A design of a dedicated positron emission imaging system for breast cancer was first presented in 1994 by Thompson [13] from the Montreal Neurological Institute of the McGill University, Canada, as a feasibility study for a positron emission mammography unit.

The developed scanner was designed to fit a mammographic unit, so that conventional mammograms could also be performed in the same gantry, thus allowing exact registration of the emission and of the conventional mammographic images [14]. For such purposes, the system included a co-registration tool to facilitate registration between radiographic and metabolic images [15]. A schematic diagram of the scanner is presented in Figure 2.

The developed scanner consists on two planar 2x2 detector arrays of blocks of bismuth germanate (BGO) crystals placed above and below the compressed breast. The detector blocks measure 36x36x20 mm3 and are segmented into 1.9x1.9 mm2 pixels [16]. The separation between the detector heads can be adjusted to match the thickness of the breast. The system uses position sensitive photomultiplier tubes (PS-PMT) that are optically coupled to the crystal blocks. Although the PS-PMTs cover a surface of 72x72 mm2 , their useful field-of-view (FOV) is only of 65x55 mm2 . The coordinates of the coincidence on opposing PS-PMT faces are decoded by the system electronics and corrected for spatial distortion and efficiency [17].

The images from this system are obtained by performing a limited-angle weighted-backpro‐ jection algorithm. This consists on dividing the image into several equidistant planes and backprojecting the lines or response (LOR) onto those planes. With this technique, the image plane closest to the site of the tumor has the most focused image, while all the other planes present more blurred images, as it can be seen in the schematic diagram of Figure 3. This is known as the focal plane effect. The reconstruction scheme is said to be 'weighted backpro‐ jection' because the values that are added to a given plane in the image matrix are weighted accordingly to the probability of detection of an annihilation in that plane, the crystals efficiencies and the photon attenuation along the path to the crystal [14].

**3. Positron emission mammography scanners**

improved early detection of disease.

**3.1. The PEM-I system**

46 Mammography Techniques and Review

measure 36x36x20 mm3

is only of 65x55 mm2

A design of a dedicated positron emission imaging system for breast cancer was first presented in 1994 as a feasibility study for a positron emission mammography unit. Since then, more than ten other systems have been developed, two of which have become commercially available [11, 12]. Those systems differ in the number, geometry and mobility of the detectors used, with consequences on the patient positioning; its ability or not to perform biopsy; the different radiation detection scheme used, including different scintillation crystals; on the strategies used for image reconstruction from the measured projections. In this section we will review the instrumentation issues that impact on the performance of the equipment that use positron emission mammography to image disease. We will emphasize on the most demand‐ ing aspects of these dedicated instruments, showing why they hold the promise for an

A design of a dedicated positron emission imaging system for breast cancer was first presented in 1994 by Thompson [13] from the Montreal Neurological Institute of the McGill University,

The developed scanner was designed to fit a mammographic unit, so that conventional mammograms could also be performed in the same gantry, thus allowing exact registration of the emission and of the conventional mammographic images [14]. For such purposes, the system included a co-registration tool to facilitate registration between radiographic and

The developed scanner consists on two planar 2x2 detector arrays of blocks of bismuth germanate (BGO) crystals placed above and below the compressed breast. The detector blocks

between the detector heads can be adjusted to match the thickness of the breast. The system uses position sensitive photomultiplier tubes (PS-PMT) that are optically coupled to the crystal

decoded by the system electronics and corrected for spatial distortion and efficiency [17].

The images from this system are obtained by performing a limited-angle weighted-backpro‐ jection algorithm. This consists on dividing the image into several equidistant planes and backprojecting the lines or response (LOR) onto those planes. With this technique, the image plane closest to the site of the tumor has the most focused image, while all the other planes present more blurred images, as it can be seen in the schematic diagram of Figure 3. This is known as the focal plane effect. The reconstruction scheme is said to be 'weighted backpro‐ jection' because the values that are added to a given plane in the image matrix are weighted accordingly to the probability of detection of an annihilation in that plane, the crystals

and are segmented into 1.9x1.9 mm2 pixels [16]. The separation

. The coordinates of the coincidence on opposing PS-PMT faces are

, their useful field-of-view (FOV)

metabolic images [15]. A schematic diagram of the scanner is presented in Figure 2.

Canada, as a feasibility study for a positron emission mammography unit.

blocks. Although the PS-PMTs cover a surface of 72x72 mm2

efficiencies and the photon attenuation along the path to the crystal [14].

**Figure 2.** Schematic drawing of the PEM-I detector plates (white areas) mounted on a conventional mammographic unit (gray areas). From [15].

**Figure 3.** Weighted backprojection used in the PEM-I scanner. From [18].

The complete system has a spatial resolution of 2.8 mm FWHM, a time resolution of 12 ns and an efficiency of 3% at a detector separation of 55 mm [19]. It is estimated that the system is not able to detect tumors with a tumor-to-background ratio lower than 6:1 [20].

The preliminary clinical trials, performed with 16 subjects, reported 80% sensitivity and 100% specificity. The accuracy of the exam, computed as the ratio of the sum of the true findings (positive and negative) to the total number of lesions, was 86% [18]. For mammography exams performed on the same subjects, those values were, respectively, 90%, 50% and 81%. The smallest cancerous lesion detected with PEM-I was 1.1x1.1x0.9 cm3 . The lower value of sensitivity with PEM, with respect to mammography, was due, according to the authors, to the small FOV of the PEM device and to the impossibility of imaging tumors localized close to the chest wall (less than 2 cm). These limitations are related to the PMTs used, whose useful field of view is significantly smaller than its area, preventing imaging near their edges. Figure 4 shows a typical set of images obtained with PEM-I, each image corresponding to a plane of the sample, with a visible site of FDG uptake in a region close to the chest wall [19].

**Figure 4.** A typical set of images obtained with the PEM-I scanner. Each image corresponds to a plane, with the left‐ most image corresponding to the image plane closer to the upper detector. A visible site of FDG uptake can be seen in a region close to the chest wall. From [19].

#### **3.2. The Naviscan PEM system**

The original idea of Thompson for a PEM system was further developed by Weinberg and colleagues, for the Naviscan PET System. The Naviscan PEM Flex consists of two 5.6×17.3 cm2 opposed detector heads [21] that can be fit on a steriotactic mammography unit [22]. This way, emission and transmission scans can be obtained. Data acquisition is performed by moving the detectors along a linear path, in order to image as much breast as possible. The PEM detectors translation allows to image an area equal to the entire X-ray field of view [23]. The system can also work separately from the mammography unit, allowing closer chest wall access. Figure 5 shows the PEM Flex system mounted in a stereotactic X-ray mammography unit.

Each detector head contains twelve 13×13 crystal blocks, each coupled to a compact PS-PMT. The crystals are 2×2×10 mm3 of a mixed-lutetium silicate [21].

For each segment of the scan, list mode data are acquired, histogrammed and reconstructed by backprojection. This allows the operator to view partial images during the scan acquisition. At the end of the entire scan, the complete list mode data are reconstructed using a maximumlikelihood expectation-maximization algorithm.

The intrinsic spatial resolution of the system is 1.5 mm FHWM [23]. The image resolution is 2.5 mm FWHM in the plane perpendicular to the displacement and 6 mm between planes. Energy resolution was measured as 14% for 511 keV. The timing window used was 9 ns.

**Figure 5.** The PEM Flex system mounted in a stereotactic X-ray mammography unit. From [22].

The preliminary clinical trials, performed with 16 subjects, reported 80% sensitivity and 100% specificity. The accuracy of the exam, computed as the ratio of the sum of the true findings (positive and negative) to the total number of lesions, was 86% [18]. For mammography exams performed on the same subjects, those values were, respectively, 90%, 50% and 81%. The

sensitivity with PEM, with respect to mammography, was due, according to the authors, to the small FOV of the PEM device and to the impossibility of imaging tumors localized close to the chest wall (less than 2 cm). These limitations are related to the PMTs used, whose useful field of view is significantly smaller than its area, preventing imaging near their edges. Figure 4 shows a typical set of images obtained with PEM-I, each image corresponding to a plane of

**Figure 4.** A typical set of images obtained with the PEM-I scanner. Each image corresponds to a plane, with the left‐ most image corresponding to the image plane closer to the upper detector. A visible site of FDG uptake can be seen in

The original idea of Thompson for a PEM system was further developed by Weinberg and colleagues, for the Naviscan PET System. The Naviscan PEM Flex consists of two 5.6×17.3 cm2 opposed detector heads [21] that can be fit on a steriotactic mammography unit [22]. This way, emission and transmission scans can be obtained. Data acquisition is performed by moving the detectors along a linear path, in order to image as much breast as possible. The PEM detectors translation allows to image an area equal to the entire X-ray field of view [23]. The system can also work separately from the mammography unit, allowing closer chest wall access. Figure 5

Each detector head contains twelve 13×13 crystal blocks, each coupled to a compact PS-PMT.

For each segment of the scan, list mode data are acquired, histogrammed and reconstructed by backprojection. This allows the operator to view partial images during the scan acquisition. At the end of the entire scan, the complete list mode data are reconstructed using a maximum-

The intrinsic spatial resolution of the system is 1.5 mm FHWM [23]. The image resolution is 2.5 mm FWHM in the plane perpendicular to the displacement and 6 mm between planes. Energy resolution was measured as 14% for 511 keV. The timing window used was 9 ns.

of a mixed-lutetium silicate [21].

shows the PEM Flex system mounted in a stereotactic X-ray mammography unit.

the sample, with a visible site of FDG uptake in a region close to the chest wall [19].

. The lower value of

smallest cancerous lesion detected with PEM-I was 1.1x1.1x0.9 cm3

a region close to the chest wall. From [19].

48 Mammography Techniques and Review

**3.2. The Naviscan PEM system**

The crystals are 2×2×10 mm3

likelihood expectation-maximization algorithm.

The clinical trials performed so far [24, 25] were all performed on patients with known breast cancer or suspected lesions. Hence, they provide little information on the specificity of the technique. In one of these studies [25], PEM was able to visualize 39 out of 44 lesions. The non visualized lesions ranged in size from a 1 mm ductal carcinoma in situ (DCIS) to a 1 cm infiltrating ductal carcinoma. Some lesions could not be visualized due to limitations on how posterior the breast tissue is observable by the device. Others, as interpreted by the authors of the study, due to the variability in the metabolic activity of breast cancer cells, similarly to what happens with whole body PET.

**Figure 6.** Image of DCIS obtained with the PEM Flex scanner a), with MRI b) and with mammography c). Neither MRI nor mammography could detect the DCIS lesion seen in the PEM image. From [25].

The most encouraging finding in this trial was the fact that PEM was able to visualize DCIS not visualized by mammography, breast ecography or MRI. An example of such a case can be seen in Figure 6. The smallest lesion detected by PEM in this study was a 2 mm duct of DCIS. This preliminary clinical trial seems to indicate that the technology is promising and worthy of further investigation.

#### **3.3. The West Virginia University — Jefferson Lab PEM system**

Another PEM system was developed and tested at the West Virginia University and at the Jefferson Laboratory by Raylman and colleagues [26]. This PEM system, which is mounted on a stereotactic biopsy table, consists of two square 10×10 cm2 detector arrays of discrete 3×3×10 mm3 GSO crystals. The scintillation light is collected by arrays of PS-PMTs. An image of the scanner mounted on the biopsy table, together with a torso phantom can be seen in Figure 7.

**Figure 7.** Image of the West Virginia University - Jefferson Laboratory PEM system. The PEM detector heads, mounted in a biopsy table, are highlighted by the black arrows. A torso phantom can be seen in the table. From [27].

Since one of the goals of the system is to perform PEM guided biopsies, a trigonometric algorithm was developed to determine the lesion stereotactic coordinates. This algorithm uses two PEM images that are acquired at two symmetric angles (±15◦).

PEM images acquired in a single detector position were initially reconstructed using a weighted backprojection algorithm similar to the used for the PEM-I system described above, or by a limited angle tomography scheme [23]. Later, the use of acquired data at two detector positions (±15◦) [28] to guide stereotactic biopsy motivated the use of an adapted Maximum Likelihood - Expectation Maximization algorithm.

The described acquisition scenario was compared with multiple acquisitions between the same limiting angles, at small uniform increments [29]. The results were somehow mixed, with no clear evidence of significant advantage of one acquisition scenario over the other, although less artifacts were observed with the multiple angle acquisition.

This lead to a study of the complete angular sampling around the breast [30] through step and shoot acquisitions. Not surprisingly, this study showed that the complete angular sampling provided better image quality with respect to a single acquisition with stationary detectors. The study also revealed some of the weaknesses of the system, such as the low rate acquisition capability and the lack of DOI information.

Posterior work reports a new design of the scanner, now named PEM-PET [31], as it means to be a tomographic system. This system has four planar detector heads that can rotate around the breast. The detector crystal used is now LYSO, with 2×2×15 mm3 individual detector elements. The PEM-PET system has 2 mm FHWM resolution, possessing, as its anterior version, the ability to guide biopsy. The initial clinical studies have shown the ability of the system to detect lesions also detected by standard methods [32].

#### **3.4. The Duke University — Jefferson Lab PEM system**

Another system was developed at the Jefferson Laboratory and Duke University to image the compressed breast [33]. This PEM system has two opposed planar 15×20 cm2 detectors that

**Figure 8.** Image of the Duke University - Jefferson Laboratory PEMsystem positioned in a mammography unit. The PEM detectors are highlighted by black arrows.From [34].

acquire data without rotational or translational movements. The detector arrays are composed of 3×3×10 mm3 of lutetium gadolinium oxyorthosilicate, LGSO. The scintillation light is collected by arrays of PS-PMTs. This system is used mounted on an X-ray mammography unit, although the PEM detector heads must be removed to acquire the X-ray image. The distance between the detector heads can be adjusted to match the size of the breast. Image reconstruction is performed by means of the backprojection scheme. The image spatial resolution varied from 4.8 mm to 6 mm, depending on the acceptance angles of the lines of response. An image of the system can be seen in Figure 8.

A pilot clinical trial was performed using this system [34]. This trial included 23 patients with suspected breast malignancies. Therefore, it does not provide meaningful information concerning the specificity of the technique. In this study, where the majority of the evaluated lesions had diameters smaller than 2.5 cm, PEM presented a sensitivity of 86%. The size of the three malignant lesions that PEM was unable to detect varied from 8 mm to 15 mm. The system was able to detect a 4 mm DCIS that was not detected by mammography.

#### **3.5. The maxPET system**

**Figure 7.** Image of the West Virginia University - Jefferson Laboratory PEM system. The PEM detector heads, mounted

Since one of the goals of the system is to perform PEM guided biopsies, a trigonometric algorithm was developed to determine the lesion stereotactic coordinates. This algorithm uses

PEM images acquired in a single detector position were initially reconstructed using a weighted backprojection algorithm similar to the used for the PEM-I system described above, or by a limited angle tomography scheme [23]. Later, the use of acquired data at two detector positions (±15◦) [28] to guide stereotactic biopsy motivated the use of an adapted Maximum

The described acquisition scenario was compared with multiple acquisitions between the same limiting angles, at small uniform increments [29]. The results were somehow mixed, with no clear evidence of significant advantage of one acquisition scenario over the other, although

This lead to a study of the complete angular sampling around the breast [30] through step and shoot acquisitions. Not surprisingly, this study showed that the complete angular sampling provided better image quality with respect to a single acquisition with stationary detectors. The study also revealed some of the weaknesses of the system, such as the low rate acquisition

Posterior work reports a new design of the scanner, now named PEM-PET [31], as it means to be a tomographic system. This system has four planar detector heads that can rotate around

elements. The PEM-PET system has 2 mm FHWM resolution, possessing, as its anterior version, the ability to guide biopsy. The initial clinical studies have shown the ability of the

Another system was developed at the Jefferson Laboratory and Duke University to image the

individual detector

detectors that

in a biopsy table, are highlighted by the black arrows. A torso phantom can be seen in the table. From [27].

two PEM images that are acquired at two symmetric angles (±15◦).

less artifacts were observed with the multiple angle acquisition.

the breast. The detector crystal used is now LYSO, with 2×2×15 mm3

compressed breast [33]. This PEM system has two opposed planar 15×20 cm2

system to detect lesions also detected by standard methods [32].

**3.4. The Duke University — Jefferson Lab PEM system**

Likelihood - Expectation Maximization algorithm.

50 Mammography Techniques and Review

capability and the lack of DOI information.

A dedicated PET camera for mammary and axillary region imaging, maxPET, was designed and constructed at the Crump Institute for Biological Imaging [35]. This group used an alternative scheme to couple the crystal arrays to the PMT's, in order to avoid the problems associated with the inactive area near the PMT edges. The maxPET system consisted of two 15×15 cm2 planar scintillation detector plates, each composed of several modular detectors. The detectors are composed of arrays of 3×3×20 mm3 LSO crystals, each crystal array being coupled to an optical fiber which in turn is coupled to a PS-PMT. The use of the optical fiber allows the exact match between the crystal area and the active PMT dimensions, thus avoiding gaps between detector modules. It also provides better imaging close to the chest wall, since the plates are active out to the edge of the field-of-view. The main disadvantage of the fiberoptic coupling is the loss of scintillation light.

The two detector plates can be mounted in a gantry allowing variable plates separation, detector plates rotation and angular motion. Based on Monte Carlo simulation, the expected intrinsic spatial resolution of the scanner was about 2.3 mm [36]. A prototype of this system was assembled but, to our knowledge, no clinical test were ever performed.

A second prototype of this detector was build, with modified geometry and electronics. The integration of this system with a dedicated CT system was exploited [37].

#### **3.6. The LBNL PEM system**

The PEM scanner developed at the Lawrence Berkeley National Laboratory (LBNL) has two major differences from the PEM scanners described here: it has a rectangular geometry, with four detector plates surrounding the breast and it has Depth of Interaction measurements capabilities [38].

The system uses a 6 ns time window and has 5% sensitivity at the center of the FOV. The measured spatial resolution of the scanner is almost uniform in the entire field-of-view, ranging from 1.9 mm FWHM at the FOV centre to 2.1 mm at the FOV corner [38]. Images of a mini-Derenzo phantom show that the smallest lesion resolved by the system is 2.4 mm in diameter.

In the context of the development of this scanner, a simulation study was done to compare the presented rectangular detector configuration with a dual stationary detector system, such as some of the systems presented above. For such purpose it was used the Fisher information matrix, an analytical computation that allows to characterize how easily a change of one parameter in the source distribution can be identified from the measured data [40]. This study has shown that the rectangular system with Depth of Interaction capability has a higher signalto-noise ratio for detection tasks and a lower bias at a given noise level for quantitation tasks. It is worth stressing that this study did not include the case of a rotating dual head scanner [39]. The LBNL PEM system consists of four detector plates that cover a rectangular 8.2×6.0×5.0 cm3 field of view. The detector modules contain arrays of 3×3×30 mm3 LSO crystals that are coupled to a single photomultiplier tube (PMT) in one end and to a photodiode array (PD) on the other end. The ratio between the signals of the PMT and the PD allow the estimation of the Depth of Interaction of the photon [41]. The achieved DOI resolution ranges from 6 mm FWHM at the PD end to 11 mm FWHM at the PMT end [42].

The image reconstruction task for this scanner has been subject of an intense work. In an initial stage, image reconstruction was performed with a filtered backprojection based reconstruction algorithm that took into account the existence of DOI information and the irregular angular sampling of the scanner [43, 44]. Later, a list mode penalized maximum likelihood algorithm using Gaussian priors was developed [40, 45, 46]. A Monte Carlo based scatter correction algorithm was also developed [46]. To our knowledge, this scanner has never been tested with clinical data.

#### **3.7. The YAP-PEM system**

The YAP-PEM prototype was developed within a collaboration of the Italian Universities of Pisa, Ferrara, Bologna and Roma [47]. The technology of this device derives from a small animal scanner previously developed by the group. The YAP-PEM scanner has been designed with the aim of detecting 5 mm breast lesions in diameter and an activity ratio of 10:1 between the cancer and the breast tissue. The device is composed of two stationary detector heads made of yttrium aluminium perovskite (YAlO3) scintillators doped with cerium (YAP:Ce). This is a scintillator crystal that produces a light output of about 20 photons/keV, has a decay constant of 30 ns and a density of 5.4 g/cm3 [48]. It has, however, a low Z number. Each detector head has a detection area of 6×6 cm2 that comprises 30×30 detection elements with 2×2×30 mm3 each. The system uses PS-PMTs to collect the scintillation light. The distance between the detectors can range from 5 to 10 cm, depending on the breast compression used.

For image reconstruction purposes, the ML-EM algorithm has been adapted to the planar nature of the acquired data, in order to obtain a pseudo-tomographic imaging method [49]. This method works on data that is converted into histograms that are indicated for planar data. These are known as planograms [50]. Geometrical symmetries are used to speed up the computations.

Monte Carlo simulation and image reconstruction studies performed for the YAP-PEM scanner indicate that the scanner is expected to have capability of discriminating 5 mm tumors in a target-to-background ratio of 10:1. However, due to the planar nature of the data, if two sources lie on the same axial plane, the system cannot discriminate them, as it can be seen in Figure 10.

**Figure 9.** Phantom images obtained with the YAP-PEM prototype. Due to the planar nature of the scanner's data, if two sources lie on a same axial plane, the system cannot discriminate them. From [49].

#### **3.8. The Clear-PEM system**

The two detector plates can be mounted in a gantry allowing variable plates separation, detector plates rotation and angular motion. Based on Monte Carlo simulation, the expected intrinsic spatial resolution of the scanner was about 2.3 mm [36]. A prototype of this system

A second prototype of this detector was build, with modified geometry and electronics. The

The PEM scanner developed at the Lawrence Berkeley National Laboratory (LBNL) has two major differences from the PEM scanners described here: it has a rectangular geometry, with four detector plates surrounding the breast and it has Depth of Interaction measurements

The system uses a 6 ns time window and has 5% sensitivity at the center of the FOV. The measured spatial resolution of the scanner is almost uniform in the entire field-of-view, ranging from 1.9 mm FWHM at the FOV centre to 2.1 mm at the FOV corner [38]. Images of a mini-Derenzo phantom show that the smallest lesion resolved by the system is 2.4 mm in

In the context of the development of this scanner, a simulation study was done to compare the presented rectangular detector configuration with a dual stationary detector system, such as some of the systems presented above. For such purpose it was used the Fisher information matrix, an analytical computation that allows to characterize how easily a change of one parameter in the source distribution can be identified from the measured data [40]. This study has shown that the rectangular system with Depth of Interaction capability has a higher signalto-noise ratio for detection tasks and a lower bias at a given noise level for quantitation tasks. It is worth stressing that this study did not include the case of a rotating dual head scanner [39]. The LBNL PEM system consists of four detector plates that cover a rectangular 8.2×6.0×5.0

 field of view. The detector modules contain arrays of 3×3×30 mm3 LSO crystals that are coupled to a single photomultiplier tube (PMT) in one end and to a photodiode array (PD) on the other end. The ratio between the signals of the PMT and the PD allow the estimation of the Depth of Interaction of the photon [41]. The achieved DOI resolution ranges from 6 mm FWHM

The image reconstruction task for this scanner has been subject of an intense work. In an initial stage, image reconstruction was performed with a filtered backprojection based reconstruction algorithm that took into account the existence of DOI information and the irregular angular sampling of the scanner [43, 44]. Later, a list mode penalized maximum likelihood algorithm using Gaussian priors was developed [40, 45, 46]. A Monte Carlo based scatter correction algorithm was also developed [46]. To our knowledge, this scanner has never been tested with

The YAP-PEM prototype was developed within a collaboration of the Italian Universities of Pisa, Ferrara, Bologna and Roma [47]. The technology of this device derives from a small animal

at the PD end to 11 mm FWHM at the PMT end [42].

was assembled but, to our knowledge, no clinical test were ever performed.

integration of this system with a dedicated CT system was exploited [37].

**3.6. The LBNL PEM system**

52 Mammography Techniques and Review

capabilities [38].

diameter.

cm3

clinical data.

**3.7. The YAP-PEM system**

The Clear-PEM system was developed within the framework of the CrystalClear collaboration, in CERN. The system, which was designed to allow the examination of the breast and the axilla regions, is composed of a dual-plate detector head that is housed in a robotic mechanical gantry, as represented in Figure 11. For the breast examination, the patient lays in the prone position with the breast hanging through an aperture in the patient. The two detector heads are positioned in each side of the breast, as represented in Figure 11, and the projection data are acquired at several angular positions. The detector heads can be positioned at different separation distances, allowing for the accommodation of different breast sizes.

**Figure 10.** Representation of the Clear-PEM system.From [51].

The detector heads cover a 16.2×14.1 cm2 FoV. Each detector head holds 96 detector modules, is constituted of a total of 3072 LYSO:Ce crystals, each crystal having 2×2×20 mm3 . A scheme of a detector head is shown in Figure 12a. The distribution of the crystals within, the detector plates is as follows. Each detector plate is constituted of a set of four structures named supermodules, each one with 14×4 cm2 , placed side by side. Each supermodule is composed of 12×2 modules that, in turn, are composed of an array of 4×8 LYSO:Ce crystals. Therefore, each detector plate is constituted of 48×64 LYSO:Ce crystals. Figure 11: Representation of the Clear-PEM system.From (51). The detector heads cover a 16.2×14.1 cm<sup>2</sup> FoV. Each detector head holds 96 detector modules, is constituted of a total of 3072 LYSO:Ce crystals, each crystal having 2×2×20 mm<sup>3</sup> . A scheme of a detector head is shown in Figure 12a). The distribution of the crystals within, the detector plates is as follows. Each detector plate is constituted of a set of four

, placed side by side. Each

structures named supermodules, each one with 14×4 cm2

supermodule is composed of 12×2 modules that, in turn, are composed of an array of 4×8 LYSO:Ce crystals. Therefore, each detector plate is constituted of 48×64 LYSO:Ce crystals.

Figure 12: Clear-PEM detectors. a) Representation of a Clear-PEM detector head, with an highlighted detector supermodule. From (51). b) Representation of a Clear-PEM detector module with the double readout scheme. From (52). The readout of each module is performed by two 32-pixel avalanche photodiodes that are optically coupled to each side of the module, as shown in Figure 12b). This double readout **Figure 11.** Clear-PEM detectors. a) Representation of a Clear-PEM detector head, with an highlighted detector super‐ module. From [51]. b) Representation of a Clear-PEM detector module with the double readout scheme. From [52].

scheme allows the DOI measure. The DOI coordinate within the crystal is estimated from the asymmetry of the collected light at the top and bottom APD pixels. Experimental results have shown that, with this scheme, it is possible to obtain a 2 mm FWHM DOI resolution (53). This measurement is important since it increases the uniformity of measure all over the The readout of each module is performed by two 32-pixel avalanche photodiodes that are optically coupled to each side of the module, as shown in Figure 12b. This double readout scheme allows the DOI measurement. The DOI coordinate within the crystal is estimated from the asymmetry of the collected light at the top and bottom APD pixels. Experimental results have shown that, with this scheme, it is possible to obtain a 2 mm FWHM DOI resolution [53]. This measurement is important since it increases the uniformity all over the field-of-view of the scanner. This feature is not common in the universe of the positron emission mammogra‐ phy dedicated scanners and therefore it is perhaps one of the most important characteristics of this scanner. The processing of the detector analogical signals, including the readout, the low noise amplification, the sampling and the storage are implemented in dedicated ASICs (Application Specific Integrated Circuits) integrated in the detection plates. The output analogue sampled pulses are digitized by Analogue Digital Converters (ADC) and transmitted to the data acquisitions system (DAQ). This system, based on FPGA (Field Programmable Gate Arrays), is responsible for the data reduction and storage. Data is send from here to a trigger system that selects two-photon events in coincidence within a programmable timing window and, at each trigger, the relevant data frames are send to the acquisition PC where energy and time information are analyzed [54]. For events with more than one active crystal in a detector head, due to Compton scattering, an event reconstruction position algorithms is used to assign the coordinates of the interaction. Those events that are within the selected energy window are validated, their final coordinates being used to define the LORs that are stored in a listmode file [53]. Images are reconstructed using 3D statistical iterative algorithms or 2D algebraic techniques [55–57]. Phantom studies showed that the scanner is suitable for milimetric tumor detection; Derenzo phantom studies showed that lesions up to 2 mm in diameter can be clearly seen; a gelatin breast phantom indicated that lesions up to 3 mm in diameter can be detected. The first prototype, installed at the Institute of Nuclear Sciences Applied to Health, Coimbra, Portugal, was used for the first tests in a preclinical environment [58].

More recently, the ClearPEM scanner has been used to create a multimodal PEM and ultrasound scanner [59]. The aim of this system is to provide high resolution, high sensitivity and high specificity metabolic information from PEM matched with 3D high resolution anatomic information. The new ClearPEM-Sonic scanner also provides elastographic information from ultrasound, further improving the specificity of the multimodality scanner. This second prototype is installed at the Hôpital Nord, in Marseille, France, and has confirmed a spatial resolution of about 1.5 mm in phantom studies. The system allows the co-registration of US/ClearPEM and elastography/ClearPEM with an alignment precision of about 2 mm. The first clinical trial has confirm the ability to detect very small lesions only seen by MRI, although lesions very close to the chest wall are left undetect‐ ed [60].

#### **3.9. The MAMMI system**

**Figure 10.** Representation of the Clear-PEM system.From [51].

mm<sup>3</sup>

each detector plate is constituted of 48×64 LYSO:Ce crystals.

The detector heads cover a 16.2×14.1 cm<sup>2</sup>

supermodules, each one with 14×4 cm2

54 Mammography Techniques and Review

The detector heads cover a 16.2×14.1 cm2 FoV. Each detector head holds 96 detector modules,

of a detector head is shown in Figure 12a. The distribution of the crystals within, the detector plates is as follows. Each detector plate is constituted of a set of four structures named

of 12×2 modules that, in turn, are composed of an array of 4×8 LYSO:Ce crystals. Therefore,

modules, is constituted of a total of 3072 LYSO:Ce crystals, each crystal having 2×2×20

supermodule is composed of 12×2 modules that, in turn, are composed of an array of 4×8 LYSO:Ce crystals. Therefore, each detector plate is constituted of 48×64 LYSO:Ce crystals.

Figure 12: Clear-PEM detectors. a) Representation of a Clear-PEM detector head, with an highlighted detector supermodule. From (51). b) Representation of a Clear-PEM detector

**Figure 11.** Clear-PEM detectors. a) Representation of a Clear-PEM detector head, with an highlighted detector super‐ module. From [51]. b) Representation of a Clear-PEM detector module with the double readout scheme. From [52].

The readout of each module is performed by two 32-pixel avalanche photodiodes that are optically coupled to each side of the module, as shown in Figure 12b. This double readout scheme allows the DOI measurement. The DOI coordinate within the crystal is estimated from the asymmetry of the collected light at the top and bottom APD pixels. Experimental results have shown that, with this scheme, it is possible to obtain a 2 mm FWHM DOI resolution [53]. This measurement is important since it increases the uniformity all over the field-of-view of the scanner. This feature is not common in the universe of the positron emission mammogra‐ phy dedicated scanners and therefore it is perhaps one of the most important characteristics of this scanner. The processing of the detector analogical signals, including the readout, the low noise amplification, the sampling and the storage are implemented in dedicated ASICs (Application Specific Integrated Circuits) integrated in the detection plates. The output

The readout of each module is performed by two 32-pixel avalanche photodiodes that are optically coupled to each side of the module, as shown in Figure 12b). This double readout scheme allows the DOI measure. The DOI coordinate within the crystal is estimated from the asymmetry of the collected light at the top and bottom APD pixels. Experimental results have shown that, with this scheme, it is possible to obtain a 2 mm FWHM DOI resolution (53). This measurement is important since it increases the uniformity of measure all over the

. A scheme of a detector head is shown in Figure 12a). The distribution of the crystals within, the detector plates is as follows. Each detector plate is constituted of a set of four

a) b)

, placed side by side. Each supermodule is composed

, placed side by side. Each

FoV. Each detector head holds 96 detector

. A scheme

is constituted of a total of 3072 LYSO:Ce crystals, each crystal having 2×2×20 mm3

Figure 11: Representation of the Clear-PEM system.From (51).

structures named supermodules, each one with 14×4 cm2

module with the double readout scheme. From (52).

MAMMI (MAMmography with Molecular Imaging) is a dedicated breast PET, commercial‐ ized by Oncovision, which has certification in Europe and has recently received FDA approval [61].

Instead of the more often used small pixelated crystal arrays, this scanner uses continuous LYSO crystals coupled to PSPMTs.

The MAMMI prototype is a full ring PET consisting on 12 detector modules forming a dodecagon with a scanner aperture of 186 mm [12]. Each detector module uses 10 mm thick scintillation crystals with 40x40mm2 face. The back face of the crystals are coupled to the PS-PMTs. The detector has a 18% energy resolution at 511 keV, an intrinsic resolution of 1.6 mm and a DOI resolution of 4 mm.

The system aperture provides a 170 mm diameter FoV. The coincidences are allowed between a detector module and its seven opposite modules, providing a transaxial FoV aperture of 170 mm diameter. The axial FoV length is 40 mm per frame; an elevator allows the sequential move of the ring detector in step and shoot mode to increase the axial FoV to 170 mm. A timing window of 5 ns is used.

During image reconstruction the crystal faces are discretized into 2x2 mm2 pixels. Images are reconstructed with standard 3D ML-EM with a voxel size of 1x1x1 mm3 . The system matrix was obtained through calculation of the solid angle of every voxel with respect to the detection surface. Image reconstruction takes into account dead time, scatter and random events correction. A method for attenuation correction without a transmission scan has been devel‐ oped and tested with the system [62].

Patients are imaged in the prone position, which is possible due to the existence of a breast aperture in the patient table. This allows to image regions close to the chest wall without breast compression.

The preliminary results using a 1 mm in diameter 22Na point like source results of 1.6 mm FWHM axial and 1.9 transaxial in the center of the FoV and less than 3 mm FWHM in most other parts of the FoV (axial) [12, 63]. The system sensitivity at the FoV center and with a wide energy window of 250-759 keV is 1 %.

A pilot study was recently conducted with 32 invasive breast cancer patients to assess the feasibility of the system for tumor detection and characterization [64]. The system sensitivity for primary tumor visualization was 97%, which equals whole body PET-CT in the same study. This included lesions close to the chest wall.

#### **4. Conclusions**

With two commercially available PEM scanners, there is now data from several clinical studies that confirm the high sensitivity and specificity values for PEM in different clinical situations [65, 66]. These data also allow a direct comparison with other techniques such as PET and MRI and seem to indicate that the promise of molecular imaging with dedicated instruments as a valuable adjunct technique for mammography holds true.

#### **Author details**

Mónica Vieira Martins1,2

Address all correspondence to<EMAIL_ADDRESS>
1 Polytechnic Institute of Portalegre, Portalegre, Portugal

2 Instituto de Biofísica e Engenharia Biomédica,Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal

#### **References**

of the ring detector in step and shoot mode to increase the axial FoV to 170 mm. A timing

was obtained through calculation of the solid angle of every voxel with respect to the detection surface. Image reconstruction takes into account dead time, scatter and random events correction. A method for attenuation correction without a transmission scan has been devel‐

Patients are imaged in the prone position, which is possible due to the existence of a breast aperture in the patient table. This allows to image regions close to the chest wall without breast

The preliminary results using a 1 mm in diameter 22Na point like source results of 1.6 mm FWHM axial and 1.9 transaxial in the center of the FoV and less than 3 mm FWHM in most other parts of the FoV (axial) [12, 63]. The system sensitivity at the FoV center and with a wide

A pilot study was recently conducted with 32 invasive breast cancer patients to assess the feasibility of the system for tumor detection and characterization [64]. The system sensitivity for primary tumor visualization was 97%, which equals whole body PET-CT in the same study.

With two commercially available PEM scanners, there is now data from several clinical studies that confirm the high sensitivity and specificity values for PEM in different clinical situations [65, 66]. These data also allow a direct comparison with other techniques such as PET and MRI and seem to indicate that the promise of molecular imaging with dedicated instruments as a

2 Instituto de Biofísica e Engenharia Biomédica,Faculdade de Ciências, Universidade de

pixels. Images are

. The system matrix

During image reconstruction the crystal faces are discretized into 2x2 mm2

reconstructed with standard 3D ML-EM with a voxel size of 1x1x1 mm3

window of 5 ns is used.

56 Mammography Techniques and Review

compression.

**4. Conclusions**

**Author details**

Mónica Vieira Martins1,2

Lisboa, Lisboa, Portugal

oped and tested with the system [62].

energy window of 250-759 keV is 1 %.

This included lesions close to the chest wall.

valuable adjunct technique for mammography holds true.

Address all correspondence to<EMAIL_ADDRESS>
1 Polytechnic Institute of Portalegre, Portalegre, Portugal

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#### **Chapter 4 Provisional chapter**

#### **Digital Mammogram Enhancement Digital Mammogram Enhancement**

Michal Haindl and Václav Remeš Michal Haindl and Václav Remeš

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60988

#### **1. Introduction**

Methods Phys Res Sect A Accel Spectrometers, Detect Assoc Equip. 2011 Aug;

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648:S75–S78.

62 Mammography Techniques and Review

Three fully automatic methods for X-ray digital mammogram enhancement based on a fast analytical textural model are presented. These efficient single and double view enhancement methods are based on the underlying two-dimensional adaptive causal autoregressive texture model. The methods locally predict breast tissue texture from single or double view mammograms and enhance breast tissue abnormalities, such as the sign of a developing cancer, using the estimated model prediction statistics. The double-view mammogram enhancement is based on the cross-prediction of two mutually registered left and right breasts' mammograms or alternatively a temporal sequence of mammograms. The single-view mammogram enhancement is based on modeling prediction error in case of not the both breasts' mammograms being available.

Breast cancer is the most common type of cancer among middle-aged women in most developed countries [1, 2].  According to the American Cancer Society [3] about 232 670 new cases of invasive breast cancer will be diagnosed in women and about 40 000 women will die from breast cancer in US alone. US mortality rate is 30% and European mortality rate is 45% [4].

To lower the mortality rate, women in the developed countries usually regularly attend a preventive mammography screening. However, around 25% of radiologically visible cancers are missed by the radiologists at screening [5]. This means that millions of cancer cases are missed and therefore even a slightest improvement in the detection methods could have a huge impact and save many lives.

The biggest problem with current Computer-Aided Diagnosis (CAD) systems is their large false negative rate and an even larger false positive rate. Most CAD systems (e.g., [1, 6]) point out 2-3 regions of interest (ROIs) per mammogram on average. Taking into account that there are about 8 malignant mammograms in 1000 [5], the radiologists consider the current CAD systems as misleading.

©2012 prezimena autora, kod vise prvi et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

An alternative way is to automatically enhance mammograms to support radiologists with their visual mammogram evaluation. Several mammogram enhancement methods have been published [7–14]. Salvado and Roque [10] use wavelet analysis to detect microcalcifications, Dippel et al. [8] compare the merits of using either Laplacian pyramids or wavelet analysis for whole mammogram enhancement, Sakellaropoulos et al. [9] designed an adaptive wavelet based method for enhancing the contrast of the whole mammograms. Mencattini et al. [13] selectively enhance segmented mammograms regions using wavelet transformation.

An approach to diagnostic evaluation of screening mammograms based on local statistical Gaussian mixture textural models was proposed in [14]. The local evaluation tool has the form of a multivariate probability density of gray levels in a suitably chosen search window. First, the density function in the form of a Gaussian mixture is estimated from data obtained by scanning the mammogram with the search window. The estimated mixture is evaluated at each position and displays the corresponding log-likelihood value as a gray level at the window center. The resulting log-likelihood image closely correlates with the structural details of the original mammogram and emphasizes unusual places, but the method is very computationally demanding.

Radiologists regularly compare the bilateral mammogram pairs during mammogram screening in search for breast abnormalities. The mutual mammograms enhancement requires accurate registration of both breast X-ray images, which is difficult due to their elasticity. Marias et al. [15, 16] use thin-plate spline transformation [17] to align the breasts and then use wavelet based feature detection to find internal landmarks. Thin-plate spline based approach is also used by Wirth et al. in [18]. Hachama [19] deals only with the comparison of temporal mammograms based on a general method for registering images with the presence of abnormalities. However, it needs the prior abnormalities distribution knowledge. The registration and transformation are based on the Bayesian maximum a posteriori probability approach and minimization of the registration and deformation energy.

The novelty of our presented method is that whereas other alternative methods usually use simple pixel difference or trivial statistics like cross-correlation to compare the left and right images, we use the mammograms of one breast as a learning sample for the 2DCAR breast texture model [20, 21] and then try to analyze the other mammogram based on this acquired information. Using the 2DCAR model for bilateral comparison, we achieve a result which is robust to inaccurate registration, very fast, and which gives improved enhancement results compare to just a single-view analysis even using similar local texture modeling.

#### **2. Public mammogram databases**

There are not many publicly available mammogram databases [22–26], older databases like DDSM, MIAS are digitized from the X-ray films, while newer databases like INbreast are already digitaly acquired.

The Digital Database for Screening Mammography (DDSM) [24] http://marathon.csee.usf. edu/Mammography/Database.html is a database of digitized from original X-ray filmscreen in different resolutions and with associated ground truth and other information. This database was completed in 1999 and contains mammograms from four different sources using four different digitizers (DBA M2100 ImageClear, Howtek 960, Lumisys 200 Laser, Howtek MultiRad850) and 12 or 16 bits quantization. The database contains normal, benign, and histologically proven cancerous mammograms in four different views (left and right cranio-caudal (CC) and medio-lateral oblique (MLO)). It contains breast imaging reporting and data system (BI-RADS) keywords and the American College of Radiology (ACR) tissue codes (Table 1).

**Table 1.** ACR and BI-RADS codes.

2 ime knjige

computationally demanding.

**2. Public mammogram databases**

already digitaly acquired.

An alternative way is to automatically enhance mammograms to support radiologists with their visual mammogram evaluation. Several mammogram enhancement methods have been published [7–14]. Salvado and Roque [10] use wavelet analysis to detect microcalcifications, Dippel et al. [8] compare the merits of using either Laplacian pyramids or wavelet analysis for whole mammogram enhancement, Sakellaropoulos et al. [9] designed an adaptive wavelet based method for enhancing the contrast of the whole mammograms. Mencattini et al. [13]

An approach to diagnostic evaluation of screening mammograms based on local statistical Gaussian mixture textural models was proposed in [14]. The local evaluation tool has the form of a multivariate probability density of gray levels in a suitably chosen search window. First, the density function in the form of a Gaussian mixture is estimated from data obtained by scanning the mammogram with the search window. The estimated mixture is evaluated at each position and displays the corresponding log-likelihood value as a gray level at the window center. The resulting log-likelihood image closely correlates with the structural details of the original mammogram and emphasizes unusual places, but the method is very

Radiologists regularly compare the bilateral mammogram pairs during mammogram screening in search for breast abnormalities. The mutual mammograms enhancement requires accurate registration of both breast X-ray images, which is difficult due to their elasticity. Marias et al. [15, 16] use thin-plate spline transformation [17] to align the breasts and then use wavelet based feature detection to find internal landmarks. Thin-plate spline based approach is also used by Wirth et al. in [18]. Hachama [19] deals only with the comparison of temporal mammograms based on a general method for registering images with the presence of abnormalities. However, it needs the prior abnormalities distribution knowledge. The registration and transformation are based on the Bayesian maximum a posteriori probability approach and minimization of the registration and deformation energy. The novelty of our presented method is that whereas other alternative methods usually use simple pixel difference or trivial statistics like cross-correlation to compare the left and right images, we use the mammograms of one breast as a learning sample for the 2DCAR breast texture model [20, 21] and then try to analyze the other mammogram based on this acquired information. Using the 2DCAR model for bilateral comparison, we achieve a result which is robust to inaccurate registration, very fast, and which gives improved enhancement results

compare to just a single-view analysis even using similar local texture modeling.

There are not many publicly available mammogram databases [22–26], older databases like DDSM, MIAS are digitized from the X-ray films, while newer databases like INbreast are

The Digital Database for Screening Mammography (DDSM) [24] http://marathon.csee.usf. edu/Mammography/Database.html is a database of digitized from original X-ray filmscreen in different resolutions and with associated ground truth and other information. This database was completed in 1999 and contains mammograms from four different sources using four different digitizers (DBA M2100 ImageClear, Howtek 960, Lumisys 200 Laser, Howtek MultiRad850) and 12 or 16 bits quantization. The database contains normal, benign,

selectively enhance segmented mammograms regions using wavelet transformation.

The Mammographic Image Analysis Society Digital Mammogram Database (miniMIAS) [22] is also digitized to 50 microns per pixel from the original X-ray filmscreen mammograms by the scanning microdensitometer SCANDIG3. MIAS mammographic images are available via the Pilot European Image Processing Archive (PEIPA) at the University of Essex http: //peipa.essex.ac.uk/ipa/info/mias.html.

The LLNL/UCSF database ftp://gdo-biomed.ucllnl.org/pub/mammo-db/ [23] contains 198 digitized films from 50 patients with 4 views per patient (but only 2 views from one mastectomy case).

The INbreast database [26] is a mammographic database, with images acquired at a Breast Centre, located in a University Hospital (Hospital de São João, Breast Centre, Porto, Portugal). INbreast has a total of 115 cases (410 images) of which 90 cases are from women with both breasts (4 images per case) and 25 cases are from mastectomy patients (2 images per case). Several types of lesions (masses, calcifications, asymmetries, and distortions) are included. Accurate contours made by specialists are also provided in the XML format.

The recent BancoWeb LAPIMO Database http://lapimo.sel.eesc.usp.br/bancoweb/ [27] was acquired in two hospitals using Senographe 500t and Senographe 600t mammographs and digitized by using two laser scanners Lumiscan 50 and Lumiscan 75.

The overview of major features of the public mammographic databases are listed in the following Table 2.

#### **3. Mammogram enhancement methods**

The mammogram enhancement methods can be roughly categorized into frequency based and spatial based methods. The frequency based methods [7, 9, 28, 29] use mostly some wavelet multiscale decomposition with modified wavelet coefficients to enhance mammogram contrast. The spatial methods [14, 30] use some nonlinear or adaptive linear filters.

We have implemented four representative mammogram enhancement methods from several published alternatives [7–10, 10–14] to compare with our novel adaptive probabilistic mammogram enhancement method.

**Table 2.** Public Mammogram Databases: where (*nmam*) is the number of mammograms, (*nviews*) number of views, (*ngl*) number of gray levels in bits, and ↓is benign without callback.

#### **3.1. Histogram equalization**

The well known gray scale image enhancement technique is histogram equalization [31], which is based on the idea of forcing the enhanced image histogram to be uniform. This is a popular technique for contrast enhancement because because of its simplicity and effectivity. However, it may overenhance the noises and sharp regions in the original images.

#### **3.2. Matting-based enhancement**

The enhancement method based on the idea of image matting was published in [32]. It works based on the idea that mammographic images (*Y*) are a superposition of some background adipose tissue (*B*) and the interesting part, which would be the mammary glands and other breast structures (*G*).

$$Y = \mathbf{G}\mathbf{c} + B(\mathbf{1} - \mathbf{c}) \tag{1}$$

The enhancement method then selectively subtracts the background tissues from the superposition, thus creating the enhanced image.

To enable this, the authors had to estimate the background (*B*) and the opacity alpha value for each pixel by which it is blended with the rest of the image (*c*). In this method the background is set as a constant value for the whole image represented by the 85% percentile of grey values of the breast part of the image.

#### **3.3. Nonlinear unsharp masking**

A nonlinear unsharp masking (NLUM) combined with nonlinear filtering for mammogram enhancement was introduced in [33]. The method embeds different types of filters into the nonlinear filtering operator within the 3 × 3 window which fuses the enhanced and original mammogram data. The unsharp masking emphasizes high-frequencies of the signal either by subtracting a low-pass filtered signal from its original or adding a scaled high-frequency factor to the measured original. NLUM eight parameters are optimized using the proposed second-derivative-like measure of enhancement (SDME) [33].

#### **3.4. Direct contrast enhancement**

4 ime knjige

DDSM ([24])

INbreast ([26])

x *resolution* 1411 − 5641 2560 − 3328 1024 y *resolution* 3256 − 7111 3328 − 4084 1024

*benign* 870 44 66

(*ngl*) number of gray levels in bits, and ↓is benign without callback.

**3.1. Histogram equalization**

**3.2. Matting-based enhancement**

superposition, thus creating the enhanced image.

of grey values of the breast part of the image.

second-derivative-like measure of enhancement (SDME) [33].

**3.3. Nonlinear unsharp masking**

breast structures (*G*).

miniMIAS ([22])

*nmam* 10480 410<PHONE_NUMBER> *nviews* 4 4 2 4 4 *ngl* 16/12 14 8 12 12

*normal* 695 70 204 38 294 ↓ *benign* 141 116 128 994

*malignant* 914 180 52 32 112 *density ACR ACR own scale no no BI-RADS yes yes no no yes*

**Table 2.** Public Mammogram Databases: where (*nmam*) is the number of mammograms, (*nviews*) number of views,

The well known gray scale image enhancement technique is histogram equalization [31], which is based on the idea of forcing the enhanced image histogram to be uniform. This is a popular technique for contrast enhancement because because of its simplicity and effectivity.

The enhancement method based on the idea of image matting was published in [32]. It works based on the idea that mammographic images (*Y*) are a superposition of some background adipose tissue (*B*) and the interesting part, which would be the mammary glands and other

The enhancement method then selectively subtracts the background tissues from the

To enable this, the authors had to estimate the background (*B*) and the opacity alpha value for each pixel by which it is blended with the rest of the image (*c*). In this method the background is set as a constant value for the whole image represented by the 85% percentile

A nonlinear unsharp masking (NLUM) combined with nonlinear filtering for mammogram enhancement was introduced in [33]. The method embeds different types of filters into the nonlinear filtering operator within the 3 × 3 window which fuses the enhanced and original mammogram data. The unsharp masking emphasizes high-frequencies of the signal either by subtracting a low-pass filtered signal from its original or adding a scaled high-frequency factor to the measured original. NLUM eight parameters are optimized using the proposed

However, it may overenhance the noises and sharp regions in the original images.

LLNL ([23])

*Y* = *Gc* + *B*(1 − *c*) (1)

LAPIMO ([27] )

An enhancement method based on wavelet transformation was described in [29]. The method performs a multi-level 2D wavelet transfomation and at each level the 3 highpass components are divided by the lowpass-lowpass component, getting a directional contrast estimate, which is further multiplied by a constant contrast enhancement factor *λ*. Starting at the deepest level of the transform, the inverse transform is performed one scale at a time. For each scale level, before the inverse transform step, the 3 modified components are multiplied by the newly computed lowpass component. This way the authors achieve a contrast enhancement without the introduction of too much of additional noise.

#### **4. Probabilistic mammogram enhancement**

These our methods use Markovian texture models for the analysis of local texture characteristics and enhancing breast tissue abnormalities such as microcalcifications and masses which could be the sign of a developing cancer. We make the presumption that left and right breasts are architecturally symmetrical. This presumption is indeed reasonable, since radiologists frequently compare double-view mammograms to find asymmetrical parts, which could indicate a developing cancer. The texture based symmetry detection neither needs to assume the pixel-wise correspondence of the both breast images, nor their ideal sub-pixel registration inside the breast area.

The double-view methods consist of three major steps: registration, model parameters adaptive estimation, and the cross-prediction based analysis.

#### **4.1. Mammogram registration**

The registration process is described for mammographic MLO views, but it can be easily adapted also for CC views. Since we compare the images based on textural features rather than pixel-wise, we do not require as precise registration as other methods, and can use a simple registration based on the affine transformation.

Three reference points are needed for the affine transformation (Figure 1). We chose the nipple and one point above and one below that are closest to the pectoral muscle.

**Figure 1.** Registered mammograms with visible reference points.

The nipple is located using the heuristic method described in [34]. It works on the idea of the nipple being a point on the skin-line of the breast which is the most distant from the line of the pectoral muscle. After the candidates for the nipple reference points have been found in both the mammograms, the position of the reference point can still slightly differ in both images. Therefore, we adjust their position by searching the neighborhood on the skin line of the breast for the most correlated window.

The remaining reference point candidates have to be further adjusted as well. Since the bilateral mammograms usually do not cover the same area of the breast, some anatomical parts of the breast can be seen only in one of the images and therefore the reference points wouldn't match. To make up for this problem, we measure the distance of the points to the nipple, weighted by the nipples distance to the pectoral muscle. The weighting compensates for the differences of positioning of the breast in the mammogram which could result in one image displaying the breast bigger than the other. We then adjust the corresponding reference points, so that they are on the skin line with the most similar weighted distance to the nipple possible.

Having found the reference points, the affine transformation is performed. Figure 1 in the leftmost images shows the images of right and left breast with marked line of the pectoral muscle (colored in red) and the distance from the pectoral muscle to the nipple. The rightmost images show the registered breasts with the reference points painted as white squares with the right breast (shown on the left side) transformed to match the left breast.

#### **4.2. Adaptive textural model**

The X-ray mammographic tissue is locally modeled by its dedicated independent Gaussian noise-driven autoregressive random field two-dimensional texture model (2DCAR), which is a rare exception among Markovian random field model family that can be completely analytically solved [35, 36]. Apart from that, this descriptive model has good modeling performance, all statistics can be evaluated recursively, and the model is very fast to evaluate.

The 2DCAR random field is a Markovian family of random variables with a joint probability density on the set of all possible realizations *Y* of the *M* × *N* lattice *I*, subject to the following condition:

$$\begin{split} p(Y \mid \gamma, \sigma^{-2}) &= (2\pi\sigma^2)^{-\frac{(MN-1)}{2}} \\ &\exp\left\{ \frac{-1}{2} \text{tr}\left\{ \sigma^{-2} \begin{pmatrix} -a \\ \gamma^T \end{pmatrix}^T \tilde{V}\_{MN-1} \begin{pmatrix} -a \\ \gamma^T \end{pmatrix} \right\} \right\} \end{split} \tag{2}$$

where *α* is a unit vector, *tr*() is a trace of the corresponding matrix, and the following notation is used

$$\begin{aligned} \tilde{V}\_{r-1} &= \sum\_{k=1}^{r-1} \begin{pmatrix} Y\_k \ Y\_k^T & Y\_k X\_k^T \\ X\_k Y\_k^T & X\_k X\_k^T \end{pmatrix} \\ &= \begin{pmatrix} \tilde{V}\_{y(r-1)} & \tilde{V}\_{xy(r-1)}^T \\ \tilde{V}\_{xy(r-1)} & \tilde{V}\_{x(r-1)} \end{pmatrix} \end{aligned}$$

Here, *r* = [*r*1,*r*2, *φ*] is spatial multiindex denoting history of movements on the rectangular lattice *I*, where *r*1,*r*<sup>2</sup> are row and column indices, and the direction of the model development is *φ* ∈ {0◦, 45◦, 90◦, 135◦, 180◦, 225◦, 270◦, 315◦} . The 2DCAR model can be expressed as a stationary causal uncorrelated noise-driven 2D autoregressive process:

$$Y\_r = \gamma\_\phi X\_r + \varepsilon\_r \tag{3}$$

where *γφ* = [*a*1,..., *aη*] is the parameter vector, *η* = *cardinality*(*I<sup>c</sup> <sup>r</sup>* ), *I<sup>c</sup> <sup>r</sup>* denotes a causal (or alternatively unilateral) contextual neighborhood (i.e., all support pixels were previously visited and thus they are known). Elements in *I<sup>c</sup> <sup>r</sup>* do not need to be topological neighbours of each other, i.e., if *s* is a neighbour of *r* then ∃*t*, *t* ∈ *I* located between *r* and *s* at a distance *<sup>δ</sup>*(*r*, *<sup>t</sup>*) *<sup>&</sup>lt; <sup>δ</sup>*(*r*,*s*) such as *<sup>t</sup>* <sup>∈</sup>/ *<sup>I</sup><sup>c</sup> <sup>r</sup>* . This type of a neighbourhood system is also called a functional neighbourhood system and its application is illustrated in Figure 2. Its optimal configuration can be found analytically using the Bayesian statistics see [36] for details. Furthermore, *er* denotes white Gaussian noise with zero mean and a constant but unknown variance *<sup>σ</sup>*2, and *Xr* is a support vector of *Yr*−*<sup>s</sup>* where *<sup>s</sup>* <sup>∈</sup> *<sup>I</sup><sup>c</sup> <sup>r</sup>* . The method uses a locally adaptive version of this 2DCAR model [36], where its recursive statistics are modified by an exponential forgetting factor, i.e., a constant smaller than 1 which is used to weight the older data.

#### *4.2.1. Parameter estimation*

Parameter estimation of the 2DCAR model using either the maximum likelihood, the least square or Bayesian methods can be found analytically. The Bayesian parameter estimates of the 2DCAR model using the normal-gamma parameter prior are:

$$
\gamma\_{r-1}^T = V\_{x(r-1)}^{-1} V\_{xy(r-1)} \quad \text{ } \tag{4}
$$

$$
\theta\_{r-1}^2 = \frac{\lambda\_{(r-1)}}{\beta(r)} \; \; \; \tag{5}
$$

where

6 ime knjige

the nipple possible.

condition:

is used

**4.2. Adaptive textural model**

*<sup>p</sup>*(*<sup>Y</sup>* <sup>|</sup> *<sup>γ</sup>*, *<sup>σ</sup>*−2)=(2*πσ*2)<sup>−</sup> (*MN*−1)

exp −1 <sup>2</sup> *tr*

*V*˜ *<sup>r</sup>*−<sup>1</sup> =

of the breast for the most correlated window.

The nipple is located using the heuristic method described in [34]. It works on the idea of the nipple being a point on the skin-line of the breast which is the most distant from the line of the pectoral muscle. After the candidates for the nipple reference points have been found in both the mammograms, the position of the reference point can still slightly differ in both images. Therefore, we adjust their position by searching the neighborhood on the skin line

The remaining reference point candidates have to be further adjusted as well. Since the bilateral mammograms usually do not cover the same area of the breast, some anatomical parts of the breast can be seen only in one of the images and therefore the reference points wouldn't match. To make up for this problem, we measure the distance of the points to the nipple, weighted by the nipples distance to the pectoral muscle. The weighting compensates for the differences of positioning of the breast in the mammogram which could result in one image displaying the breast bigger than the other. We then adjust the corresponding reference points, so that they are on the skin line with the most similar weighted distance to

Having found the reference points, the affine transformation is performed. Figure 1 in the leftmost images shows the images of right and left breast with marked line of the pectoral muscle (colored in red) and the distance from the pectoral muscle to the nipple. The rightmost images show the registered breasts with the reference points painted as white squares with the right breast (shown on the left side) transformed to match the left breast.

The X-ray mammographic tissue is locally modeled by its dedicated independent Gaussian noise-driven autoregressive random field two-dimensional texture model (2DCAR), which is a rare exception among Markovian random field model family that can be completely analytically solved [35, 36]. Apart from that, this descriptive model has good modeling performance, all statistics can be evaluated recursively, and the model is very fast to evaluate. The 2DCAR random field is a Markovian family of random variables with a joint probability density on the set of all possible realizations *Y* of the *M* × *N* lattice *I*, subject to the following

2

*r*−1 ∑ *k*=1

*V*˜

= *V*˜

 *σ*−<sup>2</sup> −*α γT <sup>T</sup> V*˜ *MN*−1

where *α* is a unit vector, *tr*() is a trace of the corresponding matrix, and the following notation

*YkY<sup>T</sup>*

*XkY<sup>T</sup>*

*<sup>y</sup>*(*r*−1) *<sup>V</sup>*˜ *<sup>T</sup>*

*xy*(*r*−1) *<sup>V</sup>*˜

*<sup>k</sup> YkX<sup>T</sup> k*

 .

*<sup>k</sup> XkX<sup>T</sup> k*

*xy*(*r*−1)

*x*(*r*−1)

 −*α γT*

, (2)

$$\begin{aligned} \lambda\_{(r-1)} &= V\_{y(r-1)} - V\_{xy(r-1)}^T V\_{x(r-1)}^{-1} V\_{xy(r-1)} \\ V\_{(r-1)} &= \tilde{V}\_{(r-1)} + V\_{(0)} \\ \beta(r) &= \beta(0) + r - 1 \end{aligned}$$

and *β*(0) is an initialization constant and submatrices in *V*(0) are from the parameter prior. The parameter estimates (4),(5) can also be evaluated recursively [36] using the proces history (Y(*r*−1)). The posterior probability density [36] of the model is:

**Figure 2.** Single-view MLO mammogram enhancement using different functional neighbourhoods consecutively rightwards - 9, 5, and 3 pixel neighbourhood distance from the enhanced pixel (blue pixels - bottom row).

$$p(Y\_r \mid Y^{(r-1)}, \hat{\gamma}\_{r-1}) = \frac{\Gamma(\frac{\beta(r) - \eta + 3}{2})}{\Gamma(\frac{\beta(r) - \eta + 2}{2}) \, \pi^{\frac{1}{2}} \, (1 + X\_r^T V\_{\mathbf{x}(r-1)}^{-1} X\_r)^{\frac{1}{2}} \, |\, \lambda\_{(r-1)}|^{\frac{1}{2}}}$$

$$\left(1 + \frac{(Y\_r - \hat{\gamma}\_{r-1} X\_r)^T \lambda\_{(r-1)}^{-1} (Y\_r - \hat{\gamma}\_{r-1} X\_r)}{1 + X\_r^T V\_{\mathbf{x}(r-1)}^{-1} X\_r}\right)^{-\frac{\beta(r) - \eta + 3}{2}}\tag{6}$$

And the conditional mean value predictor of the one-step-ahead predictive posterior density (6) for the normal-gamma parameter prior is

$$E\left\{Y\_r \mid Y^{(r-1)}\right\} = \hat{\gamma}\_{r-1} X\_r \ . \tag{7}$$

**Figure 3.** INbreast MLO mammogram enhancement comparison rightwards: the original mammogram, histogram equalization, [32], [33], [29], and the presented enhancement methods, respectively.

#### *4.2.2. Prediction*

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**Figure 2.** Single-view MLO mammogram enhancement using different functional neighbourhoods consecutively

(*Yr* <sup>−</sup> *<sup>γ</sup>*ˆ*r*−1*Xr*)*Tλ*−<sup>1</sup>

And the conditional mean value predictor of the one-step-ahead predictive posterior density

<sup>2</sup> )

*<sup>r</sup> V*−<sup>1</sup> *x*(*r*−1)

(*r*−1)

*<sup>r</sup> V*−<sup>1</sup> *x*(*r*−1) *Xr*

*Xr*) 1 <sup>2</sup> |*λ*(*r*−1)|

(*Yr* − *<sup>γ</sup>*ˆ*r*−1*Xr*)

1 2

<sup>−</sup> *<sup>β</sup>*(*r*)−*η*+<sup>3</sup> 2

(6)

= *<sup>γ</sup>*ˆ*r*−1*Xr* . (7)

<sup>2</sup> (1 + *X<sup>T</sup>*

1 + *X<sup>T</sup>*

rightwards - 9, 5, and 3 pixel neighbourhood distance from the enhanced pixel (blue pixels - bottom row).

, *<sup>γ</sup>*ˆ*r*−1) = <sup>Γ</sup>( *<sup>β</sup>*(*r*)−*η*+<sup>3</sup>

<sup>2</sup> ) *<sup>π</sup>* <sup>1</sup>

*Yr* <sup>|</sup> *<sup>Y</sup>*(*r*−1)

Γ( *<sup>β</sup>*(*r*)−*η*+<sup>2</sup>

 1 +

> *E*

*<sup>p</sup>*(*Yr* <sup>|</sup> *<sup>Y</sup>*(*r*−1)

(6) for the normal-gamma parameter prior is

The conditional mean value of the one-step-ahead predictive posterior density for the normal-gamma parameter prior is

$$E\left\{\mathbf{Y}\_{r}\mid\mathbf{Y}^{(r-1)}\right\}=\hat{\gamma}\_{r-1}X\_{r}\ .\tag{8}$$

The predictor (8) is used only for single-view mammogram enhancement. For double-view mammograms where there are available both left and right breasts mammograms the method uses the cross-prediction (10),(11).

**Figure 4.** MIAS MLO mammogram enhancement comparison rightwards: the original mammogram, histogram equalization, [32], [33], [29], and the presented enhancement methods, respectively.

#### **4.3. Enhancement methods**

Let us denote two mutually registered (e.g., left and right breasts') mammograms *Y* and *Y*˜, the local 2DCAR model parameters estimates (4), (5) computed on the mammogram image *Y γ*ˆ *<sup>T</sup> <sup>r</sup>*−1, *<sup>σ</sup>*<sup>ˆ</sup> <sup>2</sup> *<sup>r</sup>*−1. The same parameter estimates (4), (5) computed on the other mammogram *<sup>Y</sup>*˜ are denoted *γ*˜ *<sup>T</sup> <sup>r</sup>*−1, *<sup>σ</sup>*˜ <sup>2</sup> *<sup>r</sup>*−1, and the corresponding support vector is *<sup>X</sup>*˜*r*. The directional models are computed in the following angles *φ* ∈ Φ = {0◦, 45◦, 90◦, 135◦, 180◦, 225◦, 270◦, 315◦}.

#### *4.3.1. Single-view enhancement*

The single-view enhacement method is computed from up to eight directional models, i.e.,

**Figure 5.** INbreast multiple-view MLO mammogram enhancement consecutively rightwards - ground truth, pixel difference between registered LMLO and RMLO, cross-predicted gradient, and cross-prediction probability density. The upper row contains LMLO, bottom row RMLO.

$$\mathcal{Y}\_r^{\text{enh}} = \sum\_{\forall \phi \in \Phi} (\mathcal{Y}\_{r+1} - \hat{\gamma}\_{r-1} \mathcal{X}\_r) \quad , \tag{9}$$

where <sup>Φ</sup>¯ <sup>⊆</sup> <sup>Φ</sup>. All the enhanced values are normalized into the 0 <sup>−</sup> 255 range.

#### *4.3.2. Double-view enhancement*

10 ime knjige

**Figure 4.** MIAS MLO mammogram enhancement comparison rightwards: the original mammogram, histogram

Let us denote two mutually registered (e.g., left and right breasts') mammograms *Y* and *Y*˜, the local 2DCAR model parameters estimates (4), (5) computed on the mammogram image

are computed in the following angles *φ* ∈ Φ = {0◦, 45◦, 90◦, 135◦, 180◦, 225◦, 270◦, 315◦}.

The single-view enhacement method is computed from up to eight directional models, i.e.,

*<sup>r</sup>*−1. The same parameter estimates (4), (5) computed on the other mammogram *<sup>Y</sup>*˜

*<sup>r</sup>*−1, and the corresponding support vector is *<sup>X</sup>*˜*r*. The directional models

equalization, [32], [33], [29], and the presented enhancement methods, respectively.

**4.3. Enhancement methods**

*<sup>r</sup>*−1, *<sup>σ</sup>*˜ <sup>2</sup>

*4.3.1. Single-view enhancement*

*Y γ*ˆ *<sup>T</sup>*

*<sup>r</sup>*−1, *<sup>σ</sup>*<sup>ˆ</sup> <sup>2</sup>

are denoted *γ*˜ *<sup>T</sup>*

The double-view enhancement is based on statistics computed on one breast image and applied to the complementary one. The cross-prediction between images *Y*,*Y*˜ is computed as follows:

$$E\left\{\tilde{Y}\_r \mid Y^{(r-1)}\right\} = \hat{\gamma}\_{r-1}\tilde{X}\_r\tag{10}$$

and the opposite direction cross-prediction is analogously

$$E\left\{\mathbf{Y}\_{r}\mid\tilde{\mathbf{Y}}^{(r-1)}\right\}=\tilde{\gamma}\_{r-1}\mathbf{X}\_{r}\;.\tag{11}$$

The enhanced mammograms are then the corresponding cross-prediction statistics images. The corresponding cross-prediction probability densities are *p*(*Y*˜ *<sup>r</sup>* <sup>|</sup> *<sup>Y</sup>*˜(*r*−1), *<sup>γ</sup>*ˆ*r*−1) and *<sup>p</sup>*(*Yr* <sup>|</sup> *<sup>Y</sup>*(*r*−1), *<sup>γ</sup>*˜*r*−1).

The proposed double-view enhancement methods are

$$Y\_r^{com\_1} = \sum\_{\forall \phi \in \Phi} \left( \tilde{Y}\_{r+1} - \hat{\gamma}\_{r-1} X\_r \right) \quad , \tag{12}$$

$$Y\_r^{com\_2} = \sum\_{\forall \phi \in \Phi} p(\tilde{Y}\_r \mid \tilde{Y}^{(r-1)}, \hat{\gamma}\_{r-1}) \ . \tag{13}$$

#### **5. Experimental results**

The comparative experimental results (Figures 3, 4) were tested on the miniMIAS database [22] and on the state-of-the-art public digital mammogram INbreast database [26]. Comparing the alternative methods (Section 3) with our proposed adaptive enhancement, it is clearly visible that whereas these methods enhance prevailingly contrast, our method enhances textural abnormalities in the breast tissue which is more useful for the radiologists.

Our adaptive enhancement methods were also successfully tested on the Digital Database for Screening Mammography (DDSM) from the University of South Florida [24]. These results are reported elsewhere.

The spatial textural model allows seamless and natural generalization into multiple-view mammogram enhancement (be it bilateral, as presented in Figures 5, 6, or temporal). Double-view medio-lateral oblique digital mammograms' enhancements from the INbreast database (Figure 5) and the miniMIAS database (Figure 6) show the cross-prediction based enhancement performance. Comparing the cross-prediction enhancements on Figures 5, 6 respectively with the same breast single-view enhancements on Figures 3, 4, the benefits of the cross-prediction are clearly visible.

Both our double-view enhancement methods are compared with the registered image pixel difference which is standardly used for comparison ([15, 18, 19])

$$
\Delta Y\_r = \max \{ Y\_r^R - Y\_r^L, 0 \} \ . \tag{14}
$$

This standard double-view enhancement method (Figures 5, 6 - second columns) is inferior compared to the both proposed double-view enhancement methods ((12), (13)) which simultaneously exhibit more contrast and increased details' visibility.

Finally, all three proposed enhancement methods are very fast - they can be computed on the presented mammograms with a standard PC in a matter of several seconds.

**Figure 6.** Multiple-view medio-lateral mammogram (INbreast) enhancement consecutively rightwards - ground truth, pixel difference between registered LMLO and RMLO, cross-predicted gradient, and cross-prediction probability density. The upper row contains LMLO, bottom row RMLO.

#### **6. Conclusions**

12 ime knjige

*<sup>p</sup>*(*Yr* <sup>|</sup> *<sup>Y</sup>*(*r*−1), *<sup>γ</sup>*˜*r*−1).

**5. Experimental results**

are reported elsewhere.

the cross-prediction are clearly visible.

difference which is standardly used for comparison ([15, 18, 19])

simultaneously exhibit more contrast and increased details' visibility.

and the opposite direction cross-prediction is analogously

The proposed double-view enhancement methods are

*E*

The corresponding cross-prediction probability densities are *p*(*Y*˜

*<sup>Y</sup>com*<sup>1</sup> *<sup>r</sup>* <sup>=</sup> ∑

*<sup>Y</sup>com*<sup>2</sup> *<sup>r</sup>* <sup>=</sup> ∑

<sup>∀</sup>*φ*∈Φ¯

<sup>∀</sup>*φ*∈Φ¯

 *Y*˜

*p*(*Y*˜

The comparative experimental results (Figures 3, 4) were tested on the miniMIAS database [22] and on the state-of-the-art public digital mammogram INbreast database [26]. Comparing the alternative methods (Section 3) with our proposed adaptive enhancement, it is clearly visible that whereas these methods enhance prevailingly contrast, our method enhances textural abnormalities in the breast tissue which is more useful for the radiologists. Our adaptive enhancement methods were also successfully tested on the Digital Database for Screening Mammography (DDSM) from the University of South Florida [24]. These results

The spatial textural model allows seamless and natural generalization into multiple-view mammogram enhancement (be it bilateral, as presented in Figures 5, 6, or temporal). Double-view medio-lateral oblique digital mammograms' enhancements from the INbreast database (Figure 5) and the miniMIAS database (Figure 6) show the cross-prediction based enhancement performance. Comparing the cross-prediction enhancements on Figures 5, 6 respectively with the same breast single-view enhancements on Figures 3, 4, the benefits of

Both our double-view enhancement methods are compared with the registered image pixel

This standard double-view enhancement method (Figures 5, 6 - second columns) is inferior compared to the both proposed double-view enhancement methods ((12), (13)) which

Finally, all three proposed enhancement methods are very fast - they can be computed on

*<sup>r</sup>* <sup>−</sup> *<sup>Y</sup><sup>L</sup>*

<sup>∆</sup>*Yr* <sup>=</sup> *max*{*Y<sup>R</sup>*

the presented mammograms with a standard PC in a matter of several seconds.

*<sup>r</sup>*+<sup>1</sup> − *<sup>γ</sup>*ˆ*r*−1*Xr*

*<sup>r</sup>* <sup>|</sup> *<sup>Y</sup>*˜(*r*−1)

*Yr* <sup>|</sup> *<sup>Y</sup>*˜(*r*−1)

The enhanced mammograms are then the corresponding cross-prediction statistics images.

= *<sup>γ</sup>*˜*r*−1*Xr* . (11)

*<sup>r</sup>* <sup>|</sup> *<sup>Y</sup>*˜(*r*−1), *<sup>γ</sup>*ˆ*r*−1) and

, (12)

, *<sup>γ</sup>*ˆ*r*−1) . (13)

*<sup>r</sup>* , 0} . (14)

We proposed three novel fast methods for completely automatic mammogram enhancement which highlight regions of interest, detected as textural abnormalities. Cancerous areas typically manifest themselves in X-ray mammography as such textural defects which is advantageous for our methods in comparison with most alternative mammogram enhancement methods that primarily enhance only the image contrast. Thus the enhanced mammograms can help radiologists to decrease their false negative evaluation rate.

These methods are based on the underlying two-dimensional adaptive CAR texture model. Although the algorithms use random field type model, the model is very fast due to the efficient recursive model predictor estimation and therefore is much faster than the usual alternative Markov chain Monte Carlo estimation approach. The enhancement can be either single or double view depending on the available data. The single-view methods allow significant mammogram enhancement without the need of paired mammogram registration. The double-view methods benefit from mutual textural information in the registered bilateral breast pairs. Contrary to the simple pixel difference values or cross-correlations, the textural feature comparison brings increased robustness to registration inaccuracies inevitably encountered due to the elasticity of the breast. The double-view methods could alternatively be used for the enhancement of a temporal sequence of mammograms.

#### **Acknowledgements**

This research was supported by the Czech Science Foundation project GACR 14-10911S. ˇ

#### **Author details**

Michal Haindl and Václav Remeš

The Institute of Information Theory and Automation of the Czech Academy of Sciences, Prague, Czech Republic

#### **References**

[11] Yan, Z.; Zhang, Y.; Liu, B.; Zheng, J.; Lu, L.; Xie, Y.; Liang, Z.; Li, J. Extracting hidden visual information from mammography images using conjugate image enhancement software. In *Information Acquisition, 2005 IEEE International Conference on*; IEEE: 2005.

14 ime knjige

**Acknowledgements**

Michal Haindl and Václav Remeš

Alamitos, CA, USA, 2002.

[4] Kopans, D. B. *Radiology* 2010, *256,* 15–20.

*Technology Assessment* 2005, *9,*.

*International Workshop on*; 2005.

**Author details**

**References**

Prague, Czech Republic

society, 2012.

*3,* 32–46.

*48,* 787.

2002, *21,* 343–353.

inevitably encountered due to the elasticity of the breast. The double-view methods could

alternatively be used for the enhancement of a temporal sequence of mammograms.

This research was supported by the Czech Science Foundation project GACR 14-10911S.

The Institute of Information Theory and Automation of the Czech Academy of Sciences,

[1] Tweed, T.; Miguet, S. Automatic Detection of Regions of Interest in Mammographies Based on a Combined Analysis of Texture and Histogram. In *Pattern Recognition, 2002. Proceedings. 16th International Conference on*, Vol. 2; IEEE Computer Society: Los

[2] Qi, H.; Diakides, N. A. Thermal Infrared Imaging in Early Breast Cancer Detection - A Survey of Recent Research. In *Proceedings of the 25th Annual International Conference of the*

[3] ACS, "Breast cancer facts & figures 2011 -? 2012", Technical Report, American cancer

[5] Taylor, P. and Champness, J. and Given-Wilson, R. and Johnston, K. and Potts, H., *Health*

[6] Haindl, M.; Mikeš, S.; Scarpa, G. Unsupervised Detection of Mammogram Regions of Interest. In *Knowledge-Based Intelligent Information and Engineering Systems*, Vol. 4694;

[7] Chang, C.-M.; Laine, A. *IEEE Transactions on Information Technology in Biomedicine* 1999,

[8] Dippel, S.; Stahl, M.; Wiemker, R.; Blaffert, T. *Medical Imaging, IEEE Transactions on*

[9] Sakellaropoulos, P.; Costaridou, L.; Panayiotakis, G. *Physics in medicine and biology* 2003,

[10] Salvado, J.; Roque, B. Detection of calcifications in digital mammograms using wavelet analysis and contrast enhancement. In *Intelligent Signal Processing, 2005 IEEE*

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Apolloni, B.; Howlett, R. J.; Jain, L., Eds.; Springer: 2007.

ˇ

**Chapter 5**