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

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

6 Locally Adaptive Wavelet Contrast Enhancement

Lena Costaridou, Philipos Sakellaropoulos, Spyros Skiadopoulos, and George Panayiotakis

CONTENTS

6.1 Introduction6.2 Background6.3 Materials and Methods6.3.1 Discrete Dyadic Wavelet Transform Review6.3.2 Redundant Dyadic Wavelet Transform6.3.3 Wavelet Denoising

6.3.3.1 Noise Suppression by Wavelet Shrinkage6.3.3.2 Adaptive Wavelet Shrinkage

6.3.4 Wavelet Contrast Enhancement6.3.4.1 Global Wavelet Mapping6.3.4.2 Adaptive Wavelet Mapping6.3.5 Implementation

6.3.6 Test Image Demonstration and Quantitative Evaluation6.4 Observer Performance Evaluation

6.4.1 Case Sample6.4.2 Observer Performance6.4.3 Statistical Analysis6.4.3.1 Wilcoxon Signed Ranks Test6.4.3.2 ROC Analysis

6.4.4 Results6.4.4.1 Detection Task6.4.4.2 Morphology Characterization Task6.4.4.3 Pathology Classification Task6.5 Discussion

AcknowledgmentReferences2089_book.fm copy Page 225 Wednesday, May 18, 2005 3:32 PM

226 Medical Image Analysis

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-contrastcharacter of mammographic imaging, especially in the case of dense breast, account-ing for about 25% of the younger female population [6, 7]

Calcifications are calcium salts produced by processes carried out inside thebreast ductal system They are radiodense, usually appearing lighter than surroundingparenchyma, due to their inherently high attenuation of X-rays Depending on theX-ray attenuation of surrounding parenchyma (i.e., dense breast), they can be low-contrast entities, with their low-contrast resolution limited by their size Magnifica-tion 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 radiodenseregions that also appear lighter than their surrounding parenchyma due to higherattenuation 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 normaldense surrounding parenchyma The use of complementary mammographic views,craniocaudal (CC) and mediolateral (MLO), is intended to resolve tissue superim-position in different projections [8, 9]

Identification and differentiation (benign vs malignant) of MCs and masses havebeen 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 researchduring the last 20 years [10–17]

In addition to dense breast regions, mammography periphery is also poorlyimaged 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] andfor skin detection [27–29]

6.2 BACKGROUND

Digital image-enhancement methods have been widely used in mammography toenhance contrast of image features Development of mammographic image-enhance-ment methods is also motivated by recent developments in digital mammographyand soft-copy display of mammograms [30, 31] Specifically, image display andenhancement 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 graylevels for expert radiologists

Locally Adaptive Wavelet Contrast Enhancement 227

Differentalgorithms have advantages and disadvantages for thespecific tasksrequired in breast imaging: diagnosis andscreening A simple but effective methodfor image enhancement is intensity windowing (IW) [32] IW stretches a selectedrange of gray levels to the available display range However, in mammography(unlike CT), there is not an absolute correspondence between the recorded intensitiesand the underlying tissue, and thus IW settings cannot be predetermined Manualcontrast adjustment of a displayed digital mammogram with IW resembles adjust-ment of a screen-film mammogram’s contrast on a light-view box Automatedalgorithms have been developed to avoid user-dependent and time-consuming man-ual adjustments Component-based IW techniques segment the mammographicimage 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 fromdense-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 somelocal characteristics of the neighborhood around the pixel’s location Adaptive his-togram equalization (AHE) is a well-known technique that uses regional histograms

to derive local mapping functions [34] Although AHE is effective, it tends tooveremphasize noise Contrast-limited AHE (CLAHE) was designed to overcomethis problem, but the contrast-limit parameter is image and user dependent [35].Local-range modification (LRM) is an adaptive method that uses local minima-maximainformation to calculate local linear stretching functions [36] LRM enhances imagecontrast, but it tends to create artifacts (dark or bright regions) in the processed image.Spatial filtering methods, like unsharp masking (UM) [37], adaptive contrast enhance-ment (ACE) [38], multichannel filtering [39], and enhancement using first derivativeand local statistics [40] amplify mid- to high-spatial-frequency components to enhanceimage details However, these methods are characterized by noise overenhancementand ringing artifacts caused by amplification of noise and high-contrast edges [41].More complex filtering methods like contrast enhancement based on histogram trans-formation of local standard deviation [42] and just-noticeable-difference-guided ACE[41] attempt to overcome these problems by using smaller gains for smooth or high-contrast regions Adaptive neighborhood contrast enhancement (ANCE) methods[43–46] directly manipulate the local contrast of regions, computed by comparing theintensity 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 arebased on the single-scale spatial domain Due to this fact, they can only enhancethe contrast of a narrow range of sizes, as determined by the size of local-processingregion Additionally, they tend to increase the appearance of noise

To enhance features of all sizes simultaneously, multiresolution enhancementmethods, based on the wavelet transform [47], have been developed A multiscalerepresentation divides the frequency spectrum of an image into a low-pass subbandimage 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,

228 Medical Image Analysis

they are analyzed with fine spatial resolution By exploiting the location and quency–selectivity properties of the wavelet transform, we can progressively “zoom”into image features and characterize them through scale-space Mammographicimage analysis can benefit from this strategy, because mammograms contain featureswith varying scale characteristics The main hypothesis of image wavelet analysis

fre-is that features of interest reside at certain scales Specifically, features with sharpborders, like MCs, are mostly contained within high-resolution levels (small scales)

of a multiscale representation Larger objects with smooth borders, like masses, aremostly contained in low-resolution levels (coarse scales) Different features can thus

be selectively enhanced (or detected) within different resolution levels Also, a reduction stage could be applied prior to enhancement, exploiting the decorrelationproperties of the wavelet transform

noise-The main approach for wavelet-based enhancement (WE) uses a redundantwavelet transform [48] and linear or nonlinear mapping functions applied on Lapla-cian or gradient wavelet coefficients [49–52] Such methods have demonstratedsignificant contrast enhancement of simulated mammographic features [50], and alsoimproved assessed visibility of real mammographic features [51] Another approachuses a multiscale edge representation, provided by the same type of wavelet trans-form, to accentuate multiscale edges [53]

Recently, spatially adaptive transformation of wavelet coefficients has beenproposed [54] for soft-copy display of mammograms, aiming at optimized presen-tation of mammographic image contrast on monitor displays Spatial adaptivity ismotivated from the fact that mapping functions in previous methods [49, 50] aretypically characterized by global parameters at each resolution level Global param-eters fail to account for regions of varying contrasts such as fat, heterogeneouslydense, and dense in mammograms This method provides an adaptive denoisingstage, 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 unproc-essed digitized versions [46, 57–60], and a small number of intercomparison studieshas been performed [54, 61, 62] Intercomparison studies are useful in the sensethat 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 observerpreference as an initial step for selection of an appropriate contrast-enhancementmethod (i.e., those with high preference) Receiver operating characteristics (ROC)studies should be conducted as a second step for comparative evaluation of thesemethods with respect to detection and classification accuracy of each lesion type [63].Sivaramakrishna et al [61] conducted a preference study for performance eval-uation of four image contrast-enhancement methods (UM, CLAHE, ANCE, andWE) on a sample of 40 digitized mammograms containing 20 MC clusters and 20masses (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

Locally Adaptive Wavelet Contrast Enhancement 229

28% of cases, respectively For masses, the digitized (unprocessed) images and based processed images were preferred in 58% and 28% of cases, respectively Theauthors concluded that different contrast-enhancement approaches may be necessary,depending on the type of lesion

UM-Pisano et al [62] carried out a preference study for performance evaluation ofeight image contrast-enhancement methods on a sample of 28 images containing 29cancerous and 36 benign pathological findings (masses or MCs) produced from threedifferent digital mammographic units All processed images were printed on filmand compared with respect to their corresponding screen-film images Screen-filmimages were preferred to all processed images in the diagnosis of MCs For thediagnosis of masses, all processed images were preferred to screen-film images Thispreference was statistically significant in the case of the UM method For thescreening task of the visualization of anatomical features of main breast and breastperiphery, screen-film images were generally preferred to processed images Nounique enhancement method was preferred

Recently, the spatially adaptive wavelet (AW) enhancement method has beencomparedwith CLAHE, LRM, and two wavelet-based enhancement methods (globallinear 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 methodwith high performance in all tasks and types of lesions has not been developed Inaddition, the small number of preference studies is not adequate to indicate thepromising contrast-enhancement methods for clinical acceptance Further preferencestudies are needed comparing the performance of contrast-enhancement methodspresented in the literature Observer preference as well as ROC studies are not time-consuming nowadays because (a) a case sample can be selected from commonmammographic 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 6.3.1and 6.3.2 The basic principles of wavelet denoising and contrast enhancement arepresented in Sections 6.3.3.1 and 6.3.4.1, while details of an adaptive denoising andenhancement 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, bymeans of simulated MC clusters superimposed on dense breast parenchyma inSection 6.3.7 In Section 6.4, evaluation is carried out by an observer performancecomparative study between original-plus-AW-processed and original-plus-IW-pro-cessed 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 D ISCRETE D YADIC W AVELET T RANSFORM R EVIEW

The dyadic wavelet transform series of a function ƒ(x) with respect to a waveletfunction ψ(x) is defined by the convolution

230 Medical Image Analysis

(6.6)

As the scale 2j increases, more details are removed by the operator Dyadicwavelet transform series between scales 21 and 2j contain the details existing

in the S1ƒ(x) representation that have disappeared in S jƒ(x)

6.3.2 R EDUNDANT D YADIC W AVELET T RANSFORM

Redundant (overcomplete) biorthogonal wavelet representations are more suitable forenhancement compared with orthogonal, critically sampled wavelet representations

Locally Adaptive Wavelet Contrast Enhancement 231

Avoiding the downsampling step after subband filtering ensures that wavelet ficient images are free from aliasing artifacts Additionally, the wavelet representa-tion is invariant under translation [68] Smooth symmetrical or antisymmetricalwavelet functions can be used [69] to alleviate boundary effects via mirror extension

< j < +∞ has two components and is given by

j

j j

2( , )

θ

2 2

j j

(( , )x y

232 Medical Image Analysis

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 and a set of wavelet images

, which provide the details that are available in S1ƒ buthave disappeared in 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 à 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 H j(ω), G j(ω), Kj(ω), and Lj(ω) obtained by

inserting 2j − 1 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

(6.10)

Demonstrations of gradient-magnitude vector, superimposed on two

mammo-gram regions containing masses, are presented in Figure 6.3 Magnitude of the

FIGURE 6.2 Filter-bank scheme used to implement the RDWT for two scales.

G(2 ωx ) G(2ωy ) H(ωx ) H(ωy )

H(2 ωx )H( ωy )

K(2ωx )L(2ωy ) L(2ωx )K(2ωy )

H −(2ωx )H −(2ωy )

H − (ωx ) H − (ωy ) L( ωx ) K( ωy ) K( ωx ) L( ωy )

1( , ), ( , ))

2 1

gradient vector at each location corresponds to the length of the arrow, while phasecorresponds to the direction of the arrow It can be observed that the gradient-magnitude vector is perpendicular to lesion contours Because contrast enhancementshould be perpendicular to edge contours to avoid orientation distortions, subsequentprocessing is applied on the multiscale magnitude values.

6.3.3 W AVELET D ENOISING

6.3.3.1 Noise Suppression by Wavelet Shrinkage

Digitized mammograms are corrupted by noise due to the acquisition and digitizationprocess Prior to contrast enhancement, a denoising stage is desirable to avoid orreduce amplification of noise Conventional noise-filtering techniques reduce noise

by suppressing the high-frequency image components The drawback of these ods is that they cause edge blurring Wavelet-based denoising methods, however,can effectively reduce noise while preserving the edges The two main approachesfor wavelet-based noise suppression are: (a) denoising by analyzing the evolution

meth-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 multiscaleedges across scales of the wavelet transform They proved that signal singularities(edges) are characterized by positive Lipschitz exponents, and thus the magnitudevalues of edge points increase with increasing scale Noise singularities, on the otherhand, are characterized by negative Lipschitz exponents, and thus the magnitudevalues of edge points caused by noise decrease with increasing scale The algorithmcomputes Lipschitz exponents from scales 22 and 23 to eliminate edge points withnegative exponents and reconstruct the maxima at the finest scale 21, which is mostlyaffected by noise The drawback of this method is although the reconstruction fromthe multiscale edge representation produces a close approximation of the initialimage, some image details are missed It is also very computationally intensive

TABLE 6.1 Filter Coefficients for the

FIGURE 6.3 Gradient magnitude vector superimposed on mammogram regions containing

lesions.

A simpler denoising method, widely used in signal and image processing, iswavelet shrinkage [71] This method consists of comparing wavelet coefficientsagainst a threshold that distinguishes signal coefficients from noise coefficients Thisapproach is justified by the decorrelation and energy-compaction properties of thewavelet transform Signal (or image) energy in the wavelet domain is mostly con-centrated in a few large coefficients Therefore, coefficients below a threshold areattributed to noise and are set to zero Coefficients above the threshold are eitherkept unmodified (hard-thresholding) or modified by subtracting the threshold (soft-thresholding) Using the RDWT as a basis for wavelet shrinkage is beneficial becausethresholding in a shift-invariant transform outperforms thresholding in an orthogonaltransform by reducing artifacts, such as pseudo-Gibbs phenomena [72] Thresholding

is applied on gradient-magnitude values to avoid orientation distortions [50] thresholding can be mathematically described by Equation 6.11

Soft-(6.11)

where M s d (m,n) is the denoised gradient value and T s the threshold at scale s, specified

at a fixed percentile of the cumulative histogram of the gradient-magnitude subimage.The denoised image is obtained after reconstruction from the thresholded waveletcoefficients Hard-thresholding can be mathematically described as follows

(6.12)

where M s d (m,n) is the denoised gradient value and T s is the threshold at scale s,

again specified at a percentile value of the cumulative histogram of the magnitude subimage

gradient-The soft- and hard-thresholding functions are graphically displayed in Figure6.4 Soft-thresholding has the advantage that the transformation function is contin-uous and thus artifacts are avoided However, it can result in some edge blurring,especially if a large threshold is used

6.3.3.2 Adaptive Wavelet Shrinkage

The thresholding methods described above use a global threshold at each subband.Although algorithms have been proposed for its calculation, it is difficult to define

an optimal threshold Moreover, a global threshold cannot accommodate for varyingimage characteristics In smooth regions the coefficients are dominated by noise,thus most of these coefficients should be removed In regions with large variations,the coefficients carry signal information, thus they should be slightly modified topreserve signal details In this work, a spatially adaptive thresholding strategy isproposed Specifically, soft-thresholding using a local threshold is applied on wavelet

coefficient magnitudes The threshold is calculated at each (dyadic) scale and tion by applying a local window and using the formula

at each coefficient position

FIGURE 6.4 Examples of (a) soft-thresholding and (b) hard-thresholding functions.

x

(b) (a)

x −T

T m n s( , )= σN s2, /σM s, ( , )m n

j L L

After background identification, noise standard deviation at each dyadic scale(σN,s) is calculated by applying the transform on a background area of the mammo-gram and measuring the standard deviation of gradient magnitudes Denoised gra-

dient magnitudes M s d (m,n) are given by soft-thresholding using the local threshold

(6.15)

To speed up local standard deviation calculations, an interpolation procedure[34] was used Specifically, the local threshold is first calculated on a sample grid,defined from the centers of contiguous blocks (windows) Then, the local threshold

at each position is calculated using interpolation from the local thresholds assigned

to the four surrounding grid points A window size of 9 × 9 was used

6.3.4 W AVELET C ONTRAST E NHANCEMENT

6.3.4.1 Global Wavelet Mapping

In the framework of the RDWT, the main approach for contrast enhancement islinear or nonlinear mapping of wavelet coefficients [50] This approach can bejustified by the nature of wavelet coefficients The wavelet used in the RDWT is thefirst derivative of a smoothing function Consequently, wavelet coefficients are pro-portional to image-intensity variations and are related to local contrast Evidence ofthe relationship between contrast and wavelet coefficients for mammographic imageshas been provided in a recent work [73] Using the RDWT as a basis for contrastenhancement is beneficial because of the shift invariance and lack of aliasing char-acteristics of the wavelet transform Because contrast enhancement should be per-pendicular to edge contours to enhance the contrast of structures, subsequent pro-cessing is applied on the multiscale magnitude values

Contrast enhancement by linear enhancement consists of linear stretching of themultiscale gradients This ensures that all regions of the image are enhanced in thesame way It can be mathematically expressed by

(6.16)

where M s (m,n) is the enhanced gradient-magnitude value at position (m,n)-scale s, and k s > 1 is a gain parameter The gain can vary across scales to selectively enhance

features of different sizes For example a larger k1 ensures that the fine structures

will be enhanced more Usually however, the same value k is used across all scales.

Linear enhancement is equivalent to multiscale UM [50] This can be showneasily in the one-dimensional case If we denote the frequency channel responses

of the wavelet transform C m(ω) and assume that the same gain k > 1 is used for all

band-pass channels (0 ≤ m ≤ N − 1), the system-frequency response becomes

The spatial response of the system is thus

(6.18)

C N(ω) is a low-pass filter, and thus [x(m) − (x × C N )(m)] is a high-pass version of

the signal Because UM consists of adding a scaled high-pass version to the original,Equation 6.18 describes an unsharp masking operation

A drawback of linear enhancement is that it leads to inefficient usage of thedynamic range available because it emphasizes high-contrast and low-contrast edgeswith the same gain For example, a single high-contrast MC in a mammogram,enhanced by a linear enhancement, will cause gross rescaling within the availablydynamic range of the display The subtle features contained in the processed mam-mogram will have low contrast, and their detection will be difficult

To avoid the previously mentioned drawback of linear enhancement and enhancethe visibility of low-contrast regions, the mapping function must avoid overenhance-ment of the large gradient-magnitude values A nonlinear mapping function that isused to emphasize enhancement of low-contrast features has the following form

(6.19)

where M s (n,m) is the “enhanced” magnitude gradient value at position (m,n)-scale

s, k s > 1 is a gain parameter, and T s is a low-contrast threshold By selecting differentgain parameters at each dyadic scale, the contrast of specific-sized features can beselectively enhanced The low-contrast threshold parameter can be set in two ways:(a) as a percentage of the maximum gradient value in the gradient-magnitude sub-image and (b) as a percentile value of the cumulative histogram of the gradient-magnitude subimage The linear and nonlinear contrast enhancement mapping func-tions are graphically displayed in Figure 6.5

6.3.4.2 Adaptive Wavelet Mapping

With respect to wavelet contrast enhancement, in the framework of the redundantwavelet transform, the main approach is linear or nonlinear mapping of wavelet

coefficients Linear mapping uses a uniform gain G to multiply wavelet coefficients

at each scale However, linear enhancement emphasizes strong and low contrasts inthe same way When the processed image is rescaled to fit in the available displaydynamic range, weak signal features with low contrast are suppressed For this

reason, nonlinear enhancement was introduced It uses a nonlinear mapping functionthat is a piecewise linear function with two linear parts The first part has a slope

G > 1 (where G is the gain) and is used to emphasize enhancement of low-contrast features, up to a threshold T The second part has slope equal to 1, to avoid overen-

hancement of high-contrast features However, a drawback of the method is that theparameters of the transformation function at each scale are global Because mam-mograms contain regions characterized by different local energy of wavelet coeffi-

cients, a global threshold and gain cannot be optimal If a large gain G is used to

ensure that all low-contrast features are emphasized, the second part of the mappingfunction essentially clips coefficient values and thus distorts edge information A

satisfactory value for the global threshold T can also be easily determined If a large

T value is used to include a greater portion of low-contrast features to be enhanced,

the nonlinear mapping function approximates the linear one

Sakellaropoulos et al [54] tried an adaptive approach using a locally definedlinear mapping function, similar to the LRM method [36] The enhancement process

of LRM has been modified and is applied on gradient-magnitude values Theenhanced gradient-magnitude coefficient values are given by

(6.20)

The limited adaptive gain G L,s (m,n) is derived by

(6.21)

where M1,max is the maximum value of the magnitude subband image at scale 1,

M s,max (m,n) is the local maximum value in a N ×N window at the magnitude subband image at scale s and position (m,n), and L is a local gain-limit parameter Before

FIGURE 6.5 Examples of (a) linear and (b) nonlinear contrast-enhancement mapping functions.

T

k x

T

k x

Output gradient magnitude Output gradient magnitude

the application of the adaptive mapping function, a clipping of the magnitude values

at the top 2% of their histogram is performed Clipping is used to alleviate a probleminherent with the LRM method Specifically, if the unclipped maximum values areused, isolated bright points in the magnitude subband image result in a significantly

decreased gain G s (m,n) at a region around them After reconstruction, the respective

regions would appear in the processed image as blurred

Because the gradient-magnitude mapping has to be monotonically increasing,the local minimum values that are used in the LRM method are not used in Equation

6.9 The adaptive gain G L,s (m,n) forces local maxima to become equal or close to a

target global maximum Therefore, the local enhancement process stretches gradientmagnitudes in low-contrast regions However, overenhancement of contrast in such

regions can yield unnatural-looking images, thus the local gain limit parameter L is used to limit the adaptive gain Setting L equal to 20 provided satisfactory results

for all images processed in this study Use of the same target global maximum value

(M1,max) for all subband images was found to result in sharp-looking processedimages, emphasizing local details

To speed up the calculation of local maxima, the interpolation procedure lowed by the LRM method is used [36] This procedure involves two passes throughthe image In the first pass, the maximum gradient-magnitude values are found for

fol-half-overlapping windows of size N, centered at a rectangular sample grid In the

second pass, local maximum values at each pixel position are calculated by polating the maximum values assigned at the four surrounding grid points Theinterpolation procedure results in local gain varying smoothly across the image,therefore it is more preferable than direct calculation of local maximum values ateach position Calculation time is significantly reduced, even if a large window size

inter-is used The method inter-is not sensitive to the window size For the results of thinter-is study,

a constant window size of 21×21 pixels was used

The gradient-magnitude mapping function defined in Equation 6.20 can be

extended to a nonlinear one by introducing a gamma factor g, as follows

(6.22)

Note that Equation 6.20 is a special case of Equation 6.22 for g = 1 Values of the

g factor smaller than 1 favor enhancement of low-contrast features, while values of

g factor higher than 1 favor enhancement of high-contrast features In this work, only linear local enhancement (g = 1) is used.

Figure 6.6 demonstrates global nonlinear coefficient mapping vs adaptive linearmapping The magnitude subband image at scale 2 is shown It can be observed thatthe adaptive process emphasizes more the low-contrast edge information whileavoiding overenhancement of high-contrast edge information

To obtain the processed image after denoising and contrast enhancement in thewavelet domain, two more steps are needed: first, polar-to-Cartesian transformation

to calculate the horizontal and vertical wavelet coefficients from the magnitude andphase of the gradient vector, and second, reconstruction (inverse two-dimensionalDWT) from the modified wavelet coefficients

6.3.5 I MPLEMENTATION

The method was implemented in Visual C++ 6.0 and was integrated in a previouslydeveloped medical-image visualization tool [74, 75] Redundant wavelet transformroutines have been taken from the C software package “Wave2” [76] Softwareimplementation of the method was simplified by exploiting an object-oriented C++code framework for image processing that was established during the development

of the above-mentioned tool The benefits of ROI tools, wavelet coefficient display,and windowing operations have been helpful during development and refinement ofthe method In addition, the capability of the tool to execute scripts written in thestandard Windows VBscript language enabled batch processing and measurements.The methods to which the proposed method is compared are also implemented andintegrated in this tool

The computer used for processing has a P4 processor running at 1.5 GHz and

1 GB of RAM Computation time for a 1400×2300 (100-µm resolution) DDSMimage is 96 sec, and the average computation time for the image sample was 122sec The computational cost of adaptive modification of wavelet coefficients accountsfor the 25% of the total computation time For a 2800×4600 (50-µm resolution)image, the computation time scales by a factor more than four (628 sec) due toRAM size limitation

Method computation time has been kept as low as possible by exploiting polation methods and the speed offered by the C++ language In addition, to over-come virtual-memory inefficiency for limited-RAM configurations, a memory man-ager was used to swap wavelet coefficient images not currently processed to harddisk Further reductions of processing time could be accomplished by using thelifting scheme to compute the RDWT [77], by exploiting techniques such as parallelprocessing and compiling optimization, and by employing faster computer systems

inter-6.3.6 T EST I MAGE D EMONSTRATION AND Q UANTITATIVE E VALUATION

To demonstrate the effectiveness of the denoising and enhancement processes adigital phantom was created It contains five circular details, with contrasts ranging

FIGURE 6.6 Example of mapping of gradient-magnitude coefficients at scale 2

correspond-ing to a mammographic region (a) Original gradient-magnitude coefficients, (b) result of global mapping, (c) result of adaptive mapping.

from 1 to 10%, added on a uniform background Gaussian noise with normalizedstandard deviation 2% was also added The resulting image is shown in Figure 6.7.

A horizontal scan line passing through the middle of the objects was used to generateprofiles of signal and multiscale gradient magnitudes

Figure 6.8 and Figure 6.9 show the original and processed profiles for globalnonlinear and adaptive wavelet enhancement, respectively The corresponding gra-dient-magnitude values are also shown to demonstrate the effect of processing onmagnitude wavelet coefficients It can be observed that adaptive processing preservesthe sharpness of the object edges and also significantly enhances the contrast of thelowest-contrast object

The aim of the quantitative evaluation is to measure improvement of contrastfor features of interest (i.e., MCs) with respect to their background [78] However,

to measure correctly the contrast of features, an exact definition of their borders isrequired An approach to overcome this difficulty is to use simulated calcificationsand lesions, enabling for quantitative assessment of image-enhancement algorithms.This approach allows also varying quantitatively the characteristics of input featuresand thus analyzing the behavior of the enhancement Mathematical models of MCsand masses have been previously used to construct simulated lesions [49, 79] Thesimulated lesions are blended in normal mammograms, and a contrast improvementindex is derived for each type of lesion between original and processed images

In this study, we follow a similar approach to quantify contrast enhancement ofMCs A set of phantoms of simulated MC clusters was constructed, based on the

FIGURE 6.7 Digital phantom with five circular objects of varying contrast and added noise.

FIGURE 6.8 Digital phantom scan line profiles for global wavelet processing (a) Original,

(b) global denoising, and (c) global nonlinear enhancement.

enhancement

Reconstruction after inverse DWT Reconstruction after inverse

DWT

Gradient coefficients

2D DWT

assumption of Strickland and Hahn [80] that MCs can be modeled as sional Gaussian functions The input parameters for each cluster were the size andamplitude of MCs, while positions of individual MCs were randomly determinedand kept fixed In this study, we used three MC sizes (400, 600, and 800 µm) andten amplitudes (ranging linearly between 10 and 400 gray-level values) Simulatedclusters were subsequently blended into two normal mammograms characterized bydensity 3 (heterogeneously dense breast) and 4 (extremely dense breast), according

two-dimen-to Breast Imaging Reporting and Data System (BIRADS) lexicon The resultingimages were processed with IW and AW methods using the same set of parametersfor all images Following this, the contrast of each MC in the cluster was measured,and the average of contrast values was derived to determine the cluster contrast Forcontrast measurements, we adopted the optical definition of contrast introduced by

Morrow et al [45] The contrast C of an object is defined as

(6.23)

where f is the mean gray level of the object (foreground), and b is the mean gray

level of its background, defined as a region surrounding the object

Figure 6.10 and Figure 6.11 show graphs of IW and AW processed clustercontrast vs original cluster contrast (size 600 µm) It can be observed that bothmethods produce MC contrast enhancement However, the AW method is moreeffective, especially in the case of the dense breast parenchyma Similar results wereobtained for the other MC cluster sizes studied

Figure 6.12a and Figure 6.13a present two examples of original ROIs containingsimulated clusters superimposed on heterogeneously dense parenchyma and denseparenchyma, respectively Figure 6.12b, Figure 6.13b and Figure 6.12c, Figure 6.13cpresent the resulting ROIs after IW and AW processing, respectively

FIGURE 6.9 Digital phantom scan line profiles for adaptive wavelet processing (a) Original,

(b) adaptive denoising, and (c) adaptive enhancement.

= −+

FIGURE 6.10 Contrast enhancement of simulated MC cluster (600-µm size) superimposed

on dense parenchyma of B-3617_1.RMLO of DDSM database, for IW and AW enhancement methods.

FIGURE 6.11 Contrast enhancement of simulated MC cluster (600-µm size) superimposed

on heterogeneously dense parenchyma of B-3009_1.LMLO of DDSM database, for IW and

Input contrast (%)

6.4 OBSERVER PERFORMANCE EVALUATION

The objective of the observer performance evaluation study is to validate the tiveness of spatially AW enhancement and manual IW methods with respect todetection, morphology characterization, and pathology classification of MC clusters

effec-on dense breast parenchyma IW was selected as a representative of effec-one of the mosteffective contrast-enhancement methods

6.4.1 C ASE S AMPLE

Our sample consists of 86 mammographic images, 32 of density 3 and 54 of density

4 according to BIRADS lexicon Specifically, the sample consists of 43 graphic images, each one containing a cluster of MC (29 malignant and 14 benign),and 43 images without abnormalities (normal) originating from the DDSM mam-mographic database [64] Concerning MC cluster morphology, from 29 malignantand 14 benign clusters, 2 and 4 are punctuate, 24 and 5 are pleomorphic (granular),

mammo-FIGURE 6.12 ROIs with simulated MCs (600-µm size, 230 gray-level amplitude) on

heter-ogeneously dense parenchyma (a) Original region, (b) result of processing with IW ment method, and (c) result of processing with AW enhancement method.

enhance-FIGURE 6.13 ROIs with simulated MCs (600-µm size, 90 gray-level amplitude) on dense

parenchyma (a) Original region, (b) result of processing with IW enhancement method, and (c) result of processing with AW enhancement method.

3 and 3 are amorphous, as well as 0 and 2 are fine linear branching (casting),respectively, according to DDSM database Mammographic images selected corre-spond to digitization either with Lumisys or Howtek scanner, at 12 bits pixel depth,with spatial resolution of 50 µm and 43.5 µm, respectively The images weresubsampled to 100 µm to overcome restrictions in RAM and processing time.Table 6.2 provides the volume, name, and density of each mammographic image

of the sample as offered by the DDSM database for both groups (images with MCclusters and normal ones), as well as the MC cluster morphology and pathology(malignant or benign) The entire sample (86 mammographic images) has beenprocessed with two image contrast-enhancement methods, the manual IW and the

AW methods

6.4.2 O BSERVER P ERFORMANCE

Two general-purpose display LCD monitors (FlexScan L985EX, EIZO NANAOCorp., Ishikawa, Japan) were used for the observer performance study Specifically,one monitor was used for presentation of each original mammogram of the sample,and the other was used for presentation of each corresponding IW- or AW-processedversion of the mammogram The two mammograms (original plus IW-processed orAW-processed) were simultaneously presented to radiologists The evaluation studywas performed utilizing a medical-image visualization software tool developed inour department [74, 75] The sample (original-plus-IW-processed images as well asoriginal-plus-AW-processed images) was presented to two experienced, qualifiedradiologists specialized in mammography in a different, random order The radiol-ogists were asked to perform three tasks First, they rated their interpretation of theabsence or presence of a MC cluster in the mammographic image (detection task)

using a five-point rating (R) scale: 1 = definite presence of calcification clusters, 2

= probable presence, 3 = cannot determine, 4 = probable absence, and 5 = definiteabsence Second, in the case of the presence of a cluster (a rating 1 or 2 in thedetection task), they were asked to assess its morphology, according to BIRADS

a Density: 3 = heterogeneously dense breast; 4 = extremely dense breast.

b Morphology: 1 = punctuate; 2 = pleomorphic (granular); 3 = amorphous; 4 = fine linear branching (casting).

c Pathology: B = benign; M = malignant.