all objects with temperature above absolute zero ( 0 k ) radiate specific intensity of thermal energy and the amount of this radiation increases with temperature ( etehadtavakol et al . , 2010 ) . the radiation emitted by an object causes infrared energy ( griffith et al . , 2001 ) , but it is invisible to the human eye . thermography is a method which helps to display thermal energy and one of its applications is digital infrared thermal imaging ( diti ) . it is a noninvasive , non - contact method of detecting the heat coming from human body ( arora et al . , 2008 ) . breast thermography ( kennedy et al . , 2009 ) is a physiological test that displays information on temperature changes in breast tissues . the thermal information can be shown in a pseudo colored image where each color represents a specific range of temperature ( etehadtavakol et al . , 2010 ) . it is non - invasive ( ng , 2008 ) , passive , pain free , fast , low cost , sensitive and safe with no compression ( etehadtavakol et al . , 2010 ) . breast thermography can be utilized for women of all ages , with any breast size and density , for young , pregnant or nursing women . it is also effective for fibrocystic breasts and breasts with implants ( etehadtavakol et al . , 2010 ; kennedy et al . , 2009 . the procedure is based on the principle that precancerous tissue and the area around a cancerous tumor have higher temperature due to angiogenesis , and higher chemical and blood vessel activity than a normal breast ( ng and kee , 2008 ; etehadtavakol et al . , 2011 ) . studies support thermography 's potential for early detection of breast abnormalities ( kennedy et al . , 2009 ) , because it is based on detecting chemical changes and new blood vessels caused by tumor . in the other hand , mammography is an anatomical test that can find signs of cancer later than thermography . various types of image segmentation ( etehadtavakol et al . , 2010 ; gonzales and woods , 2001 ; sowmya and bhattacharya , 2005 ; etehadtavakol and ng , 2013 ; pakhira , 2009 ; ng and chen , 2006 ; ng et al . , 2001 ) methods can be applied to extract hot regions for detecting breast abnormalities and potentially suspicious tissues . shape and size of tumor region that has been diagnosed with cancer unlike benign growth tumor which is encapsulated and has a smooth boundary , malignant tumor has an irregular shape ( healthhype , 2013 ) . these facts help to distinguish the type of detected tumor from thermal image but it requires an accurate regional division . this paper is organized as follows : three image segmentation methods are reviewed in section 2 . k - means algorithm in section 2a , fuzzy c - means in 2b , and level set in section 2c . image segmentation ( etehadtavakol et al . , 2011 ) is the process by which an original image is segmented into multiple regions . the classification is based on some characteristic , such as color , intensity , texture , etc . in this paper three algorithms are described : k - means , fuzzy c - means and level set . k - means clustering ( macqueen , 1967 ) is a simple , fast and unsupervised method to classify data to a specified number of clusters ( pakhira , 2009 ) . the main idea is to define a centroid for each cluster in a way that all centroids are as far away from each other as possible , and then assign each data point to the nearest centroid . in each cycle k new centroids are re - calculated for the clusters resulting from previous step , and then data sets are categorized by minimizing the sum of squares of distances between data and the corresponding cluster centroid . as a result , k centroids change their location in each cycle until no further changes are done . 1 ) shows a set of data which is divided into three clusters , and each cluster is represented by a specific color . each data point is assigned to the nearest cluster center , such that the squared distances from the cluster are minimized . in summary , this algorithm attempts to minimize the objective function j which is the sum of the squared error . where xi is a vector of points in cluster j and cj is the cluster mean . in summary , this clustering method follows these steps ( etehadtavakol et al . , 2010 ) : choose the number of clusters ( k)selects k points as the initial cluster centers randomly ( initialization ) assign each point to the closed cluster , based upon the euclidean distance between each point and each cluster centerre - calculate the mean of each cluster as the average of the points in that clusteriterate over steps 3 and 4 until the clusters converge . convergence may be defined differently depending upon the implementation , but it normally means that no data point change clusters when these steps are repeated , and the function j reaches its minimum value . choose the number of clusters ( k ) selects k points as the initial cluster centers randomly ( initialization )   assign each point to the closed cluster , based upon the euclidean distance between each point and each cluster center re - calculate the mean of each cluster as the average of the points in that cluster iterate over steps 3 and 4 until the clusters converge . convergence may be defined differently depending upon the implementation , but it normally means that no data point change clusters when these steps are repeated , and the function j reaches its minimum value . it shows that each data element belongs to exactly one cluster , and consequently the membership function is a step function . it means that the allocation of data points is hard ( all or nothing ) . fuzzy c - means clustering ( developed by dunn ( 1973 ) and improved by bezdek ( 1981 ) ) is a class of algorithms for cluster analysis in which the allocation of data points to clusters is not hard ( 0 or 1 ) but allows one piece of data to belong to more than one cluster with a degree of membership between 0 and 1 . this algorithm assigns membership to each data point corresponding to each cluster center on the basis of distance between the cluster center and the data point . the more the data is near to the cluster center more is its membership towards the particular cluster center . fuzzy c - means is frequently used in pattern recognition ( zhang and chena , 2004 ) . this algorithm attains to minimize the objective function jm ( chuang et al . , 2006 ) where m is any real number greater than one and controls the fuzziness of the membership function , xi is a d - dimensional point , cj is the d - dimension centers vector of the cluster , each element of matrix   is a weight factor between 0 and 1 and shows the degree of membership of xi in the cluster j , such that and ||*|| is any norm expressing the similarity between any measured data and its corresponding cluster center ( etehadtavakol et al . , 2010 ) . it is an approach , where the data points have their membership values with the cluster centers , which will be updated iteratively . choose the number of clusters , c , exponent weight , m , and initialize the matrix u. 2 . iterate over steps 2 and 3 and update membership and cluster centers until the minimum value of jm is achieved or change in any element of matrix u is below a specific threshold , .   in figure 3(fig . 3 ) , twenty data and three clusters are used to initialize the algorithm and to compute the u matrix . the color of the data is that of the nearest cluster according to the membership function . in this figure , each data point does not belong exactly to a cluster , but it can be placed in a middle way . in this case , the membership function follows a smooth line to indicate that every data point may belong to several clusters with different values of the membership coefficient . active contour or snake is an energy minimizing , deformable spline influenced by constraint and image forces . they are often used in image analysis and computer vision to detect object boundaries , and to describe their shape . the main idea is to move the curve within an image under the speed f toward features of interest such as lines and edges . but the process become very complicated and hard if the snakes try to cross over themselves , or if the shape tries to break into two ( figure 4(fig . osher and sethian ( 1988 ) introduced the level set method for tracking interfaces and shapes . the central idea of this method is to represent the implicit contour as the zero level set of a higher dimensional function , referred as the level set function ( lsf ) , and to approximate the motion equations of the level set function ( osher and sethian , 1988 ) . this method provides a new framework for active contour models to overcome the problems associated with energy minimization , and instead of moving the position of contour only value of points change . as a consequence , this approach presents a major desirable feature for level set method which is the ability to handle topological merging and splitting naturally . in addition , this method works in any number of space dimensions , and is easy to program for many medical image analysis and applications of computer vision . if the level set function ,  , moves in the normal direction with a speed function f , it satisfies the partial differential equation ( pde ) : this hamilton - jacobi equation is called level set evolution equation and guides the motion of the lsf . the function can be anything as long as its zero level set gives the contour . 2 . update the function (x , y , t ) in the narrow band , based on hamilton - jacobi equation . the simulation iterates over step 2 until predefined number of iteration is reached or a desired object has been extracted . lsf is assumed as a signed distance function ( sdf ) that is negative for inside the contour and positive for outside . however , the level set evolution equation does not guarantee to preserve the lsf as a signed distance function which cause instability and numerical errors during the implementation . in references ( sethian , 1996 , 1999 ; osher and fedkiw , 2002 ) , some available methods such as fast marching algorithm periodically reinitialize the lsf to reshape the surf as a signed distance function and to reduce numerical errors . unfortunately , reinitialization may evolve the contour to an incorrect position ( sethian , 1999 ; osher and fedkiw , 2002 ) , so reinitialization should be avoided as much as possible ( xu et al . , 2010 ) . ( 2011 ) , a new type of level set evolution called distance regularized level set evolution ( drlse ) is able to maintain the desired shape of lsf near the zero level set and to eliminate the reinitialization procedure ( xu et al . , 2010 ) . conventional level set algorithms compute the sdf in the whole domain which is very time consuming . in order to improve the computational efficiency , the narrow band implementation ( adalsteinsson and sethian , 1995 ) can be applied to update only a few points close to the zero level set . for image segmentation , the speed term formulation is based on different features ; accordingly , two main categories exist for level set method : edge - based models and region - based models . edge - based models propagate the contour based on the information provided by image gradients and object boundaries , and the speed function attain zero value as it gets closer to the object boundaries . these models are adequate for images with intensity inhomogeneity , but they are sensitive to noise , dependent on initial curve placement and inaccurate for images with weak object boundaries ( li et al . , 2011 ) . the region - based models evolve the contour based on information provided by the entire region such as intensity , color or texture . mumford and shah ( 1989 ) introduced a function which is used to segment an image into sub - regions . methods aiming to find an optimal segmentation of the image i by minimizing the functional energy : the methods aiming to minimize this energy are called piecewise smooth ( ps ) . the first term is the data term , which forces u to be close to the image i , and the second term is the smoothing term , which forces u to be smooth within each of the regions separated by the contour c. the third term is introduced to regularize the contour c. |c| is the length of the contour c which separates the image domain  into disjoint regions 1 , ... , n . u is a piecewise smooth function that approximates the image i and is smooth inside the each region i . they have ability to segment images with intensity inhomogeneities ; however , sensitivity to initialization and also expensive computation are their weaknesses ( li et al . , 2011 ) . chan and vese ( 1999 ) proposed a simpler formulation to segment image i by finding the level set function  and constants c1 
 c2 that minimize the energy : where h is heaviside function , and  segments the image domain  into two disjoint regions 1 = { x: ( x ) > 0 } and 2 = { x: ( x ) > 0}. these models are termed piecewise constant ( pc ) , and are inappropriate for images with intensity inhomogeneities . ( 9 ) are the data fitting terms . while the third term , with the weight parameter  > 0 image segmentation is therefore achieved by finding the level set function  and the constants c1 and c2 that minimize the energy . the following model of intensity inhomogeneity for image i is proposed by li et al . ( 2011 ) : n is additive noise , j is true image , and b is referred to as a bias field ( or shading image ) for the intensity inhomogeneity that can be considered approximately constant in a neighborhood of   the true image j approximately takes n distinct constant values c1 , ... , cn in disjoint regions 1 , ... , n , where   therefore , the intensity of points in a neighborhood of each point can be approximated as follow :   note that the radius  of the neighborhood should be selected appropriately according to the intensity degree of inhomogeneity . the bias field varies faster for more localized intensity inhomogeneity , and therefore the approximation in eq . based on the assumption of zero - mean additive gaussian noise with small variance , intensities in the neighborhood can be classified into n distinct clusters with centers mi  b(y)ci : in li et al . ( 2011 ) , the k - means algorithm is applied to classify the local intensities . it minimizes the clustering criterion function that is described by : k(y - x ) is named kernel function which is zero for this function is chosen as a truncated gaussian function : where a is a normalization constant such that  k(u ) = 1 ,  is the standard deviation ( or the scale parameter ) of the gaussian function , and  is the radius of the neighborhood which should be selected according to the degree of the intensity . local clustering criterion function has to be minimized for all y in . therefore , energy ,  , is defined in the following form : the energy formulation is expressed in terms of n disjoint regions which makes the energy minimization difficult . therefore ,  is converted to a level set formulation with a number of level set functions and the energy minimization can be solved by using well - established variational methods . level set formulation is called two - phase for n=2 and called multiphase formulation for n>2 . in general , the energy  , can be written as the function of  = ( 1 , ... , k ) , c = c1 , ... cn ) and the bias field b :   and the membership functions are defined by : for the case of two - phase the level set function  represents the two regions 1 and 2 , therefore the energy  is a function of  and the membership functions are defined by m1( ) = h( ) and m2( ) = 1 - h( ) . the energy functional in two - phase level set formulation is defined by : and for the multiphase : are the regularization terms ( li et al . , 2011 ) . the energy minimization with respect to each variable can be achieved ( li et al . , 2011 ) . more detail can be found in ( li et al . , 2011 ; xu et al . , 2010 ) . k - means clustering ( macqueen , 1967 ) is a simple , fast and unsupervised method to classify data to a specified number of clusters ( pakhira , 2009 ) . the main idea is to define a centroid for each cluster in a way that all centroids are as far away from each other as possible , and then assign each data point to the nearest centroid . in each cycle k new centroids are re - calculated for the clusters resulting from previous step , and then data sets are categorized by minimizing the sum of squares of distances between data and the corresponding cluster centroid . as a result , k centroids change their location in each cycle until no further changes are done . 1 ) shows a set of data which is divided into three clusters , and each cluster is represented by a specific color . each data point is assigned to the nearest cluster center , such that the squared distances from the cluster are minimized . in summary , this algorithm attempts to minimize the objective function j which is the sum of the squared error . where xi is a vector of points in cluster j and cj is the cluster mean . in summary , this clustering method follows these steps ( etehadtavakol et al . , 2010 ) : choose the number of clusters ( k)selects k points as the initial cluster centers randomly ( initialization ) assign each point to the closed cluster , based upon the euclidean distance between each point and each cluster centerre - calculate the mean of each cluster as the average of the points in that clusteriterate over steps 3 and 4 until the clusters converge . convergence may be defined differently depending upon the implementation , but it normally means that no data point change clusters when these steps are repeated , and the function j reaches its minimum value . choose the number of clusters ( k ) selects k points as the initial cluster centers randomly ( initialization )   assign each point to the closed cluster , based upon the euclidean distance between each point and each cluster center re - calculate the mean of each cluster as the average of the points in that cluster iterate over steps 3 and 4 until the clusters converge . convergence may be defined differently depending upon the implementation , but it normally means that no data point change clusters when these steps are repeated , and the function j reaches its minimum value . it shows that each data element belongs to exactly one cluster , and consequently the membership function is a step function . it means that the allocation of data points is hard ( all or nothing ) . fuzzy c - means clustering ( developed by dunn ( 1973 ) and improved by bezdek ( 1981 ) ) is a class of algorithms for cluster analysis in which the allocation of data points to clusters is not hard ( 0 or 1 ) but allows one piece of data to belong to more than one cluster with a degree of membership between 0 and 1 . this algorithm assigns membership to each data point corresponding to each cluster center on the basis of distance between the cluster center and the data point . the more the data is near to the cluster center more is its membership towards the particular cluster center . fuzzy c - means is frequently used in pattern recognition ( zhang and chena , 2004 ) . this algorithm attains to minimize the objective function jm ( chuang et al . , 2006 ) where m is any real number greater than one and controls the fuzziness of the membership function , xi is a d - dimensional point , cj is the d - dimension centers vector of the cluster , each element of matrix   is a weight factor between 0 and 1 and shows the degree of membership of xi in the cluster j , such that and ||*|| is any norm expressing the similarity between any measured data and its corresponding cluster center ( etehadtavakol et al . , 2010 ) . it is an approach , where the data points have their membership values with the cluster centers , which will be updated iteratively . choose the number of clusters , c , exponent weight , m , and initialize the matrix u. 2 . iterate over steps 2 and 3 and update membership and cluster centers until the minimum value of jm is achieved or change in any element of matrix u is below a specific threshold , .   in figure 3(fig . 3 ) , twenty data and three clusters are used to initialize the algorithm and to compute the u matrix . the color of the data is that of the nearest cluster according to the membership function . in this figure , each data point does not belong exactly to a cluster , but it can be placed in a middle way . in this case , the membership function follows a smooth line to indicate that every data point may belong to several clusters with different values of the membership coefficient . active contour or snake is an energy minimizing , deformable spline influenced by constraint and image forces . they are often used in image analysis and computer vision to detect object boundaries , and to describe their shape . the main idea is to move the curve within an image under the speed f toward features of interest such as lines and edges . but the process become very complicated and hard if the snakes try to cross over themselves , or if the shape tries to break into two ( figure 4(fig . 4 ) ) . osher and sethian ( 1988 ) introduced the level set method for tracking interfaces and shapes . the central idea of this method is to represent the implicit contour as the zero level set of a higher dimensional function , referred as the level set function ( lsf ) , and to approximate the motion equations of the level set function ( osher and sethian , 1988 ) . this method provides a new framework for active contour models to overcome the problems associated with energy minimization , and instead of moving the position of contour only value of points change . as a consequence , this approach presents a major desirable feature for level set method which is the ability to handle topological merging and splitting naturally . in addition , this method works in any number of space dimensions , and is easy to program for many medical image analysis and applications of computer vision . if the level set function ,  , moves in the normal direction with a speed function f , it satisfies the partial differential equation ( pde ) : this hamilton - jacobi equation is called level set evolution equation and guides the motion of the lsf . the function can be anything as long as its zero level set gives the contour . 2 . update the function (x , y , t ) in the narrow band , based on hamilton - jacobi equation . the simulation iterates over step 2 until predefined number of iteration is reached or a desired object has been extracted . lsf is assumed as a signed distance function ( sdf ) that is negative for inside the contour and positive for outside . however , the level set evolution equation does not guarantee to preserve the lsf as a signed distance function which cause instability and numerical errors during the implementation . in references ( sethian , 1996 , 1999 ; osher and fedkiw , 2002 ) , some available methods such as fast marching algorithm periodically reinitialize the lsf to reshape the surf as a signed distance function and to reduce numerical errors . unfortunately , reinitialization may evolve the contour to an incorrect position ( sethian , 1999 ; osher and fedkiw , 2002 ) , so reinitialization should be avoided as much as possible ( xu et al . , 2010 ) . ( 2011 ) , a new type of level set evolution called distance regularized level set evolution ( drlse ) is able to maintain the desired shape of lsf near the zero level set and to eliminate the reinitialization procedure ( xu et al . , 2010 ) . conventional level set algorithms compute the sdf in the whole domain which is very time consuming . in order to improve the computational efficiency , the narrow band implementation ( adalsteinsson and sethian , 1995 ) can be applied to update only a few points close to the zero level set . for image segmentation , the speed term formulation is based on different features ; accordingly , two main categories exist for level set method : edge - based models and region - based models . edge - based models propagate the contour based on the information provided by image gradients and object boundaries , and the speed function attain zero value as it gets closer to the object boundaries . these models are adequate for images with intensity inhomogeneity , but they are sensitive to noise , dependent on initial curve placement and inaccurate for images with weak object boundaries ( li et al . , 2011 ) . the region - based models evolve the contour based on information provided by the entire region such as intensity , color or texture . mumford and shah ( 1989 ) introduced a function which is used to segment an image into sub - regions . methods aiming to find an optimal segmentation of the image i by minimizing the functional energy : the methods aiming to minimize this energy are called piecewise smooth ( ps ) . the first term is the data term , which forces u to be close to the image i , and the second term is the smoothing term , which forces u to be smooth within each of the regions separated by the contour c. the third term is introduced to regularize the contour c. |c| is the length of the contour c which separates the image domain  into disjoint regions 1 , ... , n . u is a piecewise smooth function that approximates the image i and is smooth inside the each region i . they have ability to segment images with intensity inhomogeneities ; however , sensitivity to initialization and also expensive computation are their weaknesses ( li et al . , 2011 ) . chan and vese ( 1999 ) proposed a simpler formulation to segment image i by finding the level set function  and constants c1 
 c2 that minimize the energy : where h is heaviside function , and  segments the image domain  into two disjoint regions 1 = { x: ( x ) > 0 } and 2 = { x: ( x ) > 0}. these models are termed piecewise constant ( pc ) , and are inappropriate for images with intensity inhomogeneities . while the third term , with the weight parameter  > 0 , can regularize the zero level contour . image segmentation is therefore achieved by finding the level set function  and the constants c1 and c2 that minimize the energy . the following model of intensity inhomogeneity for image i is proposed by li et al . ( 2011 ) : n is additive noise , j is true image , and b is referred to as a bias field ( or shading image ) for the intensity inhomogeneity that can be considered approximately constant in a neighborhood of   the true image j approximately takes n distinct constant values c1 , ... , cn in disjoint regions 1 , ... , n , where   therefore , the intensity of points in a neighborhood of each point can be approximated as follow :   note that the radius  of the neighborhood should be selected appropriately according to the intensity degree of inhomogeneity . the bias field varies faster for more localized intensity inhomogeneity , and therefore the approximation in eq . based on the assumption of zero - mean additive gaussian noise with small variance , intensities in the neighborhood can be classified into n distinct clusters with centers mi  b(y)ci : in li et al . ( 2011 ) , the k - means algorithm is applied to classify the local intensities . it minimizes the clustering criterion function that is described by : k(y - x ) is named kernel function which is zero for this function is chosen as a truncated gaussian function : where a is a normalization constant such that  k(u ) = 1 ,  is the standard deviation ( or the scale parameter ) of the gaussian function , and  is the radius of the neighborhood which should be selected according to the degree of the intensity . local clustering criterion function has to be minimized for all y in . therefore , energy ,  , is defined in the following form : the energy formulation is expressed in terms of n disjoint regions which makes the energy minimization difficult . therefore ,  is converted to a level set formulation with a number of level set functions and the energy minimization can be solved by using well - established variational methods . level set formulation is called two - phase for n=2 and called multiphase formulation for n>2 . in general , the energy  , can be written as the function of  = ( 1 , ... , k ) , c = c1 , ... cn ) and the bias field b :   and the membership functions are defined by : for the case of two - phase the level set function  represents the two regions 1 and 2 , therefore the energy  is a function of  and the membership functions are defined by m1( ) = h( ) and m2( ) = 1 - h( ) . the energy functional in two - phase level set formulation is defined by : and for the multiphase : are the regularization terms ( li et al . , 2011 ) . the energy minimization with respect to each variable can be achieved ( li et al . in this paper , thirty thermal images are taken from ann arbor thermography ( 2008 ) , thermal imaging lab in the san francisco bay area ( 2008 ) , american college of clinical thermology ( 2008 ) , thermography of iowa ( 2008 ) and sunstate thermal imaging center in australia ( 2009 ) . in this section , the three methods are implemented for different cases ; one fibrocystic case and four malignant cancer cases . 5 ) , the image belongs to a patient who had fibrocystic changes in left breast ( sunstate thermal imaging , 2009 ) . inflammatory breast cancer ( ibc ) is a rare and very aggressive disease in which cancer cells block lymph vessels in the skin of the breast . this type of breast cancer is called  inflammatory  because the breast often looks swollen and red , or " inflamed " ( ann arbor thermography , 2008 ) . in figure 7(fig . 7 ) , the image shows a significant increase in temperature and vascularity ( angiogenesis ) in the right breast . the patient in figure 8(fig . 8) had a thermography test with a recent mammogram that was considered watchful for an area in the left breast . a follow - up ultrasound of the left breast was also watchful for the same area . the report recommended a follow - up mammogram in 6 months to monitor the finding in the left breast . the image to the left indeed shows a noticeable increase in heat and blood vessel activity ( angiogenesis ) in the left breast when compared to the right ( thermography of iowa , 2008 ) . 9 ) shows a thermography test of a patient after having a normal mammogram and a watchful ultrasound of the left breast . the image to the left also shows a significant increase in temperature of the entire left breast along with noticeable vascularity ( angiogenesis ) ( thermography of iowa , 2008 ) . in this study , three different segmentation algorithms : k - means , fuzzy c - means and level set were applied . the implementations results of k - means algorithm are shown in part b / s of each figure . also the implementation results of fuzzy c - means algorithm are shown in part c / s ( etehadtavakol et al . , 2010 ) . level set algorithm as proposed in this paper ( li et al . , 2011 ) is a region - based segmentation method . by minimizing the energy , it is able to segment the image and estimate the bias field that can be applied for bias correction . in this implementation , ( 2011 ) , only " timestep " parameter varies in the range of [ 0.001 - 0.1 ] . the implementation results of level set algorithm are shown in part d / s of figures . 5 ) shows a comparison of segmentation results between k - means , fuzzy c - means , and level set , for a fibrocystic case . as shown in figure 5b - c(fig . 5 ) the exact shape of borders is not achieved by both the k - means and fuzzy c - means implementation . by using the level set , we are however able to elicit the exact borders where some useful features could be extracted from them . as shown in figure 5d(fig . 5 ) the borders are more similar and matching to the borders of the hottest region in original image . 9 ) present comparison of segmentation results between k - means , fuzzy c - means , and level set , when applied on malignant cancer cases . as we can see in the figures , neither k - means nor fuzzy c - means can separate the first hottest region from the second hottest region ; while level set is completely succeed in segmentation and extraction of the first hottest regions . there are several drawbacks of color segmentation of thermal infrared breast images by k and fuzzy c - means . in practice , where clusters are not disjoint and a pixel may belong to different clusters k - means clustering does not have a suitable performance . moreover , poor initial partitions can result in empty clusters ( etehadtavakol et al . , 2010 ) . in k and fuzzy c means , prior specification of the number of clusters is required . in this paper , level set technique it has preferable efficiency , accuracy , and much more robustness for initialization ( li et al . , 2011 ) . the hottest regions extracted by this method are more similar and matching to their respective original images than the k and fuzzy c - means . regarding to the suspicious region , we would be able to extract some useful information . image segmentation plays an important role in many medical imaging applications . in this paper , we present three image segmentation methods : k - means , fuzzy c - means ( fcm ) and a region - based level set for segmentation of various breast thermograms . the improved level set algorithm ( energy functional formulation ) used in this paper has preferable efficiency , accuracy , and much more robustness for initialization than the conventional level set methods . these methods have been applied to the abnormal thermal images , and the hottest regions of three different algorithms for each case are extracted and compared . experimental results have demonstrated the superior performance of level set in terms of accuracy , efficiency , and robustness . the hottest regions extracted by the level set are more similar to the original image than the other segmentation methods .
breast thermography is a physiological test that provides information based on the temperature changes in breast . 
 it records the temperature distribution of a body using the infrared radiation emitted by the surface of that body . 
 precancerous tissue and the area around a cancerous tumor have higher temperature due to angiogenesis , and higher chemical and blood vessel activity than a normal breast ; hence breast thermography has potential to detect early abnormal changes in breast tissues . 
 it can detect the first sign of forming up cancer before mammography can detect . 
 the thermal information can be shown in a pseudo colored image where each color represents a specific range of temperature . 
 various methods can be applied to extract hot regions for detecting suspected regions of interests in the breast infrared images and potentially suspicious tissues . 
 image segmentation techniques can play an important role to segment and extract these regions in the breast infrared images . 
 shape , size and borders of the hottest regions of the images can help to determine features which are used to detect abnormalities . in this paper , 
 three image segmentation methods : k - means , fuzzy c - means and level set are discussed and compared . 
 these three methods are tested for different cases such as fibrocystic , inflammatory cancer cases . 
 the hottest regions of thermal breast images in all cases are extracted and compared to the original images . according to the results , 
 level set method is a more accurate approach and has potential to extract almost exact shape of tumors .