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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

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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.

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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

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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

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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.

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(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

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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.

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‘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

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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 ,

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= 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.

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Figure 5.6 Sharpening Enhancement enlarged portions: From left toright First Column:Original, Second Column:New DT STand Third Column:NLUSM

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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

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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

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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

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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

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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

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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.

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Figure 5.10 Detection of Microcalcification: Column 1 Original,Column 2 DT ST, Column 3 USM

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Figure 5.11 Enhancement of Spiculated Masses: Column 1 Original,Column 2 CLAHE, Column 3 DT ST + CLAHE,Column 4 USM + CLAHE

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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.