Microcalcifications Segmentation using Three Edge Detection Techniques on Mammogram Images

Transcription

1 Microcalcifications Segmentation using Three Edge Detection Techniques on Mammogram Images Siti Salmah Yasiran, Abdul Kadir Jumaat, Aminah Abdul Malek, Fatin Hanani Hashim, Nordhaniah Nasrir, Syarifah Nurul Azirah Sayed Hassan, Normah Ahmad. Faculty of Computer and Mathematical Sciences Universiti Teknologi MARA 445 Shah Alam, Selangor, Malaysia. 361 Seri Iskandar, Perak. Malaysia hanani_ayg7, Rozi Mahmud Faculty of Medicine Universiti Putra Malaysia 434 Serdang, Selangor, Malaysia Abstract: - Edge detection has been widely used especially in medical image processing field. In this paper we are comparing Sobel, Prewitt and Laplacian of Gaussian (LoG) edge detection techniques in segmenting the boundary of microcalcifications. The edge detection must satisfy the breast phantom scoring criteria before the segmentation phase is carried out. Then, all of the edge detection techniques are implemented in the Enhanced Distance Active Contour (EDAC) model for the segmentation process. Results obtained from Area Under the Curve (AUC) of the Receiver Operating Characteristic (ROC) curve shows that the Prewitt edge detection has the highest value of AUC, followed by the Sobel and LoG which are.79,.7 and.71 respectively. Key-Words: - Edge Detection, Sobel, Prewitt, Laplacian of Gaussian, Segmentation, Mammogram 1 Introduction Edge detection is defined as a process of identifying and locating sharp discontinuities in an image. Classical methods of edge detection involve convolving the image with an operator, which is constructed to be sensitive to large gradients in the image while returning values of zero in uniform regions [1]. There are an extremely large number of edge detection operators available, each designed to be sensitive to certain types of edges. Edge detection is a common technique for detecting abnormalities in mammogram. A mammogram is a special type of X-ray of the breasts. Mammograms are recommended for women who have symptoms of breast cancer or who have a high risk of the disease. Mammograms are quick and easy. Patient stand in front of an X-ray machine and the radiographer helps to position breast between two plastic plates. The plates press the breast and make it flat. Mammogram images usually contain abnormalities such as microcalcifications, calcifications and masses. If the radiologist has confirmed that the mammogram shows some abnormalities, then the abnormalities should be clarified weather it is microcalcifications, calcifications or masses []. Microcalcifications are specks of calcium that may be found in an area of rapidly dividing cells. Many are seen in a cluster, they may indicate a small cancer. Since microcalcifications are small and subtle abnormalities, they may be unobserved by an examining radiologist [3] Thus, to find the exact boundary of microcalcifications in mammogram images, we used several edge detection techniques by using image processing techniques. The edge detection techniques must satisfy a test which called the Breast Phantom Test before goes to the segmentation process. ISBN:

2 The breast phantom is used to test whether the edge detection is able to detect the characteristic details which hidden behind the phantom. The characteristic details include masses, specs and fibrils. All of these characteristic details are hidden behind the breast phantom. In this study, the MRI- 156 phantom exposed at 5kv the semi-auto mode is used. At 5kv, the image has high contrasts which represent the fatty breast. This implies that the image is difficult to be differentiated between characteristic details and background. Then, a scoring will be made by a radiologist to test whether the edge detection produces a good or poor image quality. The scoring is based on American College Radiology (ACR) [4]. According to the ACR, one phantom is enough to be use to perform the scoring of breast phantom for accreditation. In this paper, three edge detections will be used; Sobel, Prewitt and Laplacian of Gaussian (LoG). These edge detections must satisfy the phantom scoring phase first. Finally, it will be applied on the Enhanced Distance Active Contour (EDAC) to segment the boundary of microcalcification on mammographic images. The performance of each edge detection technique will be measured by using the Area Under the Curve (AUC) of the Receiver Operating Characteristic (ROC) curve. The Enhanced Distance Active Contour Snake or active contour [5] is an energy minimizing spline guided by external forces and influenced by image forces, which pull it towards features such as boundaries, edges and lines. A traditional Snake [1] is represented by parametric curve v ( s) [ x( s), y( s)], s [,1 ] with x and y as the coordinates of vertices. The curve moves through the spatial domain of an image to minimize the energy function which can be represented mathematically as : E vs ( s) vss( s) Eext v( s ds 1 1 * active _ contour ) (1) The first term of Equation (1) represents the internal energy which is responsible for the smoothness and deformation process of the contour and can be expressed as:where (s) and (s) is the elasticity and rigidity parameter respectively. As the value of keep on increasing, the curve becomes straight between two points. Similarly for the large value of, it will produce a smooth curve. The external energy function attracts the deformable contour to the boundary or edge of the image. The energy functional in Equation (1) must satisfy the Euler- Lagrange equation which can be expressed as: v ( s) v ( s) E () ss ssss According to Hou and Han, [6] The Finite Difference Method (FDM) is selected due to its simplicity. Besides, the calculation is much faster compared to other method. In order to solve the matrix equations, the right hand sides of Equation () is set equal to the product of a step size γ and the negative time derivatives of the left hand side such that; E x, y x ext ext t 1 t 1 Axt xt xt 1 (3) E x, y x ext t 1 t 1 Ayt yt yt 1 (4) where A is the pentadiagonal banded matrix. The subscript t is the iterations number. Then, the vertices are calculated by: Eext xt 1, yt 1 xt A I 1 xt 1 (5) x Eext xt 1, yt 1 yt A I 1 yt 1 (6) y where I is an n x n identity matrix. Based on the history and evolution of some Active Contour models, most researchers prefer to enhance and study the GVF Active Contour [7]. In addition, [8] has present the citation occurrence of the DAC with the evolution of the Active Contour models from the year 1987 until 1. Thus, the GVF Active Contour grows to be more popular unlike the DAC which is less popular. The idea of the DAC is derived by Cohen & Cohen where the Potential force based on the Euclidean distance is used [9]. One of the reasons for choosing the DAC is that based on literature, the interest among researchers is low and limited to comparison purposes only. For instance, [7] introduced the GVF Active Contour as well as the DAC and made some comparisons. It is found that the GVF Active Contour performs much better. Then, another study is done where GGVF Active Contour is proposed to improve the GVF Active Contour. Again, the DAC is used for comparison purposes only. The Enhance Distance Active Contour (EDAC) is used to segment ISBN:

3 microcalcifications was proposed by Siti Salmah. It was obtained from modification and enhancement of the original Distance Active Contour (DAC) [8, 1]. However, the EDAC model still has some weaknesses. Based on [11], it is found that some of the results from the EDAC model could not able to differentiate between background tissue and microcalcifications. This is due to the edge detection component applied in the EDAC model. Hence, some experiment on different edge detection techniques should be conducted to. The algorithms of the EDAC model are illustrated as in Figure 1: { Step 1: read image; Step : compute edge map using Canny ; Step 3: compute the external force; Step 4: initialize the Active Contour; for i % is the number of iteration { Step 5: Active Contour deformation; } Step 6: display Active Contour result; } Fig.1 The algorithms of EDAC model. From Figure 1, the Step shows that the edge map is computed by using the Canny edge detection technique. This edge map will be replaced and computed by using different three edge detection techniques; Sobel, Prewitt and Laplacian of Gaussian (LoG). The new values of edge map obtained from each of the edge detection technique will affects the entire steps of the EDAC algorithms. 3 The Sobel, Prewitt and Laplacian of Gaussian (Log) Edge Detection The Sobel operator is based on convolving the image with a small valued filter in horizontal and vertical direction. Thus, it is relatively inexpensive in terms of computations. Another advantage of the Sobel edge detection is faster and compatible with all image resolution. It can be applied to configure any image frame size, edge threshold and data width. It is also compatible, flexible and easy to be integrated with other modules. Sobel can be applied on mammogram image to identify the outline of the object boundary [1]. The masks of its larger size provided good smoothing operation and reduce noise. Therefore, edges of microcalcifications area in mammogram can be detected. The mask of Sobel edge detection can be expressed as; 1 1 G x (7) 1 1 G y (8) where the term Gx and Gy represents the masks that run horizontally and vertically during the convolution process. The combination of these two masks is used to find the magnitude of gradient. The gradient magnitude of the edge, the formula can b expressed as: G G x G y (9) To find the angle of orientation of the edge, the formula can be expressed as: x G y tan 1 G / (1) Prewitt edge detection is also known as edge template matching. This is because a set of edge templates is matched to the image. Each represents an edge in a certain orientation. Then, it will calculate the maximum response of a set of convolution kernels to find the local edge orientation for each pixel. Prewitt edge detection produces an image where higher grey-level values indicate the presence of an edge between two objects. According to [13], the Prewitt edge detector is an appropriate way to estimate the magnitude and orientation of an edge. In addition to that, the Prewitt edge detection is simple to implement and less computational cost as compared to other edge detector. The Prewitt edge detection masks uses the two 3 by 3 templates to calculate the gradient value. The mask of Prewitt edge detection can be expressed as: M x (11) ISBN:

4 M y (1) where M x represents the image which at each point contain the horizontal approximation. Meanwhile M represents the image which at each y point contains the vertical approximation. The formula to calculate the magnitude and angle of the Prewitt edge detection is similar as in Equation (9) and (1) respectively. The Laplacian of Gaussian (LoG) used small masks called the kernel. Figure illustrates the image of kernel. 4 Materials and Method This study is mainly divided into four major stages. The first stage is data collection and preprocessing. The mammogram images are obtained from the National Cancer Society Malaysia (NCSM). In the pre-processing stage, we adjust the images by using Adobe Photoshop CS3 software. The second stage is the experiments of all edge detection technique. In this phase, we will modify all the three edge detection techniques on the EDAC model. Then, it will be tested on the breast phantom. If the technique did not pass the scoring criteria, then it will be modified again. A total of 1 is required to meet the quality imaging standards established by the American College of Radiology [15].This process will keep on repeated until the techniques pass the breast phantom scoring test. On stage three, the edge detection techniques will be implemented on mammogram to segment the boundaries of microcalcifications. Fig. : Two commonly used discrete approximations to the Laplacian filter. By using one of these kernels, Laplacian can be calculated using standard convolution methods. According to Gonzalez and Woods [14], Laplacian is combined with smoothing to find edges via zerocrossing. This can be express as in Equation (13). r r h e (13) Finally, the ROC curve will be applied on the final results of segmentation to measure the performance of the edge detection techniques. The ROC curve is a powerful method in determining the accuracy of an algorithm. This method is widely used in medical image data which associate with algorithm development [16]. The ROC curve is representing changes of the sensitivity and specificity of edge detection. Sensitivity and specificity can define by following definitions; where r x y and is the standard deviation. Equation (13) refers to Laplacian of Gaussian (LoG) which is the second derivative of h with respect to r. r r hr e 4 (14) since the LoG is the second derivative, so the image will be smoothed first. Thus, the external force of the EDAC model is much faster and easier to be calculated. True Positive (TP) when edge detection technique can segment correctly and excludes background tissue of the breast. False Positive (FP) when edge detection technique can segment correctly but includes background tissue of the breast. False Negative (FN) when edge detection technique segment incorrectly but excludes the background tissue of the breast. True Negative (TN) when edge detection technique segment incorrectly and includes background tissue of the breast. ISBN:

5 Different values of FP, TP, PN, and TN are obtained from different radiologist. The sensitivity is computed as: Spec = TP TP FN (15) where sensitivity defined as the probability edge detection segmentation result is correct and excludes the background tissue of the breast. The specificity is computed as: (a) (b) (c) Spec = TN TN FP (16) where specificity is defined as the probability edge detection segmentation result is incorrect and includes the background of the breast. The higher value of the Area Under the Curve, (AUC) the better is the performance of the edge detection technique used. The techniques are considered as good as the area of ROC approaches to 1[16]. (d) (e) (f) 5 Experimental Results A. Breast Phantom And Mammogram The results of the breast phantom scoring for the Prewitt, LoG and Sobel are as illustrated in Table 1. Tab.1 Phantom scoring for each edge detection technique Edge Detection Mass Specs Fibrils TOTAL Techniques Prewitt LoG Sobel 8 14 Since all edge detection techniques satisfy the scoring criteria, then the segmentation process phase is carried out. Some of the segmentation results are as illustrated in Figure 3. (g) (h) (i) Fig.3 Segmentation results of Prewitt (a) (c), LoG (d) (f) and Sobel (g) (i). From Figure 3, Prewitt edge detection is represented on the first row. This is followed by the results of the LoG edge detection on the second row. The third row shows the results of microcalcifications boundary segmentation for Sobel edge detection. Segmentation result on image (b), (c),(e) and (h) is considered as False Positive (FP) since the edge detection includes the background tissue of the breast. ISBN:

6 B. Receiver Operating Characteristic (ROC) Curve Radiologist will evaluate the ROC curve for each edge detection technique. Figure 4 illustrate the ROC curve of three edge detection techniques. References: [1] R. Maini and H. Aggarwal, "Study and comparison of various image edge detection techniques," International Journal of Image Processing (IJIP), vol. 3, pp. 1-11, 9. [] Cancer Research UK. (11). Mammograms in breast screening. [3] Mayo Clinic. (11). Breast calcifications. Fig.4 The ROC curve of three edge detection techniques. From Figure 4, the value of AUC for Sobel is.7, Prewitt is.79 and LoG is.71. The value AUC of Sobel is higher than LoG. Then, it shows that Sobel is better to compared to LoG technique. The AUC of Sobel is also approaching to 1 but not close as Prewitt. It shows that the Prewitt is the good technique to be used in segmenting micracalcifications. 6 Conclusion The three edge detection technique is implemented on EDAC model for segmenting the boundary of microcalcifications. In conclusion, the Prewitt shows the best edge detection technique with the highest value of AUC. This is followed by the Sobel and LoG edge detection 7 Acknowledgement This research was supported by the Universiti Teknologi MARA (UiTM) under the Research Intensive Faculty (RIF), 6-RMI/DANA 5/3/RIF (59/1). [4] American College of Radiology MammographyAccreditation: Frequently Asked Questions (1). [5] Kass, M., Witkin, A. & Terzopoulos, D. "Snakes: Active contour models," International journal of computer vision, vol. 1, pp , [6] Z. Hou and C. Han, "Force field analysis snake: an improved parametric active contour model," Pattern recognition letters, vol. 6, pp , 5. [7] X. Chenyang and J. L. Prince, "Snakes, shapes, and gradient vector flow," Image Processing, IEEE Transactions on, vol. 7, pp , [8] S. S. Yasiran, A. Ibrahim, W.E.Z.W.A. Rahman, R.Mahmud, "Efficiency of Enhanced Distance Active Contour (EDAC) for microcalcifications segmentation," 11, pp [9] L. D. Cohen and I. Cohen, "Finiteelement methods for active contour models and balloons for -D and 3-D images," Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 15, pp , ISBN:

7 [1] S. S.Yasiran, A. Ibrahim, W.E.Z.W.A. Rahman, R.Mahmud, A.K. Jumaatt "Accuracy of Enhanced Distance Active Contour (EDAC) for Microcalcifications Segmentation,"11International Conference on Biomedical Engineering and Technology. (ICBET11), p.5, 11. [11] S.S.Yasiran,"Segmenting Microcalcifications using Enhanced Distacne Active Contour (EDAC)," Msc, Center of Mathematical Studies, Universiti Teknologi MARA (UiTM), Shah Alam, 1. [1] O. Vincent and O. Folorunso, "A Descriptive Algorithm for Sobel Image Edge Detection," 9, pp [13] R. Maini, and J.S. Sohal, "Performance Evaluation of Prewitt Edge Detector for Noisy Images," vol. 6, p. 8, 6. [14] R. C. Gonzalez and R. E. Woods, "Digital image processing," Prentice Hall,. [15] G. J. Awcock, & Thomas, R., Applied Image Processing. London: The MacMillan Press Ltd., [16] J. A. Hanley and B. J. McNeil, "A method of comparing the areas under receiver operating characteristic curves derived from the same cases," Radiology, vol. 148, p. 839, ISBN: