PERFORMANCE EVALUATION OF A-TROUS WAVELET-BASED FILTERS FOR ENHANCING DIGITAL MAMMOGRAPHY IMAGES

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1 2 nd International Conference From Scientific Computing to Computational Engineering 2 nd IC-SCCE Athens, 5-8 July, 2006 IC-SCCE PERFORMANCE EVALUATION OF A-TROUS WAVELET-BASED FILTERS FOR ENHANCING DIGITAL MAMMOGRAPHY IMAGES Madoukas Theodore, Athanasiadis Emmanouil 2, Bougioukos Panagiotis 2, Kalatzis Ioannis, Dimitropoulos Nikos 3 and Cavouras Dionisis Medical Image and Signal Processing Laboratory, Department of Medical Instruments Technology, Technological Institute of Athens, Greece. theodore27@yahoo.com cavouras@teiath.gr, web page: 2 Medical Image Processing and Analysis Group, Laboratory of Medical Physics, University of Patras, Patras, Greece. 3 Medical Imaging Department, EUROMEDICA Medical Centre, 2 Mesogeion Avenue, Athens, Greece Keywords: wavelet transform, image enhancement, mammography. Abstract. The purpose of this study was to investigate the effectiveness of five a-trous wavelet transform based filters, in the task of enhancing the visualization of micro-calcifications in mammograms. Mammographic images were processed using the à-trous wavelet transform, developed in MATLAB. The detail coefficients of the wavelet transform were processed up to scale 5 using a)simple Piece-Wise Linear Mapping Function (SPWLMF), b) Hard-Threshold Function (HTF), c) Wavelet Enhancement With Noise Suppression Function (WEWNS), d) Sigmoidal non-linear Enhancement Function (SNLEF) and e) Non Linear Enhancement Function (NLEF). These five filters were applied, firstly to 23 mammograms with micro-calcifications from the MIAS database (024x024x8) and secondly to 50 mammograms from the same database with embedded simulated micro-calcifications. The processed mammograms were blind-reviewed by an experienced radiologist (D.N.). Five mammographic image parameters, such as micro-calcifications visualization, definition of masses, vessels, were evaluated and filter performances were assessed by statistical analysis of the physician s evaluation. Results: The scale-5 a-trous wavelet-based filter (SPWLMF) showed statistically significant improvement in all cases, enhancing image contrast effectively and providing better visualization of microcalcifications. INTRODUCTION Breast cancer is the leading cause of death for middle age women []. Mammography is the most effective method for early detection of breast cancer. However, normally viewed mammograms display only ab 3% of the total information they contain [2]. This is the reason why image enhancement may be beneficial in improving image quality. In the present study, a systematic evaluation of the à-trous wavelet based enhancement filters was performed, regarding the enhancement of X-ray mammographic images. These filters were: a)simple Piece- Wise Linear Mapping Function (SPWLMF), b) Hard-Threshold Function (HTF), c) Wavelet Enhancement With Noise Suppression Function (WEWNS), d) Sigmoidal non-linear Enhancement Function (SNLEF) and e) Non Linear Enhancement Function (NLEF). Moreover, an experienced radiologist (N.D.) assessed 5 mammographic image quality parameters for all the processed mammograms, in order to investigate the image-enhancing effectiveness of the 5 filters.

2 2 MATERIALS AND METHODS 2. A - trous Wavelet Transform The à-trous algorithm represents the discrete convolution between the input signal and a properly chosen mother wavelet, which refers to a low-pass filter. During discrete convolution, the distance between a central pixel and adjacent ones was 2 i- [3]. In the present study, we used a B3-Spline scaling function as mother wavelet to process the sampled data {Co(k)}. The convoluted smoothed data {Cj(k)} (at resolution j and position k) were calculated by using equation [4]: j+ j 3 j j+ C( j+ ) ( k) = C( j) ( k 2 ) + C( j) ( k 2 ) + C( j) ( k) + C( j) ( k+ 2 ) + C( j) ( k+ 2 ) () The signal difference { wj ( k )} between two resolution levels was calculated by using equation 2 : w ( k) = c ( k) c ( k) (2) j j j In the Inverse A trous algorithm, the original signal was reconstructed by adding all the differences { wj ( k )} to the last smoothed signal { cp( k ) }, as shown in equation 3: p c ( k) c ( k) w ( k) 0 = + (3) p j= j The come of the algorithm was a sequence of approximations having the same size as the original data. The extremities of the signal were handled by using the mirror effect technique [3]. In order to extend this algorithm to two dimensions, a row by row convolution followed by a column by column convolution was performed. 2.2 Wavelet-based filters The wavelet-based enhancement technique, involves three steps [5]. First, the AWT (A trous Wavelet Transform) was applied in five scales. Second, the detail coefficients of each scale were processed by using one of five different enhancement functions [5]. Finally, the enhanced mammograms were reconstructed by using the Inverse AWT (IAWT). An example of two scale decomposition procedure is schematically illustrated in Figure. st Scale 2 nd Scale 2 nd Scale st Scale Input Image Filter OutPut Image Filter AWT Image Decomposition Filtering IAWT Image Composition Figure. Wavelet-based filtering scheme

3 2.2. Simple Piece-Wise Linear Mapping (SPWLMF) Function. In SPWLMF, each detail coefficient of the à-trous wavelet transform was modified according to equation 4. W = W + T( G ) W > T W = W T( G ) W < T W = G* W W < T (4) were W denotes the put and Win the input coefficient values of the Detail Matrix. T and G are threshold and gain values respectively. An appropriate threshold value T, as well as an amplification factor G, were manually chosen by the physician. Schematically, the redistribution of the wavelet coefficients is illustrated in figure 2. Figure 2: Simple Piece-Wise Linear Mapping Function Hard-Threshold Function (HTF) Function. In HTF, the wavelet coefficients were modified in a similar way as in SPWLMF. The major difference was that the values between the thresholds T were neutralized. HTF is illustrated in equation 5 and figure 3 respectively. W = W + T( G ) W > T W = W T*( G ) Win< T W in = 0 otherwise (5) Figure 3: Hard-Threshold Function

4 2.2.3 Wavelet Enhancement With Noise Suppression (WEWNS) Function. In WEWNS, each detail coefficient of the à-trous wavelet transform was modified according to equation 6. Two independent threshold values, T and T 2, were manually selected by the physician. W denotes the put and Win the input coefficient values of the Detail Matrix. Schematically, the redistribution of the wavelet coefficients is illustrated in figure 4. W = W + ( T *( G ) ( T * G) W > T in 2 in 2 W = G*( W T) T W > T in 2 in W = 0 T W T in W = G*( W + T) T > W T2 in in W = W ( T *( G ) + ( T * G) W < T in 2 in 2 (6) Figure 4: Wavelet Enhancement With Noise Suppression Function Non Linear Enhancement (NLEF) Function. According to NLEF filter, wavelet coefficients of each scale were squared between the threshold values T as illustrated in equation 7 and figure 5. W = W + T( T) W > T W = W T*( T) W < T W = W otherwise 2 in (7) Figure 5: Non Linear Enhancement Function

5 2.2.5 A Sigmoidal Non Liner Enhancement (SNLEF) Function According to the SNLEF filter, detail coefficients of the à-trous wavelet transform were modified according to equation 8. W = a[ sigm( G( Win T)) sigm( G( Win + T))] a = sigm( G( T )) sigm( G( + T )) sigm( y) = + y e An appropriate threshold value T as well as an amplification factor G were manually chosen by the physician for optimal results. Schematically, the redistribution of the wavelet coefficients is illustrated in figure 6. (8) Figure 6: A Sigmoidal Non Liner Enhancement Function 2.3 Evaluation Twenty three real mammograms with micro-calcifications, collected from the MIAS database (024x024x8) and fifty mammograms from the same database with embedded simulated micro-calcifications, as described in previous studies [6,7], were used. The image enhancing effectiveness of the 5 filters was assessed by an experienced radiologist (N.D.) that evaluated the following image quality parameters:. Contrast between dark and light areas. 2. Improvement of normal fatty breasts. 3. Improvement of dense fibro-granular breasts. 4. Display quality and delineation of calcifications. 5. Good visualization of vessels, veins, ducts. 3 Results and discussion The results of the radiologist s evaluation are summarized in table. The performance of each filter in enhancing mammograms is illustrated in figure 7. Parameter s I NLEF II HTF III WEWNS IV SNLEF Table : Performance of each filter V SPWLMF Image contrast is a significant parameter for assess the nature of a tumor. According to our results

6 Madoukas Theodore, Athanasiadis Emmanouil, Bougioukos Panagiotis, Kalatzis Ioannis, Dimitropoulos Nikos and Cavouras Dionisis (parameter, table ), filter V managed a significant improvement of contrast between dark and light areas in 95% of the cases. Filters II, III, and IV improved mammograms adequately (7% for filters II,III and 69% for filter IV). Lowest contrast improvement was accomplished by filter I, which achieved a score of 58%. Breast structure (dense fatty tissue) is another important parameter for the physicians to take into consideration in the evaluation process. In both cases, dense and fatty tissue, filter V achieved the highest score (parameters 2 and 3, table ). It managed to enhance images in 95% of the cases. On the other hand, filters I,II,III,IV managed a satisfactory improvement of images in the case of fatty tissue and failed in the case of dense fibro-granular breasts. Visualization of micro-calcifications (parameter 4, table ), is a significant factor which indicates risk of breast cancer []. Filter V succeeded in enhancing the images in 77% of the cases. Finally, clear visualization of soft tissues, such us vessels, vein, ducts, is important in distinguishing a tumor from surrounding tissues (parameter 5, table ). In this case, filters II, III, IV, and V managed tolerable improvement, which was similar for all four filters. Filter I managed to achieve the lowest score (22% ). Original Image HTF NLEF WEWNS

7 SNLEF SPWLMF Figure 7: Original and filtered mammography images employing the SPWLMF, HTF, WEWNS, SNLEF, NLEF filters 4 CONCLUSIONS According to our results, the scale-5 à-trous wavelet-based filter (SPWLMF) showed significant improvement in almost all cases, enhancing image contrast effectively and providing better visualization of micro-calcifications. Adequate improvement was succeeded by filters I, II, III, and IV. 5 REFERENCES [] American Cancer Society http: // [2] Andrew Laine,Jian Fan and Sergio Schuler, A framework for contrast enhancement by dyadic Wavelet analysis Computer and Information Science Department, University of Florida, PO Box 620. Gainesville_ FL ,USA. [3] S. Frasher, A.K. Allen, A speckle reduction algorithm using the a trous wavelet transorm Proc.IASTED, International Conference on visualization, Imaging and Image Processing (VIIP 200), ed M.Hamza. Publ.Acta press [4] J.Campbell and F. Murtagh (998) Image Processing and Pattern Recognition with java IVS, School of Computer Science The Queen s University of Belfast [5] E. Athanasiadis,N. Piliouras, D. Glotsos, I. Kalatzis, N. Dimitropoulos, D. Cavouras (2004) Wavelet Based Filters For Enhancing Digital Mammogramms, st International Conference From science Computing to Computational Engineering (st IC-SCCE), Athens, Greece [6] Μ.Lado, A. Méndez, P. Tahoces, M. So, J. Correa,, J. Vidal Digital synthesis of microcalcifications on digital mammograms' in 8th Portuguese Conference on Pattern Recognition, Portugal, (996) [7] P. Bougioukos,,D. Glotsos, A. Daskalakis, P. Spyridonos, I. Kalatzis, N. Dimitropoulos, D. Cavouras and G. Nikiforidis, A Contextual segmentation method of micro-calcifications based on the Frequency Histogram of Connected Elements