When comparing both classifiers, this inconsistency can also be noted, since there is a large variability of results. The Random Forest presented better results for false positive rates than the SVM classifier, but the latter, on average, performed better for the false negative tests. Considering the accuracy results (overall system performace), the SVM classifier presented

Those results are corroborated when considering the AUC as a measure of the system performance. Figure 9 shows the results of AUC for the Random Forest classifier applied to the CC and MLO views independently, after the reduction procedure, parameterized by the different wavelet functions. In Figure 10, the same results of AUC are shown when applying the SVM classifier. As it can be noticed, SVM performed better for almost all cases,

Table 7. Measurements obtained with the Random Forest classifier for each view of

*Coiflet 5 Daubechies 3 Symlet 4* **CC MLO CC MLO CC MLO**

*Coiflet 5 Daubechies 3 Symlet 4* **CC MLO CC MLO CC MLO**

**3.2 Classification of CC and MLO views independently**

with the application of the Symlet 4 wavelet mother.

the exception being the Daubechies 3 wavelet on the CC view.

provided by these systems.

the better results on average.

mammogram.

#### **3.3 Classification of two-view information fusion (CC and MLO)**

Table 9 shows the number of texture data after application of the ANOVA technique in each view separately and the number of attributes after the two-view attributes fusion for each type of wavelet mother. Tables 10 and 11 show the mean values of sensitivity, specificity, accuracy

Table 9. Number of relevant textural information after application of the ANOVA technique with *p* = 1 × 10−16.

and standard deviation (*σ*) for the process of two-view information fusion, using the Random Forest and SVM classifiers, respectively.

**4. Conclusion**

Fusion of Two-View Information:

**5. References**

raise the rates of the descriptors evaluated.

evaluate possible improvements in image classification.

In this work, we develop a method for extraction and selection of attributes using the information fusion from both CC and MLO views for breast cancer classification of mammogram images. Comparing the results of Tables 7 with 10 and 8 with 11, we observe that the use of textural information, obtained from the fusion of the CC and MLO views, might

SVD Based Modeling for Computerized Classification of Breast Lesions on Mammograms

277

Experimental results showed that the three types of wavelet mother had superior performance over the area under the ROC curve for the SVM classifier. Performance evaluation was conducted in relation to the AUC and the results obtained showed that the best classification rates were obtained using the Daubechies wavelel, giving an AUC = 0.831 for the Support Vector Machine classifiers. Future experiments may use other types of feature descriptors to

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Table 10. Results for two-view fusion obtained using the Random Forest classifier.

Table 11. Results for two-view fusion obtained using the SVM classifier.

As seen on Tables 10 and 11, the results for the two classifiers using two-view CC and MLO information fusion were increased for all wavelet functions considered. As an example, for the Coiflet 5 wavelet, the fusion procedure led the sensitivity (fraction of the number of regions detected as positive against those that actually have a mass) to be increased about 5% compared to the result of the same wavelet for individual visions. The same occurred to the other two wavelets. Furthermore, the results also show an increase in the specificity

Fig. 11. Results of AUC after the two-view information fusion process for the Random Forest and SVM classifiers.

and accuracy parameters due to the two-view information fusion procedure. The results on the tables also show that the Daubechies 3 wavelet function have reached the best results compared to the other two applied wavelets. Since accuracy reflects the relation between sensitivity and specificity, that descriptor permited to note the similar overall performance between the two classifiers. This result is also visible when evaluating the AUC performance of the classifiers. Figure 11 shows the results of AUC after CC and MLO information fusion for the three different types of wavelet mother and the Random Forest and SVM classifiers.

#### **4. Conclusion**

16 Will-be-set-by-IN-TECH

**Sensitivity** 82,50 83,33 82,50 **Specificity** 81,67 82,92 80,83 **Accuracy** 82,08 83,13 81,67 *σ* 12,43 11,74 13,20

**Sensitivity** 75,83 77,08 75,00 **Specificity** 88,33 89,17 88,61 **Accuracy** 82,08 83,13 81,81 *σ* 10,77 9,89 9,94

As seen on Tables 10 and 11, the results for the two classifiers using two-view CC and MLO information fusion were increased for all wavelet functions considered. As an example, for the Coiflet 5 wavelet, the fusion procedure led the sensitivity (fraction of the number of regions detected as positive against those that actually have a mass) to be increased about 5% compared to the result of the same wavelet for individual visions. The same occurred to the other two wavelets. Furthermore, the results also show an increase in the specificity

Fig. 11. Results of AUC after the two-view information fusion process for the Random Forest

and accuracy parameters due to the two-view information fusion procedure. The results on the tables also show that the Daubechies 3 wavelet function have reached the best results compared to the other two applied wavelets. Since accuracy reflects the relation between sensitivity and specificity, that descriptor permited to note the similar overall performance between the two classifiers. This result is also visible when evaluating the AUC performance of the classifiers. Figure 11 shows the results of AUC after CC and MLO information fusion for the three different types of wavelet mother and the Random Forest and SVM classifiers.

and SVM classifiers.

Table 10. Results for two-view fusion obtained using the Random Forest classifier.

Table 11. Results for two-view fusion obtained using the SVM classifier.

*Coiflet 5 Daubechies 3 Symlet 4* **CC** + **MLO CC** + **MLO CC** + **MLO**

*Coiflet 5 Daubechies 3 Symlet 4* **CC** + **MLO CC** + **MLO CC** + **MLO** In this work, we develop a method for extraction and selection of attributes using the information fusion from both CC and MLO views for breast cancer classification of mammogram images. Comparing the results of Tables 7 with 10 and 8 with 11, we observe that the use of textural information, obtained from the fusion of the CC and MLO views, might raise the rates of the descriptors evaluated.

Experimental results showed that the three types of wavelet mother had superior performance over the area under the ROC curve for the SVM classifier. Performance evaluation was conducted in relation to the AUC and the results obtained showed that the best classification rates were obtained using the Daubechies wavelel, giving an AUC = 0.831 for the Support Vector Machine classifiers. Future experiments may use other types of feature descriptors to evaluate possible improvements in image classification.

#### **5. References**

URL: *http://www.sciencedirect.com/science/article/pii/S0895611106001029*

**Part 4**

**Emerging Technologies – Computer Aided**

**Detection, Diagnosis and Digital Mammography**

URL: *http://bjr.birjournals.org/cgi/content/abstract/68/813/958*

## **Part 4**

## **Emerging Technologies – Computer Aided Detection, Diagnosis and Digital Mammography**

18 Will-be-set-by-IN-TECH

278 Mammography – Recent Advances

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**14**

Nachiko Uchiyama

*Chuo-Ku, Tokyo,*

*Japan*

*National Cancer Center, Tsukiji,*

**Breast CAD (Computer Aided Detection)**

*Research Center for Cancer Prevention and Screening,*

**in FFDM (Full Field Digital Mammography)**

In this chapter, firstly, the author describes the differences between CAD for analog mammography and FFDM with reference to clinical workflow and physical characteristics, and secondly, addresses how the detection performance of CAD can differ in accordance with image quality utilizing different FFDM systems, including future possibilities of breast

With CAD and analog mammography the CAD device is a single, independent device (Figure 1). The quality and quantity of image data depends on the film and the digitizer. It is easy to collect and analyze digital data through a film digitizer and the CAD system is an

On the other hand, with CAD and digital mammography, it is necessary to collect so-called raw digital data from an acquisition system. To develop CAD software, it is necessary to work in conjunction with acquisition systems. Furthermore, CAD is an independent instrument with analog mammography; on the other hand, with digital mammography, CAD will be one of the interpretation functions of the reading workstation. For the most effective utilization, it is necessary to integrate CAD well with the reading workstation

Therefore, to disseminate CAD with digital mammography, we should take into consideration how to organize complete systems, including acquisition systems, reading workstations, and network systems. If the acquisition system and the reading workstation are made by the same maker, we can transfer raw image data from the acquisition system to the CAD server, and indicate Structure Report (SR) on the monitors at the reading workstation without any problems. On the other hand, when the makers are different, it may be a problem (Figure 2). For most effective utilization, it is necessary to integrate CAD

**2. Difference between CAD with analog mammography and with digital**

independent machine mainly developed by a venture company.

**1. Introduction**

**mammography in clinical workflow**

well into the reading workstation workflow [1].

CAD.

workflow.

### **Breast CAD (Computer Aided Detection) in FFDM (Full Field Digital Mammography)**

Nachiko Uchiyama

*Research Center for Cancer Prevention and Screening, National Cancer Center, Tsukiji, Chuo-Ku, Tokyo, Japan*

#### **1. Introduction**

In this chapter, firstly, the author describes the differences between CAD for analog mammography and FFDM with reference to clinical workflow and physical characteristics, and secondly, addresses how the detection performance of CAD can differ in accordance with image quality utilizing different FFDM systems, including future possibilities of breast CAD.

#### **2. Difference between CAD with analog mammography and with digital mammography in clinical workflow**

With CAD and analog mammography the CAD device is a single, independent device (Figure 1). The quality and quantity of image data depends on the film and the digitizer. It is easy to collect and analyze digital data through a film digitizer and the CAD system is an independent machine mainly developed by a venture company.

On the other hand, with CAD and digital mammography, it is necessary to collect so-called raw digital data from an acquisition system. To develop CAD software, it is necessary to work in conjunction with acquisition systems. Furthermore, CAD is an independent instrument with analog mammography; on the other hand, with digital mammography, CAD will be one of the interpretation functions of the reading workstation. For the most effective utilization, it is necessary to integrate CAD well with the reading workstation workflow.

Therefore, to disseminate CAD with digital mammography, we should take into consideration how to organize complete systems, including acquisition systems, reading workstations, and network systems. If the acquisition system and the reading workstation are made by the same maker, we can transfer raw image data from the acquisition system to the CAD server, and indicate Structure Report (SR) on the monitors at the reading workstation without any problems. On the other hand, when the makers are different, it may be a problem (Figure 2). For most effective utilization, it is necessary to integrate CAD well into the reading workstation workflow [1].

Breast CAD (Computer Aided Detection) in FFDM (Full Field Digital Mammography) 283

At present, CAD, dedicated to digital mammography, analyzes the raw imaging data and detects candidate lesions including masses and microcalcifications. As for the physical characteristics, regarding the linear attenuation coefficient for breast tissue, the differential value between breast tissue and calcification is larger than the differential value between breast tissue and mass. In the raw imaging data, mass lesions have relatively localized large areas with a smaller number of photon counts compared to surrounding breast tissue. CAD analyzes the characteristics and detects the area as a candidate mass lesion. The raw imaging data is inverted and the mass lesion is recognized clinically as a localized high density area compared to background breast tissue density. In the raw imaging data, on the other hand, the images with microcalcification lesions have localized small and clustered areas with a smaller number of photon counts compared to the background breast tissue. CAD analyzes the characteristics and detects the area as a candidate microcalcification lesion. The raw imaging data is inverted and the microcalcification lesions are recognized clinically as small and clustered areas with higher density compared to the background breast tissue density. According to the background, CAD, dedicated to FFDM, can be directly affected by the physical characteristics of the raw imaging data. Unlike the raw imaging data on hard copy, utilizing digitizers for CAD processing in the analog system by groups, in units of 8-10 bits, the raw imaging data for CAD processing in FFDM are analyzed by groups, in units of 12-14 bits, which has a much more dynamic range compared to digitized hard copy data in the analog system. According to the background, in FFDM, there are more opportunities to apply a combination of anode/filters such as W/Rh that allows us to decrease the radiation dose while keeping higher image quality in CNR (Contrast to Noise Ratio), compared to the images using Mo/Mo and Mo/Rh in the analog system [2].The raw imaging data for CAD processing with FFDM can be more strongly influenced by the different contrast and image sharpness in clinical images, compared to the CAD dedicated to an analog system. Accordingly, the detection pattern in CAD can vary even in clinical cases. The author evaluated the variety of detection performance of CAD, utilizing two different FFDM systems with reference to analysis of physical characteristics such as CNR and spectral analysis of anode/filters. This study was conducted to retrospectively evaluate the variation

of CAD performance according to different radiation exposure parameters [3,4]

This study was conducted as part of research that was approved by the IRB at our institute on June 12th in 2007. All patients that were recruited for this study gave informed consent. The clinical cases in this study were selected from screening mammograms taken from June 12th in 2007 to December 24th in 2009. Clinical image data were acquired by two different FFDM systems. One was an a-Se FFDM system with a spatial resolution of 70ìm (System A) and imaging data were acquired from June 12th in 2007 to November 24th in 2008. Another was an a-Se FFDM system with a spatial resolution of 85ìm (System B) and imaging data were acquired from December 7th in 2008 to December 24th in 2009. Mammograms were diagnosed as BI-RADS category 1 or 2 by double-reading and breast ultrasound was performed in each case and diagnosed as a normal or a benign case. The total number of

**4. Materials and methods**

**3. How can image quality affect the detection performance of breast CAD in**

**FFDM? Purpose**

Fig. 1. Example of the Workflow of the CAD System Using Analog Mammography.

#### SR: Structure Report

CAD analyzes raw data from the acquisition system in a CAD server and refers the indication of CAD results to a reading workstation.

The quality and quantity of image data depends on the acquisition system. The operating system consists of three steps: (1) an acquisition system, (2) a CAD server, and (3) a reading work station. The number of makers of CAD systems that correspond to each acquisition system is limited. It is necessary to confirm before installation whether the reading workstation can display CAD analysis results.

Fig. 2. Example of the Workflow of the CAD System Using Digital Mammography.

#### **3. How can image quality affect the detection performance of breast CAD in FFDM?**

#### **Purpose**

282 Mammography – Recent Advances

Fig. 1. Example of the Workflow of the CAD System Using Analog Mammography.

CAD analyzes raw data from the acquisition system in a CAD server and refers the indication of CAD

The quality and quantity of image data depends on the acquisition system. The operating system consists of three steps: (1) an acquisition system, (2) a CAD server, and (3) a reading work station. The number of makers of CAD systems that correspond to each acquisition system is limited. It is necessary to confirm before installation whether the reading workstation can display CAD analysis results. Fig. 2. Example of the Workflow of the CAD System Using Digital Mammography.

SR: Structure Report

results to a reading workstation.

At present, CAD, dedicated to digital mammography, analyzes the raw imaging data and detects candidate lesions including masses and microcalcifications. As for the physical characteristics, regarding the linear attenuation coefficient for breast tissue, the differential value between breast tissue and calcification is larger than the differential value between breast tissue and mass. In the raw imaging data, mass lesions have relatively localized large areas with a smaller number of photon counts compared to surrounding breast tissue. CAD analyzes the characteristics and detects the area as a candidate mass lesion. The raw imaging data is inverted and the mass lesion is recognized clinically as a localized high density area compared to background breast tissue density. In the raw imaging data, on the other hand, the images with microcalcification lesions have localized small and clustered areas with a smaller number of photon counts compared to the background breast tissue. CAD analyzes the characteristics and detects the area as a candidate microcalcification lesion. The raw imaging data is inverted and the microcalcification lesions are recognized clinically as small and clustered areas with higher density compared to the background breast tissue density. According to the background, CAD, dedicated to FFDM, can be directly affected by the physical characteristics of the raw imaging data. Unlike the raw imaging data on hard copy, utilizing digitizers for CAD processing in the analog system by groups, in units of 8-10 bits, the raw imaging data for CAD processing in FFDM are analyzed by groups, in units of 12-14 bits, which has a much more dynamic range compared to digitized hard copy data in the analog system. According to the background, in FFDM, there are more opportunities to apply a combination of anode/filters such as W/Rh that allows us to decrease the radiation dose while keeping higher image quality in CNR (Contrast to Noise Ratio), compared to the images using Mo/Mo and Mo/Rh in the analog system [2].The raw imaging data for CAD processing with FFDM can be more strongly influenced by the different contrast and image sharpness in clinical images, compared to the CAD dedicated to an analog system. Accordingly, the detection pattern in CAD can vary even in clinical cases. The author evaluated the variety of detection performance of CAD, utilizing two different FFDM systems with reference to analysis of physical characteristics such as CNR and spectral analysis of anode/filters. This study was conducted to retrospectively evaluate the variation of CAD performance according to different radiation exposure parameters [3,4]

#### **4. Materials and methods**

This study was conducted as part of research that was approved by the IRB at our institute on June 12th in 2007. All patients that were recruited for this study gave informed consent. The clinical cases in this study were selected from screening mammograms taken from June 12th in 2007 to December 24th in 2009. Clinical image data were acquired by two different FFDM systems. One was an a-Se FFDM system with a spatial resolution of 70ìm (System A) and imaging data were acquired from June 12th in 2007 to November 24th in 2008. Another was an a-Se FFDM system with a spatial resolution of 85ìm (System B) and imaging data were acquired from December 7th in 2008 to December 24th in 2009. Mammograms were diagnosed as BI-RADS category 1 or 2 by double-reading and breast ultrasound was performed in each case and diagnosed as a normal or a benign case. The total number of

Breast CAD (Computer Aided Detection) in FFDM (Full Field Digital Mammography) 285

**0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0**

**0.0 1.0 2.0 3.0 4.0**

**40mmThick**

**mGy mGy**

**40mmThick**

**0.0 1.0 2.0 3.0 4.0**

**26kv Mo/Mo 28kv Mo/Mo 30kv W/Rh**

**mGy**

**26kV Mo/Mo 26kV Mo/Rh 26kV W/Rh 28kV Mo/Mo 28kV Mo/Rh 28kV W/Rh**

**0.0**

**0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0**

**0.0 5.0 10.0 15.0 20.0 25.0 30.0**

**0.0 2.0 4.0 6.0 8.0 10.0**  **0.0 1.0 2.0 3.0 4.0**

**60mmThick**

**20mmThick**

**0.0 1.0 2.0 3.0 4.0**

**20mmThick**

**60mmThick**

**0.0 1.0 2.0 3.0 4.0**

**0.0 1.0 2.0 3.0 4.0**

**24kv Mo/Mo 26kv Mo/Mo 28kv Mo/Mo**

> **28kv Mo/Mo 30kv W/Rh 32kv W/Rh**

Fig. 4. CNR Analysis: 20mm, 40mm, and 60mmThick PMMA Phantoms in System A.

**mGy**

**0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0**

**24kV Mo/Mo 24kV Mo/Rh 24kV W/Rh**

**mGy**

Fig. 5. CNR Analysis: 20mm,40mm,and 60mm Thick PMMA Phantoms in System B.

**30kV Mo/Mo 30kV Mo/Rh 30kV W/Rh 32kV Mo/Mo 32k Mo/Rh 32kV W/Rh**

**mGy**

**5.0**

**10.0**

**15.0**

**20.0**

**25.0**

cases was 1140 cases in System A and 1178 cases in System B. The median patient age was 59.8 years old (range 40-75 years old) in System A and 60.0 years old (range 40-88 years old) in System B. To optimize radiation exposure parameters in clinical images, we measured CNR (Contrast to Noise Ratio) in accordance with EUREF (European Guidelines for Quality Assurance in Breast Cancer Screening and Diagnosis) guide lines simulating breast thickness, utilizing PMMA phantoms (20-70mm) and radiation exposure parameters, kV (24-34kV) and combinations of anode/filters (Mo/Mo, Mo/ Rh, and W/Rh). In addition, we performed spectral analysis of anode/filters (Mo/Mo, Mo/ Rh, and W/Rh) regarding both FFDM systems. A CAD dedicated to the FFDM systems was applied for the purpose of review and was verified, regarding detection areas, with reference to the diagnostic reports of the mammogram and ultrasound. The same CAD algorithm was utilized for the two FFDM systems.

#### **5. Results**

We optimized radiation exposure parameters in a clinical setting with reference to the results of the CNR analysis and dosimetry in accordance with EUREF Guidelines [5] (Fig.3.).

In System A, under 20mm breast thickness, the combination of 24kV with Mo/Mo was selected; from 21m to 30mm breast thickness, the combination of 26kV with Mo/Mo was selected; from 31mm to 40mm breast thickness, the combination of 28kV with Mo/Mo was selected; from 41to 60mm, the combination of 30kV with W/Rh was selected; from 61mm to 70mm, the combination of 32kV with W/Rh was selected; and above 70mm, the combination of 34kV with W/Rh was selected (Fig.4-5).

#### SD; Standard Deviation

Fig. 3. CNR Measurements in Accordance with EUREF.

284 Mammography – Recent Advances

cases was 1140 cases in System A and 1178 cases in System B. The median patient age was 59.8 years old (range 40-75 years old) in System A and 60.0 years old (range 40-88 years old) in System B. To optimize radiation exposure parameters in clinical images, we measured CNR (Contrast to Noise Ratio) in accordance with EUREF (European Guidelines for Quality Assurance in Breast Cancer Screening and Diagnosis) guide lines simulating breast thickness, utilizing PMMA phantoms (20-70mm) and radiation exposure parameters, kV (24-34kV) and combinations of anode/filters (Mo/Mo, Mo/ Rh, and W/Rh). In addition, we performed spectral analysis of anode/filters (Mo/Mo, Mo/ Rh, and W/Rh) regarding both FFDM systems. A CAD dedicated to the FFDM systems was applied for the purpose of review and was verified, regarding detection areas, with reference to the diagnostic reports of the mammogram and ultrasound. The same CAD algorithm was utilized for the two

We optimized radiation exposure parameters in a clinical setting with reference to the results of the CNR analysis and dosimetry in accordance with EUREF Guidelines [5] (Fig.3.). In System A, under 20mm breast thickness, the combination of 24kV with Mo/Mo was selected; from 21m to 30mm breast thickness, the combination of 26kV with Mo/Mo was selected; from 31mm to 40mm breast thickness, the combination of 28kV with Mo/Mo was selected; from 41to 60mm, the combination of 30kV with W/Rh was selected; from 61mm to 70mm, the combination of 32kV with W/Rh was selected; and above 70mm, the

combination of 34kV with W/Rh was selected (Fig.4-5).

Fig. 3. CNR Measurements in Accordance with EUREF.

FFDM systems.

SD; Standard Deviation

**5. Results**

Fig. 4. CNR Analysis: 20mm, 40mm, and 60mmThick PMMA Phantoms in System A.

Fig. 5. CNR Analysis: 20mm,40mm,and 60mm Thick PMMA Phantoms in System B.

Breast CAD (Computer Aided Detection) in FFDM (Full Field Digital Mammography) 287

Fig. 6. Spectra of Mo/Mo and W/Rh in System A.

CAD detected relatively dense areas as false-positive masses at a rate of 9.8% (448/4560 images) and fibrous tissue as false-positive microcalcifications at a rate of 0.7% (34/4560 images).

In the cases utilizing 24-28kV Mo/Mo, CAD detected masses as false positives more frequently at a rate of 12.7% (279/2196 images), compared to the cases utilizing 30-34 kV W/Rh which detected false positives at a rate of 7.1% (169/2364 images). There was a statistically significant difference (P=0.008<0.05) between the two different combinations of anode/filters. CAD detected more false-positive masses in the cases utilizing the combinations with Mo/Mo in comparison with the cases utilizing the combinations with W/Rh. On the other hand, in the cases utilizing 30-34kV W/Rh, CAD detected false-positive microcalcifications more frequently at a rate of 1.1% (26/2364 images), compared to 0.4 % (8/2196 images) detected utilizing 24-28kV Mo/Mo. There was a statistically significant difference (P=0.022<0.05) between the two combinations with different anode/filters. CAD detected more false-positive calcifications in the cases utilizing W/Rh in comparison with the cases utilizing Mo/Mo (Table 1a.). In System B, under 25mm breast thickness, the combination of 24kV with W/Rh was selected; from 26m to 35mm breast thickness, the combination of 26kV with W/Rh was selected; from 36mm to 45mm breast thickness, the combination of 28kV with W/Rh was selected; from 46 to 55mm, the combination of 30kV with W/Rh was selected; and above 56mm, the combination of 32kV-34kV with W/Rh was selected. CAD detected false-positive masses at a rate of 2.7% (129/4712 images) and falsepositive microcalcifications at a rate of 0.8% (37/4712 images) in total. With 24kV, CAD detected false-positive masses at a rate of 1.0% (5/500 images) and false-positive microcalcifications at a rate of 1.2% (6/500 images). With 26kV, CAD detected false-positive masses at a rate of 3.3% (32/960 images) and false-positive microcalcifications at a rate of 0.7% (7/960 images). With 28kV, CAD detected false-positive masses at a rate of 3.3% (48/1460 images) and false-positive microcalcifications at a rate of 1.2% (18/1460 images).With 30kV, CAD detected false-positive masses at a rate of 1.4% (16/1128 images) and false-positive microcalcifications at a rate of 0.5% (6/1128 images). With 32-34kV, CAD detected false-positive masses at a rate of 4.2% (28/664images) and 0% (0/664 images) falsepositive microcalcifications. There was no significant difference among different kV levels with the same combination of anode/filters in System B (P>0.05) (Table 1b.).

Regarding spectral analysis of anode/filters, in System A, Mo/Mo and W/Rh demonstrated different spectrum characteristic curves. In addition, the two systems showed different spectrum characteristic curves with W/Rh and the peak value in System B with W/Rh was shown at a higher kV level compared to System A (Fig.6-7).

#### **6. Discussion**

At present, CAD dedicated to digital mammography analyzes the raw imaging data and detects the candidate lesions including masses and microcalcifications. As for the physical characteristics, regarding the linear attenuation coefficient for breast tissue [6], the differential value between breast tissue and calcification is larger than the differential value between breast tissue and mass (Table2).

Mass lesions have relatively localized large areas with a smaller number of photon counts compared to surrounding breast tissue in the raw imaging data. CAD analyzes the 286 Mammography – Recent Advances

CAD detected relatively dense areas as false-positive masses at a rate of 9.8% (448/4560 images) and fibrous tissue as false-positive microcalcifications at a rate of 0.7% (34/4560

In the cases utilizing 24-28kV Mo/Mo, CAD detected masses as false positives more frequently at a rate of 12.7% (279/2196 images), compared to the cases utilizing 30-34 kV W/Rh which detected false positives at a rate of 7.1% (169/2364 images). There was a statistically significant difference (P=0.008<0.05) between the two different combinations of anode/filters. CAD detected more false-positive masses in the cases utilizing the combinations with Mo/Mo in comparison with the cases utilizing the combinations with W/Rh. On the other hand, in the cases utilizing 30-34kV W/Rh, CAD detected false-positive microcalcifications more frequently at a rate of 1.1% (26/2364 images), compared to 0.4 % (8/2196 images) detected utilizing 24-28kV Mo/Mo. There was a statistically significant difference (P=0.022<0.05) between the two combinations with different anode/filters. CAD detected more false-positive calcifications in the cases utilizing W/Rh in comparison with the cases utilizing Mo/Mo (Table 1a.). In System B, under 25mm breast thickness, the combination of 24kV with W/Rh was selected; from 26m to 35mm breast thickness, the combination of 26kV with W/Rh was selected; from 36mm to 45mm breast thickness, the combination of 28kV with W/Rh was selected; from 46 to 55mm, the combination of 30kV with W/Rh was selected; and above 56mm, the combination of 32kV-34kV with W/Rh was selected. CAD detected false-positive masses at a rate of 2.7% (129/4712 images) and falsepositive microcalcifications at a rate of 0.8% (37/4712 images) in total. With 24kV, CAD detected false-positive masses at a rate of 1.0% (5/500 images) and false-positive microcalcifications at a rate of 1.2% (6/500 images). With 26kV, CAD detected false-positive masses at a rate of 3.3% (32/960 images) and false-positive microcalcifications at a rate of 0.7% (7/960 images). With 28kV, CAD detected false-positive masses at a rate of 3.3% (48/1460 images) and false-positive microcalcifications at a rate of 1.2% (18/1460 images).With 30kV, CAD detected false-positive masses at a rate of 1.4% (16/1128 images) and false-positive microcalcifications at a rate of 0.5% (6/1128 images). With 32-34kV, CAD detected false-positive masses at a rate of 4.2% (28/664images) and 0% (0/664 images) falsepositive microcalcifications. There was no significant difference among different kV levels

with the same combination of anode/filters in System B (P>0.05) (Table 1b.).

shown at a higher kV level compared to System A (Fig.6-7).

between breast tissue and mass (Table2).

**6. Discussion**

Regarding spectral analysis of anode/filters, in System A, Mo/Mo and W/Rh demonstrated different spectrum characteristic curves. In addition, the two systems showed different spectrum characteristic curves with W/Rh and the peak value in System B with W/Rh was

At present, CAD dedicated to digital mammography analyzes the raw imaging data and detects the candidate lesions including masses and microcalcifications. As for the physical characteristics, regarding the linear attenuation coefficient for breast tissue [6], the differential value between breast tissue and calcification is larger than the differential value

Mass lesions have relatively localized large areas with a smaller number of photon counts compared to surrounding breast tissue in the raw imaging data. CAD analyzes the

images).

Fig. 6. Spectra of Mo/Mo and W/Rh in System A.

Breast CAD (Computer Aided Detection) in FFDM (Full Field Digital Mammography) 289

characteristics and detects the area as a candidate mass lesion. The raw imaging data is inverted and the mass lesion is recognized clinically as a localized high density area compared to background breast tissue density. On the other hand, the images with microcalcification lesions have localized small and clustered areas with a smaller number of photon counts compared to the background breast tissue in the raw imaging data. CAD analyzes the characteristics and detects the area as a candidate microcalcification lesion. The raw imaging data is inverted and the microcalcification lesions are recognized clinically as small and clustered areas with higher density compared to the background breast tissue density. According to the background, CAD dedicated to digital mammography can be directly affected by the physical characteristics of the raw imaging data. In this study, in System A, CAD detected more false positive masses with 24-28Kv Mo/Mo compared to those detected with 30-34Kv W/Rh. According to spectral analysis, Mo/Mo acquires a smaller number of photons compared to W/Rh . The raw imaging data with Mo/Mo has a relatively narrow range of photon counts and the differentials in the photon counts between background breast tissue and mass can be small. As a result, CAD can detect more false positive masses compared to imaging with W/Rh. On the other hand, CAD detected more false positive microcalcifications with 30-34Kv W/Rh compared to the number detected

This could be a result of the characteristics of W/Rh which can acquire a larger number of photons compared to Mo/Mo. Images with W/Rh have a much wider range of photon counts and the differential value of photon counts between background breast tissue and microcalcifications is large. As a result, imaging data with W/Rh can detect candidate microcalcification lesions with more sensitivity than imaging with Mo/Mo. Even with the same combination of anode/filters, the CAD in System A with 30-34kV W/Rh detected more false positive masses compared to System B with 30-34kV W/Rh.CAD results may differ even when the same system is used, according to which combination of anode/filter is used. On the other hand, CAD results may differ when different systems are used, even though the same combination of anode/filter is used. According to spectral analysis, the spectrum of W/Rh used in System A shows greater similarity to the spectrum of Mo/Mo than the spectrum of W/Rh used in System B. As a result, CAD detected more false positives using W/Rh with System A compared to System B. The CAD performance was

Breast Tissue 0.8

Fatty Tissue 0.45

Skin 0.8

Mass 0.85

Calcification 12.5

with 24-28Kv Mo/Mo (Fig.8-9).

Table 2. Linear Attenuation Coefficient of Breast Tissue at 20keV [6].

Linear Attenuation Coefficient(cm-1)

Fig. 7. Spectrum of W/Rh in System B.

Table 1. Clinical Radiation Exposure Setting of System A (Table 1a) and System B. (Table1b) regarding Frequency of False Positives (FPs) using CAD.

288 Mammography – Recent Advances

**24kV W/Rh 26kV W/Rh 28kV W/Rh 30kV W/Rh 32kV W/Rh 34kV W/Rh**

**keV**

**P=0.008<0.05 P=0.022<0.05**

**P>0.05 P>0.05**

**0 10 20 30 40 50**

**24-28kV Mo/Mo 12.7% (279/2196) 0.4% (8/2196)**

**30-34kV W/Rh 7.1% (169/2364) 1.1% (26/2364)**

**Total 9.8% (448/4560) 0.7% (34/4560)**

**24kV W/Rh 1.0% (5/500) 1.2% (6/500) 26kV W/Rh 3.3% (32/960) 0.7% (7/960) 28kV W/Rh 3.3% (48/1460) 1.2% (18/1460)**

**30kV W/Rh 1.4% (16/1128) 0.5% (6/1128)**

Table 1. Clinical Radiation Exposure Setting of System A (Table 1a) and System B. (Table1b)

**32-34kV W/Rh 4.2% (28/664) 0% (0/664) Total 2.7% (129/4712) 0.8% (37/4712)**

regarding Frequency of False Positives (FPs) using CAD.

**FP Mass FP Microcalcifications**

**FP Mass FP Microcalcifications**

**0**

**Table1a.**

Fig. 7. Spectrum of W/Rh in System B.

**Table1b.**

**50**

**100**

**150**

**Counts**

**200**

**250**

Linear Attenuation Coefficient(cm-1)

Table 2. Linear Attenuation Coefficient of Breast Tissue at 20keV [6].

characteristics and detects the area as a candidate mass lesion. The raw imaging data is inverted and the mass lesion is recognized clinically as a localized high density area compared to background breast tissue density. On the other hand, the images with microcalcification lesions have localized small and clustered areas with a smaller number of photon counts compared to the background breast tissue in the raw imaging data. CAD analyzes the characteristics and detects the area as a candidate microcalcification lesion. The raw imaging data is inverted and the microcalcification lesions are recognized clinically as small and clustered areas with higher density compared to the background breast tissue density. According to the background, CAD dedicated to digital mammography can be directly affected by the physical characteristics of the raw imaging data. In this study, in System A, CAD detected more false positive masses with 24-28Kv Mo/Mo compared to those detected with 30-34Kv W/Rh. According to spectral analysis, Mo/Mo acquires a smaller number of photons compared to W/Rh . The raw imaging data with Mo/Mo has a relatively narrow range of photon counts and the differentials in the photon counts between background breast tissue and mass can be small. As a result, CAD can detect more false positive masses compared to imaging with W/Rh. On the other hand, CAD detected more false positive microcalcifications with 30-34Kv W/Rh compared to the number detected with 24-28Kv Mo/Mo (Fig.8-9).

This could be a result of the characteristics of W/Rh which can acquire a larger number of photons compared to Mo/Mo. Images with W/Rh have a much wider range of photon counts and the differential value of photon counts between background breast tissue and microcalcifications is large. As a result, imaging data with W/Rh can detect candidate microcalcification lesions with more sensitivity than imaging with Mo/Mo. Even with the same combination of anode/filters, the CAD in System A with 30-34kV W/Rh detected more false positive masses compared to System B with 30-34kV W/Rh.CAD results may differ even when the same system is used, according to which combination of anode/filter is used. On the other hand, CAD results may differ when different systems are used, even though the same combination of anode/filter is used. According to spectral analysis, the spectrum of W/Rh used in System A shows greater similarity to the spectrum of Mo/Mo than the spectrum of W/Rh used in System B. As a result, CAD detected more false positives using W/Rh with System A compared to System B. The CAD performance was

Breast CAD (Computer Aided Detection) in FFDM (Full Field Digital Mammography) 291

affected by the difference in image quality produced by different radiation exposure parameters of the different anode/filters within one system and by differences in the two systems. In FFDM, CAD algorithms should be considered to vary depending on the image acquisition systems. In addition, recently, new breast image acquisition technologies, as well as digital breast tomosynthesis and dual-energy mammography, have been developed and have started to be acquired for breast diagnosis. These image acquisition approaches, utilizing new CAD techniques, will be capable of accurate volumetric measuring of breast density and microcalcifications, differently from conventional 2D images [7]-[9]. The results of this study imply that we should take into consideration the importance of analyzing physical characteristics with CAD, according to the different image quality with systems

In this section, the author addresses the issue that CAD performance is affected by the difference in image quality produced by different radiation exposure parameters of the different anode/filters within one system and by differences in the two systems; also

This study was supported by Grant-in-Aid for Scientific Research (C) (No. 23591810) in

[1] Uchiyama N.: Current status of CAD utilizing digital mammography in Japan. Breast

[2] Toroi, P., Zanca, F., Young, K. C. et al.: Experimental Investigation on the Choice of the

[3] Uchiyama N, Stoeckel J, Otsuka K, et al.:How Can Image Quality Affect the Detection

[4] Uchiyama N,Stoeckel J, Otsuka K. et al.:How Can Image Quality Affect the Detection

[5] EUREF; European Guidelines for Quality Assurance in Breast Cancer Screening and

[6] Hammerstein, G.R., Miller, D.W., et al; Absorbed Radiation Dose in Mammography.

[7] Reiser I., Nishikawa R. M., Giger M. L. et.al. Computerized Detection of Mass Lesions in

Gradient Index Segmentation.2004. Technol. Cancer Res. Treat. 3, 437–441

Digital Mammography System. 2007.Eur. Radiol.17,2368-23752.

Tungsten/Rhodium Anode/Filter Combination for an Amorphous Selenium-Based

Performance of Breast CAD (Computer Aided Detection) in FFDM (Full Field Digital Mammography)? A Comparative Study with Two Different FFDM Systems.

Performances of Breast CAD (Computer Aided Detection) in FFDM (Full Field

Digital Breast Tomosynthesis Images Using Two- and Three Dimensional Radial

variations in CAD algorithms utilizing FFDM should be taken into account.

dedicated to new image acquisition technologies.

Cancer. 2010; 17(3) 169-179.

Diagnosis 4th Edition 2006.

Radiol. 1979. 130:485-491.

Digital Mammography. 2010. 6136 288-295.

Digital Mammography)? 2009. Int J CARS;4:357-358.

**7. Conclusion**

**8. Acknowledgment**

**9. References**

Japan.

Fig. 8. Example Case with a False Positive Mass Marked by CAD.

Fig. 9. An Example Case with False Positive Calcifications Marked by CAD.

affected by the difference in image quality produced by different radiation exposure parameters of the different anode/filters within one system and by differences in the two systems. In FFDM, CAD algorithms should be considered to vary depending on the image acquisition systems. In addition, recently, new breast image acquisition technologies, as well as digital breast tomosynthesis and dual-energy mammography, have been developed and have started to be acquired for breast diagnosis. These image acquisition approaches, utilizing new CAD techniques, will be capable of accurate volumetric measuring of breast density and microcalcifications, differently from conventional 2D images [7]-[9]. The results of this study imply that we should take into consideration the importance of analyzing physical characteristics with CAD, according to the different image quality with systems dedicated to new image acquisition technologies.

### **7. Conclusion**

290 Mammography – Recent Advances

Fig. 8. Example Case with a False Positive Mass Marked by CAD.

Fig. 9. An Example Case with False Positive Calcifications Marked by CAD.

**Localized Relatively Dense Breast Tissue Detected as a**

> **Breast Fibrous Tissue Detected as False Positive**

**Calcifications**

**False Positive Mass**

In this section, the author addresses the issue that CAD performance is affected by the difference in image quality produced by different radiation exposure parameters of the different anode/filters within one system and by differences in the two systems; also variations in CAD algorithms utilizing FFDM should be taken into account.

#### **8. Acknowledgment**

This study was supported by Grant-in-Aid for Scientific Research (C) (No. 23591810) in Japan.

#### **9. References**

**0**

**15**

*Italy*

**Metrological Assessment of a CAD System**

Based on recent statistics from the International Agency for Research on Cancer (Ferlay et al., 2010), breast cancer account for 10.9% of all cancers diagnosed and ranks as the fifth cause of cancer death in the world. Although incidence rates are increasing, mortality rates are stable, representing an improved survival rate. This improvement can be attributed to effective means for the early detection as well as to significant improvement in treatment options, exposure, etc. Mammography is, at present, the only viable method for detecting most of tumors early enough for effective treatment, without unnecessary biopsies, or other invasive procedures. Therefore, screening mammography in women aged 40 to 70 years is currently the effective strategy to reduce breast cancer mortality. Early detection of invasive breast cancers is associated with better prognosis than waiting for women to become symptomatic. However, detecting the early signs of breast cancer is challenging because the cancerous structures have many features in common with normal breast tissue. Moreover, the accuracy of interpretation of screening mammograms is affected by several factors, such as image quality, the radiologist's level of expertise, and the high volume of cases. Recent statistics show that in current breast cancer screenings 10% − 25% of the tumors are missed by the radiologists (Burrell et al., 2001; Cheng, 2003; Nishikawa, 2007). Missed cancers are due to many reasons: low disease prevalence, breast structure complexity, finding subtleties, and radiologist fatigue. To accomplish with these difficulties, different methods have been analyzed: first of all, double reading, which provides either double perception or double interpretation of lesions. It has been demonstrated that a single radiologist is more accurate when reading mammograms methodically than quickly and that two observers achieve an improvement in detection rate of 5% − 15% (Mazzarella & Bazzocchi, 2007). Obviously, this procedure is too expensive, complex, and time consuming especially in screening programs where a huge number of mammographic images have to be read. The development of computerized systems as second readers represents an alternative. Researchers have been developing algorithms to detect mammographic abnormalities for more than 30 years with the aim of either automating mammographic interpretation or providing a tool that could enhance human film-reading accuracy. Computer-aided detection (CADe) and diagnosis (CADx) systems are widely used in mammography, where signs of breast cancer are often very subtle. Both systems involve the use of computer algorithms to detect patterns in images associated with signs of disease and to assign them a malignancy index. This result

**1. Introduction**

**for the Early Diagnosis of Breast Cancer**

**in Digital Mammography**

Arianna Mencattini and Marcello Salmeri

*Dept. of Electronic Engineering, Univ. of Rome Tor Vergata*

### **Metrological Assessment of a CAD System for the Early Diagnosis of Breast Cancer in Digital Mammography**

Arianna Mencattini and Marcello Salmeri *Dept. of Electronic Engineering, Univ. of Rome Tor Vergata Italy*

#### **1. Introduction**

292 Mammography – Recent Advances

[8] Chan H.P., Wei J., Zhang Y., et.al. Computer-Aided Detection of Masses in Digital

[9] Ducote J. L. and Molloi S.. 2008. Quantification of Breast Density with Dual Energy Mammography: A Simulation Study.2008.Med. Phys. 35, 5411–5418.

Phys. 35, 4087-4095.

Tomosynthesis Mammography: Comparison of Three Approaches. 2008. Med.

Based on recent statistics from the International Agency for Research on Cancer (Ferlay et al., 2010), breast cancer account for 10.9% of all cancers diagnosed and ranks as the fifth cause of cancer death in the world. Although incidence rates are increasing, mortality rates are stable, representing an improved survival rate. This improvement can be attributed to effective means for the early detection as well as to significant improvement in treatment options, exposure, etc. Mammography is, at present, the only viable method for detecting most of tumors early enough for effective treatment, without unnecessary biopsies, or other invasive procedures. Therefore, screening mammography in women aged 40 to 70 years is currently the effective strategy to reduce breast cancer mortality. Early detection of invasive breast cancers is associated with better prognosis than waiting for women to become symptomatic. However, detecting the early signs of breast cancer is challenging because the cancerous structures have many features in common with normal breast tissue. Moreover, the accuracy of interpretation of screening mammograms is affected by several factors, such as image quality, the radiologist's level of expertise, and the high volume of cases. Recent statistics show that in current breast cancer screenings 10% − 25% of the tumors are missed by the radiologists (Burrell et al., 2001; Cheng, 2003; Nishikawa, 2007). Missed cancers are due to many reasons: low disease prevalence, breast structure complexity, finding subtleties, and radiologist fatigue. To accomplish with these difficulties, different methods have been analyzed: first of all, double reading, which provides either double perception or double interpretation of lesions. It has been demonstrated that a single radiologist is more accurate when reading mammograms methodically than quickly and that two observers achieve an improvement in detection rate of 5% − 15% (Mazzarella & Bazzocchi, 2007). Obviously, this procedure is too expensive, complex, and time consuming especially in screening programs where a huge number of mammographic images have to be read. The development of computerized systems as second readers represents an alternative. Researchers have been developing algorithms to detect mammographic abnormalities for more than 30 years with the aim of either automating mammographic interpretation or providing a tool that could enhance human film-reading accuracy. Computer-aided detection (CADe) and diagnosis (CADx) systems are widely used in mammography, where signs of breast cancer are often very subtle. Both systems involve the use of computer algorithms to detect patterns in images associated with signs of disease and to assign them a malignancy index. This result

295 Metrological Assessment of a CAD System

Many of the above mentioned problems can be partially solved or at least addressed considering a further important aspect in the CAD performance evaluation and algorithms testing, that is uncertainty sources modeling and propagation. In fact, considering all the uncertainty sources that can be present in the considered context of mammography,

or in algorithms used to automatically assess the breast tissue density.

Negatives produced by the algorithms and the possible causes.

confidence in the final results produced by the CAD.

decision-making process.

of discriminating between malignant and benign abnormalities.

for the Early Diagnosis of Breast Cancer in Digital Mammography

choice and depends on who is making the evaluation.

and are often verbally reported.

should attract the clinicians' attention to potentially abnormal regions in mammograms. In the recent years, the authors have developed a CADe-CADx system (CAD in the following), called Assisted Breast Cancer Diagnosis Environment (ABCDE) (Salmeri et al., 2009), to assist radiologists in the early detection of breast cancer. Beside the development of specific algorithms for the enhancement of abnormalities and the identification of pathological structures, the performance evaluation of each block of the whole CAD system has been also performed. In order to understand the actual complexity of the complete validation of a CAD system in mammography, consider the left-hand part of the flowchart reported in Fig. 1 where all the steps involved in the early breast cancer detection and diagnosis are considered.

Fig. 1. Flowchart of the whole CAD ABCDE system. The right part shows the issues related to the uncertainty contributions handling and propagation through the blocks.

#### **2. Motivations and objectives**

This work stems from considerations of Wirth (Wirth, 2006) and Nishikawa (Nishikawa, 2007) regarding the performance evaluation of a CADe system. One of the major limitations in the design of novel computerized algorithms for breast cancer detection is related to the inherent difficulty of proving their effectiveness and improvement with respect to existing methods. In the context of performance evaluation a sequence of unresolved issues can be identified.

2 Will-be-set-by-IN-TECH

should attract the clinicians' attention to potentially abnormal regions in mammograms. In the recent years, the authors have developed a CADe-CADx system (CAD in the following), called Assisted Breast Cancer Diagnosis Environment (ABCDE) (Salmeri et al., 2009), to assist radiologists in the early detection of breast cancer. Beside the development of specific algorithms for the enhancement of abnormalities and the identification of pathological structures, the performance evaluation of each block of the whole CAD system has been also performed. In order to understand the actual complexity of the complete validation of a CAD system in mammography, consider the left-hand part of the flowchart reported in Fig. 1 where all the steps involved in the early breast cancer detection and diagnosis are considered.

Fig. 1. Flowchart of the whole CAD ABCDE system. The right part shows the issues related

This work stems from considerations of Wirth (Wirth, 2006) and Nishikawa (Nishikawa, 2007) regarding the performance evaluation of a CADe system. One of the major limitations in the design of novel computerized algorithms for breast cancer detection is related to the inherent difficulty of proving their effectiveness and improvement with respect to existing methods. In the context of performance evaluation a sequence of unresolved issues can be identified.

to the uncertainty contributions handling and propagation through the blocks.

  -

**2. Motivations and objectives**

Many of the above mentioned problems can be partially solved or at least addressed considering a further important aspect in the CAD performance evaluation and algorithms testing, that is uncertainty sources modeling and propagation. In fact, considering all the uncertainty sources that can be present in the considered context of mammography,

robust validation and testing procedures should consider images either from SFM and from FFDM. In order to map gray-levels to optical density the calibration curve of each acquisition system is used. Each acquisition system In particular, in this work we will consider three databases: the Digital Database for Screening Mammography (DDSM) (Heath et al., 1998), the Mammographic Image Database (MIAS) (Suckling et al., 1994), and a FFDM database from the San Paolo Hospital in Bari (Mencattini et al., 2011d). In the following, we briefly

297 Metrological Assessment of a CAD System

The Mammographic Image Analysis Society (MIAS) is an organization of UK research groups interested in the understanding of mammograms and has generated a public database of digital mammograms available via the Pilot European Image Processing Archive (PEIPA) of the University of Essex, at: *http://peipa.essex.ac.uk/info/mias.html*. Films taken from the UK National Breast screening Programme have been digitized to 50 *μ*m pixel edge with a Joice-Loebl scanning microdensitometer, a device linear in the optical density range [0 − 3.2] and representing each pixel with an 8-bit word. The original database has been reduced to a 200 *μ*m pixel edge and padded/clipped so that all the images are 1024 × 1024 and the mammogram is centered in the matrix. Fig. 2 reports four examples of images taken from

Fig. 2. Examples of mammographic images from the MiniMIAS database. (Figures-left) Normal case, right (mdb053) and left (mdb054) mammograms. (Figures-right) bilateral

The Digital Database for Screening Mammography (DDSM) (Heath et al., 1998) was completed in 1999 and contains a total of 2620 cases. Primary support for this project was a grant from the Breast Cancer Research Program of the U.S. Army Medical Research and Materiel Command. The DDSM project is a collaborative effort involving co-p.i.s at the Massachusetts General Hospital (D. Kopans, R. Moore), the University of South Florida (K. Bowyer), and Sandia National Laboratories (P. Kegelmeyer). Additional cases from Washington University School of Medicine were provided by Peter E. Shile, MD,

asymmetry case, right (mdb081) and left (mdb082) mammograms.

describe the characteristics of the three databases.

for the Early Diagnosis of Breast Cancer in Digital Mammography

**3.1 MiniMIAS database**

MiniMIAS database.

**3.2 DDSM database**

performing a detailed modelization of each of them, constructing a dedicated propagation procedure through each block of the CAD, according to the uncertainty nature, will allow us to address the following topics:

In light of this, we have already partially addressed some of the above cited issues: breast masses automatic segmentation (Mencattini et al., 2011d; Rabottino et al., 2008) and the uncertainty propagation through the algorithm (Mencattini et al., 2010b), microcalcifications classification (Ferrero et al., 2010), performance evaluation of an automatic tumoral masses identification algorithm (Mencattini et al., 2010a), uncertainty propagation through the classification of breast masses (considering also the features extraction and the feature selection procedures), the uncertainty propagation by Random Fuzzy Variables (RFVs) through a denoising and enhancement procedure for the detection of microcalcifications (Mencattini et al., 2009b), and the noise variance estimation results under the assumption of signal-dependent noise (.Mencattini et al., 2007; Salmeri et al., 2008).

#### **3. Materials**

The digital mammographic image can be obtained using Full-Field Digital Mammography (FFDM) or it can be obtained by digitizing a Screen Film Mammogram (SFM). The two kinds of images exhibit very different properties in linearity (relationship between pixel intensity and exposure to X-ray detector), contrast (contrast in SFM at low and high exposures is reduced with respect to FFDM), spatial resolution (40 − 50 *μ*m in SFM, 100 *μ*m in FFDM), and noise: in linear FFDM noise is proportional to the square root of the X-ray exposure, while at low exposures electronic noise is dominant; conversely, for logarithmic FFDM noise is proportional to the inverse of the square root of the X-ray exposure to the detector. The same holds for SFM, but changed according to the characteristic curve. Owing to these differences, robust validation and testing procedures should consider images either from SFM and from FFDM. In order to map gray-levels to optical density the calibration curve of each acquisition system is used. Each acquisition system In particular, in this work we will consider three databases: the Digital Database for Screening Mammography (DDSM) (Heath et al., 1998), the Mammographic Image Database (MIAS) (Suckling et al., 1994), and a FFDM database from the San Paolo Hospital in Bari (Mencattini et al., 2011d). In the following, we briefly describe the characteristics of the three databases.

#### **3.1 MiniMIAS database**

4 Will-be-set-by-IN-TECH

performing a detailed modelization of each of them, constructing a dedicated propagation procedure through each block of the CAD, according to the uncertainty nature, will allow us

In light of this, we have already partially addressed some of the above cited issues: breast masses automatic segmentation (Mencattini et al., 2011d; Rabottino et al., 2008) and the uncertainty propagation through the algorithm (Mencattini et al., 2010b), microcalcifications classification (Ferrero et al., 2010), performance evaluation of an automatic tumoral masses identification algorithm (Mencattini et al., 2010a), uncertainty propagation through the classification of breast masses (considering also the features extraction and the feature selection procedures), the uncertainty propagation by Random Fuzzy Variables (RFVs) through a denoising and enhancement procedure for the detection of microcalcifications (Mencattini et al., 2009b), and the noise variance estimation results under the assumption of signal-dependent noise (.Mencattini et al., 2007; Salmeri et al., 2008).

The digital mammographic image can be obtained using Full-Field Digital Mammography (FFDM) or it can be obtained by digitizing a Screen Film Mammogram (SFM). The two kinds of images exhibit very different properties in linearity (relationship between pixel intensity and exposure to X-ray detector), contrast (contrast in SFM at low and high exposures is reduced with respect to FFDM), spatial resolution (40 − 50 *μ*m in SFM, 100 *μ*m in FFDM), and noise: in linear FFDM noise is proportional to the square root of the X-ray exposure, while at low exposures electronic noise is dominant; conversely, for logarithmic FFDM noise is proportional to the inverse of the square root of the X-ray exposure to the detector. The same holds for SFM, but changed according to the characteristic curve. Owing to these differences,

physician and with the developers is simple and constructive.

to address the following topics:

sections.

**3. Materials**

uncertainty sources.

The Mammographic Image Analysis Society (MIAS) is an organization of UK research groups interested in the understanding of mammograms and has generated a public database of digital mammograms available via the Pilot European Image Processing Archive (PEIPA) of the University of Essex, at: *http://peipa.essex.ac.uk/info/mias.html*. Films taken from the UK National Breast screening Programme have been digitized to 50 *μ*m pixel edge with a Joice-Loebl scanning microdensitometer, a device linear in the optical density range [0 − 3.2] and representing each pixel with an 8-bit word. The original database has been reduced to a 200 *μ*m pixel edge and padded/clipped so that all the images are 1024 × 1024 and the mammogram is centered in the matrix. Fig. 2 reports four examples of images taken from MiniMIAS database.

Fig. 2. Examples of mammographic images from the MiniMIAS database. (Figures-left) Normal case, right (mdb053) and left (mdb054) mammograms. (Figures-right) bilateral asymmetry case, right (mdb081) and left (mdb082) mammograms.

#### **3.2 DDSM database**

The Digital Database for Screening Mammography (DDSM) (Heath et al., 1998) was completed in 1999 and contains a total of 2620 cases. Primary support for this project was a grant from the Breast Cancer Research Program of the U.S. Army Medical Research and Materiel Command. The DDSM project is a collaborative effort involving co-p.i.s at the Massachusetts General Hospital (D. Kopans, R. Moore), the University of South Florida (K. Bowyer), and Sandia National Laboratories (P. Kegelmeyer). Additional cases from Washington University School of Medicine were provided by Peter E. Shile, MD,

Fig. 4. Four FFDM images containing a massive lesion whose boundary has been drawn by a

299 Metrological Assessment of a CAD System

Recent reference documents (JCGM, 2008) revised almost totally the formal and practical definitions concerning measurement uncertainty, its modelization and propagation, as a part in the measurand estimation. There are two types of measurement error quantity that can occur during a measurement process: *systematic* and *random*. A systematic error (an estimate of which is known as a measurement bias) is associated with the fact that a measured quantity value contains an offset (that can be unpredictable and uncontrollable). A random error relies on the fact that when a measurement is repeated it will generally provide a measured quantity value that is different from the previous value. It is random in that the next measured quantity value cannot be predicted exactly from previous such values. The GUM (JCGM, 2008) provided a different way of thinking about measurement and in how to express the perceived quality of the result of a measurement. Rather than express the result of a measurement by providing a best estimate of the measurand, along with information about systematic and random error values (in the form of an "error analysis"), the GUM approach aims at expressing the result of a measurement as a best estimate of the measurand, along with an

Let us denote with *Xi* any input quantities (measurands) and with *Y* the output quantity about which information is required. The output *Y* should be related to the inputs *X*1,..., *XN* by a measurement models that can be explicitly formulated *Y* = *f*(*X*1,..., *XN*) or implicitly defined *h*(*X*1,..., *XN*,*Y*) = 0. Functions *f*(·) and *h*(·) should be estimated. The main stages

of uncertainty evaluation are formulation, propagation, and summarizing.

distribution to those input quantities that are not independent).

**4. A Monte Carlo approach for CAD performance assessment**

for the Early Diagnosis of Breast Cancer in Digital Mammography

radiologist.

associated *measurement uncertainty*.

Assistant Professor of Radiology and Internal Medicine. Additional collaborating institutions include Wake Forest University School of Medicine (Departments of Medical Engineering and Radiology), Sacred Heart Hospital and ISMD, Incorporated. Each study includes two images of each breast, along with some associated patient information (age at time of study, ACR breast density rating, subtlety rating for abnormalities, ACR keyword description of abnormalities) and image information (scanner, spatial resolution, bpp). Images containing suspicious areas have associated pixel-level "ground truth" information about the locations and types of suspicious regions. Unfortunately, lesion boundary drawn by radiologists are not always reliable and often include also pixels from normal tissue. The images are digitized by four different scanners (HOWTEK-A/D, LUMISYS, and DBA) using spatial resolution equal to [43.5, 50, 42] *μ*m and a pixel resolution equal to 12 bpp for scanners (HOWTEK-A/D and LUMISYS) and equal to 16 bpp for scanner DBA. Each study contains four screening views, left and right mediolateral oblique (MLO) and cranio-caudal views (CC). Figure 3 reports three pairs of mammograms from DDSM, one for each scanner.

Fig. 3. Three pairs of DDSM images from three different scanners (a) DBA, (b) HOWTEK-A, (c) LUMISYS.

Images from scanner HOWTEK-D presents the same characteristics of scanner HOWTEK-A and are omitted.

#### **3.3 FFDM database**

Thanks to a collaboration with the San Paolo Hospital in Bari and with the Dept. of Mathematics at the University of Bari, we have access to Full Field Digital Mammographic (FFDM) images acquired using the Senograph 2000D ADS 17.3, GE Medical Systems, at a spatial resolution of 94 *μ*m and a pixel resolution of 12 bpp. Each study contains two relevant series: a series including the four standard views (CC and MLO) for presentation state and a series including, if present, a screen save image reporting the lesion boundary manually drawn by radiologists. Currently, these images are used for the development and testing of an algorithm for the automatic extraction of the lesions boundary in order to assign a malignancy degree to each lesion detected by a radiologist. At the moment, the dataset includes 196 mammograms containing one or more benign or malignant massive lesions. The malignancy assessment is a part of the CADx section in ABCDE and is currently based on fractal analysis (Giuliato & Rangayyan, 2011; Mencattini et al., 2011d; Raguso et al., 2010). Figure 4 reports four FFDM images from San Paolo Hospital.

6 Will-be-set-by-IN-TECH

Assistant Professor of Radiology and Internal Medicine. Additional collaborating institutions include Wake Forest University School of Medicine (Departments of Medical Engineering and Radiology), Sacred Heart Hospital and ISMD, Incorporated. Each study includes two images of each breast, along with some associated patient information (age at time of study, ACR breast density rating, subtlety rating for abnormalities, ACR keyword description of abnormalities) and image information (scanner, spatial resolution, bpp). Images containing suspicious areas have associated pixel-level "ground truth" information about the locations and types of suspicious regions. Unfortunately, lesion boundary drawn by radiologists are not always reliable and often include also pixels from normal tissue. The images are digitized by four different scanners (HOWTEK-A/D, LUMISYS, and DBA) using spatial resolution equal to [43.5, 50, 42] *μ*m and a pixel resolution equal to 12 bpp for scanners (HOWTEK-A/D and LUMISYS) and equal to 16 bpp for scanner DBA. Each study contains four screening views, left and right mediolateral oblique (MLO) and cranio-caudal views (CC). Figure 3 reports

Fig. 3. Three pairs of DDSM images from three different scanners (a) DBA, (b) HOWTEK-A,

Images from scanner HOWTEK-D presents the same characteristics of scanner HOWTEK-A

Thanks to a collaboration with the San Paolo Hospital in Bari and with the Dept. of Mathematics at the University of Bari, we have access to Full Field Digital Mammographic (FFDM) images acquired using the Senograph 2000D ADS 17.3, GE Medical Systems, at a spatial resolution of 94 *μ*m and a pixel resolution of 12 bpp. Each study contains two relevant series: a series including the four standard views (CC and MLO) for presentation state and a series including, if present, a screen save image reporting the lesion boundary manually drawn by radiologists. Currently, these images are used for the development and testing of an algorithm for the automatic extraction of the lesions boundary in order to assign a malignancy degree to each lesion detected by a radiologist. At the moment, the dataset includes 196 mammograms containing one or more benign or malignant massive lesions. The malignancy assessment is a part of the CADx section in ABCDE and is currently based on fractal analysis (Giuliato & Rangayyan, 2011; Mencattini et al., 2011d; Raguso et al., 2010).

three pairs of mammograms from DDSM, one for each scanner.

Figure 4 reports four FFDM images from San Paolo Hospital.

(c) LUMISYS.

and are omitted.

**3.3 FFDM database**

Fig. 4.

#### **4. A Monte Carlo approach for CAD performance assessment**

Recent reference documents (JCGM, 2008) revised almost totally the formal and practical definitions concerning measurement uncertainty, its modelization and propagation, as a part in the measurand estimation. There are two types of measurement error quantity that can occur during a measurement process: *systematic* and *random*. A systematic error (an estimate of which is known as a measurement bias) is associated with the fact that a measured quantity value contains an offset (that can be unpredictable and uncontrollable). A random error relies on the fact that when a measurement is repeated it will generally provide a measured quantity value that is different from the previous value. It is random in that the next measured quantity value cannot be predicted exactly from previous such values. The GUM (JCGM, 2008) provided a different way of thinking about measurement and in how to express the perceived quality of the result of a measurement. Rather than express the result of a measurement by providing a best estimate of the measurand, along with information about systematic and random error values (in the form of an "error analysis"), the GUM approach aims at expressing the result of a measurement as a best estimate of the measurand, along with an associated *measurement uncertainty*.

Let us denote with *Xi* any input quantities (measurands) and with *Y* the output quantity about which information is required. The output *Y* should be related to the inputs *X*1,..., *XN* by a measurement models that can be explicitly formulated *Y* = *f*(*X*1,..., *XN*) or implicitly defined *h*(*X*1,..., *XN*,*Y*) = 0. Functions *f*(·) and *h*(·) should be estimated. The main stages of uncertainty evaluation are formulation, propagation, and summarizing.

uncertainty, uncertainty sources related to the patient, model uncertainty related to the CAD parameters selection, uncertainty sources related to the input provided by the radiologist during the system development and validation steps (reference values etc.), the uncertainty sources related to the possible interaction among the CAD and the physician who is manually

301 Metrological Assessment of a CAD System

• GROUP 1: image acquisition and digitalization process (i.e., spatial resolution, geometric distortion, noise, pixel quantization, film degradation, artifacts introduction, etc.); • GROUP 2: biological and patient variability (related to both pathological or normal cases);

• GROUP 3: model uncertainty due to the unperfect or incomplete knowledge about algorithm parameters values and their influence on the final results. Major concern should be paid to algorithm with a random initialization, where some parameters are initially set

• GROUP 4: human observer subjective interpretation of the image according to his/her experience, in providing reference boundary, malignancy degree, reference region of

• GROUP 5: interaction between the human observer and the image data, in manually enhancing the image contrast, selecting Region Of Interest, manually sectioning the breast

Some of these sources of uncertainty (GROUPS 1 and 3) can be reasonably modelled and considered in the uncertainty estimation process (Mazzarella & Bazzocchi, 2007), while some other (GROUPS 2, 4, and 5) have unknown nature and are difficult to be embedded, even if noteworthy. As a consequence of the large subjectivity in using the CAD system in this context, a metrological validation of medical image processing approaches is required to highlight the intrinsic characteristics and behavior of a method, to evaluate its performance

In the following sections, we will describe with more details a possible modelization of the uncertainty contributions summarized above, providing examples taken from ABCDE's

Each step that contributes to the final digital mammographic image influences the global uncertainty in a different way: the formation process, based on X-ray exposure, introduces a noise contribution that is intensity dependent (e.g., photon noise), the microscopic structure of the impressed film introduces the so-called *film grain noise*, finally the digitalization process when performed through scanner devices, introduces an uncertainty contribution that is related to the number of bit per pixel (bpp) used in the conversion, or an uncertainty term that presents systematic periodic patterns (Mencattini et al., 2009b) superimposed to the image. Photon noise is the dominant random contribution in this context, since the bpp is usually 12 − 16, but other relevant noise contributions can be present at low and high exposures. Consequently, as suggested in (Jain, 1989), we consider an *heteroscedastic noise model* for the random contribution assuming that the noise variance depends on the intensity of each pixel, and it is not constant within the image. The noise model can be represented as follows:

˜*I*(*n*, *m*) = *I*(*n*, *m*) + *η*1(*n*, *m*), (1)

setting the algorithm parameters during the system operation.

for the Early Diagnosis of Breast Cancer in Digital Mammography

to a value randomly selected in a certain interval.

region for inspection etc., during the operation of the system.

**5.1 GROUP 1: Noise contribution in mammographic images**

and limitations, and to compare the method with different existing approaches.

investigation, useful for the CAD validation.

functionalities.

intrinsic and unpredictable data variability (e.g., patient movement);

probability density function (pdf) for *Y*; uncertainty propagation based on replacing the model by a first-order Taylor series approximation (also called the the law of propagation of uncertainty); numerical methods that implement the propagation of distributions, specifically using Monte Carlo method, that will be described in the following.

Monte Carlo method provides a general approach to obtain an approximate numerical representation of the distribution function *FY* for *Y*. The heart of the approach is repeated sampling from the pdfs for the *Xi*. The implementation of the method is summarized below:

Step f) is crucial because it can be formulated as a constrained minimization problem. In fact, given a coverage probability *p*, the associated confidence interval [*y*1, *y*2]*p* is obtained as the minimum interval [*a*, *b*] such that *G*−1(*b*) − *G*−1(*a*) = *p*. When the pdf of *Y* is symmetric the solution is trivial an equal to *G*−1((1 + *p*)/2) − *G*−1((1 − *p*)/2). Some relevant features of Monte Carlo method are: a reduction in the analysis effort required for complicated or non-linear models, especially since the partial derivatives of first- or higher-order of the model are not needed; generally improved estimate of *Y* for non-linear models; improved standard uncertainty associated with the estimate of *Y* for non-linear models, especially when the *Xi* are assigned non-Gaussian (e.g. asymmetric) pdfs, without the need to provide derivatives of higher order1; provision of a confidence interval corresponding to a stipulated coverage probability when the pdf for *Y* cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution, i.e. when the central limit theorem does not apply.

Being the measurement uncertainty modeling a central part in the assessment of the CAD performance, in the following section, we will describe the major sources of uncertainty that can be identified in a CAD for mammography.

#### **5. Uncertainty modeling in a CAD**

Numerous sources of uncertainty have to be taken into account in a medical image processing system for breast cancer detection and diagnosis, both in the system development step and in the operating conditions. Keeping in mind the two different situations, here below, we recall the most relevant sources of uncertainty subdividing them into five groups: instrumental

1 This point is crucial when an evident asymmetric pdf should be assigned to the input quantity such as for photon noise.

8 Will-be-set-by-IN-TECH

specifically using Monte Carlo method, that will be described in the following.

a) select the number *M* of Monte Carlo trials to be made;

input quantities *Xi*;

probability *p*.

provide the estimation *G* of *FY*;

can be identified in a CAD for mammography.

**5. Uncertainty modeling in a CAD**

for photon noise.

probability density function (pdf) for *Y*; uncertainty propagation based on replacing the model by a first-order Taylor series approximation (also called the the law of propagation of uncertainty); numerical methods that implement the propagation of distributions,

b) generate *M* vectors, by sampling from the assigned pdfs, as realizations of the (set of *N*)

c) for each such vector, form the corresponding model value of *Y*, yielding *M* model values; d) sort these *M* model values into strictly increasing order, using the sorted model values to

e) use *G* to form an estimate *y* of *Y* and the standard uncertainty *u*(*y*) associated with *y*. f) use *G* to form an appropriate confidence interval for *Y*, for a stipulated coverage

Step f) is crucial because it can be formulated as a constrained minimization problem. In fact, given a coverage probability *p*, the associated confidence interval [*y*1, *y*2]*p* is obtained as the minimum interval [*a*, *b*] such that *G*−1(*b*) − *G*−1(*a*) = *p*. When the pdf of *Y* is symmetric the solution is trivial an equal to *G*−1((1 + *p*)/2) − *G*−1((1 − *p*)/2). Some relevant features of Monte Carlo method are: a reduction in the analysis effort required for complicated or non-linear models, especially since the partial derivatives of first- or higher-order of the model are not needed; generally improved estimate of *Y* for non-linear models; improved standard uncertainty associated with the estimate of *Y* for non-linear models, especially when the *Xi* are assigned non-Gaussian (e.g. asymmetric) pdfs, without the need to provide derivatives of higher order1; provision of a confidence interval corresponding to a stipulated coverage probability when the pdf for *Y* cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution, i.e. when the central limit theorem does not apply.

Being the measurement uncertainty modeling a central part in the assessment of the CAD performance, in the following section, we will describe the major sources of uncertainty that

Numerous sources of uncertainty have to be taken into account in a medical image processing system for breast cancer detection and diagnosis, both in the system development step and in the operating conditions. Keeping in mind the two different situations, here below, we recall the most relevant sources of uncertainty subdividing them into five groups: instrumental

1 This point is crucial when an evident asymmetric pdf should be assigned to the input quantity such as

uncertainty, uncertainty sources related to the patient, model uncertainty related to the CAD parameters selection, uncertainty sources related to the input provided by the radiologist during the system development and validation steps (reference values etc.), the uncertainty sources related to the possible interaction among the CAD and the physician who is manually setting the algorithm parameters during the system operation.

Some of these sources of uncertainty (GROUPS 1 and 3) can be reasonably modelled and considered in the uncertainty estimation process (Mazzarella & Bazzocchi, 2007), while some other (GROUPS 2, 4, and 5) have unknown nature and are difficult to be embedded, even if noteworthy. As a consequence of the large subjectivity in using the CAD system in this context, a metrological validation of medical image processing approaches is required to highlight the intrinsic characteristics and behavior of a method, to evaluate its performance and limitations, and to compare the method with different existing approaches.

In the following sections, we will describe with more details a possible modelization of the uncertainty contributions summarized above, providing examples taken from ABCDE's functionalities.

#### **5.1 GROUP 1: Noise contribution in mammographic images**

Each step that contributes to the final digital mammographic image influences the global uncertainty in a different way: the formation process, based on X-ray exposure, introduces a noise contribution that is intensity dependent (e.g., photon noise), the microscopic structure of the impressed film introduces the so-called *film grain noise*, finally the digitalization process when performed through scanner devices, introduces an uncertainty contribution that is related to the number of bit per pixel (bpp) used in the conversion, or an uncertainty term that presents systematic periodic patterns (Mencattini et al., 2009b) superimposed to the image. Photon noise is the dominant random contribution in this context, since the bpp is usually 12 − 16, but other relevant noise contributions can be present at low and high exposures. Consequently, as suggested in (Jain, 1989), we consider an *heteroscedastic noise model* for the random contribution assuming that the noise variance depends on the intensity of each pixel, and it is not constant within the image. The noise model can be represented as follows:

$$\tilde{I}(n,m) = I(n,m) + \eta\_1(n,m),\tag{1}$$

Fig. 5. The noise variance estimation algorithm.

for the Early Diagnosis of Breast Cancer in Digital Mammography

*B* with the same evidence.

seconds are needed in order to form a single mammographic image), to artifacts that can be present in the final image, due to dust, fingerprints, scratch, and to the non random contribution introduced by the scanner itself, such as the spatial non uniformity introduced in the luminance. For example, the images database we consider, e.g., the Digital Database for Screening Mammography (DDSM) (Heath et al., 1998) uses the three scanners DBA, HOWTEK, and LUMISYS to digitalize more than 4000 mammographic images. We can notice that the final images are corrupted by a periodic pattern contribution that we assumed to be systematic. An example is shown in Fig. 6(a)-(b) where two regions are extracted from the same mammographic image. Region *A* is dark and it is evident that there is an overlying periodic pattern that here is also emphasized by an histogram stretching. On the contrary, region *B* is corrupted by noise but the periodic pattern is much more subtle. In Fig. 6(c) the two-dimensional Fourier Transforms of the two regions are also shown proving that there is a unidirectional periodic pattern overlying region *A* and that the same does not hold for region

303 Metrological Assessment of a CAD System

It is well known that systematic effects have to be corrected before performing a reliable uncertainty propagation of random effects (Santo et al., 2004). Unfortunately, as a consequence of the previous considerations, this kind of contributions is both luminance and spatial dependent so that it is very difficult to evaluate and correct it. Moreover, from both medical and visual viewpoints, it could be dangerous to preliminarily correct the images from non random contribution thus altering the final aspects of the images and falsifying the correct diagnosis of microcalcifications. In this regard, the new version of International Vocabulary of Metrology (VIM) (see (*International vocabulary of metrology. Basic and general concepts and associated terms (VIM)*, 2008) paragraph 2.26) states that *Sometimes, estimated systematic effects are not corrected for but, instead, associated measurement uncertainty components are incorporated*. Finally, scanner devices used in medical laboratories are not completely characterized from a metrological point of view thus making the exact evaluation of these effects for correction impossible. As a possible solution, we assume to treat non random contributions as systematic

where ˜*I*(*n*, *m*) is the noisy image, *I*(*n*, *m*) is the noise-free image, *η*1(*n*, *m*) is a zero mean non stationary random process given by *η*1(*n*, *m*) = *η* · *σ*(*n*, *m*) with *η* ∼ N (0, 1) a normal random process with zero mean and unitary variance, and *σ*2(*n*, *m*) the spatial-dependent variance of the process *η*1(*n*, *m*).

The assumption of a normal random process with non constant variance is fully justified (Jain, 1989) for luminance values in the subrange [0.2 − 0.8] that corresponds to what we are interested in; actually, dark or very bright pixels are corrupted by a saturated gaussian noise with cut tails. This problem could occasionally produce an underestimation of the noise variance we perform, but involving regions far from the regions of interest.

It is well known that the noise variance *σ*2(*n*, *m*) depends on the intensity *I*(*n*, *m*). In particular, we get that *σ*2(*n*, *m*) = *αI*(*n*, *m*)*β* for scanner devices and *σ*2(*n*, *m*) = *γ* · log10(*I*(*n*, *m*)) − *d*0 for photographic films. Consequently, an estimation procedure is needed in order to estimate the unknown dependence of the noise variance *σ*2(*n*, *m*) on the intensity *I*(*n*, *m*). To do this, we implement the noise estimation introduced in (Gravel et al., 2004), later extended and improved in (.Mencattini et al., 2007; Salmeri et al., 2008). The strength of the estimation algorithm is that it can be applied to very different kind of medical images (MRI, ultrasound images, etc.) where noise is signal dependent following different probability distribution (Rician noise, Rayleigh, etc). In case of homoscedastic noise (where noise variance is constant through the image) the estimation algorithm still provides an accurate estimation of the noise variance, needed in many algorithms for image denoising and enhancement (Mencattini et al., 2010b; 2008). Here below, we only report a sketch of the whole estimation algorithm.

A block diagram of the whole algorithm is reported in Fig. 5.

Unfortunately, uncertainty contribution do not embed only random effects, related to noise. In fact, in medical diagnosis, it is often crucial to take into account also non random contributions that can occur during the exposure, the acquisition and the digitalization of the image. We refer for example to physiological movements of the patient (a few 10 Will-be-set-by-IN-TECH

where ˜*I*(*n*, *m*) is the noisy image, *I*(*n*, *m*) is the noise-free image, *η*1(*n*, *m*) is a zero mean non stationary random process given by *η*1(*n*, *m*) = *η* · *σ*(*n*, *m*) with *η* ∼ N (0, 1) a normal random process with zero mean and unitary variance, and *σ*2(*n*, *m*) the spatial-dependent variance of

The assumption of a normal random process with non constant variance is fully justified (Jain, 1989) for luminance values in the subrange [0.2 − 0.8] that corresponds to what we are interested in; actually, dark or very bright pixels are corrupted by a saturated gaussian noise with cut tails. This problem could occasionally produce an underestimation of the noise

It is well known that the noise variance *σ*2(*n*, *m*) depends on the intensity *I*(*n*, *m*). In particular, we get that *σ*2(*n*, *m*) = *αI*(*n*, *m*)*β* for scanner devices and *σ*2(*n*, *m*) = *γ* · log10(*I*(*n*, *m*)) − *d*0 for photographic films. Consequently, an estimation procedure is needed in order to estimate the unknown dependence of the noise variance *σ*2(*n*, *m*) on the intensity *I*(*n*, *m*). To do this, we implement the noise estimation introduced in (Gravel et al., 2004), later extended and improved in (.Mencattini et al., 2007; Salmeri et al., 2008). The strength of the estimation algorithm is that it can be applied to very different kind of medical images (MRI, ultrasound images, etc.) where noise is signal dependent following different probability distribution (Rician noise, Rayleigh, etc). In case of homoscedastic noise (where noise variance is constant through the image) the estimation algorithm still provides an accurate estimation of the noise variance, needed in many algorithms for image denoising and enhancement (Mencattini et al., 2010b; 2008). Here below, we only report a sketch of the

a) Extract low-frequency components from the image containing homogeneous regions. This step is performed by applying a low pass gaussian filter to the original noisy image

b) Evaluate the high frequency components of the image by the subtraction of the smoothed image to the original one. Obviously this image contains both small details, boundaries,

c) Eliminate edges by applying a robust edge detector to the original image. This further step is needed in order to eliminate edges from the estimation procedure, that would decrease noise variance estimation accuracy. Then, by thresholding we obtain a binary mask of

d) Build an histogram of relating each bin to the intensity of image considering pixels at the

e) Evaluate the standard deviation of each bin by a Median Absolute Deviation (MAD)

f) Perform a robust regression analysis by Cubic Smoothing Spline in order to fit the data

Unfortunately, uncertainty contribution do not embed only random effects, related to noise. In fact, in medical diagnosis, it is often crucial to take into account also non random contributions that can occur during the exposure, the acquisition and the digitalization of the image. We refer for example to physiological movements of the patient (a few

same position in the smoothed image and in the noise image.

A block diagram of the whole algorithm is reported in Fig. 5.

variance we perform, but involving regions far from the regions of interest.

the process *η*1(*n*, *m*).

whole estimation algorithm.

and noise.

estimator.

principal edges.

extracted at step (e).

obtaining a smoothed orignal image.

Fig. 5. The noise variance estimation algorithm.

seconds are needed in order to form a single mammographic image), to artifacts that can be present in the final image, due to dust, fingerprints, scratch, and to the non random contribution introduced by the scanner itself, such as the spatial non uniformity introduced in the luminance. For example, the images database we consider, e.g., the Digital Database for Screening Mammography (DDSM) (Heath et al., 1998) uses the three scanners DBA, HOWTEK, and LUMISYS to digitalize more than 4000 mammographic images. We can notice that the final images are corrupted by a periodic pattern contribution that we assumed to be systematic. An example is shown in Fig. 6(a)-(b) where two regions are extracted from the same mammographic image. Region *A* is dark and it is evident that there is an overlying periodic pattern that here is also emphasized by an histogram stretching. On the contrary, region *B* is corrupted by noise but the periodic pattern is much more subtle. In Fig. 6(c) the two-dimensional Fourier Transforms of the two regions are also shown proving that there is a unidirectional periodic pattern overlying region *A* and that the same does not hold for region *B* with the same evidence.

It is well known that systematic effects have to be corrected before performing a reliable uncertainty propagation of random effects (Santo et al., 2004). Unfortunately, as a consequence of the previous considerations, this kind of contributions is both luminance and spatial dependent so that it is very difficult to evaluate and correct it. Moreover, from both medical and visual viewpoints, it could be dangerous to preliminarily correct the images from non random contribution thus altering the final aspects of the images and falsifying the correct diagnosis of microcalcifications. In this regard, the new version of International Vocabulary of Metrology (VIM) (see (*International vocabulary of metrology. Basic and general concepts and associated terms (VIM)*, 2008) paragraph 2.26) states that *Sometimes, estimated systematic effects are not corrected for but, instead, associated measurement uncertainty components are incorporated*. Finally, scanner devices used in medical laboratories are not completely characterized from a metrological point of view thus making the exact evaluation of these effects for correction impossible. As a possible solution, we assume to treat non random contributions as systematic

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

for the Early Diagnosis of Breast Cancer in Digital Mammography

Fig. 7. Noise variance modeling for scanners HOWTEK-A and LUMISYS (left) and DBA (right). A Cubic Smoothing Spline regression is applied with a smoothing parameter equal to 0.9999 for scanners HOWTEK-A and LUMISYS and to 0.999 to scanner DBA. The systematic

this case, photon noise is the dominant contribution. The digital mammography device has a

1

2

σ2(I)

Fig. 8. Noise variance modeling for Joice-Loebl scanning microdensitometer (a) and for GE Senograph 2000D ADS 17.3 (b). A Cubic Smoothing Spline regression is applied with a smoothing parameter equal to 0.999. The systematic noise variation is marked by the arrows. It can be noted that the noise dependence from the pixel intensity strongly varies across different digitalization devices, according to pixel quantization, spatial resolution, scanner calibration curve, etc. Also, the systematic noise variation is different across the devices.

Uncertainty sources due to biological and patient variability are probably the most difficult kind of uncertainty to consider because it groups together unpredictable variations in patient

3

4 x 10-4

1

σ2(I)

305 Metrological Assessment of a CAD System

2 x 10-4

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

Luminance I

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

Luminance I

(b)

Luminance I

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0

Luminance I

(a)

**5.2 GROUP 2: biological and patient variability**

noise variation is marked by the arrows.

logarithmic characteristic curve.

1

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10-5

σ2(I)

σ

2(I)

2 x 10-4

Fig. 6. (a) A mammographic image with a dark region (A) exhibiting a periodic pattern and a bright region (B) in which the same effect is much more subtle. (b) A zoom of the two regions A and B. (c) The 2D-FFT of the regions A and B respectively.

effects and to embed them in a unified uncertainty model, implementing an uncertainty propagation through a suitable method.

A viable solution is to use information extracted by the estimation procedure performed for the noise variance modeling. In this way, by merging different images coming from the same scanner or digitalization device, we are able to provide more accurate limits for the systematic contribution. In the following, we will provide an example for the whole noise estimation procedure considering the three different databases: MiniMIAS, DDSM, and San Paolo FFDM images.

Fig. 7 reports the noise variance modeling considering DDSM images for the three different scanners HOWTEK-A, LUMISYS, and DBA at different spatial and pixel resolution. Note that for low luminance values electronic noise in HOWTEK-A and in DBA is the dominant noise contribution, while photon noise due to X-ray exposure has a small variance at high and low exposure. Noise variance related to photon noise has a maximum value in the range [0.4 − 0.6] for scanners LUMISYS, HOWTEK-A, and DBA. Fig. 8(a) shows the noise variance estimation for images from MiniMIAS database. Photon noise is low at high and low exposure and the noise variance has a maximum value in the same range as above. Both LUMISYS, HOWTEK-A, and MIAS scanning device have a linear characteristic curve. Conversely, scanner DBA has a logarithmic response. Finally, Fig. 8(b) reports the noise variance estimation performed on the FFDM images from the San Paolo Hospital. Also in 12 Will-be-set-by-IN-TECH

Fig. 6. (a) A mammographic image with a dark region (A) exhibiting a periodic pattern and a bright region (B) in which the same effect is much more subtle. (b) A zoom of the two regions

effects and to embed them in a unified uncertainty model, implementing an uncertainty

A viable solution is to use information extracted by the estimation procedure performed for the noise variance modeling. In this way, by merging different images coming from the same scanner or digitalization device, we are able to provide more accurate limits for the systematic contribution. In the following, we will provide an example for the whole noise estimation procedure considering the three different databases: MiniMIAS, DDSM, and San Paolo FFDM

Fig. 7 reports the noise variance modeling considering DDSM images for the three different scanners HOWTEK-A, LUMISYS, and DBA at different spatial and pixel resolution. Note that for low luminance values electronic noise in HOWTEK-A and in DBA is the dominant noise contribution, while photon noise due to X-ray exposure has a small variance at high and low exposure. Noise variance related to photon noise has a maximum value in the range [0.4 − 0.6] for scanners LUMISYS, HOWTEK-A, and DBA. Fig. 8(a) shows the noise variance estimation for images from MiniMIAS database. Photon noise is low at high and low exposure and the noise variance has a maximum value in the same range as above. Both LUMISYS, HOWTEK-A, and MIAS scanning device have a linear characteristic curve. Conversely, scanner DBA has a logarithmic response. Finally, Fig. 8(b) reports the noise variance estimation performed on the FFDM images from the San Paolo Hospital. Also in

FFT of a region without any evident periodic pattern

FFT of a region exhibiting a unidirectional periodic pattern

A and B. (c) The 2D-FFT of the regions A and B respectively.

propagation through a suitable method.

images.

Fig. 7. Noise variance modeling for scanners HOWTEK-A and LUMISYS (left) and DBA (right). A Cubic Smoothing Spline regression is applied with a smoothing parameter equal to 0.9999 for scanners HOWTEK-A and LUMISYS and to 0.999 to scanner DBA. The systematic noise variation is marked by the arrows.

this case, photon noise is the dominant contribution. The digital mammography device has a logarithmic characteristic curve.

Fig. 8. Noise variance modeling for Joice-Loebl scanning microdensitometer (a) and for GE Senograph 2000D ADS 17.3 (b). A Cubic Smoothing Spline regression is applied with a smoothing parameter equal to 0.999. The systematic noise variation is marked by the arrows.

It can be noted that the noise dependence from the pixel intensity strongly varies across different digitalization devices, according to pixel quantization, spatial resolution, scanner calibration curve, etc. Also, the systematic noise variation is different across the devices.

#### **5.2 GROUP 2: biological and patient variability**

Uncertainty sources due to biological and patient variability are probably the most difficult kind of uncertainty to consider because it groups together unpredictable variations in patient

developed by Ferrero and Salicone (Ferrero & Salicone, 2009; Salicone, 2007) and it is still under investigation the possible application of the method to iterative and more complex

307 Metrological Assessment of a CAD System

*Context* Handling and propagation of random uncertainty contributions due to image noise through the automatic segmentation and classification of massive lesions in mammographic

*Algorithm* Segmentation is performed by an iris detection algorithm, an iterative region-growing procedure is applied to extract the mass boundary, geometric and textural (Haralick) features are computed for each segmented lesion, and finally a Bayes linear classifier is applied to assign a malignancy degree to each lesion (Mencattini et al., 2009a).

*Method* Monte Carlo simulations using 50 trials on ROIs 1000 × 1000. The AUC-based performance assessment has been performed. Fig. 9 reports the cumulative distribution function and the histogram of the AUC obtained after the trials. Note that the AUC parameter

has a clear non-Gaussian probability distribution, such that the confidence interval for *p* = 0.9

*Context and Algorithm* An analogous study has been developed in collaboration with the San Paolo Hospital and the Dept. of Mathematics University of Bari, using the active contour algorithm developed by Chan and Vese (Chan & Vese, 2001) for the segmentation step, the fractal analysis and support vector machines for the malignancy assessment. Preliminary

*Materials* San paolo FFDM Images and DDSM images containing malignant and benign

*Context* Conditional statements in a fuzzy logic inference system for pattern classification (Ferrero et al., 2010; Mencattini & Salmeri, 2011a). The pattern classification step is an important section of a CAD because it is use in many functionalities: in the automatic identification of lesions a classifier is used to reduce false positive lesion candidates discriminating them from true lesions; in the malignancy assessment a classification step

is very different than the interval obtained under the assumption of normality.

elaboration units.

**5.3.2 Iterative elaboration units**

images (Mencattini et al., 2009a; 2010a; Rabottino et al., 2011).

for the Early Diagnosis of Breast Cancer in Digital Mammography

Fig. 9. AUC cumulative distribution function and histogram.

results can be found in (Mencattini et al., 2011d).

*Method* Monte Carlo simulations using 100 trials.

massive lesions histologically proven.

**5.3.3 Conditional elaboration units**

*Materials* DDSM Images containing malignant and benign massive lesions.

physiological status and position. Fortunately, the protocol that regulates mammography provides a set of rules that allow you to control many of these sources of uncertainty: the breast is compressed and locked during exposure to X-rays, reducing the possible involuntary movements also due to the simple respiratory motion; the hormonal changes that may occur during the patient's mammography are also controlled as much as possible through detailed recommendations about the optimal time to perform the examination in relation to the menstrual cycle. In any case, a complete and accurate CAD system should also provide the possibility to receive and process information relating to the phase of the woman's life: at puberty, lactation, or menopause, in order to adapt algorithm parameters such as for example those related to fibro-glandular disk extraction in bilateral asymmetry detection.

#### **5.3 GROUP 3: model uncertainty**

A CAD for mammography consists of several blocks, as already shown in the introduction. The correct functioning and adaptation of each block involve the use of inline tuned parameters that are initialized to a certain value (randomly or not) and can be changed during the system functioning, according to the image characteristics (adaptation) or according to pre-specified rules. The CAD developers identify these rules during the system development and validation steps, using large datasets of mammographic images, but a complete knowledge of the behavior of the selected parameters is not realistic. In light of this, a formal way to deal with this incomplete knowledge is to perform an analysis of sensitivity, that, considering a parameter at a time, introduces small perturbation of it and evaluate the final effect on the block output. By an iterative procedure, the developer can assign an interval of values to each block output with a dual effect: quantifying the most critical parameters that most influence the output and modify the block in order to improve the robustness of the whole system to unpredictable parameters variations.

The CAD elaboration units can be divided into three categories:

According to the typology, different kind of uncertainty modelling should be performed. Here below, we provide some examples already investigated by the authors in previous works. In Section 6 will be described in more detail a recent study in the context of the identification of bilateral asymmetry.

#### **5.3.1 Direct elaboration units**

*Context* Handling and propagation of random and systematic uncertainty contributions due to image noise through a wavelet-based enhancement and denoising procedure for microcalcification detection (Mencattini et al., 2009b).

*Materials* DDSM Images containing malignant and benign calcifications.

*Method* Random Fuzzy Variables able to simultaneously represent and propagate through dedicated mathematical operators random and systematic terms. The method has been developed by Ferrero and Salicone (Ferrero & Salicone, 2009; Salicone, 2007) and it is still under investigation the possible application of the method to iterative and more complex elaboration units.

#### **5.3.2 Iterative elaboration units**

14 Will-be-set-by-IN-TECH

physiological status and position. Fortunately, the protocol that regulates mammography provides a set of rules that allow you to control many of these sources of uncertainty: the breast is compressed and locked during exposure to X-rays, reducing the possible involuntary movements also due to the simple respiratory motion; the hormonal changes that may occur during the patient's mammography are also controlled as much as possible through detailed recommendations about the optimal time to perform the examination in relation to the menstrual cycle. In any case, a complete and accurate CAD system should also provide the possibility to receive and process information relating to the phase of the woman's life: at puberty, lactation, or menopause, in order to adapt algorithm parameters such as for example

A CAD for mammography consists of several blocks, as already shown in the introduction. The correct functioning and adaptation of each block involve the use of inline tuned parameters that are initialized to a certain value (randomly or not) and can be changed during the system functioning, according to the image characteristics (adaptation) or according to pre-specified rules. The CAD developers identify these rules during the system development and validation steps, using large datasets of mammographic images, but a complete knowledge of the behavior of the selected parameters is not realistic. In light of this, a formal way to deal with this incomplete knowledge is to perform an analysis of sensitivity, that, considering a parameter at a time, introduces small perturbation of it and evaluate the final effect on the block output. By an iterative procedure, the developer can assign an interval of values to each block output with a dual effect: quantifying the most critical parameters that most influence the output and modify the block in order to improve the robustness of the

According to the typology, different kind of uncertainty modelling should be performed. Here below, we provide some examples already investigated by the authors in previous works. In Section 6 will be described in more detail a recent study in the context of the identification of

*Context* Handling and propagation of random and systematic uncertainty contributions due to image noise through a wavelet-based enhancement and denoising procedure for

*Method* Random Fuzzy Variables able to simultaneously represent and propagate through dedicated mathematical operators random and systematic terms. The method has been

those related to fibro-glandular disk extraction in bilateral asymmetry detection.

**5.3 GROUP 3: model uncertainty**

nonlinear operators;

bilateral asymmetry.

**5.3.1 Direct elaboration units**

whole system to unpredictable parameters variations.

change during the block functioning;

or changing during the functioning).

microcalcification detection (Mencattini et al., 2009b).

*Materials* DDSM Images containing malignant and benign calcifications.

The CAD elaboration units can be divided into three categories:

*Context* Handling and propagation of random uncertainty contributions due to image noise through the automatic segmentation and classification of massive lesions in mammographic images (Mencattini et al., 2009a; 2010a; Rabottino et al., 2011).

*Algorithm* Segmentation is performed by an iris detection algorithm, an iterative region-growing procedure is applied to extract the mass boundary, geometric and textural (Haralick) features are computed for each segmented lesion, and finally a Bayes linear classifier is applied to assign a malignancy degree to each lesion (Mencattini et al., 2009a).

*Materials* DDSM Images containing malignant and benign massive lesions.

*Method* Monte Carlo simulations using 50 trials on ROIs 1000 × 1000. The AUC-based performance assessment has been performed. Fig. 9 reports the cumulative distribution function and the histogram of the AUC obtained after the trials. Note that the AUC parameter

has a clear non-Gaussian probability distribution, such that the confidence interval for *p* = 0.9 is very different than the interval obtained under the assumption of normality.

*Context and Algorithm* An analogous study has been developed in collaboration with the San Paolo Hospital and the Dept. of Mathematics University of Bari, using the active contour algorithm developed by Chan and Vese (Chan & Vese, 2001) for the segmentation step, the fractal analysis and support vector machines for the malignancy assessment. Preliminary results can be found in (Mencattini et al., 2011d).

*Materials* San paolo FFDM Images and DDSM images containing malignant and benign massive lesions histologically proven.

*Method* Monte Carlo simulations using 100 trials.

#### **5.3.3 Conditional elaboration units**

*Context* Conditional statements in a fuzzy logic inference system for pattern classification (Ferrero et al., 2010; Mencattini & Salmeri, 2011a). The pattern classification step is an important section of a CAD because it is use in many functionalities: in the automatic identification of lesions a classifier is used to reduce false positive lesion candidates discriminating them from true lesions; in the malignancy assessment a classification step

operator (Ferrero et al., 2010). The evaluation of the two antecedents, *number of calcifications in a cluster is HIGH* and *number of calcifications in a cluster is HIGHLY significant for diagnosis MALIGNANT* involves the definition of the fuzzy variable *number of calcifications*, and consequently of the fuzzy sets *HIGH number of calcifications* and *LOW number of calcifications*. This definition consists in the construction of two trapezoidal Membership Functions (MFs) as those reported in Fig. 10 for the two symptoms *number of calcifications* (*Sj*) and *mean entropy of calcifications* (*Sk*). The two MFs are superimposed on the corresponding histograms. Note that,

309 Metrological Assessment of a CAD System

for the Early Diagnosis of Breast Cancer in Digital Mammography

*j M S* μ

*k S*

increases toward the unity and *μB*

*k M S* μ

*S*¯ *j*

*Sj* of a symptom *Sj* for a

decreases

*k B S* μ

*j B S* μ

Fig. 10. Examples of MF construction for symptom *Sj* (number of calcifications) and *Sk* (mean

*J* of the first symptom, the system assigns two degrees of membership

to the class MALIGNANT (M) and BENIGN (B) respectively. As long as the

entropy of calcifications). The magenta bars identify the class *M* while the blue bars

*S*¯ *j*

toward zero. The opposite happens when *Sj* decreases from *x*2 to *x*1. It is evident that each of the two MFs depends on the two parameters *x*1 and *x*2 which are extracted from the distribution of the feature for the different classes. In particular, *x*1 is the maximum value of *Sj* for benign cases such that all the *Sj* for malignant cases are greater than *x*1. Conversely, *x*2 is the minimum value of *Sj* for malignant cases such that all the *Sj* values for benign cases are smaller than *x*2. The evaluation of *x*1 and *x*2 is performed after outliers elimination on each feature *Sj*. Parameters *x*1 and *x*2 influences the final class membership function and an

The second antecedent *number of calcifications is HIGHLY significant for diagnosis MALIGNANT*

diagnosis *Di*, where in the considered example *Di* is *M* or *B*. It represents the degree of influence that a symptom *Sj* can have on a certain diagnosis *Di* and a degree of correlation among them. This correlation is evaluated according to physician's experience or again from the distribution of the symptom's values for each class. Two examples of this calculation are reported in Fig. 11 for the number of calcifications in a cluster and for the mean entropy of calcifications for the two classes Malignant and Benign. In particular, we get for symptom *Sj*

*j S*

represent the class *B*. for a certain value *S*¯

value of *Sj* increases from *x*1 to *x*2 then *μM*

analysis of sensitivity should be implemented for them.

involves the computation of what we called *Incidence Level ILDi*

and *μB S*¯ *j*

*μM S*¯ *j*

is used to assign the malignancy degree to each considered suspicious lesion; lastly, in the identification of bilateral asymmetry the classifier assigns the asymmetry degree to each pair of mammograms under test. Many different classifiers exist in the literature and have been used in developing a CAD for mammography: Bayesian classifier, decision trees, artificial neural networks, logistic regression, support vector machine, fuzzy logic inference systems are the most popular approaches. Each of them has its own peculiarity. For example, SVM is excellent for small training dataset, while artificial neural network has great flexibility to very large datasets. However, most of them can be considered as completely black boxes able to learn from examples and to produce a final class membership. None of them, excluding fuzzy inference systems and decision trees, produces simple classification rules that can be easily understood by physicians. Finally, only fuzzy inference systems can be directly modified by physicians who can add classification rules, according to his/her experience. *Algorithm* Since the method uses a non-standard fuzzy logic system, in the following we will provide a brief introduction of the method. A Fuzzy Inference System (FIS) for medical diagnosis is a nonstandard FIS firstly proposed by Andersson in (Andersson, 2007). The core of such a system is a simple structure composed of three agents: the patient (the mammogram in our context), the symptoms (in our context the features extracted to characterize the object to be classified), and finally the diagnosis (in our context the class, normal or abnormal tissue, benign or malignant lesions, normal or asymmetric breast, etc.). The architecture of such a FIS involves three kind or relations: two input relationships (the relation Mammogram-Features and the relation Features-Diagnosis) and a third relation (the Mammogram-Diagnosis relation) that is derived by the first two relations using a specific inference process. The first relation is built by physicians in the patient-history or anamnesis process, while is learnt by the CAD during the features extraction and training steps. The second relation is derived by the physician according to his/her experience, retrospective study and clinical trials in which a symptom has been confirmed to be significant for a certain diagnosis (e.g., spiculated margins of a mass represent the infiltrating properties of the lesion and a sign of possible malignancy). Finally, the third relation assigns a final class membership to a mammogram or simply to a region of interest (*P* in the following), according to the features extracted on it and on their significance for a certain class. Such a system has been already applied in different situations: the malignancy assessment of calcifications clusters (Ferrero et al., 2010), the false positive reduction in the automatic mass identification (Mencattini & Salmeri, 2011b), the development of a novel scoring system to measure the severity of illness of patients admitted in Intensive Care Units (Mencattini et al., 2011e). In this section, we will consider in details the malignancy assessment of calcifications.

A FIS rule has an IF-THEN structure, an example of two distinct rules is reported below.

IF *number of calcifications in a cluster is HIGH in mammogram P* AND *number of calcifications is HIGHLY significant for diagnosis MALIGNANT* THEN *mammogram P contains a MALIGNANT cluster of calcifications*

IF *mean entropy of calcifications is HIGH in mammogram P* AND *mean entropy of calcifications is HIGHLY significant for diagnosis BENIGN* THEN *mammogram P contains a BENIGN cluster of calcifications*

Each rule is preliminarily evaluated computing the two antecedents according to specific mathematical fuzzy operators and then the rules are aggregated through a weighted average 16 Will-be-set-by-IN-TECH