early detection and eradication of malignant tumors at an early stage before metastasize and spread to neighboring areas , can be prevented from threats and problems later . during 20032007
almost 0.0% , 0.9% , 6.0% , 15.0% , 20.8% , 19.7% , 22.6% and 15.1% of mortality has occurred in the following order , 20 yr , 2034 , 3544 , 4554 , 5564 , 6574 , 7584 and above 85 yr(1 ) .
report submitted shows that 0% detection has been possible in those under the age of 20 . while 1.9% , 10.2% , 22.6% , 24.4% , 19.7% , 15.5% and 5.6% of diagnosis has been possible in the inside groups ranging , 3444 , 4554 , 5564 , 6574 , 7584 and above 85 yr ( 1 ) .
early detection of breast cancer is one of the most important issues that researchers have always sought .
pathological mechanism of breast cancer is formed in this manner while cancerous cells produce nitric oxide ( no ) in the proliferative phase ( proliferative ) .
the chemicals cause difficulties in neural control , and thus lead to regional artery dilatation in the early stages of cancer cells growth .
this angiogenesis causes increment in the local temperature even a few years earlier than tumor formation .
deep lesions can cause changes in skin temperature ( 3 , 4 ) . based on the features listed above
, this concept means that , some features used in the diagnosis of breast cancer , entail geometric size , location , shape , topology as well as the thermal features . because , doctors are interested in the thermal imaging after a long time , which comprise the following : 1 ) progress done in the technology of infrared cameras ; 2 ) creation of standard rules for thermal imaging ; 3 ) accurate calibration of the camera .
breast thermography is a potential technique with useful protocol ( 5 ) , which has advantages such as noninvasive , non - radiation , passive , quick , painless , inexpensive , and non - contact camera ( 611 ) .
breast thermography is suitable for women of all ages , including pregnant and nursing women and women with dense tissue in their breast ( 12 ) .
thermogram of a patient provides the distribution of heat in the body . due to the high metabolic rate and progression of vascular angiogenesis ,
thus , cancer cells in infrared images can be indicated in the form of critical focus .
thermography is better than the method of mammography in predicting breast cancer in its early stages , even when the tumor is at the initial stage of formation .
medical thermography could not progress for a long time because of the dependency on hardware and software fields and limitations concerning existing .
recently hardware limitations have declined with the improvements made in the field of photo detectors and pcs .
all the items listed , indicate the success related to the use of thermal images in medicine ( 5 ) .
recently , case studies have been implemented on breast cancer detection in large - scale by thermal imaging , mostly indicate average sensitivity and specificity of 90% ( 7 ) .
thermal imaging is employed in diverse medical applications such as breast cancer detection ( 14 ) , pain management ( 15 ) , and diabetes ( 16 ) .
methods are proposed for the analysis of image processing algorithms such as abnormal statistical methods , thermal asymmetric methods and descriptive matching ( 1719 ) .
although the image processing techniques are important for the analysis of medical thermography , many of these methods are not sensitive enough or delicate algorithms are not applied extensively for independent detection by using of computer .
the purpose of this paper is to provide a diagnostic tool by using computer based on thermal model ( 7 ) .
one of the primary problems for the clustering and detecting breast cancer in thermal imaging is that both of breast areas must first be segmented so that the image processing be performed on it ( 20 ) . since thermal images have diverse formats ( small or large , condensation , etc . )
, separating special area whit high accuracy is very difficult . on the other hand ,
some papers ( 21 ) have used asymmetry of the two regions and moments . in the proposed method ,
the problem has been fixed and there is no requirement to separate the breast from the beginning .
identification of the correct boundary and image segmentation is one of the most important issues in the utilization of machine vision applications , such as traffic monitoring in urban transport systems ( 22 , 23 ) , medical applications ( 24 ) , video monitoring and target identification in air defense weapons ( 25 ) .
one problem in computer analysis of the thermal images is that the images should be obtained directly from the patient to avoid encountering with the problems during the analysis of such asymmetry .
it is difficult to separate cancerous tissue in thermal images ; the goal of this paper is to solve this problem .
the proposed models are the combination of surf and sift which are related to feature extraction .
whit regard to computer vision ; contour models describe the boundaries of shapes within an image .
few papers are in the field of thermography have used active contour method to separate but these are not pertinent to breast cancer .
active contour method has been adopted for segmenting masses on breast ultrasound images ( 26 ) .
previous models were not related to infrared image within the scope of breast cancer . and finally in the proposed method , lyapunov exponent has been used for detecting benign and malignant cancer .
lyapunov exponents are quantities that characterize the average rate of divergence or convergence of two neighboring trajectories in the ps .
the proposed method requires that body organs in the thermal image be separated into distinct parts . for this purpose , firstly
after thermogram someone took pictures from a patient , the image must be converted to gray image format using an appropriate threshold , so we can , the main organ extract from image by using of active contour for later analysis .
otsu s technique is adopted to obtain the optimal level of threshold in order to minimize the intra - class variance ( 29 ) .
detection of corners has been used in many aspects of image processing and machine vision ( fig .
1 ) . images obtained the method of edge detection finding all the corners , measure of the exact position of the corner and robustness of algorithm against noise is resistant to noise , are important in edge detection . by using specific characteristics , simpler picture of the structure of image
the corner is one of the special features widely used in the analysis of sense .
some of the important criteria for detection of corner includes : a ) all corners should be detected ; b ) anything wrong corner is not found ; c ) corners should be evident in their exact position ; f ) the corner detector should be robust against noise ( 3033 )
. methods of corner detection including the curvature , model of corner , peripheral curve . in this paper , using methods based on scale space , the corner position is extracted .
scale space allows the edges of the space with carefully down the space with high accuracy to be examined .
this work is done by applying the gaussian filter with different standard deviation ( 34 ) .
k is calculated by the following equation ( 35 ) : 
 k(u,)=x(u,)y(u,)x(u,)y(u,)(x(u,)2y(u,)2)1.5 
 where : 
 x(u,)=x(u)g(u,)x(u,)=x(u)g(u,)y(u,)=y(u)g(u,)y(u,)=y(u)g(u, ) 
 and  is the convolution operator , g(u, ) is gaussian function with standard deviation ,(u, ) , , g(u, ) , are the first and second derivatives of the gaussian function respectively . the original algorithms of css
are used the following for detecting corner points of an image : 
 canny edge detector is applied on the image gray levels and a binary edge map obtained.perimeter of edges is extracted from the map of edge , and distances between places are replenished , t connections are found.the curvature in a large scale ( high ) , is calculated for the environment of each edge.local maximum points are selected as the point s initial corner points .
the absolute size of curvature related to points must be higher than national threshold t and twice as one of local minimum of its neighbors.following corner points are applied in the largest scale to the smallest scale for improving their posture.comparison of t - fitting with the other corner and deletion of one corner points that is too close .
canny edge detector is applied on the image gray levels and a binary edge map obtained .
perimeter of edges is extracted from the map of edge , and distances between places are replenished , t connections are found . the curvature in a large scale ( high ) , is calculated for the environment of each edge .
the absolute size of curvature related to points must be higher than national threshold t and twice as one of local minimum of its neighbors . following corner points are applied in the largest scale to the smallest scale for improving their posture . comparison of t - fitting with the other corner and deletion of one corner points that is too close .
the scale - related algorithm has been used for finding the corner points and from multi- scale for establishing the corner points . among corner points of candidate , although some are a local maximum , but most of them will be removed with the help of the local threshold .
the endowment threshold is as follows : 
 t(u)=ck=c1l1+l2 + 1i = ul2u+l1k(i ) the average value of k , was used to display average curvature of covered area of ros .
this area is defined as the minimum of the local curvature adjacent to the next . in general
, a good corner must have been the desired angle , in order to be in a specific range .
this angle ( ci ) can be obtained from the following equation : 
 ci|tan1y1x1tan1y2x2| 
 in which : 
   x1=1l1i = u+1u+l1x(i)x(u)  y1=1l1i = u+1u+l1y(i)y(u)  x2=1l2i = ul2u1x(i)x(u)  y2=1l2i = ul2u1y(i)y(u ) after this step , the set of candidate points is changed ; several iterations must be done for converting the points . using this criterion ,
segmented corner points may be removed due to noise and edgy detail and feature points of several sizes remain ( fig .
2 ) . finding the main points in the thermal image coordinate of a point 9 and 10 are maximum points in image of edge detection .
coordinates of the point s m , n , o , p , q can be calculated by the following equations .
currently methods used for feature extraction in thermal images for analysis , include geometrical features and wavelet moment ( 3641 ) . to be able to extract features that are resistant to the angle and rotation ,
our proposal is to use surf descriptor , this descriptor is an extended form of sift , and much more ( about 10 times ) is faster than sift algorithm . sift algorithm can calculate the gradient of any area in the size 16  16 , then it is normalized , while the surf algorithm is used by estimating the second order derivative of gaussian function , convolved in image(42 ) .
moreover instead of using time consuming calculations of sift , quick estimate , is used .
although surf and sift have their advantages and disadvantages , but surf algorithm works based on estimating the gradient of image pixels .
although the nature of the pixels change slightly ( due to convolution of gaussian function ) , it is desirable in other words , the pixel values remain constant ( 43,44 ) .
sift makes the pyramids of the image for finding the candidate points makes , each layer filters gauss law with increasing values of sigma and its acquired differences . on the other hand , surf makes use from hessian s matrix for selecting the candidate points with different sizes , as it is used in the hessian laplace . dominant angle over feature descriptor vector
is obtained , using haar - wavelet filters and employing the integral image . finally , using haar - wavelet filters
3 ) . feature extraction by using surf algorithm totally , surf utilizes a hessian based blob detector to find interest points .
the determinant of a hessian matrix expresses the extent of the response and is an expression of the local change around the area ( 45 ) .
the heart of the surf detection is non - maximal - suppression of the determinants of the hessian matrices . by determining a unique orientation for an interest point
finally , the descriptor is normalized , to achieve invariance to contrast those variations that will represent themselves as a linear scaling of the descriptor .
the interest points detected in the infrared image asmyd s assessment of the key point s detectors ( 46 ) shows that although harris s detector , is not robust enough to changes scale , it has superior performance compared to the rest of detectors .
the second moment matrix is used often for detection of features or to describe the internal structure of the image .
this matrix must be adjusted to changes in scale , so it makes in depend of the accuracy and picture clarity .
the second moment matrix is defined as follows ( 47 ) : 
 (x,i,d)=[11122122]=d2g(i)[lx2(x,d)lxly(x,d)lxly(x,d)ly2(x,d ) ]  is integrated scale , d is differenced scale .
then the derivative is made average in the vicinity of point by smoothing with gaussian window to the size 1 .
eigen values of this matrix show the variation of the two signals in the neighborhood of a point .
larger value of this feature indicates that its point is high in both major curve ( such as corners , connector locations , etc . ) .
harris combines trace and second moment matrix determinant in the following form ( 48 ) : 
 r = det((x,1,d))trace2((x,1,d ) ) local maximum of harris ( r ) makes clear the location of the critical point .
harris detector is stable even in the presence of light that can provide same points .
also , harris s detector can reveal the same points even when there are changes in the angle of view ( 48 , 49 ) .
5 . detected points by a harris s method in the next step , points of interest identified by the surf and corner algorithm , combined and then used to segment cancerous tissue .
however , it is possible that some parts of the features obtained from the corner method , are not important .
so in the proposed method it is needed that the extracted features are combined together and used in both methods ( surf and sift ) .
initially extracted skeleton is partitionedand thenextracted features from the two methods are combined ( fig .
6 , areas 4 and 6 needs to be reviewed , because breast cancer is noticeable in 3 , 4 , 5 and 6 districts .
in addition , because areas 4 , 6 are common so next focus will be on this area .
the next step requires that the cancerous cancer be segmented from image , done using active contour methods .
active contour models are powerful tools for identifying and tracking images , used extensively in applications of machine vision and image processing . object detection with the help of active contour models is done based on tracking the boundaries of the target object . in this method ,
the contour curve is defined by the user or automatically around the target object , used from the extracted features for contour curves in this paper .
then this contour is deformed effected by the energy function , to be adapted with boundaries of target object ( 50 , 51 ) .
s(u)=i(x(u),y(u ) )  u= this curve is transformed under the influence of an energy function , and is guided towards the features of interest in an image .
points of contour moves in the space coordinates ( x , y ) , as long as curve is coincided to the favorite features of the desired object .
the energy function is defined as follows ( 5253 ) : 
 e=01esnake(s(u))du which includes the internal energy and the energy of the image : 
 e=01eint(s(u))+eimg(s(u))du it is best boundaries for contour , which has the lowest energy ( fig .
7 ) , so finding the boundary of the object , is equivalent to minimizing the energy function of contour .
segmentation by using a parametric active contour model ( 54 ) in which internal energy depends on the internal features of the contour such as elasticity rate and curvature , calculated as follows : 
 eint=2|us(u)|2  du+2|2u2s(u)|2  du the first part of the internal energy causes the contour , act like a spring in order to determine the elastic curve .
the second part determines the internal energy curve of the rate of resistance against bending . in the above equation , the coefficients  , 
energy of image , direct the contour curves to the favorite features and distinct image such as edges , lines , corners and etc . and is calculated as follows ( 52 ) : 
 eimg = eedge=p|i(s)|2 parameter p is a huge amount of image energy  , indicates the gradient operator .
hence , the total energy of the active contour is defined as follows : 
 e=2|us(u)|2du+2|2u2s(u)|2du+eedge(s(u))du if there is a visual prominent feature ( strong edge ) , energy function guides the contour curve towards the target correctly . unfortunately in the absence of strong edges , curve of contour becomes difficult to find the target object . for overcoming this problem ,
the new energy has been used called the strain energy of color , and is replaced by edge energy in equation 7(5557 ) .
this energy produces a compressive force , and contour is condensed toward the target object ( or is expanded ) .
the pressure energy of color can be defined as following : 
 epressure = p  g(i(s))(su) where p is a parameter that determines the magnitude of the pressure energy and is loaded by the user .
g is a function , in accordance with equation 18 as ( 56 ) : 
 g(i(s))={+1  if  it1  otherwise t is the intensity threshold of image .
considering that most features are in the district 4 , therefore the initial active contour should be created in the district 4 . the final frontier of active contour , as can be seen in fig .
adaptation of surf & sift algorithm with active contour implementation of active contours in steps 100 , 130 , 200 , 250 and extraction of the cancerous area from the thermal image as can be seen in fig .
the detection is performed using lyapunov exponent test el . by this test it is possible to distinguish accidental from non - accidental time series without statistical distribution .
we can express the similarity of data in a time series , so that period of effect data appears to predict the future .
suppose we have n observation of a chaotic time series available as follows : 
 xk ,  k=1,2,  ,n in this case , to obtain the lyapunov exponent , divided m vectors is initially formed from these time series as follows : 
 xim=(xi , xi+1, 
,xi+m1 ) ;  i=1,2,  ,nm+1 then among these vectors , all pairs of vectors proved in the following equation , are determined : 
 r0(m;i , j)=|ximxjm|r where r is a small positive number and || .
now with transfer time to the n - step ahead , this distance is computed again , thus : 
 dn(m;i , j)=rn(m;i , j)r0(m;i , j)=xi+nmxj+nmximxjm if these vectors are far apart we result that dn is the larger than one otherwise , smaller than 1 .
thus , the largest lyapunov exponent is calculated as follows : 
 l(m , n)=ijlog[dn(m;i , j)]n(n1 ) the positive value of l indicates that time series is chaotic and predicted in divergent way .
the negative value of l represents a definitive nature for time series and long - term predictability .
so if l accepts positive values close to zero , the system are weakly chaotic and medium - term prediction is possible , but predicted long - term is impossible . up to now
first distance of center related to the segmented area from it edge is calculated as time series and distance values are written in the same way , then lyapunov exponent test is employed .
in this section , the results of the proposed method are compared with mammography results .
bar chart on pixel area traced by radiologist versus balloon snake for validating the overall performance of the proposed method , the breast tumor regions obtained by the proposed method were compared with those plotted by the radiologist .
three error metrics were defined : the true - positive ratio ( tp ) , the false - positive ratio ( fp ) and the false - negative ratio ( fn ) ( 60 ) .
let aa be the pixel set of the rois determined by the proposed method and am be the pixel set of the rois determined manually by the radiologist ; the three error metrics are calculated as : 
 tp=|amaa||am|fp=|amaaam||am|fn=|amaaaa||am| when the tp ratio is higher and the fn ratio is lower , more real tumor regions are classified as 
breast lesion  regions , and when the fp ratio is lower , fewer normal tissue regions are classified as  breast lesion  regions .
lyapunov exponent for the segmented areas results that the rate of chaos for benign case is much less than the malignant cases . in another words ,
mammography can be considered as the golden standard method for breast cancer detection . applying mammographic screening
additional screening methods such as the use of thermograms may help lower the death rate from the breast cancer .
cancerous and pre - cancerous tissues have a higher metabolic rate resulting in the growth of new blood vessels to supply nutrients to the cancerous cells .
consequently , the temperature of the tissue surrounding the pre - cancerous tissue is higher than the other regions .
hence , pre - cancerous and cancerous tissues appear as hot spots in breast thermal images .
mammography detects anatomical changes while thermography detects physiological changes that occur much earlier than anatomical changes .
a combination of mammography and thermography methods can perform better in detecting invasive cancer and multifocal diseases .
the keys to obtaining higher accuracy would be ( a ) high sensitivity imaging to obtain reliable hot spot information related to metabolic activity in the breast , ( b ) to process thermogram to isolate these regions from the background , ( c ) to use a feature extraction algorithm such as the one described here that will capture information about the spatial distribution of these regions while being robust to translation and scale changes and ( d ) to use a good feature selection , fusion and classification algorithm such as ad boost .
the features extracted from a collection of images can be used for training and clustering of systems .
many previous studies have used only the difference in temperature between the affected area and normal ( asymmetric techniques ) , for breast cancer detection .
some researchers have suggested that  distribution  of the actual temperature difference between the thermal image and temperature data normalization ( ideally ) is a better way to detect cancerous areas ( 58 ) .
recently , intelligent computers that have features such the support of multimedia and data - mining have assisted the radiologist ( 59 ) .
although breast cancer is not a new disease , it has been increased in women to an unprecedented level in the world in recent decades .
if it is diagnosed early , it can be treated easily . in previous research , many methods have been proposed to form a mathematical model for pattern classification . in this paper
, we presented a method of completely automatic segmentation that can diagnose the breast cancer core in the breast thermal images .
this paper drew one combination model of feature extraction related to surf and corner algorithm that are robust .
ethical issues ( including plagiarism , informed consent , misconduct , data fabrication and/or falsification , double publication and/or submission , redundancy , etc . ) have been completely observed by the authors .
 background : the segmentation of cancerous areas in breast images is important for the early detection of disease . 
 thermal imaging has advantages , such as being non - invasive , non - radiation , passive , quick , painless , inexpensive , and non - contact . 
 imaging technique is the focus of this research.methods:the proposed model in this paper is a combination of surf and corners that are very resistant . 
 obtained features are resistant to changes in rotation and revolution then with the help of active contours , this feature has been used for segmenting cancerous areas.results:comparing the obtained results from the proposed method and mammogram show that proposed method is accurate and appropriate . 
 benign and malignance of segmented areas are detected by lyapunov exponent . 
 values obtained include tp=91.31% , fn=8.69% , fp=7.26%.conclusion : the proposed method can classify those abnormally segmented areas of the breast , to the benign and malignant cancer . 
Introduction
Materials and Methods
Results
Discussion
Conclusions
Ethical considerations