Phương pháp chẩn đoán hình ảnh medical image analysis methods (phần 6)

Phương pháp chẩn đoán hình ảnh medical image analysis methods (phần 6)

2089_book.fm copy Page 225 Wednesday, May 18, 2005 3:32 PM Locally Adaptive Wavelet Contrast Enhancement Lena Costaridou, Philipos Sakellaropoulos, Spyros Skiadopoulos, and George Panayiotakis CONTENTS 6.1 6.2 6.3 Introduction Background Materials and Methods 6.3.1 Discrete Dyadic Wavelet Transform Review 6.3.2 Redundant Dyadic Wavelet Transform 6.3.3 Wavelet Denoising 6.3.3.1 Noise Suppression by Wavelet Shrinkage 6.3.3.2 Adaptive Wavelet Shrinkage 6.3.4 Wavelet Contrast Enhancement 6.3.4.1 Global Wavelet Mapping 6.3.4.2 Adaptive Wavelet Mapping 6.3.5 Implementation 6.3.6 Test Image Demonstration and Quantitative Evaluation 6.4 Observer Performance Evaluation 6.4.1 Case Sample 6.4.2 Observer Performance 6.4.3 Statistical Analysis 6.4.3.1 Wilcoxon Signed Ranks Test 6.4.3.2 ROC Analysis 6.4.4 Results 6.4.4.1 Detection Task 6.4.4.2 Morphology Characterization Task 6.4.4.3 Pathology Classification Task 6.5 Discussion Acknowledgment References Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 226 Wednesday, May 18, 2005 3:32 PM 226 Medical Image Analysis 6.1 INTRODUCTION Breast cancer is the most frequently occurring cancer in women [1–3] Detecting the disease in its early stages increases the rate of survival and improves the quality of patient life [4, 5] Mammography is currently the technique with the highest sensitivity available for early detection of breast cancer on asymptomatic women Detection of early signs of disease, such as microcalcifications (MCs) and masses in mammography programs, is a particularly demanding task for radiologists This is attributed to the high volume of images reviewed as well as the low-contrast character of mammographic imaging, especially in the case of dense breast, accounting for about 25% of the younger female population [6, 7] Calcifications are calcium salts produced by processes carried out inside the breast ductal system They are radiodense, usually appearing lighter than surrounding parenchyma, due to their inherently high attenuation of X-rays Depending on the X-ray attenuation of surrounding parenchyma (i.e., dense breast), they can be lowcontrast entities, with their low-contrast resolution limited by their size Magnification of mammographic views, characterized by improved signal-to-noise ratio, result in improved visualization of MCs Masses, which represent a more invasive process, are compact radiodense regions that also appear lighter than their surrounding parenchyma due to higher attenuation of X-rays The major reason for the low contrast of malignant masses is the minor difference in X-ray attenuation between even large masses and normal dense surrounding parenchyma The use of complementary mammographic views, craniocaudal (CC) and mediolateral (MLO), is intended to resolve tissue superimposition in different projections [8, 9] Identification and differentiation (benign vs malignant) of MCs and masses have been the major subject of computer-aided diagnosis (CAD) systems that are aimed at increasing the sensitivity and specificity of screening and interpretation of findings by radiologists CAD systems in mammography have been an active area of research during the last 20 years [10–17] In addition to dense breast regions, mammography periphery is also poorly imaged due to systematic lack of compressed breast tissue in this region [18, 19] Although periphery visualization is associated with more advanced stages of disease, such as skin thickening and nipple retraction, it has attracted research attention, either as a preprocessing stage of CAD system [10] or enhancement [18–26] and for skin detection [27–29] 6.2 BACKGROUND Digital image-enhancement methods have been widely used in mammography to enhance contrast of image features Development of mammographic image-enhancement methods is also motivated by recent developments in digital mammography and soft-copy display of mammograms [30, 31] Specifically, image display and enhancement methods are needed to optimally adapt the increased dynamic range of digital detectors, up to 212 gray levels, to the human dynamic range, up to 27 gray levels for expert radiologists Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 227 Wednesday, May 18, 2005 3:32 PM Locally Adaptive Wavelet Contrast Enhancement 227 Different algorithms have advantages and disadvantages for the specific tasks required in breast imaging: diagnosis and screening A simple but effective method for image enhancement is intensity windowing (IW) [32] IW stretches a selected range of gray levels to the available display range However, in mammography (unlike CT), there is not an absolute correspondence between the recorded intensities and the underlying tissue, and thus IW settings cannot be predetermined Manual contrast adjustment of a displayed digital mammogram with IW resembles adjustment of a screen-film mammogram’s contrast on a light-view box Automated algorithms have been developed to avoid user-dependent and time-consuming manual adjustments Component-based IW techniques segment the mammographic image into its components (background, uncompressed-fat, fat, dense, and muscle) and adjust IW parameters to emphasize the information in a single component Mixture-modeling-based IW [33] uses statistical measures to differentiate fat from dense-component pixels to accentuate lesions in the dense part of the mammogram A preprocessing step is applied to separate the edge border Adaptive local-enhancement methods modify each pixel value according to some local characteristics of the neighborhood around the pixel’s location Adaptive histogram equalization (AHE) is a well-known technique that uses regional histograms to derive local mapping functions [34] Although AHE is effective, it tends to overemphasize noise Contrast-limited AHE (CLAHE) was designed to overcome this problem, but the contrast-limit parameter is image and user dependent [35] Local-range modification (LRM) is an adaptive method that uses local minima-maxima information to calculate local linear stretching functions [36] LRM enhances image contrast, but it tends to create artifacts (dark or bright regions) in the processed image Spatial filtering methods, like unsharp masking (UM) [37], adaptive contrast enhancement (ACE) [38], multichannel filtering [39], and enhancement using first derivative and local statistics [40] amplify mid- to high-spatial-frequency components to enhance image details However, these methods are characterized by noise overenhancement and ringing artifacts caused by amplification of noise and high-contrast edges [41] More complex filtering methods like contrast enhancement based on histogram transformation of local standard deviation [42] and just-noticeable-difference-guided ACE [41] attempt to overcome these problems by using smaller gains for smooth or highcontrast regions Adaptive neighborhood contrast enhancement (ANCE) methods [43–46] directly manipulate the local contrast of regions, computed by comparing the intensity of each region with the intensity of its background Region growing is used to identify regions and corresponding backgrounds A common characteristic of the above-mentioned techniques is that they are based on the single-scale spatial domain Due to this fact, they can only enhance the contrast of a narrow range of sizes, as determined by the size of local-processing region Additionally, they tend to increase the appearance of noise To enhance features of all sizes simultaneously, multiresolution enhancement methods, based on the wavelet transform [47], have been developed A multiscale representation divides the frequency spectrum of an image into a low-pass subband image and a set of band-pass subband images, indexed by scale s and orientation The spatial and frequency resolution of the subband images are proportional to 1/s and s, respectively Because sharp image variations are observed at small scales, Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 228 Wednesday, May 18, 2005 3:32 PM 228 Medical Image Analysis they are analyzed with fine spatial resolution By exploiting the location and frequency–selectivity properties of the wavelet transform, we can progressively “zoom” into image features and characterize them through scale-space Mammographic image analysis can benefit from this strategy, because mammograms contain features with varying scale characteristics The main hypothesis of image wavelet analysis is that features of interest reside at certain scales Specifically, features with sharp borders, like MCs, are mostly contained within high-resolution levels (small scales) of a multiscale representation Larger objects with smooth borders, like masses, are mostly contained in low-resolution levels (coarse scales) Different features can thus be selectively enhanced (or detected) within different resolution levels Also, a noisereduction stage could be applied prior to enhancement, exploiting the decorrelation properties of the wavelet transform The main approach for wavelet-based enhancement (WE) uses a redundant wavelet transform [48] and linear or nonlinear mapping functions applied on Laplacian or gradient wavelet coefficients [49–52] Such methods have demonstrated significant contrast enhancement of simulated mammographic features [50], and also improved assessed visibility of real mammographic features [51] Another approach uses a multiscale edge representation, provided by the same type of wavelet transform, to accentuate multiscale edges [53] Recently, spatially adaptive transformation of wavelet coefficients has been proposed [54] for soft-copy display of mammograms, aiming at optimized presentation of mammographic image contrast on monitor displays Spatial adaptivity is motivated from the fact that mapping functions in previous methods [49, 50] are typically characterized by global parameters at each resolution level Global parameters fail to account for regions of varying contrasts such as fat, heterogeneously dense, and dense in mammograms This method provides an adaptive denoising stage, taking into account recent works for wavelet-based image denoising [55, 56], in addition to locally adaptive linear enhancement functions Performance of contrast-enhancement methods is important for soft-copy display of mammograms in the clinical environment It is usually differentiated with respect to task (detection or characterization) or type of lesion (calcifications or masses) Several enhancement methods have been evaluated as compared with their unprocessed digitized versions [46, 57–60], and a small number of intercomparison studies has been performed [54, 61, 62] Intercomparison studies are useful in the sense that they are a first means of selecting different contrast-enhancement methods to be evaluated later on, carried out with an identical sample of original (unprocessed) images and observers These intercomparison studies are usually based on observer preference as an initial step for selection of an appropriate contrast-enhancement method (i.e., those with high preference) Receiver operating characteristics (ROC) studies should be conducted as a second step for comparative evaluation of these methods with respect to detection and classification accuracy of each lesion type [63] Sivaramakrishna et al [61] conducted a preference study for performance evaluation of four image contrast-enhancement methods (UM, CLAHE, ANCE, and WE) on a sample of 40 digitized mammograms containing 20 MC clusters and 20 masses (10 benign and 10 malignant in each lesion type) In the case of MCs, processed images based on the ANCE and WE methods were preferred in 49% and Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 229 Wednesday, May 18, 2005 3:32 PM Locally Adaptive Wavelet Contrast Enhancement 229 28% of cases, respectively For masses, the digitized (unprocessed) images and UMbased processed images were preferred in 58% and 28% of cases, respectively The authors concluded that different contrast-enhancement approaches may be necessary, depending on the type of lesion Pisano et al [62] carried out a preference study for performance evaluation of eight image contrast-enhancement methods on a sample of 28 images containing 29 cancerous and 36 benign pathological findings (masses or MCs) produced from three different digital mammographic units All processed images were printed on film and compared with respect to their corresponding screen-film images Screen-film images were preferred to all processed images in the diagnosis of MCs For the diagnosis of masses, all processed images were preferred to screen-film images This preference was statistically significant in the case of the UM method For the screening task of the visualization of anatomical features of main breast and breast periphery, screen-film images were generally preferred to processed images No unique enhancement method was preferred Recently, the spatially adaptive wavelet (AW) enhancement method has been compared with CLAHE, LRM, and two wavelet-based enhancement methods (global linear and nonlinear enhancement methods) in a sample of 18 MC clusters [54] The AW method had the highest preference The results of these preference studies show that a contrast-enhancement method with high performance in all tasks and types of lesions has not been developed In addition, the small number of preference studies is not adequate to indicate the promising contrast-enhancement methods for clinical acceptance Further preference studies are needed comparing the performance of contrast-enhancement methods presented in the literature Observer preference as well as ROC studies are not timeconsuming nowadays because (a) a case sample can be selected from common mammographic databases (e.g., Digital Database for Screening Mammography — DDSM [64, 65], Mammographic Image Analysis Society — MIAS [66, 67]) and (b) high-speed processors can be used for lower computational times A brief summary of redundant dyadic wavelet analysis is given in Sections 6.3.1 and 6.3.2 The basic principles of wavelet denoising and contrast enhancement are presented in Sections 6.3.3.1 and 6.3.4.1, while details of an adaptive denoising and enhancement approach are provided in Sections 6.3.3.2 and 6.3.4.2 The performance of the AW method is quantitatively assessed and compared with the IW method, by means of simulated MC clusters superimposed on dense breast parenchyma in Section 6.3.7 In Section 6.4, evaluation is carried out by an observer performance comparative study between original-plus-AW-processed and original-plus-IW-processed images with respect to three tasks: detection, morphology characterization, and pathology classification of MC clusters on dense breast parenchyma 6.3 MATERIALS AND METHODS 6.3.1 DISCRETE DYADIC WAVELET TRANSFORM REVIEW The dyadic wavelet transform series of a function ƒ(x) with respect to a wavelet function ψ(x) is defined by the convolution Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 230 Wednesday, May 18, 2005 3:32 PM 230 Medical Image Analysis W2 j f ( x ) = f ∗ ψ j ( x ) (6.1) where ψ j ( x ) = − j ψ (2 − j x ) is the dilation of ψ(x) by a factor of 2j In general, ƒ(x) can be recovered from its dyadic wavelet transform from the summation +∞ f ( x) = ∑W 2j f ∗ χ2 j ( x ) (6.2) j =−∞ where the reconstruction wavelet χ(x) is any function whose Fourier transform satisfies +∞ ∑ ψˆ (2 ω)χˆ (2 ω) = j j (6.3) j=−∞ The approximation of ƒ(x) at scale 2j is defined as S2 j f ( x ) = f ∗ φ2 j ( x ) (6.4) where φ(x) is a smoothing function called the scaling function that satisfies the equation φˆ (ω ) = +∞ ∑ ψˆ (2 ω)χˆ (2 ω) j j (6.5) j =1 In practice, the input signal is measured at a certain resolution, and thus the wavelet transform cannot be computed at any arbitrary fine scale However, a discrete periodic signal D, derived from a periodic extension of a discrete signal, can be considered as the sampling of a smoothed version of a function ƒ(x) at the finest scale 1: ∀n ∈ Z , S1 f ( n ) = d n (6.6) As the scale 2j increases, more details are removed by the S2 j operator Dyadic wavelet transform series W2 j f ( x ) between scales 21 and 2j contain the details existing in the S1ƒ(x) representation that have disappeared in Sjƒ(x) 6.3.2 REDUNDANT DYADIC WAVELET TRANSFORM Redundant (overcomplete) biorthogonal wavelet representations are more suitable for enhancement compared with orthogonal, critically sampled wavelet representations Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 231 Wednesday, May 18, 2005 3:32 PM Locally Adaptive Wavelet Contrast Enhancement 0.4 0.8 0.35 0.6 0.3 231 0.4 0.25 0.2 0.2 0.15 0.1 −0.2 0.05 −0.4 −0.6 −0.05 −0.1 −2 −1.5 −1 −0.5 0.5 (a) 1.5 −0.8 −2 −1.5 −1 −0.5 0.5 (b) 1.5 FIGURE 6.1 (a) A cubic spline function and (b) a wavelet that is a quadratic spline of compact support Avoiding the downsampling step after subband filtering ensures that wavelet coefficient images are free from aliasing artifacts Additionally, the wavelet representation is invariant under translation [68] Smooth symmetrical or antisymmetrical wavelet functions can be used [69] to alleviate boundary effects via mirror extension of the signal Mallat and Zhong have defined a fast, biorthogonal, redundant discrete wavelet transform (RDWT) that can be used to derive multiscale edges from signals [48] It is based on a family of wavelet functions ψ(x) with compact support that are derivatives of corresponding Gaussian-like spline functions θ(x) Fourier transforms of these functions are defined as follows  sin(ω / 4)  ψˆ (ω ) = ( jω )   ω /   sin(ω / 4)  θˆ (ω ) =   ω /  n +2 (6.7) n +2 (6.8) By choosing n = 1, we obtain a wavelet function ψ(x) that is a quadratic spline, while θ(x) is a cubic spline These functions are displayed in Figure 6.1 For this particular class of wavelet functions, the wavelet transform series of ƒ(x, y) for −∞ < j < +∞ has two components and is given by W 1j ( x, y )  j =2  W2 j ( x, y )   f ∗ ψ j ( x, y )  j =2   f ∗ ψ j ( x, y )  Copyright 2005 by Taylor & Francis Group, LLC ∂  ∂x  ∂  ∂y   f ∗ θ j ( x, y )     j  = ⋅ ∇( f ∗ θ2 j )( x, y ) (6.9)   f ∗ θ j ( x, y )     2089_book.fm copy Page 232 Wednesday, May 18, 2005 3:32 PM 232 Medical Image Analysis Decomposition Reconstruction f (m, n) = S0(m, n) W 1(m, n) G(ωx) K(ω x) L(ω y) W 1(m, n) G(ω y) S1(m, n) G(2ω x) H(ω x) H(ω y) G(2ω y) L(ω x) K(ω y) f(m, n) + W 2(m, n) K(2ω x)L(2ω y) W2(m, n) L(2ω x)K(2ω y) H−(ω x) H−(ω y) + S2(m, n) H−(2ω x)H−(2ω y) H(2ω x)H(ω y) FIGURE 6.2 Filter-bank scheme used to implement the RDWT for two scales The discrete wavelet transform is a uniform sampling of the wavelet transform series, discretized over the scale parameter s at dyadic scales 2j (wavelet transform series) The analyzing wavelets ψ1(x,y) and ψ2(x,y) are partial derivatives of a symmetrical, smoothing function θ(x,y) approximating the Gaussian and j the dyadic scale The DWT is calculated up to a coarse dyadic scale J Therefore, the original image is decomposed into a multiresolution hierarchy of subband images, consisting of a coarse approximation image S2 J f (m, n ) and a set of wavelet images W21j f (m, n), W22j f (m, n)) 1≤ j ≤ J , which provide the details that are available in S1ƒ but have disappeared in S2 J f All subband images have the same number of pixels as the original, thus the representation is highly redundant Figure 6.2 shows the filter bank scheme used to implement the DWT (two dyadic scales) The transform is implemented using a filter bank algorithm, called algorithme trous (algorithm with holes) [70], which does not involve subsampling The filter bank is characterized by discrete filters H(ω), G(ω), K(ω), and L(ω) All filters have compact support and are either symmetrical or antisymmetrical At dyadic scale j, the discrete filters are Hj(ω), Gj(ω), Kj(ω), and Lj(ω) obtained by inserting 2j − zeros (“holes”) between each of the coefficients of the corresponding filters The coefficients of the filters are listed in Table 6.1 Equation 6.9 shows that the DWT computes the multiscale gradient vector Coefficient subband images are proportional to the sampled horizontal and vertical components of the multiscale gradient vector, and thus they are related to local contrast The magnitude-phase representation of the gradient vector, in the discrete case, is given by ( ) M j (m, n ) = W21j (m, n ) + W22j (m, n )  W 2j (m, n )  , A2 j (m, n ) = arctan  21   W2 j (m, n )  (6.10) Demonstrations of gradient-magnitude vector, superimposed on two mammogram regions containing masses, are presented in Figure 6.3 Magnitude of the Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 233 Wednesday, May 18, 2005 3:32 PM Locally Adaptive Wavelet Contrast Enhancement 233 TABLE 6.1 Filter Coefficients for the Filters — H(n), G(n), K(n), and L(n) — Corresponding to the Quadratic Spline Wavelet of Figure 6.1 N H(n) G(n) K(n) L(n) −3 −2 −1 — — 0.125 0.375 0.375 0.125 — — — — 2.0 −2.0 — — 0.0078125 0.0546875 0.171875 −0.171875 −0.0546875 −0.0078125 — 0.0078125 0.046875 0.1171875 0.65625 0.1171875 0.046875 0.0078125 gradient vector at each location corresponds to the length of the arrow, while phase corresponds to the direction of the arrow It can be observed that the gradientmagnitude vector is perpendicular to lesion contours Because contrast enhancement should be perpendicular to edge contours to avoid orientation distortions, subsequent processing is applied on the multiscale magnitude values 6.3.3 WAVELET DENOISING 6.3.3.1 Noise Suppression by Wavelet Shrinkage Digitized mammograms are corrupted by noise due to the acquisition and digitization process Prior to contrast enhancement, a denoising stage is desirable to avoid or reduce amplification of noise Conventional noise-filtering techniques reduce noise by suppressing the high-frequency image components The drawback of these methods is that they cause edge blurring Wavelet-based denoising methods, however, can effectively reduce noise while preserving the edges The two main approaches for wavelet-based noise suppression are: (a) denoising by analyzing the evolution of multiscale edges across scales [48] and (b) denoising by wavelet shrinkage [71] The algorithm of Mallat and Hwang [48] is based on the behavior of multiscale edges across scales of the wavelet transform They proved that signal singularities (edges) are characterized by positive Lipschitz exponents, and thus the magnitude values of edge points increase with increasing scale Noise singularities, on the other hand, are characterized by negative Lipschitz exponents, and thus the magnitude values of edge points caused by noise decrease with increasing scale The algorithm computes Lipschitz exponents from scales 22 and 23 to eliminate edge points with negative exponents and reconstruct the maxima at the finest scale 21, which is mostly affected by noise The drawback of this method is although the reconstruction from the multiscale edge representation produces a close approximation of the initial image, some image details are missed It is also very computationally intensive Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 234 Wednesday, May 18, 2005 3:32 PM 234 Medical Image Analysis FIGURE 6.3 Gradient magnitude vector superimposed on mammogram regions containing lesions Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 256 Wednesday, May 18, 2005 3:32 PM 256 Copyright 2005 by Taylor & Francis Group, LLC Medical Image Analysis FIGURE 6.16 (c) (b) (a) Copyright 2005 by Taylor & Francis Group, LLC (e) (f) FIGURE 6.16 (continued) (a) Original mammogram (A-1185_1.RCC) containing MC cluster (arrow); (b, c) results of processing with the IWand the AW-enhancement methods, respectively; (d–f) magnified ROIs containing the MC cluster for original, IW-processed, and AW-processed image, respectively MC cluster was detected in both enhancement methods, but improved detection performance was obtained for the method based on original-plus-AW-processed image (d) 2089_book.fm copy Page 257 Wednesday, May 18, 2005 3:32 PM Locally Adaptive Wavelet Contrast Enhancement 257 2089_book.fm copy Page 258 Wednesday, May 18, 2005 3:32 PM 258 Medical Image Analysis TABLE 6.7 Individual and Averaged Number (N) and Percentage of True Responses in Morphology Characterization of 43 Microcalcification Clusters for Two Radiologists Using the Original-Plus-IW and Original-Plus-AW Methods Radiologist A Radiologist B Average Enhancement Method N Percentage N Percentage N Percentage Original plus intensity windowing Original plus adaptive wavelet 30 37 69.8 86.0 28 37 65.1 86.0 29 37 67.4 86.0 TABLE 6.8 Frequency of Shiftings in Morphology Characterization of Microcalcification Clusters for TIW and TAW Methods as Applied by Two Radiologists Morphology Shifting 2→1 Radiologist A Radiologist B TIW TIW TAW TAW 1: Punctuate 0 0→2 1→2 3→2 4→2 2: Pleomorphic (granular) 0 0 1→3 2→3 4→3 3: Amorphous 0 1 0 1→4 3→4 Total 4: Fine Linear Branching (casting) 1 0 13 15 Note: TIW (true intensity windowing) shows frequency of shiftings from adaptive wavelet method to intensity windowing one; TAW (true adaptive wavelet) shows frequency of shiftings from intensity windowing method to adaptive wavelet one Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 259 Wednesday, May 18, 2005 3:32 PM Locally Adaptive Wavelet Contrast Enhancement 259 TABLE 6.9 Individual and Averaged Percentage of True Responses in Pathology Classification (benign or malignant) of the 43 Microcalcification Clusters for Two Radiologists Using Two Contrast-Enhancement Methods Enhancement Method Radiologist A Original plus intensity windowing Original plus adaptive wavelet Original DDSM assessmenta 62.8 65.1 — Radiologist B Average 74.4 76.7 — 69.8 72.1 62.8 a Corresponding percentage derived by radiologists’ assessments provided by the Digital Database for Screening Mammography (DDSM) TABLE 6.10 Frequency of Benign and Malignant Microcalcification Clusters of the Case Sample with Respect to Difference in Confidence Levels (D = LIW − LAW) between the Original-Plus-IW and the Original-Plus-AW Methods in the Microcalcification-Cluster Classification Task for Two Radiologists Benign Cluster D = LIW – LAW D>0 D=0 D 0) is almost equal to the number of negative differences (D < 0) for both benign and malignant MC clusters for each of the two radiologists In the case of no difference in confidence levels (D = 0), Table 6.11 shows the numbers of correctly classified (true) and misclassified (false) cases for benign and malignant clusters of the sample for both radiologists For benign clusters, the true classification cluster rate is sufficiently low, 43% for radiologist A and 33% for radiologist B In case of malignant clusters, the true classification cluster rate is sufficiently high, 100% for radiologist A and 87% for radiologist B As a result, both contrast-enhancement methods misclassified the same number of clusters, especially benign ones Table 6.12 shows the distribution of the differences between the two methods for benign and malignant clusters for both radiologists Concerning benign clusters, the frequency of positive differences (D > 0) represents the number of clusters where the AW method is superior to the IW method The frequency of negative differences (D < 0) represents the number of images where the IW method is superior to the AW method The total number of positive differences (D > 0) is higher than the total number of negative differences (D < 0) for radiologist A and is equal for radiologist B Specifically, 83% (5/6) and 62% (5/8) of the differences were obtained from one level difference (D = ±1) for radiologist A, and two levels difference (D = ±2) for radiologist B, respectively The only significant difference for the two methods is that both radiologists accurately classified two more benign MC clusters by means of the AW method Specifically, the confidence levels of radiologist A for these two clusters were (additional diagnostic workup is required) and (definitely malignant) for the IW method, and the corresponding confidence levels were (probably benign) in both clusters for the AW method The confidence levels of radiologist B for the two clusters were (probably malignant) and (definitely malignant) for the IW method, and the corresponding confidence levels were (probably benign) in both clusters for the AW method Concerning malignant clusters, the frequency of negative differences (D < 0) represents the number of images where the AW method is superior to the IW method, and the opposite occurs for positive differences (D > 0) The total number of negative differences (D < 0) is lower than the total number of positive differences (D > 0) for radiologist B and Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 261 Wednesday, May 18, 2005 3:32 PM Locally Adaptive Wavelet Contrast Enhancement 261 TABLE 6.12 Frequency of Differences in Confidence Levels (D = LIW − LAW) between the Original-Plus-IW and the Original-Plus-AW Methods in the Microcalcification-Classification Task for Benign and Malignant Clusters of the Case Sample for Two Radiologists Benign Cluster Malignant Cluster Radiologist A Radiologist B D = LIW − LAW D>0 D0 Radiologist A Radiologist B D0 D0 2→1 3→2 4→3 5→4 0 0 0 0 0 0 0 4→2 5→3 0 0 D = ±2 2→4 3→5 4→1 5→2 0 D = ±3 1→4 2→5 0 0 1 5→1 Total D = ±4 1→5 Total 7 D 0) represents the number of clusters that the AW method is superior to the IW method; the opposite occurs for negative differences (D < 0) However, for malignant clusters, the frequency of negative differences (D < 0) represents the number of clusters that the AW method is superior to the IW method; the opposite occurs for positive differences (D > 0) equal for radiologist A Specifically, 64% (9/14) and 50% (6/12) of the differences were obtained from one level difference (D = ±1) for radiologist A, and two levels difference (D = ±2) for radiologist B, respectively There is no significant difference between the two methods with respect to malignant clusters The statistical results using the Wilcoxon signed ranks test for paired data are presented in Table 6.13 Statistical analysis was performed for benign and malignant clusters, as well as for the entire abnormal sample (benign plus malignant clusters) for both radiologists The differences are not statistically significant (p > 0.05), indicating that the two contrast-enhancement methods are equivalent with respect to pathology classification performance of MC clusters In other words, use of the IW-processed images with original ones aids the pathology classification (benign vs malignant) of MC clusters in a similar way as the AW-processed images Representative examples of original, IW-processed, and AW-processed ROIs of mammographic images containing MC cluster (arrows) are presented in Figure 6.17 Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 262 Wednesday, May 18, 2005 3:32 PM 262 Medical Image Analysis TABLE 6.13 Results of Wilcoxon Statistical Test for Pathology-Classification Task for Two Radiologists Radiologist A Benign Malignant Entire sample Radiologist B Na SI b p-value c SD d Na 06 14 20 T+: 18 T+: 42 z: 0.26 0.1562 0.5416 0.7948 NS NS NS 08 12 20 SI b T+: 20 T+: 32.5 z: 0.28 p-value c SD d 0.8438 0.7054 0.7794 NS NS NS a N: number of mammographic images SI statistical index The statistical index T+ (sum of positive ranks) was used for small samples (benign and malignant), and the statistical index z-value, which assumes a normal distribution, was used for large samples (entire sample) c p-value: probability values were calculated for two-tailed statistical tests d SD: statistical differences are not significant (NS) b and Figure 6.18 In Figure 6.17, the benign MC cluster was misclassified by both radiologists in the method based on original-plus-IW-processed images (confidence level 5: definitely malignant) In the method based on original-plus-AW-processed images, the two radiologists rated the MC cluster with confidence level (probably benign) In Figure 6.18, the MC cluster was correctly classified as malignant in both methods (confidence level for each radiologist), but was incorrectly classified as probably benign (short-interval follow-up) by radiologists’ assessment provided by the DDSM database 6.5 DISCUSSION Multiscale wavelet processing is one of the most promising approaches to mammographic image enhancement The spatially adaptive wavelet (AW) enhancement method attempts to optimize medical-image contrast by local adaptive transformation of gradient-magnitude values obtained by the redundant wavelet transform of Mallat and Zhong The method is generic and can also be applied to medical images or other imaging modalities Emphasis in this work is directed to finding the best way to treat wavelet coefficients However, the identification of the most appropriate basis functions for enhancing specific types of mammographic features needs further investigation Denoising performance, and specifically local threshold estimation, could benefit from recent advances in the wavelet denoising field, such as context modeling to group coefficients according to their activity level and estimate the local standard deviation of the signal from coefficients belonging to the same context group, as proposed by Chang et al [90] In addition, a noise equalization preprocessing step would be beneficial because mammographic noise often has a dependence on the gray level and signal activity [91], especially in the case of certain digitizers [92, 93] Copyright 2005 by Taylor & Francis Group, LLC (b) (c) FIGURE 6.17 Magnified ROIs containing a benign MC cluster from (a) original, (b) IW-processed, and (c) AW-processed mammographic image (B-3425.1_LCC) The MC cluster was correctly classified only in the method based on original-plus-AW-processed image Radiologists’ assessment for the method based on original-plus-IW-processed image, as well as radiologists’ assessment provided by DDSM database was false (positive), since they both misclassified as definitely malignant and suspicious abnormality the MC cluster, respectively 2089_book.fm copy Page 263 Wednesday, May 18, 2005 3:32 PM Locally Adaptive Wavelet Contrast Enhancement Copyright 2005 by Taylor & Francis Group, LLC (a) 263 (b) (c) Medical Image Analysis FIGURE 6.18 Magnified ROIs containing a malignant MC cluster from (a) original, (b) IW-processed, and (c) AW-processed mammographic image (D-4110.1_RMLO) The MC cluster was correctly classified in both enhancement methods, in contrast to radiologists’ assessment provided by DDSM database, rated as probably benign 2089_book.fm copy Page 264 Wednesday, May 18, 2005 3:32 PM 264 Copyright 2005 by Taylor & Francis Group, LLC (a) 2089_book.fm copy Page 265 Wednesday, May 18, 2005 3:32 PM Locally Adaptive Wavelet Contrast Enhancement 265 Beyond image contrast enhancement, a more interesting extension could be toward lesion-specific enhancement by exploiting interscale analysis [94] or orientation information [95, 96] In this study, the effectiveness of the AW enhancement method was assessed and compared with the IW enhancement method with respect to detection, morphology characterization, and pathology classification of MC clusters on dense breast parenchyma The detection accuracy of the method based on original-plus-AW-processed images is higher than those of the method based on original-plus-IW-processed images, but the differences in ratings (Wilcoxon signed ranks test), as well as in Az values (ROC test), are not statistically significant, indicating that the two contrast-enhancement methods have similar detection performance The detection performance of both contrast-enhancement methods is high (>0.93) in a difficult task, such as MC clusters on dense breast parenchyma With respect to morphology characterization of MC clusters, the method based on originalplus-AW-processed images is more accurate (18.6% increase), but the differences between the two methods are not statistically significant, as proved by two-tailed sign statistical test Concerning the pathology classification task, similar performance (≈70%) was achieved with both contrast-enhancement methods (Wilcoxon signed ranks test) Although this classification accuracy is relatively low, it is higher than those derived by radiologists’ assessments of DDSM database (≈63%), indicating the increased difficulty of classifying as benign or malignant MC clusters on dense parenchyma The advantage of the AW enhancement method is the use of adaptive denoising and enhancement stages, which make the enhancement method less dependent on method parameter settings, an issue frequently associated with the performance of image postprocessing techniques [35, 58–62, 97–99], such as the manual IW enhancement method studied However, the AW method, besides enhancing MC clusters, inevitably enhances the MCs’ background parenchyma within the adapting window Further refinement of the method to selective lesion vs background adaptation is expected to further improve its performance Finally, a more complete evaluation study should consider: (a) a larger case sample, (b) participation of more radiologists, (c) detection and classification tasks for different types of lesions, such as circumscribed and stellate masses, and (d) intercomparisons with other contrast-enhancement methods proposed for soft-copy display of mammograms ACKNOWLEDGMENT This work is supported by the European Social Fund (ESF), the Operational Program for Educational and Vocational Training II (EPEAEK II), and particularly the Program PYTHAGORAS and by the Caratheodory Programme (2765) of the University of Patras We also thank the staff of the Department of Radiology at the University Hospital of Patras for their contribution to this work Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 266 Wednesday, May 18, 2005 3:32 PM 266 Medical Image Analysis REFERENCES Dean, P.B., Overview of breast cancer screening, in Proc 3rd Int Workshop on Digital Mammography, Doi, K., Giger, M.L., Nishikawa, R.M., and Schmidt, R.A., Eds., Elsevier Science, Amsterdam, 1996, p 19 Landis, S.H et al., Cancer statistics, Cancer J Clin., 48, 6, 1998 Smigel, K., Breast cancer death rates decline for white women, J Nat Cancer Inst., 87, 73, 1995 Candelle, L.A et al., Update on breast cancer mortality, Health Reports, 9, 31, 1995 Schneider, M.A., Better detection: improving our chances, in Proc 5th Int Workshop on Digital Mammography, Yaffe, M.J., Ed., Medical Physics Publishing, Madison, WI, 2000, p Page, D.L and Winfield, A.C., The dense mammogram, AJR, 147, 487, 1986 Jackson, V.P et al., Imaging of the radiographically dense breast, Radiology, 188, 297, 1993 Tabar, L and Dean, P.B., Anatomy of the breast, in Teaching Atlas of Mammography, 2nd ed., Frommhold, W and Thurn, P., Eds., Thieme, New York, 1985, chap Dahnert, W., Breast, in Radiology Review Manual, Dahnert, W., Ed., Williams and Wilkins, Baltimore, 1996, chap 10 Giger, M.L., Huo, Z., Kupinski, M., and Vyborny, C.J., Computer-aided diagnosis in mammography, in Handbook of Medical Imaging, Vol 2, Medical Image Processing and Analysis, Sonka, M and Fitzpatrick, J.M., Eds., SPIE Press, Bellingham, WA, 2000, p 915 11 Karssemeijer, N., Computer-aided detection and interpretation in mammography, in Proc 5th Int Workshop on Digital Mammography, Yaffe, M.J., Ed., Medical Physics Publishing, Madison, WI, 2000, p 243 12 Birdwell, R.L et al., Mammographic characteristics of 115 missed cancers later detected with screening mammography and the potential utility of computer-aided detection, Radiology, 219, 192, 2001 13 Freer, T.W and Ulissey, M.J., Screening mammography with computer-aided detection: prospective study of 12,860 patients in a community breast center, Radiology, 220, 781, 2001 14 Nishikawa, R., Assessment of the performance of computer-aided detection and computer-aided diagnosis systems, Semin Breast Disease, 5, 217, 2002 15 Nishikawa, R.M., Detection of microcalcifications, in Image-Processing Techniques for Tumor Detection, Strickland, R.N., Ed., Marcel Dekker, New York, 2002, chap 16 Karssemeijer, N., Detection of masses in mammograms, in Image-Processing Techniques for Tumor Detection, Strickland, R.N., Ed., Marcel Dekker, New York, 2002, chap 17 Kallergi, M., Computer-aided diagnosis of mammographic microcalcifications clusters, Med Phys., 31, 314, 2004 18 Panayiotakis, G et al., Valuation of an anatomical filter-based exposure equalization technique in mammography, Br J Radiol., 71, 1049, 1998 19 Skiadopoulos, S et al., A phantom-based evaluation of an exposure equalization technique in mammography, Br J Radiol., 72, 977, 1999 20 Bick, U et al., Density correction of peripheral breast tissue on digital mammograms, RadioGraphics, 16, 1403, 1996 21 Byng, J.W., Critten, J.P., and Yaffe, M.J., Thickness-equalization processing for mammographic images, Radiology, 203, 564, 1997 Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 267 Wednesday, May 18, 2005 3:32 PM Locally Adaptive Wavelet Contrast Enhancement 267 22 Panayiotakis, G., Equalization techniques in mammography, in Proc VI Int Conf on Med Phys., Kappas, C et al., Eds., Monduzzi Editore, Bologna, 1999, p 163 23 Highnam, R and Brady, M., Mammographic Image Analysis, Kluwer Academic, Dordrecht, Netherlands, 1999 24 Stefanoyiannis, A.P et al., A digital density equalization technique to improve visualization of breast periphery in mammography, Br J Radiol., 73, 410, 2000 25 Attikiouzel, Y and Chandrasekhar, R., DSP in mammography, in Proc 14th Int Conf on Digital Signal Processing, Vol 1, Skodras, A.N and Constantinides, A.G., Eds., Typorama, Greece, 2002, p 29 26 Stefanoyiannis, A et al., A digital equalization technique improving visualization of dense mammary gland and breast periphery in mammography, Eur J Radiol., 45, 139, 2003 27 Mendez, A et al., Automatic detection of breast border and nipple in digital mammograms, Comp Meth Prog Biom., 49, 253, 1996 28 Chandrasekhar, R and Attikiouzel, Y., A simple method for automatically locating the nipple in mammograms, IEEE Trans Medical Imaging, 16, 483, 1997 29 Katartzis, A et al., Model-based technique for the measurement of skin thickness in mammography, Med Biol Eng Comp., 40, 153, 2002 30 Yaffe, M.J., Technical aspects of digital mammography, in Proc Int Workshop on Digital Mammography, Doi, K et al., Eds., Elsevier Science, Amsterdam, 1996, p 33 31 Evertsz, C.J.G et al., Soft-copy reading environment for screening mammographyscreen, in Proc 5th Int Workshop on Digital Mammography, Yaffe, M.J., Ed., Medical Physics Publishing, Madison, WI, 2000, p 566 32 Castleman, K.R., Digital Image Processing, Prentice Hall, Englewood Cliffs, NJ, 1979 33 Aylward, S.R., Hemminger, M.B., and Pisano, E.D., Mixture modelling for digital mammogram display and analysis, in Proc 4th Int Workshop on Digital Mammography, Karssemeijer, N et al., Eds., Kluwer Academic, Dordrecht, Netherlands, 1998, p 305 34 Pizer, S.M et al., Adaptive histogram equalization and its variations, Comput Vision Graph Image Process., 39, 355, 1987 35 Pisano, E.D et al., Contrast-limited adaptive histogram equalization image processing to improve the detection of simulated spiculations in dense mammograms, J Digit Imaging, 11, 193, 1998 36 Fahnestock, J.D and Schowengerdt, R.A., Spatially variant contrast enhancement using local range modification, Opt Eng., 22, 378, 1983 37 Levi, L., Unsharp masking and related image-enhancement techniques, Comput Graph Image Proc., 3, 163, 1974 38 Lee, J.S., Digital image enhancement and noise filtering by using local statistics, IEEE Trans Pattern Anal Machine Intell., 2, 165, 1980 39 Tahoces, P et al., Enhancement of chest and breast radiographs by automatic spatial filtering, IEEE Trans Medical Imaging, 10, 330, 1991 40 Kim, J.K et al., Adaptive mammographic image enhancement using first derivative and local statistics, IEEE Trans Medical Imaging, 16, 495, 1997 41 Ji, T.L., Sundareshan, M.K., and Roehrig, H., Adaptive image contrast enhancement based on human visual properties, IEEE Trans Medical Imaging, 13, 573, 1994 42 Chang, D and Wu, W., Image contrast enhancement based on a histogram transformation of local standard deviation, IEEE Trans Medical Imaging, 17, 518, 1998 43 Dhawan, A.P., Buelloni, G., and Gordon, R., Enhancement of mammographic features by optimal adaptive neighborhood image processing, IEEE Trans Medical Imaging, 5, 8, 1986 Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 268 Wednesday, May 18, 2005 3:32 PM 268 Medical Image Analysis 44 Dhawan, A.P and Royer, E.L., Mammographic feature enhancement by computerized image processing, Comput Methods Programs Biomed., 27, 23, 1998 45 Morrow, W.M., Paranjape, R.B., and Rangayyan, R.M., Region-based contrast enhancement of mammograms, IEEE Trans Medical Imaging, 11, 392, 1992 46 Rangayyan, R.M et al., Region-based adaptive contrast enhancement, in ImageProcessing Techniques for Tumor Detection, Strickland, R.N., Ed., Marcel Dekker, New York, 2002, chap 47 Mallat, S., A Wavelet Tour of Signal Processing, Academic Press, London, 1998 48 Mallat, S and Zhong, S., Characterisation of signals from multiscale edges, IEEE Trans Pattern Anal Machine Intell., 14, 710, 1992 49 Laine, A et al., Mammographic feature enhancement by multiscale analysis, IEEE Trans Medical Imaging, 13, 725, 1994 50 Laine, A., Fan, J., and Yang, W., Wavelets for contrast enhancement of digital mammography, IEEE Eng Med Biol., 14, 536, 1995 51 Laine, A et al., Mammographic image processing using wavelet processing techniques, Eur Radiol., 5, 518, 1995 52 Sakellaropoulos, P., Costaridou, L., and Panayiotakis, G., Integrating wavelet-based mammographic image visualisation on a Web browser, in Proc Int Conf Image Proc., 2, 873, 2001 53 Lu, J and Heally, D.M., Contrast enhancement of medical images using multiscale edge representation, Opt Eng., 33, 2151, 1994 54 Sakellaropoulos, P., Costaridou, L., and Panayiotakis, G., A wavelet-based spatially adaptive method for mammographic contrast enhancement, Phys Med Biol., 48, 787, 2003 55 Chang, S., Yu, B., and Vetterli, M., Image denoising via lossy compression and wavelet thresholding, IEEE Trans Image Proc., 9, 1532, 2000 56 Chang., S., Yu, B., and Vetterli, M., Spatially adaptive wavelet thresholding with context modeling for image denoising, IEEE Trans Image Proc., 9, 1522, 2000 57 Kallergi, M et al., Interpretation of calcifications in screen/film, digitized, and wavelet-enhanced monitor-displayed mammograms: a receiver operating characteristic study, Acad Radiol., 3, 285, 1996 58 Pisano, E.D et al., The effect of intensity windowing on the detection of simulated masses embedded in dense portions of digitized mammograms in a laboratory setting, J Digit Imaging, 10, 174, 1997 59 Pisano, E.D et al., Does intensity windowing improve the detection of simulated calcifications in dense mammograms? J Digit Imaging, 10, 79, 1997 60 Mekle, R., Laine, A.F., and Smith, S.J., Evaluation of a multiscale enhancement protocol for digital mammography, in Image-Processing Techniques for Tumor Detection, Strickland, R.N, Ed., Marcel Dekker, New York, 2002, chap 61 Sivaramakrishna, R et al., Comparing the performance of mammographic enhancement algorithms: a preference study, Acad J Radiol., 175, 45, 2000 62 Pisano, E.D et al., Radiologists’ preferences for digital mammographic display, Radiology, 216, 820, 2000 63 Wagner, R.F et al., Assessment of medical imaging and computer-assist systems: Lessons from recent experience, Acad Radiol., 8, 1264, 2002 64 Heath, M et al., The digital database for screening mammography, in Proc 5th Int Workshop on Digital Mammography, Yaffe, M.J., Ed., Medical Physics Publishing, Madison, WI, 2000, p 212 65 DDSM: Digital Database for Screening Mammography; available on-line at http:// marathon.csee.usf.edu/Mammography/Database.html last accessed March 2005 Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 269 Wednesday, May 18, 2005 3:32 PM Locally Adaptive Wavelet Contrast Enhancement 269 66 Suckling, J et al., The mammographic image analysis society digital mammographic database, in Proc 2nd Int Workshop on Digital Mammography, Gale, A.G., Ed., Elsevier Science, York, U.K., 1994, p 375 67 MIAS: Mammographic Image Analysis Society; available on-line at http://www.wiau man.ac.uk/services/MIAS/MIASweb.html last accessed March 2005 68 Simoncelli, E.P et al., Shiftable multiscale transforms, IEEE Trans Inform Theory, 38, 587, 1992 69 Vetterli, M and Kovacevi, J., Wavelets and Subband Coding, Prentice Hall, Englewood Cliffs, NJ, 1995 70 Shensa, M.J., The discrete wavelet transform: wedding the trous and Mallat algorithms, IEEE Trans Signal Proc., 40, 2464, 1992 71 Donoho, D.L., Denoising by soft-thresholding, IEEE Trans Inform Theory, 41, 613, 1995 72 Coifman, R.R and Donoho, D.L., Translation-invariant denoising, in Wavelets and Statistics, Antoniadis, A and Oppenheim, G., Eds., Springer-Verlag, Berlin, 1995 73 Costaridou, L et al., Quantifying image quality at breast periphery vs mammary gland in mammography using wavelet analysis, Br J Radiol., 74, 913, 2001 74 Sakellaropoulos, P., Costaridou, L., and Panayiotakis, G., An image visualisation tool in mammography, Med Inform., 24, 53, 1999 75 Sakellaropoulos, P., Costaridou, L., and Panayiotakis, G., Using component technologies for Web-based wavelet enhanced mammographic image visualization, Med Inform., 25, 171, 2000 76 Bacry, E., Fralen, J., Kalifa, J., Pennec, E.L., Hwang, W.L., Mallat, S and Zhong, S., Lastwave 2.0 Software, Centre de Mathématiques Appliquees, France; available on-line at http://www.cmap.polytechnique.fr/~bacry/Lastwave last accessed March 2005 77 Stoffel, A., Remarks on the unsubsampled wavelet transform and the lifting scheme, Signal Proc., 69, 177, 1998 78 Bovis, K and Singh, S., Enhancement technique evaluation using quantitative measures on digital mammograms, in Proc 5th Int Workshop on Digital Mammography, Yaffe, M.J., Ed., Medical Physics Publishing, Madison, WI, 2000, p 547 79 Skiadopoulos, S et al., Simulating mammographic appearance of circumscribed lesions, Eur Radiol., 13, 1137, 2003 80 Strickland, R.N and Hahn, H.I., Detection of microcalcifications in mammograms using wavelets, in Proc SPIE Conf Wavelet Applications in Signal and Image Processing II, 2303, 430, 1994 81 Siegel, S and Castellan, N.J., The case of one sample, two measures or paired replicates, in Nonparametric Statistics for the Behavioral Sciences, 2nd ed., McGrawHill, New York, 1988, p 87 82 Goodenough, D.J., Rossmann, K., and Lusted, L.B., Radiographic applications of receiver operating characteristic (ROC) curves, Radiology, 110, 89, 1974 83 Metz, C.E., ROC methodology in radiologic imaging, Invest Radiol., 21, 720, 1986 84 Erkel, A.R and Pattynama, P.M., Receiver operating characteristic (ROC) analysis: basic principles and applications in radiology, Eur J Radiol., 27, 88, 1998 85 Medical Image Perception Society; available on-line at http://www.mips.ws/ last accessed March 2005 86 Metz, C.E., University of Chicago; available on-line at http://www-radiology uchicago.edu/krl/roc_soft.htm last accessed March 2005 87 Metz, C.E., Rockit version 0.9B, User’s Guide, Department of Radiology, University of Chicago, 1998 Copyright 2005 by Taylor & Francis Group, LLC 2089_book.fm copy Page 270 Wednesday, May 18, 2005 3:32 PM 270 Medical Image Analysis 88 Dorfman, D.D and Alf, E., Maximum likelihood estimation of parameters of signal detection theory and determination of confidence intervals: rating data method, J Math Psychol., 6, 487, 1969 89 Metz, C.E., Quantification of failure to demonstrate statistical significance: the usefulness of confidence intervals, Invest Radiol., 28, 59, 1993 90 Chang, S., Yu, B., and Vetterli, M., Spatially adaptive wavelet thresholding with context modeling for image denoising, IEEE Trans Image Proc., 9, 1522, 2000 91 Veldkamp, W and Karssemeijer, N., Normalization of local contrast in mammograms, IEEE Trans Medical Imaging, 19, 731, 2000 92 Poissonnier, M and Brady, M., “Noise equalization” for microcalcification detection? in Proc 5th Int Workshop on Digital Mammography, Yaffe, M.J., Ed., Medical Physics Publishing, Madison, WI, 2000, p 334 93 Efstathopoulos, E.P et al., A protocol-based evaluation of medical image digitizers, Br J Radiol., 74, 841, 2001 94 Heinlein, P., Drexl, J., and Schneider, W., Integrated wavelets for enhancement of microcalcifications in digital mammography, IEEE Trans Medical Imaging, 22, 402, 2003 95 Koren, I., Laine, A., and Taylor, F., Enhancement via fusion of mammographic features, in Proc IEEE Int Conf on Image Proc., 2, 722, 1998 96 Wang, Y.P., Wu, Q., and Castleman, K., Image enhancement using multiscale oriented wavelets, in Proc Int Conf on Image Processing, Greece, Thessaloniki, October 2001, 1, 610 97 Costaridou, L., Computer methods in mammography, in Proc VI Int Conf on Med Phys., Kappas, C et al., Eds., Monduzzi Editore, Bologna, Italy, 1999, p 201 98 Hemminger, B.M et al., Improving the detection of simulated masses in mammograms through two different image-processing techniques, Acad Radiol., 8, 845, 2001 99 Cole, E.B et al., Diagnostic accuracy of digital mammography in patients with dense breasts who underwent problem-solving mammography: effects of image processing and lesion type, Radiology, 226,153, 2003 Copyright 2005 by Taylor & Francis Group, LLC