A semi-supervised fuzzy GrowCut algorithm to segment and classify regions of interest of mammographic images

A Semi-Sup ervised F uzzy Gro wCut Algorithm to Segmen t and Classify Regions of In terest of Mammographic Images Filip e R. Cordeiro a , W ellington P . Santos b, ∗ , Ab el G. Silv a-Filho a a Informatics Center, F e der al University of Pernambuc o, Br azil b Dep artment of Biomedic al Engineering, F e der al University of Pernambuc o, Br azil Abstract A ccording to the W orld Health Organization, breast cancer is the most com- mon form of cancer in women. It is the second leading cause of death among w omen round the world, b ecoming the most fatal form of cancer. Despite the existence of sev eral imaging tec hniques useful to aid at the diagnosis of breast cancer, x-ra y mammograph y is still the most used and effective imaging technol- ogy . Consequen tly , mammographic image segmentation is a fundamental task to support image analysis and diagnosis, taking in to accoun t shap e analysis of mammary lesions and their b orders. Ho wev er, mammogram segmen tation is a v ery hard pro cess, once it is highly dep endent on the types of mammary tissues. The GrowCut algorithm is a relatively new metho d to p erform general image segmen tation based on the selection of just a few p oints inside and outside the re- gion of interest, reaching go o d results at difficult segmentation cases when these p oin ts are correctly selected. In this work we present a new semi-sup ervised segmen tation algorithm based on the mo dification of the Gro wCut algorithm to p erform automatic mammographic image segmentation once a region of interest is selected b y a sp ecialist. In our prop osal, we used fuzzy Gaussian memb ership functions to mo dify the ev olution rule of the original GrowCut algorithm, in order to estimate the uncertain ty of a pixel b eing ob ject or background. The ∗ Corresponding author. Email addr esses: frc@cin.ufpe.br (Filip e R. Cordeiro), wellington.santos@ufpe.br (W ellington P . Santos), agsf@cin.ufpe.br (Ab el G. Silv a-Filho) Pr eprint submitte d to Exp ert Systems with Applic ations January 8, 2018 main impact of the prop osed method is the significan t reduction of exp ert effort in the initialization of seed p oin ts of GrowCut to p erform accurate segmenta- tion, once it remov es the need of selection of bac kground seeds. F urthermore, the prop osed method is robust to wrong seed positioning and can b e extended to other seed based techniques. These characteristics hav e impact on expert and in telligent systems, once it helps to develop a segmentation metho d with lo wer required sp ecialist knowledge, b eing robust and as efficient as state of the art techniques. W e also constructed an automatic p oin t selection pro cess based on the simulated annealing optimization metho d, av oiding the need of human in terven tion. The prop osed approac h w as qualitativ ely compared with other state-of-the-art segmen tation techniques, considering the shap e of segmen ted regions. In order to v alidate our prop osal, w e built an image classifier using a classical multila yer perceptron. W e used Zernik e moments to extract segmented image features. This analysis employ ed 685 mammograms from IRMA breast cancer database, using fat and fibroid tissues. Results sho w that the prop osed tec hnique could ac hiev e a classification rate of 91.28% for fat tissues, evidencing the feasibility of our approac h. Keywor ds: breast cancer, mammographic image analysis, semi-sup ervised image segmentation, GrowCut algorithm, fuzzy segmen tation, simulated annealing 1. In tro duction Breast cancer is the most common cancer in women w orldwide: the W orld Health Organization (WHO) estimates the o ccurrence of 1.1 million new cases eac h y ear (Mathers et al., 2008). Surviv al rates for breast cancer can v ary from 80%, in high-income countries, to b elo w 40% in low-income nations (Coleman et al., 2008). The low surviv ability in some coun tries is related to the lac k of screening programs whic h assist in the early detection of cancers. Early detection has an important impact on the successful treatmen t of cancer, once medical treatment b ecomes harder in late stages. One of the most effectiv e 2 metho ds for breast cancer analysis is digital mammograph y (Maitra et al., 2011). Ho wev er, mammography visual understanding and analysis can be a hard task ev en to a sp ecialist, once suc h a pro cedure can b e affected by image qualit y asp ects, radiologist exp erience, and tumor shape. A realistic estimative of the p eriod that comprises the b eginning of the tu- mor and its growth un til it b ecomes palpable, reaching around 1 cm, is ab out 10 years (Allred et al., 1998). During this p erio d, breast imaging is essential for tumor monitoring. Correct ev aluation of tumor size takes an imp ortant role at planning breast cancer treatmen ts and a voiding mutilating surgeries, e.g. mas- tectom y (Litière et al., 2012). Nev ertheless, imaging devices used b y the BMH (Brazilian Ministry of Health) (Costa et al., 2004) for the detection of breast cancer, which in v olve manual iden tification of the no dule size, are quite ineffi- cien t at the ev aluation. These methods dep end substantially on the professional examiners exp erience (Costa et al., 2004) . F urthermore, image diagnosis is a complex task due to the large v ariability of clinical cases. Many cases seen in clinic practice do not fit classic images and descriptions precisely (Juhl et al., 2000). F or these reasons, mammograph y computer aided diagnosis (CAD) has b een playing an imp ort role to assist radiologists in improving the accuracy of their diagnosis. Consequently , traditional tec hniques in image pro cessing ha v e b een applied in the medical field to mak e diagnosis less susceptible to errors through accurate identification of anatomic anomalies (Da-xi et al., 2010)(Y e et al., 2010). The shape of the segmented tumor is a determinan t factor in the mammo- gram diagnosis. It is related to the gravit y of the tumor and the difference of a few centimeters in the maxim um diameter can determine if it is necessary do a surgery or not. How ever, it can be very difficult to detect the con tour of the tumor accurately depending on several factors, such as shap e of the tumor, densit y , size, location and image qualit y . Some c hallenges in tumor segmen- tation include lo w contrast images, in tensit y levels which v ary greatly across differen t regions, p o or illumination and high noise levels, non-defined contours, and masses which are not alw a ys obviously detected (Raman et al., 2011). 3 The Gro wCut algorithm is a relativ ely new metho d to perform general image segmen tation based on the selection of just a few points inside and outside the region of interest, reac hing goo d results at difficult segmentation cases when these p oin ts are adequately selected 1. In this work we presen t a new semi-sup ervised segmen tation algorithm based on the modification of the GrowCut algorithm to perform semi-automatic mam- mograph y image segmen tation. In our prop osal, we used fuzzy Gaussian mem- b ership functions to mo dify the ev olution rule of the original GrowCut algo- rithm, in order to estimate the uncertaint y of a pixel b eing ob ject or bac kground. Once p oin t selection can b e considered an imp ortant disadv antage of Gro wCut, w e also constructed an automatic p oin t selection pro cess based on the simu- lated annealing optimization metho d, a voiding the need of human interv ention. The proposed approac h w as qualitativ ely compared with other state-of-the-art segmen tation tec hniques, considering the shape of segmented regions. In order to v alidate our prop osal, we built an image classifier using a classical multila y er p erceptron. W e used Zernik e moments to extract segmented image features. This analysis emplo y ed 685 mammograms from IRMA breast cancer database, using fat and fibroid tissues. This work has impact in the con text of exp ert systems once it turns an exp ert system less dep enden t on the user knowledge, b esides turning the pro cess more robust to incorrect initialization. Moreov er, the prop osed method can b e extended and applied to other exp ert systems, in other areas of application. This work is organized as follo wing: in section 2 we presen t the related w ork; in section 3 w e present our segmentation prop osal based on the mo dification of Gro wCut algorithm using fuzzy Gaussian membership functions and the clas- sical sim ulated annealing algorithm; in section 5 w e present our exp erimental qualitativ e and quantitativ e results and p erform some commen ts; finally , in sec- tion 7 we present general conclusions and some p ersp ectiv es of future works. 4 2. Related W orks Recen t w orks ha ve pro vided go od accuracy in identifying the lo cation of tu- mors (Liu et al., 2011)(Mohamed et al., 2009), ho wev er relativ ely little researc h has b een done to verify the quality of segmentation. Oliver et al. (2010) makes a review of state of art and shows that related works are divided in to edge-based segmen tation, region-based segmen tation and adaptive threshold. In edge-based segmentation, it is difficult to determine the b oundary of the tumor due to some ill-defined edges lesions. Region-based segmentation are more suitable for mass detection, since regions of tumor are usually brighter than their surrounding tissue, hav e an almost uniform density and a fuzzy boundary (Raman et al., 2011). Recen t studies for tumor segmentation hav e b een successfully applied to region-based techniques for tumor segmentation. Lewis and Dong (2012) uses W atershed to automatically segment tumor candidate regions, ac hieving an o verall detection rate for mass tumors of 90%. Ho w ever, the metric of anal- ysis that w as used was based only on the location of the tumor and not on the qualit y of segmen tation. Eltoukh y and F a y e (2013) use an adaptive threshold technique, ac hieving 100% sensitivity , with an av erage of 1.87 false p ositiv es, when applied to 188 images. How ever, the v alue of sensitivity v aries depending on the false p ositive rate, and each work uses a differen t rate. Susp ect regions usually are brigh ter than neigh b or regions and with a uni- form density (Hong and Sohn, 2010). How ev er, usually lesion regions do not hav e a w ell-defined contour. Due to this fact, seed-based tec hniques, i.e. tec hniques in whic h users lab el the initial seeds, show a b etter qualit y in the final seg- men tation. Gro wCut tec hnique has b een applied to successful segment medical images, such as kidney (Dai et al., 2013), brain (Y amasaki et al., 2012) and ver- tebral b ody segmentation (Egger et al., 2013). Cordeiro et al. (2012) apply the classical Gro wCut to segmen t masses in mammograms, obtaining goo d results in terms of quality of segmentation. Zheng et al. (2013) employ a random-w alk 5 based segmentation, which also uses seeds provided by the user, to achiev e a go od segmen tation. Ho wev er, they do not pro vide a quantitativ e analysis of the results. Despite seed based techniques hav e shown suitable p erformance for mass segmen tation, they require a high level of specialist kno wledge about the problem in order to select these seeds. Unsup ervised and Semi-Supervised tec hniques try to reduce the required sp ecialist kno wledge about the tumor region. Ghosh et al. (2011) proposes an unsup ervised Gro wCut applied to medical images, but it is used for clustering and not for sp ecific segmen tation. Ramathi et. al use A ctive Contours (Rahmati et al., 2012) to segmen t masses, ac hieving 86.85% of accuracy using an o v erlap measure betw een segmen t images and ground truth. Chakraborty et al. apply Multilev el threshold (Chakrab ort y et al., 2012) combined with region growing to perform segmentation for w ell-defined edge con tours, but b oth techniques sho w difficulties in defining spiculated contours or ill-defined edges. Hao et al. (2012) attempt an automated seed generation com bining iso con tour maps with random walks and active contours, achieving high accuracy for the metric of area ov erlap measure. Ho wev er, this metric alone does not reflect precisely the qualit y of segmen tation. Al-Na jdawi et al. (2015) et. al prop oses an image visual enhancement and mass segmentation, obtaining tumor classification accuracy of 90.7%. Ho wev er, the segmentation step is mainly based on thresholding, whic h do es not guar- an tee correct segmentation for ill-defined edges, even with image enhancement. Dong et al. (2015) prop oses and automated for mass segmentation, using active con tours to perform the segmentation. Nevertheless, it uses the information pro vided by the database to identify the lo cation of the mass, which does not happ ens in practice. Xie et al. (2016) use a Pulse Coupled Neural Netw ork algorithm to obtain a scheme for correct initialization for level set e v olution. Ho wev er, the w ork do es not explore the limitation of the algorithm to wrong initialization, once the level set segmen tation depends on that. Although it impro ves the lev el set segmentation, the algorithm is still dep enden t of a go od initialization. 6 As describ ed previously , most of recen t work in literature which are based on seeds selection are dependent on correct initialization in order to the algorithm p erform accurately . But a correct seed p ositioning requires high user kno wledge ab out the problem, to the most complex images. Although new metho ds with a high segmen tation accuracy ha v e been prop osed, they are still high dep enden t on the user kno wledge to obtain goo d results. The unsup ervised methods pro- p osed in literature ha ve tw o main approaches: obtaining an automatic threshold v alue to p erform the segmen tation or generating the seeds automatically . The metho ds based on a threshold may ha ve difficulties to p erform segmentation in more complex images, with ill-defined edges . The techniques based on auto- matic seeding must guaran tee that all the seeds are correctly p ositioned. The prop osed metho d contributes and differs from state of art techniques by reduc- ing the kno wledge necessary to p erform segmentation, using as case of study the Gro wCut technique. The prop osed tec hniques eliminate the need of selec ting bac kground seeds and makes the metho d more robust to wrong initialization. This has an impact of using unsupervised segmen tation methods easier and more tolerant to differen t initializations. F urthermore, the prop osed approach can b e extended to other tec hniques and other kind of image. As observed by Raman et al. (Raman et al., 2011), related works results differ significantly , and are often based on visual sub jectiv e opinion with very little quan titativ e endorsemen t. F urthermore, most studies describ e an accuracy of the techniques based only on the lo calization of the tumor and not on its shap e and contour, though these characteristics are very imp ortant for accurate diagnoses. Herein this work we prop ose a new approach based on automatic selection of seeds, making comparisons b et w een our prop osal and other state- of-the-art techniques, analyzing the qualit y of segmen tation of each technique. 3. Metho ds In terms of the methodology , the segmen tation can be though t of a pro cess whic h consists of tw o tasks: the localization of the anatom y of interest and 7 its delineation. The prop osed metho dology aims to provide assistance to the sp ecialist to find an accurate delineation of the mass. Therefore, it assumed that a region of in terest was previously selected by a sp ecialist and provided to the proposed system to perform a high quality segmen tation. Therefore, the ob jectiv e of the prop osed metho d is not to segment the mass from a full mammogram, but to help the professional to iden tify the correct measure of the mass. Once the region on interest (ROI) is used as input, the segmen tation task is p erformed automatically . The metho d is called semi-sup ervised b ecause of the need of selection of the region of interest by a sp ecialist. But once the R OI is given as input to the prop osed system, the segmentation is p erformed automatically . The flow c hart of Figure 1 illustrates the prop osed metho d. Aut om a t i c S e e ds S e l e ct i on F e a t ur e E x t r a ct i on us i ng Ze r n i k e M om e nt s ML P Cl a s s i fi c a t i o n R e gi on of I nt e r e s t Aut om a t i c S e e ds S e l e ct i on F e a t ur e E x t r a ct i on us i ng Ze r n i k e M om e nt s Aut om a t i c S e e ds S e l e ct i on F e a t ur e E x t r a ct i on us i ng Ze r n i k e M om e nt s R e gi o n o f In t e r e s t RO I P a t ch Da t a b a s e B e n i gn M a l i gn a n t Pr o p o s e d Se gm e n t a t i o n Mo d e l Fe a t u r e E x t r a ct i o n u s i n g Ze r n i k e Mo m e n t s Se gm e n t e d I m a ge A u t o m a t i c Se e d s Se l e c t i o n P r op os e d S y s t e m In p u t ( s e l e c t e d b y a s p e c i a l i s t ) Ou t p u t Ou t p u t Figure 1: Flow c hart of the prop osed method. The metho dology starts from an initial region of interest that corresp onds to a previous selection made b y a sp ecialist or p erformed by a computational algorithm. In this work, R OIs are provided by the IRMA (Deserno et al., 2011) database, which contains patches of the suspicious image regions. After this, automatic selection of seeds is p erformed using Sim ulated Annealing (Dowsland and Thompson, 2012), which mo dels the lo calization of seed in an optimization problem, in which the ob jectives are to maximize the in tensity of seed pixels and minimize the distance b et ween them. After the seed pixels are obtained, they are used as inputs to the prop osed segmentation mo del, in order to generate the segmen ted image. Therefore, once giv en a region of interest, the segmen tation pro cess is p erformed automatically . As the IRMA database do es not pro vide the 8 ground truth of the images of interest, w e decided to use a classifier to v alidate the segmen tation through the iden tification of the segmen ted images based on their shap e and edge c haracteristics. If the classifier is able to identify the type of tumor of segmented images accurately , we consider the segmentation suitable enough for the problem. Therefore, after the segmented images are obtained, the feature selection stage starts. In this stage, the prop osed feature extractor calculates attributes related to shape and margin of the segmen ted regions us- ing the Zernike Moments. Subsequen tly , a classifier is applied to identify the segmen ted images as b enign or malignant tumors. After the classification step, w e p erform the analysis of results. 3.1. Pr op ose d Se gmentation Mo del The prop osed mo del is based on the Gro wCut (V ezhnevets and Konouc h- ine, 2005) algorithm, a user interactiv e approach employ ed to p erform image pro cessing tasks, such as noise reduction and morphological and edge detection. Gro wCut is a technique based on cellular automata (Hernandez and Herrmann, 1996), represen ted by grids of cells, where each cell can assume a finite num ber of states, which can v ary according to the neighborho o d rules. The neighbor- ho od consists of a selection of neigh b or pixels of a determined image, and can b e defined by using Neumann and Mo ore neighborho o d mo dels (Nay ak et al., 2014), for example. All the cells update their states according to the same up- date rule, based on the v alues of neighbor cells. Eac h time a rule is applied to a grid, a new iteration b egins. The GrowCut technique, as a user-interactiv e based approach, uses the con- cept of a seed pixel, in which the user initially lab els a set of pixels in differen t classes of in terest and, based on these seeds, the algorithm tries to lab el all the pixels of the image. In GrowCut, eac h cell has a strength v alue and, at eac h iteration, the neigh b or cells try to dominate this sp ecific cell, changing its lab el. If a defender cell has a higher strength than its dominators, then it contin ues with the same lab el. Otherwise, the sp ecific cell inherits the dominators’ cell lab el. The pro cess contin ues until the algorithm reaches conv ergence and all 9 the cells stop changing their states. The pseudo-code of Gro wCut is described in Algorithm 1. Algorithm 1 Gro wCut evolution rule 1: for all p ∈ P do 2: l t +1 p ← l t p 3: Θ t +1 p ← Θ t p 4: for all q ∈ N ( p ) do 5: if g (    ~ C p − ~ C q    2 ) · Θ t q > Θ t p then 6: l t +1 p ← l t q 7: Θ t +1 p ← g (    ~ C p − ~ C q    2 ) · Θ t q 8: end if 9: end for 10: end for A ccording to the Algorithm 1, for each cell p in a P space of cells, previous states are copied, up dating the label v alue of cell p in iteration t+1 , represented as l t +1 p , and the strength v alue of cell p in iteration t+1 , as Θ t +1 p . Next, for eac h cell q belonging to a neighbor of cell p , represented as N(p) , the up date lab el condition is chec ked. In the condition of line 5, ~ C p and ~ C q are intensit y v ectors of the pixels p and q in the gray-scale space of colors, resp ectively , and Θ t q and Θ t p are v alues of strength of cells q and p in iteration t . F unction g , in lines 5 and 7, is a decreasing monotonic function, represen ted by Equation 1. g ( x ) = 1 max    ~ C    2 (1) Finally , label and strength of cells are up dated if the domination rule is satisfied, and the process repeats until the algorithm con verges. In Gro wCut, as in the ma jorit y of seed-based techniques, the qualit y of segmen tation depends directly on the positions of the initial seeds. Therefore, it dep ends on the user’s knowledge to select appropriately seeds next to the edge of the ob ject to b e segmen ted. In the case in whic h some seeds are initially lab eled 10 incorrectly , the algorithm may p erform an undesired and p o or segmentation. The proposed mo del aims to reduce the need for initial kno wledge about the con tour of the ob ject, b esides reducing the effort of selection of seeds. More- o ver, the proposed mo del aims to be fault toleran t, allowing it to reco v er from incorrect seed selection. In GrowCut all the initial seeds selected by the user hav e maximum strength v alue, assigning a high weigh t to the seeds with incorrect lab els. Unlik e Grow- Cut, the proposed mo del is based on the selection of seeds of only one class: the ob ject of in terest. The traditional Gro wCut only works with t wo classes, and if the bac kground class is not close to the edges of tumor it do es not provide a go od segmentation, as describ ed by Cordeiro et al. (Cordeiro et al., 2012). In our approach, w e discard the selection of a background class because, from the seeds of ob ject class, we can estimate a frontier region separating ob ject and bac kground. How ever, instead of assigning all the lab eled cells with max- im um strength, all the cells are initialized with zero strength, except the cell corresp onding to the center of mass of input seeds. Consequently , we assign maxim um v alue to the cell of cen ter of mass b ecause we assume that it has a higher chance of having a correct lab el. The initialization is p erformed using the following Equation 2. ∀ p ∈ P , l p = 0 , Θ p = 0 , l cm = l ob , Θ cm = 1; (2) where p is a cell in space P of cells, and l p and Θ p are the lab els and strengths of cell p , respectively . The lab el and strength of the cell w hic h corresponds to the center of mass of the seeds are represen ted by l c m and Θ c m , resp ectiv ely . The prop osed mo del makes a mo dification in the update rule of the cells of Gro wCut, in a wa y that the attac k of each cell is based in a region modeled by a Gaussian function. The strength of the mo del will b e equal to 1 if the degree of mem b ership of the sp ecific cell to the background is higher than its complement, i.e. the degree of mem bership of the sp ecific cell to the ob ject of in terest. Otherwise, the strength of the mo del assumes the strength of the curren t cell. 11 The up date algorithm of the prop osed metho d is shown in Algorithm 2. Algorithm 2 Prop osed Algorithm evolution rule 1: for all p ∈ P do 2: l t +1 p ← l t p 3: Θ t +1 p ← Θ t p 4: Calculate Θ t M ,p 5: for all q ∈ N ( p ) do 6: Calculate Θ t M ,q 7: if g (    ~ C p − ~ C q    2 ) · Θ t M ,q > Θ t M ,p then 8: Calculate l t M ,p,q 9: l t +1 p ← l t M ,p,q 10: Θ t +1 p ← g (    ~ C p − ~ C q    2 ) · Θ t M ,q 11: end if 12: end for 13: end for In Algorithm 2, Θ t M ,p and Θ t M ,q are the strengths of the mo del for the cells p and q , resp ectively , being represented b y Equations 3 to 5. Θ M ,i =    1 , µ Bkg ( i ) > µ Ob j ( i ) Θ i , µ Bkg ( i ) ≤ µ Ob j ( i ) , (3) µ Bkg ( i ) = 1 − µ Ob j ( i ) , (4) µ Ob j ( i ) = exp  − ( x i − x m ) 2 2 α x s 2 x  exp  − ( y i − y m ) 2 2 α y s 2 y  , (5) where µ Bkg ( i ) is the the fuzzy mem b ership degree asso ciated to the uncertain ty of the i -th cell b elongs to the image background, whilst µ Ob j ( i ) is the the fuzzy mem b ership degree associated to the uncertain t y of the i -th b elongs to the ob ject of interest. These fuzzy membership functions are Gaussian functions whose v ariables x i and y i corresp ond to the co ordinates of the i -th cell in the grid, whereas x m and y m are the co ordinates of the cen ter of mass for the 12 initially selected seeds; s x and s y are the standard deviation of initial p oin ts, whilst α x and α y are the weigh ts of tuning of the Gaussian function, empirically determined according to the problem of interest. The lab el of eac h q -th cell, l M ,p,q , is up dated according to the following expression of Equation 6 l M ,p,q =    l p , µ Bkg ( q ) > µ Ob j ( q ) l q , µ Bkg ( q ) ≤ µ Ob j ( q ) . (6) T able 1 mak es a comparison betw een the GrowCut algorithm and the pro- p osed mo del. T able 1: Comparison betw een Gro wCut and the Prop osed Algorithm. Characteristic Gro wCut Prop osed Mo del Selection of Seeds Selection of seeds of ob ject class and bac kground class. Selection of seed only of ob ject class. Initialization All the seeds hav e strength v alue equal to 1. Only the cell corresponding to the center of mass of points has strength v alue equal to 1. Segmentation Based on knowledge of seeds lo- calization pro vided b y the user. Based on knowledge of seeds; lo- calization and in the Gaussian model that separates the region of foreground and bac kground region. F ault T olerance to seeds localization Low High The initial impact of the prop osed approach is the reduction of the effort to select the initial seeds, in which it is necessary to use only the seeds of the ob ject of in terest. The bac kground region is obtained through the Gaussian mo del, regulating the strength of eac h cell in the up date labeling process. The Gaussian mo del allo ws the pro cess to b e tolerant to incorrect selection of initial seeds, once it is based on the center of mass of the seeds. Consequently , the algorithm b ecomes less dep enden t on the user sp ecialist kno wledge, b eing more appropriate for the process of semi-sup ervised seed selection. 13 3.2. A utomatic Sele ction of Se e ds The selection of seeds consists of identifying initial pixels lo cated in re gions of tumor and non-tumor. In many seed-based techniques, such as Random W alks (Grady, 2006) and Graph Cut (Vicen te et al., 2008), seeds are selected man ually b y a sp ecialist. In this work, the tec hnique Sim ulated Annealing (Dowsland and Thompson, 2012) is used to automatically find the seeds in the region of in terest. As usually , mass regions ha ve higher in tensity pixel v alues. Therefore, the problem of finding a set of seeds was conv erted into an optimization problem, where the algorithm optimizes the set of seeds by the intensit y v alues, aiming to get the seed inside the mass areas. As the Sim ulated Annealing is a v alidated optimization algorithm, it is used to find a set of seeds, trying to minimize the fitness function describ ed by equation 7: f itness = α n − 1 X j =1 d j n − β n X j =1 I j , (7) where d j n is the Euclidian distance b etw een seed j and seed n , and I j is the in tensity v alue of seed j . Hence, the fitness function ev aluates the in tensity lev els of the set of seeds and the distance b etw een them. As it is also imp ortant that the seeds are spread throughout the region of interest, the distance betw een p oin ts is ev aluated in the fitness function. P arameters α and β are used to adjust the impact of distance and in tensit y of the seeds, resp ectiv ely . The higher the v alue, the higher the influence of the distance of intensit y in the fitness function. How ev er, we recommend the v alues to be b et ween 1 and 2. F or the present application, we empirically defined the following standard v alues: α = 1 and β = 1 . 5 . An imp ortan t asp ect of the prop osed algorithm is that it is not necessary to select non-tumor seeds, once our algorithm can adjust its fuzzy Gaussian frontier based only on the seeds of the tumor region. Figure 2 illustrates the steps of the segmentation pro cess for some images of the database. Columns a and d of Figure 2 represen ts the initial region of in terest selected from the IRMA database. Columns b and e shows the seed p oints obtained from automatic seeds selection, represen ted b y the red 14 p oin ts, and the fuzzy Gaussian region, represen ted by red ellipses. Regions inside ellipse hav e a higher probability of finding pixels of tumor mass. The size of the Gaussian region is based on the location and distribution of the seed p oin ts. The adv an tage of the prop osed tec hnique is that it requires only seeds of the tumor region, different from most of techniques. Finally , columns c and f shows the final segmen tation of the prop osed approac h, represen ted by green con tours. (a) (b) (c) (d) (e) (f ) Figure 2: Segmentation pro cess of the prop osed approach for images of IRMA database. (a) and (d) Original Images; (b) and (e) Automatic generated seeds and F uzzy-Gaussian region; (c) and (f ) Final segmentations. 15 4. Exp eriments 4.1. Exp erimental Envir onment Our prop osal w as ev aluated using the IRMA (Deserno et al., 2011) (De Oliv eira et al., 2010) (Deserno et al., 2012) database, whic h was developed from a pro ject p erformed b y Aac hen Univ ersit y (R WTH Aac hen). The database is composed b y regions of interest of mammograms, whic h were classified by radiologists and resized to 128 × 128 pixels. The database is comp osed by 2.796 mam- mograms images of four repositories: 150 images from Mini-MIAS database (Suc kling et al., 1994), 2.576 images from DDSM (Heath et al., 2000), 1 from LLN database, and 69 from R WTH database. The images from IRMA hav e four t yp es of tissue densit y , whic h are classified in four t yp es, according to the classi- fication of BI-RADS (D’Orsi, 1998): fat tissue (T yp e I), fibroid tissue (Type I I), heterogeneous dense tissue (Type I II) and extremely dense tissue (Type IV). In this w ork, we analyzed images of fat transparent and fibroid glands systems, for masses classified as circumscrib ed, spiculated, and other mass, according to the database description. F or exp erimen tal ev aluations, we used 685 mammograph y patc hes, which corresponds to all images of fat and fibroid tissues which lesions of type circumscrib ed, spiculated and other mass. 4.2. F e atur e Extr action F eature extraction used in this work is based on the calculation of Zernike Momen ts (T ahmasbi et al., 2011). The Zernik e Moments are image descriptors of shap e and margin and inv arian t to rotation, non-redundan t, and robust to noise and shap e (W ang et al., 2009)(Hwang and Kim, 2006), and they had already been used successfully to identify masses by T ahmasbi et al. (T ahmasbi et al., 2011). The Zernik e Moments are defined as pro jections of the in tensity function of an image, represented by f : S → W , ov er the orthogonal basis functions, whic h are the Zernik e p olynomials. The calculation of Zernik e Moments to a digital image f is represented by Equation 8. 16 Z n,m = n + 1 π ( N − 1) X u ∈ S f ( u ) V n,m ( ρ, θ ) , (8) where ρ = √ x 2 + y 2 N and θ = tan − 1( y /x ) . The v ariable n is a natural num b er denominated momen t order and m is a p ositive or negativ e in teger, named rep etition, which satisfies the restriction n − | m | = pair , and | m | ≤ n . The v ariable V n,m is the Zernike p olynomials family , defined by the Equation 9 and Equation 10. V n,m ( ρ, θ ) = R n,m ( ρ ) − j mθ , (9) R n,m = n −| m | 2 X s =0 ( − 1) s ( n − s )! s !( n + | m | 2 − s )!( n −| m | 2 − s )! ρ n − 2 s . (10) T o calculate the Zernik e Moments of an image, its center is considered as a cen ter of an unitary disk. The Zernik e Momen ts are divided in 64 descriptors, whic h are divided in t w o groups of 32 elements, defined as lo w order and high order moments. 4.3. Classific ation In order to perform the classification of the suspicious regions of in terest, we used a classical Multilay er Perceptron (MLP) (Jain et al., 1996), which is an extensiv ely v alidated neural netw ork based classifier. The inputs of the MLP are the Zernike momen ts extracted from the segmented images. W e employ ed the following architecture: 64 inputs, t wo neurons in the output la yer (benign and malignan t finding classes), and tw o hidden la yers with 30 neurons each one. T raining and test stages were performed using k-fold cross-v alidation, with 10 folds. The classifier was used to indirectly ev aluate the quality of segmentation through the features of shap e and margin extracted using Zernik e moments. 4.4. Evaluation W e ev aluate the qualit y of segmentation of the implemented tec hniques b y analyzing if the con tour of the segmentation is well-defined enough to makes 17 p ossible the correct identification of the type of tumor using the MLP classi- fier. W e chose this ev aluation b ecause the IRMA database do es not pro vide the segmen tation ground truth. F urthermore, it would b e unfeasible to a sp ecialist man ually segment all the images. Additionally , if the contour of the segmen- tation is suitable enough to turns p ossible the classifier identify the type of tumor, we can consider the segmentation has a go od quality and is useful to b e emplo yed in clinical practice. Our prop osal w as compared to six state-of-the-art w orks: BEMD (Jai-Andaloussi et al., 2013), BMCS (Berb er et al., 2013), LBI (Sharma and Khanna, 2013), MCW (Lewis and Dong, 2012), T opographic Approach (Hong and Sohn, 2010) and W a velet Analysis (P ereira et al., 2014). Eac h technique w as implemented using the parameters pro vided by each article. Although some w orks w ere used for different databases and considering the full mammogram, the tuning was based on the parameters suggest in each work. A comparison with the classical Gro wCut was not feasible due to necessity of selection of seed points of 685 images, whic h the database do es not pro vide the ground truth. F urthermore, it is more suitable the comparison b etw een semi-sup ervised tec hniques, as ev aluated in this work. 5. Results This section shows the results of the state of the art techniques applied to segmen t lesions of mammograms, from IRMA database, from fat transparen t and fibroid tissues, corresp onding to 685 images divided in to circumscrib ed, spiculated and other mass. The prop osed approach was compared with state of the art techniques and the results of the segmentation of each technique were ev aluated through the metric describ ed previously . Figure 3 shows the results of segmentation of all tec hniques analyzed for the images of IRMA database. Figure 3 sho ws 8 patc hes from IRMA database and the segmentation of eac h analyzed tec hnique. The region of interest from the database is shown in column (a), where in the other columns the segmentation of eac h technique is 18 (a) (b) (c) (d) (e) (f ) (g) Figure 3: Comparison of segmentation of analyzed tec hniques. (a) Region of Interest; (b)Proposed Metho d; (c) T op ographic; (d) W avelet; (e) BEMD; (f ) BMCS; (g) MCW. represen ted in green. As can b e observed, the prop osed metho d and T opographic approac h obtained a w ell-defined segmentation for most of cases of Figure 3. As describ ed in the ev aluation section, the segmented images of eac h tec h- nique were submitted to a classifier to identify the t yp e of lesion according to its features of shap e and margin. The classifier used was a MLP , whic h classi- fies the region of in terest in b enign or malignan t. The analysis was separated according to the type of tissue and for eac h tissue it was divided analyzing t w o scenarios: a)circumscrib ed and spiculated lesions and b) circumscrib ed, spicu- lated and other masses. The results of classification for each scenario desc ribed 19 are shown in T able 2. T able 2: Classification accuracy rate using the segmented images of the analyzed techniques, for fat and fibroid tissue. T echniques F at Tissue Fibroid Tissue circ.+spic. circ.+spic.+other circ.+spic. circ.+spic.+other BEMD 75.93 ± 3.47% 75.32 ± 3.60% 78.22 ± 3.8% 75.64 ± 3.11% BMCS 76.15 ± 3.21% 72.07 ± 2.41% 85.50 ± 4.42% 72.37 ± 2.96% MCW 69.52 ± 3.49% 70.01 ± 3.18% 86.17 ± 3.47% 70.91 ± 4.29% Proprosed 85.83 ± 5.67% 75.93 ± 3.94% 84.30 ± 1.95% 72.48 ± 3.83% T opographic 76.82 ± 4.85% 77.00 ± 4.15% 84.61 ± 5.94% 76.81 ± 4.61% W av elet 81.64 ± 5.35% 75.48 ± 5.51% 84.84 ± 5.96% 76.32 ± 5.97% The b o xplot of results sho wed in T able 2 is illustrated in Figure 4. Figure 4: Boxplot of the classification rate of the tec hniques analyzed. As can b e observ ed in Figure 4, the ma jor difference of results b etw een tec hniques w as in the first scenario, when using fat tissue and only circumscrib ed and spiculated masses, where the prop osed approach had higher classification rate. T o ev aluate if the results were statistically different, it was p erformed a h yp othesis test. The h yp othesis test w as done using Studen t’s t-test (Sam uels et al., 2012), considering null h ypothesis with equal p opulation mean, using a confidence level of 95%. The Student’s t-test was done comparing the results of the prop osed technique against the other ones. The results of this test is sho wn in T able 3. 20 T able 3: P-v alue of Student’s t-test comparing the prop osed approach with the analyzed techniques. Comparison F at Tissue Fibroid Tissue circ.+spic. circ.+spic.+other circ.+spic. circ.+spic.+other T opographic 1.4418E-08 0.3082 0.7908 0.0002 W av elet 0.00469 0.7162 0.0067 0.0046 BEMD 1.3128E-10 0.5363 5.4451E-10 0.0068 BMCS 1.9458E-10 3.4508E-05 0.1830 0.9035 MCW 6.9151E-18 3.5855E-08 0.0131 0.1405 The b old v alues in T able 3 represen t the situations in which the null hypoth- esis were rejected. This means that the prop osed approach and the compared tec hnique are statistically differen t. F or the other cases it means that they are statistically similar. Although most of the techniques obtained a go o d classification rate using the Zernik e moments to the segmented images, it is not guaranteed that the edges of the segmented image are well defined. Therefore, another analysis was done focusing on the quality of segmentation and the classification rate using only the well segmented images. This does not in v alidate the first analysis, b ecause results show ed that the obtained segmentation is suitable for the correct iden tification of tumors in b enign or malignan t, once it provides the contour features necessary to classify the tumor. How ev er, for a more sp ecific analysis ab out the quality of segmen tation, it w as separated the w ell segmented images obtained for each technique. F or this purp ose, it w as considered that a well segmen ted image was that ones in which more than 50% of the edges w ere not touc hing the edges of the region of interest. This decision w as made b ecause it was assumed that it is necessary to ha ve more than 50% of a w ell-defined edge to b e considered as a go o d segmen tation. Based on this, the next analysis ev aluates the classification accuracy rate based only on the selected well-defined segmen tations. This aims to analyze the amoun t of images selected as go o d segmen tation for each technique and the classification rate for this selection. The pro cess of selection w as p erformed automatically based on edges of the 21 tumor. The results for this analysis is sho wed in T able 4. T able 4: Classification rate of the analyzed techniques, when using the segmented images with a w ell-defined margin. T echnique F at Tissue Fibroid Tissue circ. + spic. circ. + spic. + other circ. + spic. circ. + spic. + other Classification Rate Selection Classification Rate Selection Classification Rate Selection Classification Rate Selection BEMD - 20/152 - 46/345 - 13/198 - 23/340 BMCS - 12/152 - 28/345 - 10/198 - 33/340 MCW 85.69 ± 6.03% 78/152 86.12 ± 4.23% 169/345 89.77 ± 4.41% 81/198 90.11 ± 3.44% 128/340 Proposed 91.28 ± 2.96% 87/152 88.34 ± 5.03% 186/345 89.27 ± 4.12% 125/198 85.52 ± 4.39% 211/340 T op ographic 84.20 ± 5.33% 143/152 83.49 ± 4.34% 317/345 86.97 ± 5.21% 185/198 81.56 ± 6.35% 313/340 W avelet 89.81 ± 3.29% 67/152 90.16 ± 3.83% 125/345 89.76 ± 3.95% 55/198 90.60 ± 4.13% 87/340 In T able 4, the BEMD and BMCS approac hes do not ha ve a classification rate because the amoun t of selected images was to o lo w to the classifier training pro cess. That means that few images of BEMD and BMCS had more than 50% of the edges w ell defined. 6. Discussion This work presents a metho dology for delineating masses on R OIs of digital mammograms, aiming to help the sp ecialist in the identification of the lesion. The delineation approach is based on a mo dification of the seeded region based metho d Gro wCut. In this mo dification the up dated ev olution rule employ ees a fuzzy Gaussian membership function. This mo dification reduces the effort of seeds selection, once only the foreground seeds are necessary to estimate the region of the lesion. F urthermore, it facilitates the use of unsup ervised methods to select the seeds, as prop osed in this work. In this section w e discuss the results show ed previously , analyzing the p erformance of the algorithms and the results obtained. In Figure 3, the prop osed technique, in column b , obtained a con tour close to the edges of the tumor for the images presen ted. The T op ographic approac h, in column c , also obtained a go od segmentation for most of cases, but it w as not so well defined in some cases, like in the first, second and last image, w ere 22 the segmentation was wrong. The W a v elet based approach, in column d did not obtain a go od segmentation for some cases where the contour was ill-defined. The other techniques, in column e , f and g did not segmen t well for most of the cases, segmenting the en tire region of interest. The analysis w as made for the 685 images, but the examples shown in Figure 3 illustrates the quality of segmen tation of the prop osed segmen tation mo del. T able 2 sho ws that the prop osed approach achiev es a higher accuracy when using the classifier to classify the segmented images in b enign or malignant, applied to fat tissues and using circumscrib ed and spiculated masses. When including also other masses, in the third column, the av erage of classification is close to the T opographic and W a velet approaches. F or fibroid tissues, all tec hniques, except BEMD, obtained similar p erformance when considering only circumscrib ed and spiculated masses. With the addition of other masses for fibroid tissue, the T opographic approach obtained higher result. Can also b e observ ed that not necessarily an algorithm that detect masses on fibroid tissue has a higher performance compared to one that identifies masses in fat tissue. F or the cases analyzed, the MCW approach had a b etter p erformance for fibroid tissue when compared to the proposed approac h, whereas for fat tissue the prop osed approac h had better results. In T able 3, the results of second column means that for fat tissue, using only circumscrib ed and spiculated masses, the prop osed approach has statistically differen t results when compared to the other techniques. Therefore, can b e said that the prop osed technique obtained a high accuracy when used its segmented images with the classifier. F or fat tissue, including other masses, it w as sta- tistically differen t when compared to BMCS and MCW approaches. How ev er, it had no statistical evidence that it was different from T opographic, W a v elet and BEMD approaches. This means that despite T op ographic approach had a higher av erage classification rate, it was not statistically differen t from the prop osed metho d. F or fibroid tissue, the W a v elet based tec hnique w as statisti- cally different, having higher slight higher accuracy when using circumscrib ed and spiculated masses. When adding other masses, T op ographic, W a v elet and 23 BEMD approach were statistically sup erior. T able 4 shows the classification rate and the amoun t of selected images, for eac h technique, for fat and fibroid tissues. The dataset for each technique is the same, how ev er it was p erformed a selection of images based on the qualit y of segmen tation. This is done because the ob jective is to ev aluate the confi- dence level of each technique, showing a relation b et w een the amount of well segmen ted images and its accuracy for this set. If a tec hnique has a high accu- racy when using the classifier, this indicates that the quality of segmen tation is high. Therefore, if a tec hnique has few w ell segmented images, but the classifi- cation rate is high, this means a high quality of segmentation and the confidence lev el of its segmen tation is high. On the other hand, if a technique has sev eral w ell segmented images, but the classification rate is low, the confidence level of its segmentation is lo w. In the second column of T able 4, the prop osed ap- proac h reaches 91.28% of classification rate, having 87 of 152 images considered as ha ving a w ell-defined contour, as show ed in the third column of T able 4. The T op ographic approac h, despite ha ving a higher num b er of images selected, it had a lo w er classification rate. Therefore, the analysis shows the relation b et w een the amount of well segmented images and the classification rate when used only the images considered with well defined con tour. F rom the first case of fat tissue, the proposed approac h had low er num b er of w ell segmen ted images, but the classification rate shows that the qualit y of segmentation w as b etter. The second case, where the circumscribed, spiculated and other masses were analyzed, for fat tissue, the W a velet based approac h had a higher classification rate. How ever, the prop osed approach had a close rate with a higher num b er of well segmented images. F or fibroid tissue the proposed and the T op ographic approac h had a go od tradeoff betw een classification rate and num b er of selected images. Exp erimen tal outcomes indicate that using the segmentation generated by the proposed method will lead to a b etter classification rate for fat tissues. This represen ts that the segmen tation pro vided b etter c haracteristics to the classifier distinguish b etw een tumor and not tumor for this type of tissue. This 24 results also suggest that the qualit y of segmen tation w as b etter when using F uzzy GrowCut. One of the asp ects that makes the F uzzy Gro wCut obtain b etter segmentation results is that the metho d is less dep endent on a correct initialization when compared to state-of-art techniques. Therefore, even if the unsup ervised step of generation of seed is not perfect, the algorithm can pro vide an accurate segmentation. Moreov er, it do es not rely on a threshold v alue, as found in T opographic Approach and BMCS. The reduction of dep endence on initialization has high implications on segmentation tasks where user knowledge is required, but not guaran teed that is correct. F urthermore, the proposed metho d can be extended to other kind of medical images. This explanation w as added to the discussion section. One of the main strengths of the prop osed metho d is that it is flexible to the seeds’ initialization. This happ ens b ecause the propagation of seeds is based on the center of mass of all seeds, and not on the seeds individually . With the addition of a F uzzy membership function, the segmentation pro cess b ecomes more flexible, different from state-of-art tec hniques whic h uses the seeds as re- liable information. Therefore, b esides reducing specialist knowledge necessary to initialization and remo ving the need of selecting background seeds, it has as consequence the reduction of weigh t related to the correct generation of seeds in an unsup ervised approac h. In state of the art seed based techniques, such as Random W alks, it is hard to adapt the metho d to an unsup ervised approach, once the automatic generation of seeds cannot con tain incorrect lab elling. On the other hand, of the w eakness of the proposed approac h is that it requires more computational time compared to state of the art techniques. 7. Conclusion Herein this work w e proposed a new approac h to segment masses in digital mammograph y images. This approach is based on a semi-sup ervised mo difi- cation of Gro wCut segmen tation algorithm, using fuzzy Gaussian membership functions in the new evolution rule. With suc h a fuzzy function we were able 25 to deal with complex non-defined tumor b oundaries, as our qualitativ e results demonstrate. In order to surpass GrowCut limitation of needing human in- terv ention at selecting internal and external p oin ts to train the segmen tation metho d, w e included a non-sup ervised previous stage with the ability to au- tomatically select internal p oin ts using the classical sim ulated annealing algo- rithm. Our fuzzy approac h av oids the need of selecting external p oints. The proposed technique was ev aluated with 685 images from the IRMA database and compared with the follo wing tec hniques: BEMD, BMCS, LBI, MCW, T opographic Approach and W av elet Analysis. The ev aluation was done applying the Zernike moments on the segmented images and using the MLP to classify the images in b enign or malignan t. This estimates the qualit y of segmen- tation, sin ce the database do es not pro vided the ground truth. The ev aluation w as p erformed for images of fat tissue and fibroid tissue, using circumscrib ed, spiculated and other masses. Results show ed that the prop osed approach had b etter results on av erage for fat tissue, obtaining 85.83% of classification rate. W e also emplo y ed Student’s t- test to iden tify differences among the several metho ds we implement, and results p oin ted that our approach is significantly different from others in this scenario. When including other masses, for fat tissue, the metho d we prop osed can b e considered statistically equiv alen t to others. F or fibroid tissue, the W a v elet and T opographic approaches had a slightly higher classification rate. When analyz- ing the qualit y of segmented images, the prop osed approach obtained 91.28% of classification rate for fat tissue, having a go o d tradeoff betw een well segmented images and classification rate. F or fibroid tissues, the proposed approach had a go od balance b et ween classification rate and w ell segmented images, equiv alent to the T op ographic approach. F rom these results, we can conclude that our semi-sup ervised mo dification of GrowCut, with automatic seed selection using simulated annealing and al- tered evolution rule based on fuzzy Gaussian mem b ership functions, is feasible and suitable for breast tumor segmentation, mainly b ecause it do es not require additional h uman in terv ention once suspicious lesion areas are already clinically 26 determined as input data in this application. Considering qualitative results, our prop osal was able to p erform go od lesion segmentation for circumscrib ed and spiculated mammary lesions, having b etter qualitative segmen tation than the state-of-the-art tec hniques we implemented, considering fat mammary tis- sues. This approach can b e extended for other biomedical image applications where fuzzy-boundaries ob jects hav e to be segmen ted. 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