73
CHAPTER 5
DIRECTIONLET BASED ENHANCEMENT METHOD
5.1 INTRODUCTION
Early detection of breast cancer is important and mammography is
the primary imaging technique for the detection and diagnosis of breast
lesion. The primary goal of mammography screening is to detect small, non-
palpable cancers in its early stage. Due to poor visibility, low contrast and
noisy nature of mammograms, it is difficult to interpret the pathological
changes of the breast. Thus, enhancing the contrast of the images becomes
very important while screening mammograms.
Contrast enhancement is an essential technical aid in applications
where human visual perception remains the primary approach to extract
relevant information from images. On the other hand, the contrast between
malignant tissue and normal dense tissue may below the threshold of human
perception (Ji 1996). Emphasis at this stage is to provide superior image for
screening purpose. In the past, several contrast enhancement methods have
been proposed. Although, varieties of contrast enhancement algorithms are
present in the literature, development of methods dealing with image
consisting of fine details such as mammogram is still a research issue.
The main contribution of this work is that ST uses multidirection
multiscale anisotropic features provided by DT. Using these anisotropic
74
features, the developed algorithm sharpens the mammogram images in
selective regions, and controls the noise effect using scale multiplication.
The sharpened images are given as the input to AHE algorithms to
avoid the flat handling of textured mammogram thereby improves their
performance. The enhanced images are applied with simple threshold to
detect the microcalcification in mammogram images. While sharpening the
image, the noise also enhanced (i.e.) the invisible noise in the image is
amplified, thus distortions in areas that are looked smooth in the original
images. Depending upon the local image variance, this algorithm
discriminates the homogeneous and non-homogeneous regions and applies the
enhancement process selectively. In addition, this method enhances the edges
moderately and avoids unnatural pronounced edges. Being multidirectional,
anisotropic characteristics of this algorithm, it preserves the local features
than commonly used enhancement algorithms.
5.2 MULTISCALE AND MULTIDIRECTION EDGE
EXTRACTION
The linear structures such as edges and textures are important
features in the mammogram images. Image textures have sharp intensity
variations that are often not considered as edges. The discrimination between
edges and textures depends on the scale of analysis. While enhancing, suitable
importance must be given to both objects and textures present in mammogram
images. This motivates researchers to detect image variations at different
scales and directions. Wavelet is an important tool to analyze scale space
representation of images. This section explains the extraction of scale space
features using isotropic wavelets and anisotropic directionlets.
75
5.2.1 Wavelet filters and Edge Extraction
The sharpening enhancement intensifies the higher frequency (HF)
components that represent the image edges. The Wavelet coefficients provide
the explicit information on the location and the type of edges in the form of
signal singularities. The decomposition coefficients of a signal in a basis
highlight on localized signal structures. Edge Detection by canny operator
detects points of sharp variation in an image f(x ,x ) by calculating the
modulus of its gradient vector. The partial derivative of f in the = (x , x )
plane is calculated as an inner product with the gradient vector. A multiscale
version of this edge detector is implemented by smoothing the surface with a
convolution kernel (x) that is dilated. This is computed with two wavelets
that are the partial derivatives of (x). and . For1 <
, denote for different orientation with scale . Edges
and textures synthesized and discriminated with oriented two dimensional
wavelet transforms. The wavelet transform of f(x , x ) at = (u , u ) is
W f( , s) = f( ) ) = f ( ) ( ) (5.1)
The equation (5.1) gives direct insight that various oriented wavelet functions
( ) convolved with image f( ) provide the multiscale and multidirectional
edge as well as texture information. However, they have limited directions
and fail to capture anisotropic features that are important in image processing
applications.
5.2.2 Directionlet Filters and Edge Extraction
Isotropy and anisotropy are the two types of basis functions to
represent the simple image discontinuity along a smooth curve. Isotropic basis
functions generate a large number of significant coefficients around the
76
discontinuity Figure 5.1. Anisotropic basis functions trace the discontinuity
line and produce just few significant coefficients. Although, wavelets
efficiently represent the point singularities (i.e.) edges, but fails to achieve the
curve like linear structures. In addition, discontinuity curves present in the
images are highly anisotropic and they are characterized by a geometrical
coherence. These features are not properly captured by the standard WT that
uses isotropic basis functions and they fail to represent the edges and contours
effectively. On the other hand anisotropic wavelets (i.e.) contourlets,
directionlet etc, are capable to overcome this insufficiency as in Figure 5.1.
Anisotropic Basis Isotropic Basis
Figure 5.1 Two types of basis function representing ‘curve’ like feature
Anisotropic skewed and elongated basis functions in various scales
used in DT efficiently represent the edges. The seven Haar based DT basis
functions specified in (Vladan 2006, 2009) are considered in this method are
shown in Figure 5.2. In this scheme, these Haar DT functions are convolved
with the mammogram images to obtain the anisotropic features. These DT
functions not only provide point singularities but also collect the linked
correlations among point singularities. In addition to anisotropy, DT has
multiscale and multidirectional properties that are helpful in this sharpening
enhancement process of mammogram images. The directionality provides
variety of directions, much more than the few directions offered by separable
wavelets. Since anisotropic basis elements use variety of elongated shapes
with different aspect ratios, they capture smooth contours in images. It is
straightforward to express DT equation as
77
DT f(u, s) = f( ) ) = f ( ) ( ) (5.2)
where ( ) are the directionlets with directions k=1, 2, 3…etc. and scales
s = 0, 1, 2, 3 …etc. From the equation (5.2), it is easy to understand that the
image f( ) convolved with DT ( ) kernels results directional responses of
the image.
Figure 5.2 Seven First level Directionlet – skewed and elongatedbasis functions for ‘Haar’
Due to multidirection and multiscale characteristics, the new DT
ST provides effective anisotropic edge structures that are helpful in the
enhancement algorithms. The significance of the image geometrical features
increased with the number of scales and directions as illustrated in Figure 5.3.
In the Figure 5.3(a), the average information increases while the number of
directions and scales increases. In Figure 5.3(b), the mean square error
decreases while the number of directions and scales increases.
78
(a) (b)
Figure 5.3 Illustration of the quantity improvement of the anisotropicgeometrical edge features in multiple scales and multipleorientations
5.3 MAMMOGRAM ENHANCEMENT METHOD
Enhancing the sharpness by accentuating the edges may thus
contribute to a more pleasing subjective appearance of an image. The
recognition of shapes or objects in an image starts from identification of sharp
edges and their poor presentations are felt as lack of details. The degrees of
low sharpness around the borders are formulated as slowly varying intensities
in the spatial domain. In the frequency domain, it is a low distribution of
missing HF components.
This developed method overcomes the noise influences in smooth
regions by sharpening the image where more edge information is present. The
anisotropic features are obtained by DT functions that are convolved with
image is to be enhanced. The directional filter responses of various scales are
obtained by applying dilated basis functions. The oriented and scaled
79
anisotropic responses from the convolution results need to be combined to get
complete HF components. This is performed by taking either modulus
maxima or maximum of the absolute values or sum of all oriented responses.
This developed method formulated a new approach of ST to focus on
selective enhancement at object boundaries, noise suppression in smooth area
while sharpening. The enhanced image (u, v) from various scales ‘a’ and
directions of DT is defined as
f(u, v) =f(u, v) y (u, v)in(f (u, v)
f(u, v)otherwise (5.3)
wherey (u, v) = DT (u, v) . f(u, v) is the image to be
enhanced, is the parameter that can be used to determine the fraction of
y(u, v) that is to be added with original for sharpening process. and are
local standard deviation of oriented response images and original image
respectively. f (u, v) and f(u, v) are the smoothed image and original image.
The parameter‘ ’ depends upon the noise present and can be fixed with
respect to‘ ’. Here noise component refers to image noise that included in
capturing process itself. f (u, v) is the low pass subband of DT structure. The
new method tackles three different situations effectively. The min(
guarantees that the sharpening will process only on the high gray variance
image area (i.e.) where the edge information is present. The has the value
between 0 and 1 and if > 1, the edge will predominate in enhancement
process and results in unnatural edges. Thus the value of is important
and = 0, the enhanced image equal to original. fixes the weights for
oriented responses, generally it is related by 1/ , where is the number of
DTs applied. The equation (5.3) splits the image into three regions and
depends upon the enhancement requirements to treat them individually.
80
‘Sharp’, ‘smooth’ and ‘keep as it is’ are the three regions. It is easy to
interpret the term y(u, v) is a weighted HP filter and its addition with
original will act as USM. Since it incorporates the oriented and multiscale
anisotropic edge information, this ST provides objective and subjective
improvement in sharpening enhancement of mammogram images. The
functional Block diagram of new DT ST is shown in Figure 5.4. H (z) and
H (z) denotes Haar scaling and wavelet filter coefficients respectively and
horizontal and vertical denotes direction of convolution operation on 2D
discrete image dataZ (z , z ).
Figure 5.4 Block diagram of DT based Mammogram ImageSharpening Enhancement
Vertical
H0(z1)
Vertical
H1(z1)
MammogramImages
SharpeningEnhanced
MammogramImagesSharpening
Methodequation
(5.3)
H1(z1)
H0(z1)
H1(z1)
H0(z1)
H1(z1)
H0(z1)
Horizontal
Horizontal
H1(z2)
H0(z2)
H1(z2)
H0(z2)
H1(z1)
H0(z1)
Horizontal
Horizontal
Horizontal
81
Stepwise procedure for this method as follows
Step 1: Decompose the mammogram image into various sub bands as
shown figure 5.4, which contains anisotropic features. Anisotropy is
obtained by an unbalanced iteration of transform steps along two
transform directions. The transform is applied more along one than
along the other direction as in Figure 2.3(b).
Step 2: Compute y(u, v) = DT (u, v)
Step 3: Substitute y(u, v) in developed equation (5.3) to get the
enhanced mammogram image f(u, v)
Collecting anisotropic features from the directionlets and assimilate them by
developed equation, equation (5.3) is the novelty of this method of
enhancement.
5.4. RESULTS AND PERFORMANCE COMPARISON
This section presents the experimental results of applying this new
DT ST enhancement of mammogram images. The objective and subjective
results are given. The new enhancement results are compared with NLUSM
(Karen 2011). Twenty-three images are selected from microcalcification
category of MIAS database and used in the tests. The DT is applied on the
images to group the nearby locally correlated coefficients, which signify the
smoothness of the contours and gather the nearby edge features into linear
structures. The DT filter coefficients obtained from the Haar basis functions
are convolved on the images to get corresponding directional responses.
Equation (5.1) is applied on DT coefficients (sub bands) to get the sharpening
enhanced images. This experiments performed with the scalea = 2 , D= 7 ,
82
= 0.2, = 1and = 1/7. Figure 5.5 shows the mammogram images that
are obtained from new algorithm and NLUSM.
Figure 5.5 Sharpening Enhancement of mdb 248 and mdb 256: fromleft to right-Original, New DT ST and USM
The NLUSM is implemented by using optimized parameters as given in
Karen (2011). From the Figure 5.6, it is recognized that DT ST provides more
efficient sharpened edge structure with less noise effect than NLUSM,
because the DT ST method extract the edge information from two-scale
multiplication. The scale multiplication in wavelet domain reduces the noise
effect.
83
Figure 5.6 Sharpening Enhancement enlarged portions: From left toright First Column:Original, Second Column:New DT STand Third Column:NLUSM
84
It is difficult to measure the improvement in images after
enhancement. A processed image is said to be enhanced over the original
image, if it allows the observer to perceive the desirable information better in
that image. In images, the improved perception is difficult to quantify. There
is no universal measure, which can specify both the objective and subjective
validity of the enhancement method. In practice, many definitions of the
contrast measure are used. This evaluation uses Enhancement Measure
(Agaian 2001) (EME) to measure the enhancement and tabulated in Table 1.
It compares the performance of NLUSM and DT ST.
Table 5.1 EME Comparison of DT ST and NLUSM Algorithms
Image DT ST NLUSM Image DT ST NLUSMmdb209(2.88) 5.82 5.29 mdb236(1.99) 4.03 2.12mdb211(1.43) 3.34 1.95 mdb238(1.45) 3.16 1.55mdb213(1.29) 2.38 1.34 mdb239(2.53) 4.35 2.58mdb216(2.00) 3.90 2.85 mdb240(2.23) 4.00 2.53mdb218(2.09) 4.06 2.23 mdb241(1.13) 2.19 1.17mdb219(1.77) 3.45 2.05 mdb245(1.44) 2.78 2.26mdb222(1.90) 3.58 2.22 mdb248(3.40) 5.62 6.76mdb223(1.20) 2.37 1.24 mdb249(1.84) 3.52 1.95mdb226(2.28) 5.61 5.37 mdb252(1.86) 3.69 2.02mdb227(1.08) 2.14 1.20 mdb253(2.05) 3.87 2.02mdb231(2.76) 4.43 3.89 mdb256(2.04) 4.88 3.56mdb233(1.60) 3.25 2.36
EME is an enhancement measure, its high value indicates the
enhancement in the output image and low value EME indicates hidden
information is not significantly enhanced. On the other hand, it is necessary to
have an optimum value of EME in order to have both contrast enhancement
and preserving more local details of the mammogram images. From the
85
experimental results, it is clear that DT ST gives optimum level of
enhancement without compromising the fine detail information. Although the
DT ST technique provides stronger contrast enhancement while preserving
more local information, the quality of the original do not affect. To verify this
property, enhanced image quality is measured by reduced reference entropic
differences (RRED) for image quality assessment index proposed in (Rajiv
2012). The quality indices for DTST enhanced image and NLUSM enhanced
image are tabulated in Table 5.2. The higher index value of enhanced images
indicates the enhancement process that does not affect the quality. From the
both subjective and objective measures, it is observed that the DT ST method
preserves local features and brings out the fine hidden details.
Table 5.2 RRED Index of DT ST and NLUSM Enhanced images
Image DT ST NLUSM Image DT ST NLUSMmdb209 1.201922 1.028682 mdb236 1.099423 0.865482mdb211 1.474552 1.225304 mdb238 1.521192 1.351191mdb213 1.108111 1.09039 mdb239 1.071037 0.986785mdb216 1.443599 1.206165 mdb240 1.512335 1.222201mdb218 1.28055 1.211519 mdb241 1.234238 1.107956mdb219 1.376216 1.088411 mdb245 1.261939 1.11406mdb222 1.384845 1.140495 mdb248 1.022991 0.887609mdb223 0.990273 1.035259 mdb249 1.513749 1.273498mdb226 1.351161 1.102013 mdb252 1.095996 1.032293mdb227 1.425647 1.210992 mdb253 1.494145 1.433008mdb231 1.228933 1.101739 mdb256 1.282377 1.093498mdb233 1.44315 1.215829
86
Table 5.3 SSIM of DT ST and NLUSM Enhanced images
Image DTST NLUSM Image DTST NLUSMmdb209 0.696 0.711 mdb236 0.769 0.643mdb211 0.783 0.753 mdb238 0.818 0.697mdb213 0.842 0.773 mdb239 0.737 0.660
mdb216 0.752 0.702 mdb240 0.777 0.669mdb218 0.785 0.629 mdb241 0.828 0.779mdb219 0.715 0.664 mdb245 0.831 0.788mdb222 0.808 0.731 mdb248 0.758 0.685mdb223 0.824 0.770 mdb249 0.783 0.728mdb226 0.778 0.786 mdb252 0.797 0.731mdb227 0.818 0.784 mdb253 0.762 0.645mdb231 0.725 0.657 mdb256 0.761 0.704mdb233 0.802 0.768
In addition, enhanced results are tested with Structural Similarity
measure (SSIM) (Wang 2004). Structural Similarity SSIM index is an
objective performance parameter under the assumption that human visual
perception is highly adapted for extracting structural information from a
scene. This quality assessment based on the degradation of structural
information provides quantitative measures that can automatically predict
perceived image quality. The index will be in between the values -1 to +1 and
ideal index is equal to one. The SSIM index for new DT ST method and
NLUSM method is tabulated in Table 5.3. It is observed that this new
algorithm is not degrading the structural information while performing
enhancement.
In order to prove the DT ST ability in preserving local features and
brings out the fine hidden fine details, the new sharpened image as the input
to CLAHE algorithms. This sharpening followed by CLAHE improves the
87
performance of CLAHE to bring out fine details as demonstrated in
Figure 5.7 and Figure 5.8. While USM based sharpened images are given to
CLAHE the noise dominates and it is clearly perceived from the Figure 5.7
and Figure 5.8 Column ‘3’. In particular, CLAHE using DTST image as the
input preserves the local features than the common CLAHE.
Figure 5.7 Enhancement Results of CLAHE (enlarged portions)Column ‘1’- CLAHE, Column ‘2’ - DT ST and CLAHEColumn ‘3’ – USM and CLAHE
88
Figure 5.8 Enhancement Results of CLAHE: Column ‘1’- CLAHE,Column ‘2’ - DT ST and CLAHE Column ‘3’ – USM andCLAHE
Figure 5.9 mdb006’ image’s 200th row gray level intensity profile of ‘ofOriginal, CLAHE and ST CLAHE
89
5.5 DETECTION OF MICROCALCIFICATION AND
SPICULATED MASSES
Mammogram enhancement increase radiologist’s detection /
characterization efficiency or as preprocessing stage of a system that aimed at
the detection of microcalcification and spiculated masses in mammograms.
Microcalcifications are deposits of calcium that they may indicate an early
sight of cancer. Screening mammography involves the detection of
abnormalities like lesions, characterized by their shape and margin.
Spiculated lesions are highly suspicious signs of breast cancer. The enhanced
results can be used to detect the small-sized and low-contrast
microcalcifications that could be missed or misinterpreted by medical experts.
A fixed threshold (i.e.) by keeping 10% larger gray value pixels, is applied to
various enhanced images and the results are presented in Figure 5.10. Thus
the results, strongly suggest that the DT ST method provides considerable
improvement in microcalcification detection over USM and CLAHE
methods. Similarly, from the results, spiculated masses present in the
mammogram (obtained from MIAS speculated category) are easily identified.
The results are presented in Figure 5.11.
90
Figure 5.10 Detection of Microcalcification: Column 1 Original,Column 2 DT ST, Column 3 USM
91
Figure 5.11 Enhancement of Spiculated Masses: Column 1 Original,Column 2 CLAHE, Column 3 DT ST + CLAHE,Column 4 USM + CLAHE
92
5.6 SUMMARY
Classical sharpening techniques fail to capture the anisotropic
features and amplify the noise while enhancing. Mammography images are
enhanced using anisotropic directionlet (DT) based image-sharpening
algorithm. This method not only provided the useful geometric features but
also have effective noise control. The skewed, elongated, directional DT basis
functions are applied on the mammogram images to obtain the multiscale
multidirectional anisotropic geometrical features. The new sharpening method
equation (5.3) aggregated the effective linear and geometrical features that are
provided by DT. The performances are compared with non-linear Unsharp
masking. This chapter also analysis a way to improve the CLAHE algorithm
by providing the DT ST image as the input. Thus, the preprocessed CLAHE
well preserve the local information than the CLAHE. Enhancement Measure
and SSIM index evaluates the effectiveness of this method. It is observed that
the new DT ST methodology produces better image quality, less error and
noise control with high structural similarity. The enhanced images help to
detect the microcalcification and view the speculated masses.