ENHANCEMENT OF MAMMOGRAPHIC IMAGES FOR DETECTION OF MICROCALCIFICATIONS Damir Seršiæ and Sven Lonèariæ Department of Electronic Systems and Information Processing, Faculty of Electrical Engineering and Computing, University of Zagreb, Vukovar Avenue 39, CROATIA Tel: +385 1 6129973; fax: +385 1 6129652 e-mail: Sven.Loncaric@FER.hr ABSTRACT A novel approach to image enhancement of digital mammography images is introduced, for more accurate detection of microcalcification clusters. In original mammographic images obtained by X-ray radiography, most of the information is hidden to the human observer. The method is based on redundant discrete wavelet transform due to its good properties: shift invariance and numeric robustness. The procedure consists of three steps: low-frequency tissue density component removal, noise filtering, and microcalcification enhancement. The experimental results have shown good properties of the proposed method. 2. INTRODUCTION Many authors deal with the problem of automatic segmentation of microcalcification clusters in digital mammography. Presence of microcalcifications and skin thickening is an indirect sign of malignant masses. Unfortunately, mammograms (obtained by breast radiography) as normally viewed, display only about 3% of the information they detect [Laine, Fan, and Yang, 1995]. Main obstacle lays in low contrast between normal and malignant glandular tissues, especially in younger women. On the other hand, calcifications have high attenuation properties, which is a good visibility property. The problem is in their very small size, especially in the early stage of tumor development, making them extremely difficult to view. A number of digital image processing techniques have been applied to mammography, to address the mentioned problems. Several authors used adaptive neighborhood image processing techniques to enhance mammographic features while reducing noise [Gorden and Rangayyan, 1984, Dhawan and Le Royer, 1988, etc.], or spatial filtering [Tahoces et al. 1991]. Recent discoveries show that a multiresolution approach exists in human vision system, thus leading to an idea of using wavelet based multiresolution analysis for mammographic image processing. Wavelet approach has been used by [Strickland and Hahn, 1997] for detection of microcalcifications, while [Qian et al. 1993] used wavelets and tree-structured nonlinear filtering for microcalcification segmentation. [Laine, Fan, and Yang, 1995] used wavelets for contrast enhancement in digital mammography, as well as many other authors. Microcalcifications usually come in clusters, having very sharp edges, and usually irregular shape of very small size. Due to their high attenuation properties, they appear as white (or high intensity) spots on mammograms. There are two goals of this work: enhancement of mammographic images to achieve better visibility of the observed phenomena to the human observer (radiologist), and processing of mammograms to enable automatic detection of micro-calcifications, as a first step to the "automated second-opinion" procedure. To achieve both goals, we first used redundant wavelet transform applied to suspicious cutouts of mammograms. 3. A METHOD FOR MAMMOGRAM ENHANCEMENT In this work, we developed a specific wavelet-based scheme for image enhancement and compared different wavelet choices, as well as different filtering procedures applied to wavelet coefficients. A quality measure is developed for comparison of the processed image to the binary, human made drawing of microcalcifications. The measure is based on relative energy comparison between microcalcification area and its complement. 2.1 Non-decimated wavelet transform Among other linear transforms, wavelets have a number of useful properties: they can successfully represent smooth functions, as well as singularities; expansion functions are local - so the algorithms based on wavelet coefficients are adaptive to inhomogeneities; wavelets are computationally inexpensive and near optimal for statistical estimation, signal recovery and data compression.
Discrete time wavelet transform expands analyzed signals into components with different shifts and scales, where scales are usually chosen from a dyadic set: X m,n = <x, ψ m,n >, ψ m,n =2-1/2 ψ(2 -m x - n). (1) Hence, ψ m,n are shifted, expanded or shrank versions of a mother wavelet ψ. Mother wavelet function ψ is typically chosen to achieve desired localization properties in time and frequency domain. There are many choices of wavelets that lead to orthogonal or biorthogonal expansions, some of them realizable by FIR perfect reconstruction wavelet filter banks. The number of calculated wavelet coefficients decreases with enlarged scale, which corresponds to decimation in wavelet filter banks: Figure 2 Non-decimated analysis wavelet filter bank H(z 2 ), H(z 4 ), H(z 8 ),... can be easily realized by inserting zeros between samples of h(k) in the time domain ("algorithm á trous"). Most of numerical simulation software tools spend processor's time even for multiplications by zero, so we rather use recursive subsampling-upsampling structure illustrated in the following figure: Figure 1 Decimated analysis wavelet filter bank H and L filters are related to mother wavelet ψ and its associated scaling function φ respectively, while "detail" coefficients d 1, d 2, d n,... correspond to the wavelet coefficients in different scales (m=0, 1,...). The set of wavelet coefficients for orthogonal or biorthogonal decompositions is minimum size, equal to the length of analyzed signal x. The number of necessary calculations is O(N), which is computationally very inexpensive when compared to other linear transforms. On the other hand, such wavelet coefficients are shift dependent, in the sense that time shifts of the original signal result in different sets of wavelet coefficients, with different statistical properties. That fact has been noticed as a significant drawback, especially in detection problems, as well as in de-noising and compression applications. All-shifts DWT expansion is redundant, but shift-invariant in the previously mentioned sense: ψ m,n =2-1/2 ψ(2 -m (x - n)). (2) By calculating all shifts, orthogonal expansions turn to frames, withholding reconstruction properties. Frames (due to their redundancy) bring numerical robustness [Daubechies, 1992], which will show its value in nonlinear wavelet coefficient processing. [Beylkin, 1992] has shown that the order of computation can be reduced to O(N log N) operations using corresponding nondecimated wavelet filter bank, instead of O(N 2 ) operations, which follows from equation (2). Figure 3 Recursive subsampling-upsampling structure The last branch filters in recursion structure are H(z), applied to l-times decimated input. In the linear phase case, symmetry of coefficients can be used to reduce the number of multiplications (by factor of 2 or 4, for 1-D or 2-D case, respectively). Shift-invariant wavelet expansion can be easily extended to the two-dimensional (2-D) case: Figure 4 Filter bank implementation of the 2-D nondecimated wavelet decomposition using 1-D filters. Both analysis and reconstruction sides in a level l are shown. The single level expansion results in 3 "details" images: d HH, d HL, and d LH, (shorter: HH, HL, LH) covering independent bands in the frequency domain. The "approximation" a LL (or LL) is a low-pass component, which is passed to the next level of decomposition.
2.2 Application to mammograms At first, 5-levels redundant wavelet decomposition of the original mammogram cutout is performed. Mammogram images were obtained by scanning the X-ray images in 30µm x 30µm resolution, 12 bits per pixel. Typical size of microcalcification varies from 0.1 mm to more than 1 mm, which corresponds to the range from the smallest 3 x 3 pixel round objects to more than 30 pixels wide irregular shapes. The 5-octaves analysis is taken to cover the whole range. Density of the breast tissue varies across different parts of the mammogram, thus increasing the dynamic range of the image. Fine breast tissue structure and microcalcifications are almost invisible in dense parts of the original image, especially if gray-value does not cover the necessary dynamic range. Several wavelet choices were taken in consideration, but B-spline wavelets yield the best results, due to their linear phase and symmetry, as well as some similarity to observed calcifications (which complies to [Strickland and Hahn, 1997] ). Visual inspection of wavelet coefficient images shows that first-level detail coefficients (HH, HL and LH) contain mostly noise. Detail coefficients in levels 2-5 contain fine breast structure and microcalcifications (together with some noise). Finally, level 5 approximation coefficients (LL) contain low frequency background, which corresponds to the tissue density. Reconstructed sub-images (after applying reconstruction part of filter bank) are additive components of the original image, so the reconstructed details HH r, HL r and LH r at observed level were added in a single representation D r. To enhance the image for a human observer, several r actions have been taken. Subtraction of the reminder A 5 shrinks the dynamic range of the image and makes the fine structure more visible, as well as microcalcifications. But, the image is still noised, and small microcalcifications are hardly visible. [Donoho and Johnstone, 1994] suggest a denoising scheme by killing and shrinking wavelet coefficients. If we assume additive noise in the form: x i = s i + σ n n i, i = 1,..., N; (3) where signal s i is corrupted by zero mean, Gaussian noise n i with standard deviation σ n, then the risk (l 2 measure of error between estimated and original signal s) of the so called soft - thresholding scheme: X = DWT( x), ( ) ( ) sign X X thr X thr X$ ( ), = 0, otherwise 1 s$ = DWT X$, is within a logarithmic factor log N of ideal minimum risk. A good choice for threshold thr is: (4) thr = σ n N log N, where σ n is standard deviation of noise, and N is number of wavelet coefficients. We used a robust estimation of σ n, calculated from detail wavelet coefficients of an additional decomposition of x: σ median d / 0. (6) ˆ n = 1 ( ) 6745 Such estimation is insensitive to presence of strong outliers (as the microcalcifications are). Denoising scheme confirms that decomposition at level 1 contains "pure" noise, and should be killed. Notice that our sampling interval was 30 µm, and if the same decomposition would have been applied to the images sampled in 100µm resolution, (like University Hospital Nijmegen images), level 1 decomposition would contain signal information as well. Applied to other levels, denoising enhances the reconstructed images, especially in higher frequency subbands (level 2 and 3). Results of denoising in level 2 are visible in figure (5). Figure 5 Denoissed detail reconstruction D 2 r image Finally, we would like to amplify the microcalcifications. [Strickland and Hahn, 1997] have shown that redundant wavelet transform by itself act as a multiscale matched filter. B-spline redundant wavelets closely approximate the prewhitening matched filter for detecting Gaussian objects in Markov noise. Small microcalcifications are blob-like objects that fit in the assumed scheme, and the background can be modeled as a combination of separable and non-separable Markov noise. Microcalcifications are well represented by the non-decimated B-spline wavelet decomposition. If the scales match, coefficients show a huge peak at the locations of calcifications. [Burley and Darnell, 1997] analyze the suppression of impulse noise using wavelets, and suggest a kind of reversed scheme of [Donoho, 1995]. If the signal is corrupted by additive Gaussian noise and impulse noise m i : x i = s i + σ n n i + m i, i = 1,..., N; (7) they propose shrinking of wavelet coefficients larger then 3.3 σ n to the Donoho level. The procedure is eliminating coefficients who belong to the impulse noise, and preserve Gaussian signal which is under the threshold. Wavelet coefficients that correspond to microcalcifications have huge peaks in all scales, thus behaving similarly as they were impulse noise. We used a reversed scheme to amplify their contribution to the final image. We estimated the variance of the background signal using (5)
our robust estimator (insensitive to peaks), and then calculated upper threshold. Almost all coefficients belonging to the fine tissue structure are bellow the upper threshold. The "upper" images (soft thresholded images using upper threshold) in all scales are good candidates for the feature vector representation for detection of calcifications. If the upper sub-images are added to denoised sub-images, a visible enhancement of calcification areas will be done. 4. RESULTS AND DISCUSSION Analysis has been taken on a number of mammograms, all containing microcalcifications showing presence of tumors (either benign or malign). Figure 6 Original mammogram cutout Figure 7 Enhanced image, reconstructed from levels 2-5 Figure 8 Microcalcifications, marked by human Figure 9 Upper image, reconstructed from levels 2-5 It is clearly visible that "upper" image is nearly a detector of microcalcifications. We convert the upper image to the binary form, and estimate the similarity to human drawn calcifications, by calculating the energy of the difference. The similarity is higher for B-spline (linear phase) wavelets, and somewhat less for a simple Haar decomposition. 5. CONCLUSION A new method for enhancement of mammogram images is presented in the paper. The method has been applied to a number of mammogram images and has shown good results. 1. REFERENCES [Laine, Fan, and Yang, 1995] A. Laine, J. Fan, and W. Yang: Wavelets for contrast enhancement of digital mammography, IEEE Engineering in Medicine and Biology Magazine, vol 14, no. 5, pp. 536-550, 1995 [Dhawan and Le Royer, 1988] A.P. Dhawan, E. Le Royer: Mammographic feature enhancement by computerized image processing, Computer Methods and Programs in Biomedicine, vol. 27, pp. 23, 1988 [Tahoces et al. 1991] P.G. Tachoes, J. Correa, M. Souto, C. Gonzales, L. Gomez, J. Vidal: Enhancement of chest and breast radiographs by automatic spatial filtering, IEEE Transactions on Medical Imaging, vol. MI-10(3), pp. 330-335, 1991 [Strickland and Hahn, 1997] R. N. Strickland and H. I. Hahn: Wavelet Transform Methods for Object Detection and Recovery, IEEE Transactions on image processing, vol 6, no 5. pp 724-735, 1997 [Qian et al. 1993] W. Chian, L. P. Clarke, M.Kallergi, H. D. Li, R. P. Velthuizen, R. A. Clarke, and M. L. Silbigier: Tree-structured nonlinear filter and wavelet transform for microcalcification segmentation in mammography, Biomed. Image Processing and Biomed. Visualization, Proc. SPIE 1905, pp. 509-521, 1993 [Donoho 1995] D. L. Donoho: De-noising by softthresholding, IEEE Transactions on Information Theory, 41(3): 613-627, 1995 [Donoho and Johnstone, 1994] D. L. Donoho and I. M. Johnstone: Ideal spatial adaptation via wavelet shrinkage, Biometrika, 91:425-455, 1994 [Gorden and Rangayyan, 1984] R. Gorden, R. M. Rangayyan: Feature enhancement of film mammograms using fixed and adaptive neghborhoods, Applied Optics, vol 23, pp. 560, 1984 [Daubechies, 1992] I. Daubechies: Ten lectures on wavelets, SIAM, Philadelphia, PA, 1992
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