A Novel Breast Mass Diagnosis System based on Zernike Moments as Shape and Density Descriptors

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1 A Novel Breast Mass Diagnosis Syste based on Zernike Moents as Shape and Density Descriptors Air Tahasbi 1,2, *, Fateeh Saki 2, Haed Aghapanah 3, Shahriar B. Shokouhi 2 1 Departent of Electrical Engineering, The University of Texas at Dallas, Richardso TX 75080, USA 2 Departent of Electrical Engineering, Iran University of Science and Technology, Narak, Tehran 16844, Iran 3 Departent of Electrical Engineering and Coputer Science, Tarbiat Modares University, Tehran 14115, Iran * a.tahasbi@utdallas.edu Abstract In this paper, a novel Coputer-aided Diagnosis (CADx) syste has been proposed for ass diagnosis in aography iages. Zernike oents are utilized as descriptors of shape and density characteristics in order to iprove the overall accuracy. The input Regions of Interest (ROI) are segented and subjected to soe preprocessing stages. The outcoe of preprocessing stage is a gray-scale iage containing co-scaled translated ass which contains both shape and density characteristics of the ass. Two groups of Zernike oents have been extracted fro the preprocessed iages. Considering the perforance of the overall syste the ost effective oents have been chosen and applied to a Multi-layer Perceptron (MLP) classifier. The Receiver Operational Characteristics (ROC) plot and the perforance of overall CADx syste are analyzed for each group of features. The average achieved area under ROC curve (Az) and False Positive Rate (FPR) for high-order oents are and 18.34%, respectively. Besides, for low-order oents those are equal to and 15.44%, respectively. Keywords-Coputer aided diagnosis; aography; ulti layer Perceptron; Zernike oents I. INTRODUCTION Breast cancer has always been one of the ost perilous diseases aong woen [1]. Despite technology developent in the fields of aography [2] and other anticancer ethodologies in recent years, breast cancer is still an unresolved proble. Maography has been one of the ost reliable ethods for early detection and diagnosis of breast cancer [3]; expert radiologists focus on three different types of features including shape, argi and density while visually searching the aogras [2]. Mass shape can be round, oval, lobulated, or irregular [1]. Moreover, ass argin can be circuscribed, icrolobulated, indistinct, or spiculated [1]. Breast Iaging-Reporting and Data Syste (BI-RADS) categorizes the breast density into four groups of high density, isodense, low density, and radiolucent [2]. Current research is directed toward the developent of a CADx syste for breast ass diagnosis eploying Zernike oents as shape and density descriptors. Zernike oents are the apping of an iage onto a set of coplex Zernike polynoials [4]. Since Zernike polynoials are orthogonal to each other, Zernike oents can represent the properties of an iage with no redundancy or overlap of inforation between the oents [4]. Because of such iportant characteristics, Zernike oents have been used widely in different types of applications. For instance, they have been utilized in shape-based iage retrieval [5]. However, the ost iportant drawback of Zernike oents is the large coputational coplexity aking the unsuitable for real-tie applications [6]. In our previous work, Zernike oents were utilized as shape and argin descriptors of asses [7], [8]. In fact, the input ROIs were subjected to two different groups of preprocessing stages resulting in generating two distinct output iages which were called Mass Shape Iage (MSI) and Mass Margin Iage (MMI). The forer was a binary iage describing shape characteristics while the latter was a grayscale iage describing argin characteristics [7]. The Zernike oents were extracted fro each iage separately so that the extracted oents could be effective shape and argin descriptors. Although the accuracy and False Negative Rate (FNR) of the proposed syste were acceptable, there were a nuber of drawbacks. Firstly, the syste could not be used in real-tie applications due to the large coputational coplexity. Indeed, there were two parallel paths of preprocessing stages as well as 4 different groups of features each containing 32 oents. Thus, the coputational coplexity was large in both preprocessing and feature extraction stages [7]. Secondly, the centroids of asses were calculated using MSI, which is a binary iage. In other words, the gray level inforation were not utilized in centroid finding and object translating [8]. The last but not least proble was that Zernike oents describing ass argin inforation were not good descriptor of ass alignancy; hence, they had better be discarded. In this paper, it has been tried to develop a novel aography CADx syste based on Zernike oents that can resolve the above probles. On the one hand, the input ROI has been segented; on the other hand, its histogra has been equalized. The the resulting iages have been coposed into one coplex iage. The coplex iage is translated based on an intensity-weighted centroid and coscaled. Finally, the Zernike oents are extracted as the descriptors of ass shape and density and applied to an MLP classifier. The results and perforances have been evaluated. Furtherore, in order to analyze the effect of orders of Zernike oents on the perforance of the overall syste, a group of /11/$ IEEE 100

2 high-order as well as low-order Zernike oents have been separately extracted fro ROIs. The the ROC curve of each group has been evaluated. In this research, the MIAS database has been used to provide the aography iages [9]. It contains 322 digital aogras belonging to right and left breasts of 161 different woen. The MIAS database includes 209 noral breasts, 67 ROIs with benign lesions and 54 ROIs with alignant lesions [9]. The outline of this paper is as follows. In the next sectio the proposed approach has been discussed in ore detail. In section III, the experients and results are reported and copared with other recent approaches and finally, in the last section a conclusion has been ade. II. METHODOLOGY Fig. 1 represents the processing stages of the proposed approach. The input data is an ROI which is a suspected part of a aogra and contains only one ass. Each stage is explained in detail as follows. Fig. 2. a) Input ROI containing only one ass. b) Manual segentation of ass by an expert radiologist. c) Input ROI after histogra equalization which is called g(. d) The negative for of input ROI after segentation and filling which is called not(f(). f (, f ( ( g( in{ f (, g( } = (1) x, y g(, f ( > ( g( y ( N 1) where x and y denote the pixel indices and the size of the ROI is N N. The resulting coplex iage is shown in Fig. 3. The ost iportant benefit of this iage is that it contains both shape and density inforation of asses. Zernike oents are dependent on the translation and scaling of asses in ROIs [5], [7], [8]. Thus, these sufferings had better be copensated in the preprocessing stage. In fact, the centroid of each ass should be translated into the center of ROI and the radii of asses should be co-scaled. Fig. 1. The flowchart of proposed CADx syste including preprocessing, feature extractio feature selection and classification stages A. Segentation and Preprocessing In this paper, each ROI has been segented by two different expert radiologists and the final boundary of ass has been calculated using radial averaging [8]. The the ass has been filled which results in generating f(. On the other hand, the input ROI is subjected to histogra equalization which leads to calculating g(. Fig. 1 illustrates this procedure. Fig. 2 represents two different ROIs each containing one ass in different steps of preprocessing stage. Note that Fig. 2 c illustrates g( whereas Fig. 2 d depicts the negative for of f(. In the previous work, each of these iages were subjected to other preprocessing stages such as translation and co-scaling and further the proposed features were extracted separately fro each one. However, in this paper f( and g( are coposed into one coplex iage using in operator; its definition is given as follows: Fig. 3. The resulting coplex iage, which contains both shape and density inforatio before subjecting to translation and co-scaling The Intensity-weighted centroid ethod [10] is used in order to find the centroid of asses instead of siple binary centroid which were utilized in the previous work [7]. This helps us not to lose any of density inforation of asses. The the centroid of each ass has been translated into the center of ROI eploying an appropriate vector (v). The average radius of each ass has been calculated using Noralized Radial Length (NRL) vector [11]. The a suitable scaling coefficient (k) has been coputed for each ass which results in equalizing the average radii of all asses. A ore detailed explanation of proposed translation and co-scaling stages can be found in [7], [8],[11]. Eventually, the output of the preprocessing stages is a grayscale iage which contains a co-scaled translated ass; the proposed iage is a good descriptor of shape and density inforation and called Shape and Density Descriptor Iage (SDDI). 101

3 B. Feature Extraction and selection The coputation of Zernike oents fro an input iage includes three steps: coputation of radial polynoials, coputation of Zernike basis functions and coputation of Zernike oents by projecting the iage onto the Zernike basis functions [4], [7], [8]. Fig. 4 illustrates the agnitude response of two Zernike basis functions with different orders and itterations. The discrete for of the Zernike oents for an iage with the size N N is expressed as follows: Z n + 1 = λ N 1N 1 n + 1 * = f ( V ( λ (2) N N c= 0 r= 0 N 1N 1 c= 0 r= 0 f ( R ( ρ ) xy e jθ cr where 0 ρ xy 1, and λ N is a noralization factor. n is a non-negative integer representing the order of the radial polynoial. is an integer satisfying constraints n - = even and n representing the repetition of the aziuthal angle. R n, is radial polynoial and V n, is 2-D Zernike basis function. A detailed description of calculating Zernike oents can be found in our previous works [7], [8]. High order Zernike oents not only have a large coputational coplexity [6], but also represent a high sensitivity to noise [9]. However, they ight be better descriptors of shape and density characteristics than the loworder Zernike oents. Thus, in order to analyze the effect of orders of Zernike oents on the perforance of the overall syste, a group of high-order Zernike oents as well as a group of low-order Zernike oents have been extracted fro SDDI, separately. The proposed groups of Zernike oents are tabulated in Table I. The first group includes 32 low-order oents which satisfy the following conditions: { Z } Group1 = 3 n 10 n n = 2k k Ν Moreover, the second group includes 32 high-order oents which satisfy the following conditions: { Z } Group2 = 10 n 17 n n = 4k k Ν Note that the conditions are found experientally [8]. C. Classification Artificial Neural Networks (ANNs) have been used widely in edical diagnosis of aography iages. For instance, (3) (4) Fig. 4. The agnitude response of two Zernike basis functions with different orders and itterations TABLE I THE PROPOSED ZERNIKE MOMENTS Group Order (n) Iteration () Nuber of oents , 3 4 0, 2, 4 5 1, 3, 5 6 0, 2, 4, 6 7 1, 3, 5, 7 8 0, 2, 4, 6, 8 9 1, 3, 5, 7, , 2, 4, 6, 8, , 6, , 7, , 4, 8, , 5, 9, , 6, 10, , 7, 11, , 4, 8, 12, , 5, 9, 13, 17 they have been utilized in diagnosis of icro-calcifications [12]. According to literature, MLP has always been a good classifier in the aography iage processing applications [12]. Hence, in this research, an MLP classifier is eployed for categorizing input patterns into Benign and Malignant classes. In this research 40% of input patterns are dedicated to the training set, 30% of the are dedicated to the validation set and also the reaining 30% are dedicated to the testing set. The proposed MLP classifier has been trained using the training set so that the suitable weights are found. Moreover, the nuber of hidden layers and their nodes are being changed until the best network topology, which yields the best accuracy as well as sall aount of FNR, is found. Not to ention the fact that in order to find the best topology and avoid over-training, the accuracy on validation set has been evaluated every 1000 training epochs. After finding the best topology and appropriate nuber of training epochs with the aid of validation set, the testing patterns, which are unseen for the trained classifier, are applied to the classifier and the perforance has been evaluated

4 The input layer has 32 nodes which equals to the nuber of utilized features. The sigoid function has been utilized as the activation function of all internal nodes. The output layer has only one node that uses a linear activation function. This increases the dynaic range of output node, so the ROC curve can be coputed ore precisely. III. EXPERIMENTS AND RESULTS Both high-order and low-order oents have been applied to MLP classifiers with different structures and the results are reported in Table II. The first colun is the nae of each syste while the second colun represents the orders (n) of the utilized Zernike oents. The third colun reports the nuber of eployed Hidden layers (HL) in each syste. The other coluns denote False Positive Rate (FPR), False Negative Rate (FNR), Accuracy and Az which are benchark functions of a aography CADx syste [2], [8]. The first four rows of the table are those systes that eploy high-order Zernike oents. H1, H2, H3 and H4 are four exaple systes whereas HA reports the average values of benchark paraeters for ore than 20 systes that utilize high-order Zernike oents. Fig. 5 illustrates the ROC plots for these systes. Furtherore, the last four rows of the table are those systes that eploy low-order Zernike oents. L1, L2, L3 and L4 are four exaple systes whereas LA reports the average values of benchark paraeters for ore than 20 systes that utilize low-order Zernike oents. These systes show alost the sae behavior as the ones expressed in the previous paragraph. The ROC plots of the are illustrated in Fig. 6. The average FNR and Az for HA are 17.6 % and 0.872, respectively. In additio the entioned paraeters for LA syste are equal to 23.8% and 0.824, respectively. It eans that those systes which utilize high-order Zernike oents yield a higher Az as well as a lower FNR than those systes eploying low-order Zernike oents. Furtherore, the average nuber of hidden layers needed for the high-order Zernike systes is slightly larger than that of low-order Zernike systes. In other words, they have larger coputational coplexity in the feature extraction and classification stages. According to our previous works, utilizing Zernike oents as argin descriptors does not yield satisfactorily results [7]. In fact, the achieved Az for low and high-order Zernike oents as argin descriptors were and 0.547, respectively [7], [8]. Hence, the Achieved Az for LA and HA, TABLE II FINAL RESULTS Nae n HL FPR FNR Accuracy Az H % 20.1 % % H % 00.0 % % H % 20.0 % % H % 29.9 % % HA % 17.6 % % L % 19.9 % % L % 20.0 % % L % 30.0 % % L % 20.0 % % LA % 23.8 % % Fig. 5. ROC plot for H1, H2, H3 and H4. All of the utilize high-order Zernike oents Fig. 6. ROC plot for L1, L2, L3, and L4. All of the utilize low-order Zernike oents which are equal to and 0.872, surpass the argin descriptors. It can be inferred that the new developed syste, which eploys Zernike oents as shape and density descriptors, has already gained two benefits: discarding argin descriptor oents which are useless; enhancing Az by iparting density inforation. As it entioned before, the coputational coplexity of the syste is reduced by coposing both shape and density inforation of asses into one coplex iage. In other words, the coputational coplexity of preprocessing and feature extraction stages is divided by two as we do not need to process two parallel iages anyore. Eventually, a brief coparison is perfored to evaluate the developed syste s perforance. Table III shows the perforances of soe recently developed CADx systes vs. the proposed syste. Nevertheless, a precise coparison of the systes is ipossible since different researchers have eployed different aography databases and ost of paraeters are not reported. It can be seen that the proposed 103

5 TABLE III THE PROPOSED CADX SYSTEM IN COMPARISON WITH OTHER CADX SYSTEMS Reference Year Feature Extraction Technique Database FPR FNR Accuracy This research (HA) 2011 Zernike Moents as shape and density descriptors MIAS This research (H1) 2011 Zernike Moents as shape and density descriptors MIAS A. Rojas et al [13] 2009 Spiculation easure, fuzziness of ass argins DDSM, MIAS T. Mu et al [14] 2008 Fourier factor, Spiculation inde fractal diension MIAS R. M. Rangayyan et al [15] 2007 Fractal diensio Fractional concavity MIAS Az approach yields an acceptable perforance in coparison with other reported approaches. IV. CONCLUSION In this paper, a novel CADx syste has been introduced for ass diagnosis in aography iages using Zernike oents as shape and density descriptors. In fact, it has been tried to develop a novel CADx syste that can enhance our previous work and resolve its probles. The input ROIs are subjected to a nuber of preprocessing stages; the the resulting iages coposed into one coplex iage called SDDI. After special translation and co-scaling stages, two groups of Zernike oents with different orders are extracted fro SDDI and applied to an MLP classifier with different structures. The average Az and FPR for high-order oents are and 18.34%, respectively. Besides, for low-order oents those are equal to and 15.44%, respectively. It is worth entioning that the density inforation of asses are not discarded in the translation stage as we have utilized intensity weighted centroid ethod instead of siple binary centroid calculation. Finally, the argin inforation which were not useful for the diagnosis process have been discarded. REFERENCES [1] Aerican Cancer Society, Breast Cancer Facts & Figures , Atlanta, [2] Alan C. Bovik, Handbook of Iage and Video Processing, 2 nd ed., Elsevier Acadeic Press, 2005, pp [3] H.D. Cheng et al, Approaches for autoated detection and classification of asses in aogras, J. Pattern Recognitio vol. 39, pp , [4] W. Wang, J. E. Mottershead, and C. Mares, Mode-shape recognition and finite eleent odel updating using the zernike oent descriptor, J. Mechanical Systes and Signal Processing, vol. 23, pp , [5] Sh. Li, M. Ch. Lee, and Ch. M. Pu Coplex Zernike oents features for shape-based iage retrieval, IEEE Trans. Systes, a Cybernetics. Part A. Systes and Huans, vol. 39, no. 1, pp , [6] S. K. Hwang, W. Y. Ki, A novel approach to the fast coputation of zernike oents, J. Pattern Recognitio vol 39, pp , [7] A. Tahasbi, F. Saki, S. B. Shokouhi, An Effective Breast Mass Diagnosis Syste using Zernike Moents, in Proc. IEEE, 17 th Iranian Conf. on Bioedical Engineering (ICBME 2010), Isfaha Ira 2010, pp [8] A. Tahasbi, F. Saki, S. B. Shokouhi, Classification of benign and alignant asses based on Zernike oents, J. Coputers in Biology and Medicine, vol. 41, no. 8, pp , [9] J. Suckling et al, The Maographic Iage Analysis Society digital aogra database, Exerpta Medica, Int. Congress Series 1069, 1994, pp [10] C. R. Maure et al, Registration of 3-D Iages using Weighted Geoetrical Features, IEEE Trans. Medical Iaging, vol. 15, no. 6, pp , [11] A. Tahasbi, F. Saki, S. B. Shokouhi, Mass Diagnosis in Maography Iages using Novel FTRD Features, in Proc. IEEE, 17 th Iranian Conf. on Bioedical Engineering (ICBME 2010), Isfaha Ira 2010, pp [12] L. Wei et al, A study on several achine-learning ethods for classification of alignant and benign clustered icrocalcifications, IEEE Trans. Medical Iaging, vol. 24, no. 3, pp., , [13] A. Rojas-Doinguez, and A. K. Nandi, Developent of Tolerant Features for Characterization of Masses in Maogras, J. Coputers in Biology and Medicine, vol. 39, pp , [14] T. Mu, A. K. Nandi, R. M. Rangayya Classification of Breast Masses Using Selected Shape, Edge-sharpness, and Texture Features with Linear and Kernel-based Classifiers, J. Digital Iaging, vol. 21, no. 2, pp , [15] R. M. Rangayya T. M. Nguye Fractal Analysis of Contours of Breast Masses in Maogras, J. Digital Iaging, vol. 20, no. 3, pp ,