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

6

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 2 j ( x )

(6.1)

where ψ 2 j ( x ) = 2 − 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) = 1
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
2

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

0.1

−0.2

0.05

−0.4

0

−0.6

−0.05
−0.1
−2 −1.5 −1 −0.5 0 0.5
(a)

1

1.5

2

−0.8
−2 −1.5 −1 −0.5 0 0.5
(b)

1

1.5

2

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 / 4 
 sin(ω / 4) 
θˆ (ω ) = 
 ω / 4 

2 n +2

(6.7)

2 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
=2
 2
W2 j ( x, y ) 

 f ∗ ψ 1 j ( x, y ) 
j
2
=2


2
 f ∗ ψ 2 j ( x, y ) 

Copyright 2005 by Taylor & Francis Group, LLC

∂
 ∂x

∂
 ∂y


 f ∗ θ j ( x, y )  
2


j
 = 2 ⋅ ∇( f ∗ θ2 j )( x, y ) (6.9)

 f ∗ θ j ( x, y ) 
2





2089_book.fm copy Page 232 Wednesday, May 18, 2005 3:32 PM

232

Medical Image Analysis

Decomposition

Reconstruction
1

f (m, n) =
S0(m, n)

W 1(m, n)

G(ωx)

K(ω x) L(ω y)

2
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)
+

1

W 2(m, n)
K(2ω x)L(2ω y)
2
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 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 Hj(ω), Gj(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

(

)

M 2 j (m, n ) =

2

W21j (m, n ) + W22j (m, n )

2

 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
1
2
3

—
—
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 235 Wednesday, May 18, 2005 3:32 PM

Locally Adaptive Wavelet Contrast Enhancement

235

A simpler denoising method, widely used in signal and image processing, is
wavelet shrinkage [71]. This method consists of comparing wavelet coefficients
against a threshold that distinguishes signal coefficients from noise coefficients. This
approach is justified by the decorrelation and energy-compaction properties of the

wavelet transform. Signal (or image) energy in the wavelet domain is mostly concentrated in a few large coefficients. Therefore, coefficients below a threshold are
attributed to noise and are set to zero. Coefficients above the threshold are either
kept unmodified (hard-thresholding) or modified by subtracting the threshold (softthresholding). Using the RDWT as a basis for wavelet shrinkage is beneficial because
thresholding in a shift-invariant transform outperforms thresholding in an orthogonal
transform by reducing artifacts, such as pseudo-Gibbs phenomena [72]. Thresholding
is applied on gradient-magnitude values to avoid orientation distortions [50]. Softthresholding can be mathematically described by Equation 6.11
 M (m, n ) − Ts , if M s (m, n ) > Ts
M sd (m, n ) =  s
0,
otherwise


(6.11)

where Msd (m,n) is the denoised gradient value and Ts 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 wavelet
coefficients. Hard-thresholding can be mathematically described as follows
 M (m, n ), if M s (m, n ) > Ts
M sd (m, n ) =  s
0,
otherwise


(6.12)

where Msd (m,n) is the denoised gradient value and Ts is the threshold at scale s,
again specified at a percentile value of the cumulative histogram of the gradientmagnitude subimage.
The soft- and hard-thresholding functions are graphically displayed in Figure
6.4. Soft-thresholding has the advantage that the transformation function is continuous 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 varying
image 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 to
preserve signal details. In this work, a spatially adaptive thresholding strategy is
proposed. Specifically, soft-thresholding using a local threshold is applied on wavelet
Copyright 2005 by Taylor & Francis Group, LLC


2089_book.fm copy Page 236 Wednesday, May 18, 2005 3:32 PM

Output gradient magnitude

Medical Image Analysis

Output gradient magnitude

236

x −T

x

T Input gradient magnitude (x)

T Input gradient magnitude (x)

(b)

(a)

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

coefficient magnitudes. The threshold is calculated at each (dyadic) scale and position by applying a local window and using the formula
Ts (m, n ) = σ 2N ,s / σ M ,s (m, n )

(6.13)

where σN,s is noise standard deviation at scale s, and σM,s (m,n) is the signal standard
deviation at scale s, position (m,n). This formula has been proposed by Chang et al.
[55] with the assumption that wavelet coefficients can be modeled as generalized
Gaussian distribution random variables and the noise as Gaussian distribution.
Local standard deviation of the signal is calculated from a local window, centered
at each coefficient position
1
σ M ,s (m, n ) = 2
N

L

L

∑ ∑ M (m, n)
s

2

− σ 2N ,s

(6.14)

i =− L j =− L

where N = 2L + 1 is the window size, and Ms(m,n) is the gradient magnitude at
position (m,n). The term σ2N,s is subtracted because gradient magnitudes are noisy,
and the noise is considered independent of the signal. Noise standard deviation σN,s
is estimated from the mammogram background area. An automatic procedure is
used to define a background area, used for noise estimation. Specifically, a rectangular window with size equal to the 20% of the mammogram width scans the image,
and two metrics are measured: mean value of gradient magnitudes and the 98%
percentile of gradient magnitudes. At the position where the two metrics are minimized, the area under the window defines the background area. Use of the 100%
percentile (maximum) is avoided to exclude bright pixels caused by artifacts. This
background identification process has been accurate in all cases tested.
Copyright 2005 by Taylor & Francis Group, LLC


2089_book.fm copy Page 237 Wednesday, May 18, 2005 3:32 PM

Locally Adaptive Wavelet Contrast Enhancement

237

After background identification, noise standard deviation at each dyadic scale
(σN,s) is calculated by applying the transform on a background area of the mammogram and measuring the standard deviation of gradient magnitudes. Denoised gradient magnitudes Msd(m,n) are given by soft-thresholding using the local threshold
 M (m, n ) − Ts (m, n ), if M s (m, n ) > Ts (m, n )
M sd (m, n ) =  s
0,
otherwise



(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 WAVELET CONTRAST ENHANCEMENT
6.3.4.1 Global Wavelet Mapping
In the framework of the RDWT, the main approach for contrast enhancement is
linear or nonlinear mapping of wavelet coefficients [50]. This approach can be
justified by the nature of wavelet coefficients. The wavelet used in the RDWT is the
first derivative of a smoothing function. Consequently, wavelet coefficients are proportional to image-intensity variations and are related to local contrast. Evidence of
the relationship between contrast and wavelet coefficients for mammographic images
has been provided in a recent work [73]. Using the RDWT as a basis for contrast
enhancement is beneficial because of the shift invariance and lack of aliasing characteristics of the wavelet transform. Because contrast enhancement should be perpendicular to edge contours to enhance the contrast of structures, subsequent processing is applied on the multiscale magnitude values.
Contrast enhancement by linear enhancement consists of linear stretching of the
multiscale gradients. This ensures that all regions of the image are enhanced in the
same way. It can be mathematically expressed by
M se (m, n ) = ks M s (m, n )

(6.16)

where Mse (m,n) is the enhanced gradient-magnitude value at position (m,n)-scale s,
and ks > 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 shown
easily in the one-dimensional case. If we denote the frequency channel responses
of the wavelet transform Cm(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
Copyright 2005 by Taylor & Francis Group, LLC


2089_book.fm copy Page 238 Wednesday, May 18, 2005 3:32 PM

238

Medical Image Analysis

N −1

U (ω ) =

∑

N

kC m (ω ) + C N (ω ) = k

m =0

∑C

m

(ω ) − ( k − 1)C N (ω ) =

m =0

(6.17)

k − ( k − 1)C N (ω ) = 1 + ( k − 1)[1 − C N (ω )]
The spatial response of the system is thus
y (m ) = x (m ) + ( k − 1)  x (m ) − ( x ∗ C N )(m ) 

(6.18)

CN(ω) is a low-pass filter, and thus [x(m) − (x × CN)(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 the
dynamic range available because it emphasizes high-contrast and low-contrast edges
with the same gain. For example, a single high-contrast MC in a mammogram,
enhanced by a linear enhancement, will cause gross rescaling within the availably
dynamic range of the display. The subtle features contained in the processed mammogram will have low contrast, and their detection will be difficult.
To avoid the previously mentioned drawback of linear enhancement and enhance
the visibility of low-contrast regions, the mapping function must avoid overenhancement of the large gradient-magnitude values. A nonlinear mapping function that is
used to emphasize enhancement of low-contrast features has the following form

M se (n, m) = 


ks M s (n, m),
if M s (n, m) ≤ Ts
M s (n, m) + (ks -1)Ts , if M s (n, m) ≥ Ts

(6.19)

where Mse (n,m) is the “enhanced” magnitude gradient value at position (m,n)-scale
s, ks > 1 is a gain parameter, and Ts is a low-contrast threshold. By selecting different
gain parameters at each dyadic scale, the contrast of specific-sized features can be
selectively 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 subimage and (b) as a percentile value of the cumulative histogram of the gradientmagnitude subimage. The linear and nonlinear contrast enhancement mapping functions 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 redundant
wavelet 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 in
the same way. When the processed image is rescaled to fit in the available display
dynamic range, weak signal features with low contrast are suppressed. For this
Copyright 2005 by Taylor & Francis Group, LLC


2089_book.fm copy Page 239 Wednesday, May 18, 2005 3:32 PM

Output gradient magnitude

Output gradient magnitude

Locally Adaptive Wavelet Contrast Enhancement

kx

239

x + (k − 1)T

kx

T Input gradient magnitude (x)
(a)

T

Input gradient magnitude (x)
(b)

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

reason, nonlinear enhancement was introduced. It uses a nonlinear mapping function
that 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 overenhancement of high-contrast features. However, a drawback of the method is that the
parameters of the transformation function at each scale are global. Because mammograms contain regions characterized by different local energy of wavelet coefficients, 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 mapping
function 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 defined
linear mapping function, similar to the LRM method [36]. The enhancement process
of LRM has been modified and is applied on gradient-magnitude values. The
enhanced gradient-magnitude coefficient values are given by
M se (m, n ) = GL ,s (m, n ) ⋅ M s (m, n )

(6.20)

The limited adaptive gain GL,s(m,n) is derived by
G (m, n ) ≡ M 1,max / M s ,max (m, n ), if
GL ,s (m, n ) =  s
L, otherwise


Gs (m, n ) < L

(6.21)

where M1,max is the maximum value of the magnitude subband image at scale 1,
Ms,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
Copyright 2005 by Taylor & Francis Group, LLC


2089_book.fm copy Page 240 Wednesday, May 18, 2005 3:32 PM

240

Medical Image Analysis

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 problem
inherent with the LRM method. Specifically, if the unclipped maximum values are
used, isolated bright points in the magnitude subband image result in a significantly
decreased gain Gs(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 GL,s(m,n) forces local maxima to become equal or close to a
target global maximum. Therefore, the local enhancement process stretches gradient
magnitudes 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 processed
images, emphasizing local details.
To speed up the calculation of local maxima, the interpolation procedure followed by the LRM method is used [36]. This procedure involves two passes through
the image. In the first pass, the maximum gradient-magnitude values are found for
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 interpolating the maximum values assigned at the four surrounding grid points. The
interpolation procedure results in local gain varying smoothly across the image,
therefore it is more preferable than direct calculation of local maximum values at
each position. Calculation time is significantly reduced, even if a large window size
is used. The method is not sensitive to the window size. For the results of this 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
g

M se (m, n ) =  M s (m, n ) / M s ,max (m, n )  GL ,s (m, n ) M s ,max (m, n )

(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 linear
mapping. The magnitude subband image at scale 2 is shown. It can be observed that
the adaptive process emphasizes more the low-contrast edge information while
avoiding overenhancement of high-contrast edge information.
To obtain the processed image after denoising and contrast enhancement in the
wavelet domain, two more steps are needed: first, polar-to-Cartesian transformation
to calculate the horizontal and vertical wavelet coefficients from the magnitude and
phase of the gradient vector, and second, reconstruction (inverse two-dimensional
DWT) from the modified wavelet coefficients.
Copyright 2005 by Taylor & Francis Group, LLC


2089_book.fm copy Page 241 Wednesday, May 18, 2005 3:32 PM

Locally Adaptive Wavelet Contrast Enhancement

(a)

(b)

241

(c)

FIGURE 6.6 Example of mapping of gradient-magnitude coefficients at scale 2 corresponding to a mammographic region. (a) Original gradient-magnitude coefficients, (b) result of
global mapping, (c) result of adaptive mapping.

6.3.5 IMPLEMENTATION
The method was implemented in Visual C++ 6.0 and was integrated in a previously
developed medical-image visualization tool [74, 75]. Redundant wavelet transform

routines have been taken from the C software package “Wave2” [76]. Software
implementation 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 of
the method. In addition, the capability of the tool to execute scripts written in the
standard Windows VBscript language enabled batch processing and measurements.
The methods to which the proposed method is compared are also implemented and
integrated 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) DDSM
image is 96 sec, and the average computation time for the image sample was 122
sec. The computational cost of adaptive modification of wavelet coefficients accounts
for 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 to
RAM size limitation.
Method computation time has been kept as low as possible by exploiting interpolation methods and the speed offered by the C++ language. In addition, to overcome virtual-memory inefficiency for limited-RAM configurations, a memory manager was used to swap wavelet coefficient images not currently processed to hard
disk. Further reductions of processing time could be accomplished by using the
lifting scheme to compute the RDWT [77], by exploiting techniques such as parallel
processing and compiling optimization, and by employing faster computer systems.

6.3.6 TEST IMAGE DEMONSTRATION

AND

QUANTITATIVE EVALUATION

To demonstrate the effectiveness of the denoising and enhancement processes a
digital phantom was created. It contains five circular details, with contrasts ranging
Copyright 2005 by Taylor & Francis Group, LLC

2089_book.fm copy Page 242 Wednesday, May 18, 2005 3:32 PM

242

Medical Image Analysis

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

Original (noisy) scan line profile

Global denoising

Global nonlinear
enhancement

2D DWT
Gradient coefficients

Reconstruction after inverse
DWT

(a)

(b)

Reconstruction after
inverse DWT

(c)

FIGURE 6.8 Digital phantom scan line profiles for global wavelet processing. (a) Original,
(b) global denoising, and (c) global nonlinear enhancement.

from 1 to 10%, added on a uniform background. Gaussian noise with normalized
standard 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 generate
profiles of signal and multiscale gradient magnitudes.
Figure 6.8 and Figure 6.9 show the original and processed profiles for global
nonlinear and adaptive wavelet enhancement, respectively. The corresponding gradient-magnitude values are also shown to demonstrate the effect of processing on
magnitude wavelet coefficients. It can be observed that adaptive processing preserves
the sharpness of the object edges and also significantly enhances the contrast of the
lowest-contrast object.
The aim of the quantitative evaluation is to measure improvement of contrast
for 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 is
required. An approach to overcome this difficulty is to use simulated calcifications
and lesions, enabling for quantitative assessment of image-enhancement algorithms.
This approach allows also varying quantitatively the characteristics of input features
and thus analyzing the behavior of the enhancement. Mathematical models of MCs
and masses have been previously used to construct simulated lesions [49, 79]. The
simulated lesions are blended in normal mammograms, and a contrast improvement
index is derived for each type of lesion between original and processed images.
In this study, we follow a similar approach to quantify contrast enhancement of
MCs. A set of phantoms of simulated MC clusters was constructed, based on the
Copyright 2005 by Taylor & Francis Group, LLC


2089_book.fm copy Page 243 Wednesday, May 18, 2005 3:32 PM

Locally Adaptive Wavelet Contrast Enhancement

Original (noisy) scan line profile

Adaptive denoising

243

Adaptive enhancement

2D DWT
Gradient coefficients

Reconstruction after inverse
DWT

Reconstruction after inverse
DWT

(b)

(c)

(a)

FIGURE 6.9 Digital phantom scan line profiles for adaptive wavelet processing. (a) Original,
(b) adaptive denoising, and (c) adaptive enhancement.

assumption of Strickland and Hahn [80] that MCs can be modeled as two-dimensional Gaussian functions. The input parameters for each cluster were the size and

amplitude of MCs, while positions of individual MCs were randomly determined
and kept fixed. In this study, we used three MC sizes (400, 600, and 800 µm) and
ten amplitudes (ranging linearly between 10 and 400 gray-level values). Simulated
clusters were subsequently blended into two normal mammograms characterized by
density 3 (heterogeneously dense breast) and 4 (extremely dense breast), according
to Breast Imaging Reporting and Data System (BIRADS) lexicon. The resulting
images were processed with IW and AW methods using the same set of parameters
for 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. For
contrast measurements, we adopted the optical definition of contrast introduced by
Morrow et al. [45]. The contrast C of an object is defined as
C=

f −b
f +b

(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 cluster
contrast vs. original cluster contrast (size 600 µm). It can be observed that both
methods produce MC contrast enhancement. However, the AW method is more
effective, especially in the case of the dense breast parenchyma. Similar results were
obtained for the other MC cluster sizes studied.
Figure 6.12a and Figure 6.13a present two examples of original ROIs containing
simulated clusters superimposed on heterogeneously dense parenchyma and dense
parenchyma, respectively. Figure 6.12b, Figure 6.13b and Figure 6.12c, Figure 6.13c
present the resulting ROIs after IW and AW processing, respectively.
Copyright 2005 by Taylor & Francis Group, LLC

2089_book.fm copy Page 244 Wednesday, May 18, 2005 3:32 PM

244

Medical Image Analysis

16
14

Output contrast (%)

12
10
AW

8

IW
6
4
2
0
0

0.5

1

1.5
2
Input contrast (%)

2.5

3

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.

16
14

Output contrast (%)

12
10
AW

8

IW
6
4
2
0
0

0.5

1

1.5
2
Input contrast (%)

2.5

3

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
AW enhancement methods.
Copyright 2005 by Taylor & Francis Group, LLC


2089_book.fm copy Page 245 Wednesday, May 18, 2005 3:32 PM

Locally Adaptive Wavelet Contrast Enhancement

(a)

(b)

245

(c)

FIGURE 6.12 ROIs with simulated MCs (600-µm size, 230 gray-level amplitude) on heterogeneously dense parenchyma. (a) Original region, (b) result of processing with IW enhancement method, and (c) result of processing with AW enhancement method.

(a)

(b)

(c)

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.

6.4 OBSERVER PERFORMANCE EVALUATION
The objective of the observer performance evaluation study is to validate the effectiveness of spatially AW enhancement and manual IW methods with respect to
detection, morphology characterization, and pathology classification of MC clusters
on dense breast parenchyma. IW was selected as a representative of one of the most
effective contrast-enhancement methods.

6.4.1 CASE SAMPLE
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 mammographic images, each one containing a cluster of MC (29 malignant and 14 benign),
and 43 images without abnormalities (normal) originating from the DDSM mammographic database [64]. Concerning MC cluster morphology, from 29 malignant
and 14 benign clusters, 2 and 4 are punctuate, 24 and 5 are pleomorphic (granular),
Copyright 2005 by Taylor & Francis Group, LLC


2089_book.fm copy Page 246 Wednesday, May 18, 2005 3:32 PM

246

Medical Image Analysis

TABLE 6.2
Volume, Density, Morphology, and Pathology of Each Microcalcification
Cluster for the 86 Mammographic Images (43 abnormal and 43 normal)
Images with Cluster (abnormal)
A/A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23

24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41

Volume
Cancer 01
Cancer 01
Cancer 01
Cancer 06
Cancer 06
Cancer 06
Cancer 06
Cancer 06
Cancer 06
Cancer 07

Cancer 07
Cancer 07
Cancer 08
Cancer 08
Cancer 08
Cancer 12
Cancer 12
Cancer 12
Cancer 12
Cancer 14
Cancer 14
Cancer 14
Cancer 14
Cancer 14
Cancer 15
Cancer 15
Cancer 15
Cancer 15
Cancer 15
Cancer 01
Benign 04
Benign 04
Benign 04
Benign 04
Benign 06
Benign 06
Benign 06
Benign 06
Benign 06
Benign 06

Benign 06

Mammogram
B-3005_1.LCC
B-3009_1.RCC
B-3009_1.RMLO
A-1113_1.RCC
A-1113_1.RMLO
A-1152_1.LCC
A-1152_1.LMLO
A-1185_1.RCC
A-1188_1.RMLO
A-1220_1.RCC
A-1238_1.LCC
A-1238_1.LMLO
A-1508_1.RCC
A-1517_1.RCC
A-1517_1.RMLO
D-4110_1.RCC
D-4110_1.RMLO
D-4158_1.LCC
D-4158_1.LMLO
A-1897_1.LCC
A-1897_1.LMLO
A-1905_1.LCC
A-1905_1.LMLO
A-1930_1.LMLO
B-3002_1.LCC
B-3440_1.RCC
B-3440_1.RMLO

B-3509_1.LCC
B-3510_1.LCC
B-3030_1.RMLO
B-3120_1.RCC
B-3120_1.RMLO
B-3363_1.RCC
C-300_1.LCC
B-3418_1.LCC
B-3418_1.LMLO
B-3419_1.RCC
B-3422_1.RCC
B-3423_1.LCC
B-3425_1.LCC
B-3425_1.LMLO

Copyright 2005 by Taylor & Francis Group, LLC

Images without Cluster (normal)

D a M b P c A/A
3
3
3
4
4
4
4
4
4
4

4
4
3
4
4
3
3
4
4
4
4
3
3
4
4
4
4
3
3
3
4
4
4
3
3
3
4
3
3
4

4

3
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
2
2
2
2
2
2
2
2
1
1
2

2
2
1
1
2
2
3
3
2
2
1
4
4

M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M

M
M
M
M
M
M
M
M
M
M
M
M
M
B
B
B
B
B
B
B
B
B
B
B
B

1
2
3
4

5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34

35
36
37
38
39
40
41

Volume
Cancer 01
Cancer 01
Cancer 01
Cancer 06
Cancer 06
Cancer 06
Cancer 06
Cancer 06
Cancer 07
Cancer 07
Cancer 08
Cancer 08
Cancer 08
Cancer 12
Cancer 12
Cancer 12
Cancer 14
Cancer 14
Cancer 14
Cancer 14
Cancer 15

Cancer 15
Cancer 15
Benign 04
Benign 04
Benign 04
Benign 04
Benign 06
Benign 06
Benign 06
Benign 06
Benign 06
Benign 06
Benign 06
Benign 06
Normal 07
Normal 07
Normal 07
Normal 07
Normal 09
Normal 09

Mammogram
B-3005_1.RCC
B-3009_1.LCC
B-3009_1.LMLO
A-1113_1.LCC
A-1113_1.LMLO
A-1152_1.RMLO
A-1185_1.LMLO
A-1188_1.LMLO

A-1220_1.LCC
A-1238_1.RCC
A-1508_1.LCC
A-1517_1.LCC
A-1517_1.LMLO
D-4110_1.LCC
D-4110_1.LMLO
D-4158_1.RMLO
A-1897_1.RCC
A-1897_1.RMLO
A-1905_1.RMLO
A-1930_1.RMLO
B-3509_1.RCC
B-3440_1.LCC
B-3440_1.LMLO
B-3120_1.LCC
B-3120_1.LMLO
B-3363_1.LCC
C-300_1.RCC
B-3418_1.RCC
B-3418_1.RMLO
B-3419_1.LCC
B-3422_1.LCC
B-3423_1.RCC
B-3425_1.RCC
B-3425_1.RMLO
B-3426_1.RCC
D-4506_1.RCC
D-4522_1.LCC
D-4582_1.RCC

D-4591_1.LCC
B-3606_1.RCC
B-3614_1.LMLO

Da
3
3
3
4
4
4
4
4
4
4
3
4
4
3
3
4
4
4
3
4
3
4
4
4
4

4
3
3
3
4
3
3
4
4
3
4
4
4
4
4
4


2089_book.fm copy Page 247 Wednesday, May 18, 2005 3:32 PM

Locally Adaptive Wavelet Contrast Enhancement

247

TABLE 6.2
Volume, Density, Morphology, and Pathology of Each Microcalcification
Cluster for the 86 Mammographic Images (43 abnormal and 43 normal)
Images with Cluster (abnormal)
A/A
42

43

Volume

Mammogram

Benign 06
Benign 06

B-3426_1.LCC
C-407_1.RMLO

Images without Cluster (normal)

D a M b P c A/A
3
3

1
3

B
B

42
43

Volume
Normal 09
Normal 09

Mammogram
B-3617_1.RMLO
B-3653_1.RMLO

Da
4
4

a

Density: 3 = heterogeneously dense breast; 4 = extremely dense breast.
Morphology: 1 = punctuate; 2 = pleomorphic (granular); 3 = amorphous; 4 = fine linear branching
(casting).
c Pathology: B = benign; M = malignant.
b

3 and 3 are amorphous, as well as 0 and 2 are fine linear branching (casting),
respectively, according to DDSM database. Mammographic images selected correspond 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 were
subsampled 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 MC
clusters and normal ones), as well as the MC cluster morphology and pathology
(malignant or benign). The entire sample (86 mammographic images) has been
processed with two image contrast-enhancement methods, the manual IW and the
AW methods.

6.4.2 OBSERVER PERFORMANCE
Two general-purpose display LCD monitors (FlexScan L985EX, EIZO NANAO

Corp., 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-processed
version of the mammogram. The two mammograms (original plus IW-processed or
AW-processed) were simultaneously presented to radiologists. The evaluation study
was performed utilizing a medical-image visualization software tool developed in
our department [74, 75]. The sample (original-plus-IW-processed images as well as
original-plus-AW-processed images) was presented to two experienced, qualified
radiologists specialized in mammography in a different, random order. The radiologists were asked to perform three tasks. First, they rated their interpretation of the
absence 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 = definite
absence. Second, in the case of the presence of a cluster (a rating 1 or 2 in the
detection task), they were asked to assess its morphology, according to BIRADS
Copyright 2005 by Taylor & Francis Group, LLC


2089_book.fm copy Page 248 Wednesday, May 18, 2005 3:32 PM

248

Medical Image Analysis

lexicon, using one of four categories: 1 = punctate, 2 = pleomorphic (granular), 3
= amorphous, and 4 = fine linear branching (casting). The third task for each
radiologist was to classify each MC cluster with respect to pathology, benign or
malignant (classification task), according to BIRADS lexicon, using again five levels
(L) of confidence: level 1, definitely benign; level 2, probably benign, suggest shortinterval follow-up; level 3, cannot determine, additional diagnostic workup required;
level 4, probably malignant, biopsy should be considered; level 5, definitely malignant, biopsy is necessary.
Radiologists were informed of the percentages (half images with clusters and

half normal images) of the sample. Missed detections, namely cases with calcification clusters rated as 5, 4, or 3 in the detection process, were not classified in the
classification process. During reading, the room illumination was dimmed and kept
constant, while reading time and radiologist-monitor distance were not restricted.

6.4.3 STATISTICAL ANALYSIS
In this study, three (null) hypotheses were tested:
1. There is no difference between the method based on original-plus-IWprocessed images and the method based on original-plus-AW-processed
images with respect to MC detection (presence or absence) task.
2. There is no difference between the two above-mentioned methods with
respect to MC morphology task.
3. There is no difference between the two methods with respect to MC
pathology-classification (benign or malignant) task.
Two statistical analyses were used. One was based on a nonparametric statistical
test (Wilcoxon signed ranks test), and the other was based on ROC curves. Both of
them are briefly described in the following subsections.
6.4.3.1 Wilcoxon Signed Ranks Test
The Wilcoxon signed ranks test [81] was selected for the analysis of radiologists’
responses because the data can be transformed as difference responses/scores from
two related subsamples. (One subsample consists of the original-plus-IW-processed
images and the other of original-plus-AW-processed images). For each case of the
sample (abnormal or normal original mammogram), two responses are provided,
one response from the original-plus-IW-processed image (RIW), and one from the
original-plus-AW-processed image (RAW). Then the difference in responses is given
by D = RIW − RAW for each case (paired data). These differences indicate which
member of a pair is “greater than” (i.e., the sign of the difference between any pair)
and also can be ranked in order of absolute size. In the statistical analysis, pairs
with D = 0 are not taken into account. This test is used for statistical analysis of
radiologists’ responses in MC clusters detection task as well as pathology classification task, because these two tasks employ two related subsamples and yield
difference scores that can be ranked in order of absolute magnitude.
Copyright 2005 by Taylor & Francis Group, LLC

2089_book.fm copy Page 249 Wednesday, May 18, 2005 3:32 PM

Locally Adaptive Wavelet Contrast Enhancement

249

6.4.3.2 ROC Analysis
ROC analysis is a statistical method used in evaluation of medical images [82–84].
This method analyzes observer responses usually obtained from a five- or six-point
rating scale (or confidence levels). There are several free software packages available
for the analysis of ROC data [85, 86]. In this study, concerning the MC clusters
detection task, the radiologists’ responses were analyzed using the ROCKIT program
(Metz CE, University of Chicago, IL) [87]. A conventional binormal ROC curve
was individually fitted to the scores of each radiologist with a maximum-likelihood
procedure, and the area under the estimated ROC curve (Az), standard error (SE),
as well as the asymmetric 95% confidence interval (CI) was calculated [88, 89].
Differences in Az value, both for the responses of each radiologist independently
and combining the responses of the two radiologists (pooled data), were statistically
analyzed using two-tailed student’s t-test. Derived values of p < 0.05 indicate
superiority of one contrast-enhancement method against the other, whereas values
of p > 0.05 indicate no difference between the two methods.

6.4.4 RESULTS
6.4.4.1 Detection Task
Table 6.3 shows the number of cases per category of difference with respect to the
rating (R) between the IW and the AW methods (D = RIW − RAW) for the MC cluster
detection task. In this table, we observe that more differences are zero (D = 0), and
the number of “positive” differences (D > 0) is almost equal to the number of

“negative” differences (D < 0) for both abnormal and normal mammographic images
for each of the two radiologists.
More analytically, the distribution of the differences between the two methods for
abnormal and normal images for both radiologists is provided in Table 6.4. Concerning abnormal images, the frequency of positive differences (D > 0) represents
the number of images where the AW method is superior to the IW method. The
frequency of negative differences (D < 0) represents the number of images where

TABLE 6.3
Frequency of Abnormal and Normal Images with Respect to Differences
in Ratings (D = RIW − RAW) between the Original-Plus-IW and the
Original-Plus-AW Methods in the Microcalcification-Cluster Detection
Task for Two Radiologists
Radiologist A
D = RIW – RAW
D>0
D=0
D<0
Total

Radiologist B

Abnormal

Normal

Total

Abnormal

Normal

Total

6
31
6
43

9
22
12
43

15
53
18
86

7
29
7
43

7
27
9
43

14
56

16
86

Copyright 2005 by Taylor & Francis Group, LLC