breast cancer is one of the major causes of mortality in middle - aged women , especially in developed countries . at present , there are no effective ways to prevent breast cancer since its cause remains unknown . therefore , early detection becomes the key to improving the breast cancer prognosis and reducing the mortality rates .
mammography has been widely recognized as being one of the most effective imaging modalities for early detection of breast cancer .
however , it is a hard work for radiologists to provide both accurate and uniform evaluation for the enormous number of mammograms generated in widespread screening .
a computer - aided detection or diagnosis ( cad ) system , which uses computer technologies to detect the typical signs of breast cancer , has been developed to provide a  second opinion  for radiologists and to improve the accuracy and stability of diagnosis . in general
, there are three signs of breast cancer in a mammogram : microcalcification clusters ( mcs ) , architectural distortions , and masses . in this paper
, we particularly focus on the detection of mcs since they appear in 3050% of mammographic diagnosed cases and show a high correlation with breast cancer .
according to the breast image reporting and data system ( bi - rads ) lexicon , mcs are tiny calcium deposits that appear as small bright spots in mammograms . as an example , figure 1 shows an mc in a mediolateral - oblique ( mlo ) mammogram .
it is often hard for radiologists to find individual mcs in mammograms because they are very small ( typically , 0.051  mm ) in the size and the contrast between the mcs and the surrounding breast tissue is not high enough .  
over the past two decades , there has been extensive research focused on developing the cad tools for automatic detection of mcs in mammograms .
several review papers have also been published on this topic [ 2 , 48 ] .
as described in , mc detection can be classified into four categories : ( 1 ) image enhancement methods [ 913 ] ; ( 2 ) multiscale decomposition methods [ 1417 ] ; ( 3 ) stochastic modeling methods [ 18 , 19 ] ; and ( 4 ) machine learning methods [ 2028 ] . in , a performance evaluation was summarized using free - response receiver operating characteristic ( froc ) in which a support vector machine ( svm ) approach   is found to be superior to conventional methods and is capable of achieving a true positive rate of approximately 90% when the false - positive ( fp ) rate is on average of 1.1 fp clusters per image .
however , such fp is not low enough for clinical application .   in this paper
, we present a new method based on a hybrid method which combines a morphological technique   and wavelet decomposition processing for detecting the mcs in mammograms .
compared with previous methods , the proposed method can achieve not only a high sensitivity but also a lower fp . in the proposed method , we first use a multistructuring - elements ( ses- ) based top - hat transform to enhance the intensity of microcalcification .
subsequently , we employ a wavelet decomposition to refine the enhanced results for removing the false enhanced microcalcifications .
then , based on the feature of malignant mcs , threshold processing is used to segment the mcs from mammograms .   
the rest of paper is organized as follows : section 2 presents a morphological processing technique to enhance the mcs in mammogram . in section 3
section 4 presents the detection of the mcs and gives the experimental results by using the proposed method .
as mentioned in section 1 , the mcs appear as small bright spots in mammograms . in this sense , mcs can be directly segmented by using a threshold process . however , since most mammograms have a low dynamical rang and the intensity contrast between mcs and surrounding tissue is quite low , selection of a threshold for the whole image is not an easy task . as a solution ,
the difference of gaussian ( dog- ) based method which approximates the individual microcalcification as a two - dimensional ( 2d ) gaussian kernel has been reported in , but this method only is suitable for detecting the microcalcifications with approximate circle shape .   in this section
, we propose a new method which is based on a morphological filtering technique   to enhance the individual microcalcifications for mc detection .
the basic idea of the method is to use a set of top - hat transforms based on multi - structuring elements ( ses ) of which sizes and shapes are fitted to the individual microcalcifications to enhance them .
the top - hat transform of a gray - scale image f is defined as f minus its opening by structuring element b : 
 ( 1)t = f(f  b ) , 
 where  denotes the opening operation ; the difference operation yields an image in which only the components fitting to the se remain .  
figure 2 illustrates the concept of the top - hat transform in one dimension .  
in the top - hat transform , selection of an appropriate se fitting to the target objects is the key . since
individual microcalcifications in mammograms frequently vary both in size and shape , it is imposable to use a single se to remove all of them . to solve this problem
, we use a multi - ses - based method which uses eight different flat ses , denoted as bi  ( i = 1,2 ,  , 8) to remove the individual microcalcifications in the opening processing . in this paper
, the ses are a set of lines revolving around its center in a 15  15 array . for a mammogram image with resolution 0.05  mm / pixel
, the 15  15 array indicates that the objects whose size are larger than 0.75  0.75  mm will be removed in the opening operation .  
figure 3 shows the flat ses used in the top - hat transform where the dots denote the centers of the ses .   for each se bi ,  i = 1,2 ,  , 8
, the opening operation yields an image , denoted by ( f  bi ) , in which the individual microcalcifications fitting to the se are removed .
then , in order to enhance these individual microcalcifications removed by the opening operation , we use a subtraction between the original image and the maximum of the opening results to obtain an image , given by 
 ( 2)e = fargmax(f    bi ) . 
figure 4 shows an original mammogram and an enhanced image obtained from ( 2 ) . comparing figure 4(b ) with figure 4(a )
, we can see that individual microcalcifications appearing on a complex background were enhanced successfully .
these results indicate that the microcalcifications can be easily segmented by using a threshold process .
however , the top - hat transform also enhances some undesired objects in the mammograms , such as mammary glands , vessels , and so on .
therefore , a refinement processing is required to remove these undesirable objects from the enhanced mammogram images .
as mentioned above , although the top - hat transform is capable of enhancing microcalcifications varying in size and shape , a side effect is that the undesirable objects are also enhanced .
based on an investigation , we found that these unwanted objects are mainly caused by the soft tissues , such as mammary glands and vessels .
the typical feature of them is that they have a relatively higher intensity compared with their surrounding area as well as an inner nonhomogeneous intensity .  
figure 5 shows a comparison between the microcalcification and the mammary gland after the top - hat transform . comparing figures 5(c ) and 5(g ) , we find that the intensity of microcalcification in the enhanced image approximately equals that of the mammary glands .
however , since the individual microcalcification has almost homogeneous intensity , the size of the enhanced microcalcification is generally larger than that of the mammary gland . figures 5(d ) and 5(e ) show the expanded view of the dashed rectangles in figures 5(c ) and 5(g ) , respectively . we can find that the size of the microcalcification is almost twice as large as the size of the mammary gland .
therefore , the enhanced mammary glands can be treated as noise that can be removed according to their size . in this paper
, we employ a wavelet denoising method to remove the mammary glands because the wavelet decomposition can easily separate them according to their particular size .  
the wavelet - based procedure for denoising the image consists of the following four steps . 

a four - scale wavelet transform is used to decompose the image obtained from the top - hat transform .
symlet-2 ,  as the decomposition filters since they have the least asymmetry and highest number of vanishing moments .
figures 6(a ) and 6(b ) show the scaling function and wavelet function used in the decomposition filtering .  
figure 7 shows the decomposition results in which w(4 , m , n ) ,  w(4 , m , n ) ,  and w(4 , m , n ) denote the detail coefficients at level 4 size of half the original image . 
 
a four - scale wavelet transform is used to decompose the image obtained from the top - hat transform .
symlet-2 ,  as the decomposition filters since they have the least asymmetry and highest number of vanishing moments .
figures 6(a ) and 6(b ) show the scaling function and wavelet function used in the decomposition filtering .  
figure 7 shows the decomposition results in which w(4 , m , n ) ,  w(4 , m , n ) ,  and w(4 , m , n ) denote the detail coefficients at level 4 size of half the original image . 

since the size of the microcalcification is almost twice as large as the size of the mammary gland , the noise caused by the mammary gland can be decomposed in level 4 .
therefore , we set the detail coefficients at level 4 as well as the approximation coefficients at level 1 to zeros .  
figure 7 shows the result of the four - scale wavelet transform in which the shaded coefficients marked are set to zero . 
  thresholding the approximation and detail coefficients .
since the size of the microcalcification is almost twice as large as the size of the mammary gland , the noise caused by the mammary gland can be decomposed in level 4 .
therefore , we set the detail coefficients at level 4 as well as the approximation coefficients at level 1 to zeros .  
figure 7 shows the result of the four - scale wavelet transform in which the shaded coefficients marked are set to zero . 

figures 8(a ) and 8(b ) show the results of the inverse wavelet transform of the microcalcification and mammary gland in figures 5(d ) and 5(h ) .
we see that the intensity of the mammary gland is clearly reduced so that the microcalcifications and mammary glands can be easily separated using a threshold . 
 
figures 8(a ) and 8(b ) show the results of the inverse wavelet transform of the microcalcification and mammary gland in figures 5(d ) and 5(h ) .
we see that the intensity of the mammary gland is clearly reduced so that the microcalcifications and mammary glands can be easily separated using a threshold .  

, we use a thresholding processing to obtain a binary image in which each microcalcification is segmented as connected components . 
 
we use a thresholding processing to obtain a binary image in which each microcalcification is segmented as connected components .
in this section , we introduce a procedure that segments the mcs from the mammogram image obtained from the above sections and give some experimental results by using the proposed method .
as mentioned in section 1 , the mcs are tiny calcium deposits clustering together in the mammogram images . based on an investigation on the bi - rads
, we found that a typical mc generally has the following two features:(1)an mc usually consists of four or more individual microcalcifications;(2)an mc generally appears within a limited area of size 10  10  mm in mammogram images .
an mc usually consists of four or more individual microcalcifications ; an mc generally appears within a limited area of size 10  10  mm in mammogram images . 
 according to these two features , we use the following two steps to detect the mcs .
first , the binary image is subdivided into blocks that overlap their neighbors both horizontally and vertically .
the blocks are of size 200  200 pixels ; for each pair of overlapping blocks , the overlapping boundary region is of size 100  100 pixels .
second , for each block , if the total number of the connected components is larger than three , this block will be labeled as an mc .
we developed and tested the proposed method using a database collected by the tohoku university school of medicine .
these mammograms are of size 4740  3540 pixels , with a spatial resolution of 0.05  mm / pixel and 16-bit grayscale .  
the performance of the proposed method is summarized by the true positive rate and false positive cluster per image .  
table 1 summarizes the experimental results of the proposed method comparing with several previous methods [ 8 , 9 , 13 , 14 , 32 , 33 ] .
the proposed method is capable of detecting 92.9% of true microcalcification clusters with an average of 0.08 false microcalcification clusters detected per image . to our best knowledge
, this performance is better than most state - of - the - art methods in mc detection [ 2 , 34 ] . in the experiments
, we found that the fps are mainly caused by the linear - structure tissues interlacing with each other or benign calcifications with nonhomogenous intensity .  
since the characteristics of linear - structure tissues are quite different with that of the mcs , we consider that fps can still be reduced by using a statistic classifier , such as a support vector machine ( svm ) .
in this paper , we presented a high - accuracy method for the detection of mcs in mammograms .
the proposed method combined a multi - ses top - hat transform and a wavelet - based denoising approach to enhance the individual microcalcifications in mammograms .
experimental results demonstrated that the proposed method is capable of detecting the mcs in mammograms with high accuracy .   in further work
, we will conduct more experiments on a wider database and improve its performance both in accuracy and computational cost .
 the presence of microcalcification clusters ( mcs ) in mammogram is a major indicator of breast cancer . 
 detection of an mc is one of the key issues for breast cancer control . in this paper 
 , we present a highly accurate method based on a morphological image processing and wavelet transform technique to detect the mcs in mammograms . 
 the microcalcifications are firstly enhanced by using multistructure elements morphological processing . 
 then , the candidates of microcalcifications are refined by a multilevel wavelet reconstruction approach . finally , mcs are detected based on their distributions feature . 
 experiments are performed on 138 clinical mammograms . 
 the proposed method is capable of detecting 92.9% of true microcalcification clusters with an average of 0.08 false microcalcification clusters detected per image . 