M 2 presentation(final)

Microcalcification identification
in digital mammogram for early
detection of breast cancer
Masters -2 Presentation
Nashid Alam
Registration No: 2012321028
annanya_cse@yahoo.co.uk
Supervisor: Prof. Dr. M. Shahidur Rahman
Department of Computer Science And Engineering
Shahjalal University of Science and Technology
Wednesday, April 15, 2015
Driving research for better breast cancer treatment
“The best protection is early detection”

Introduction
Breast cancer:
The most devastating and deadly diseases for women.
o Computer aided detection (CADe)
o Computer aided diagnosis (CADx) systems
Computerize Breast cancer Detection System:
Steps to control breast cancer:
1) Prevention
2) Detection
3) Diagnosis
4) Treatment
We will emphasis on :
1) Detection
2) Diagnosis

Background Interest
Ultrasound/ Sonogram MRI

Background Interest
Interest comes from two primary
backgrounds
Improvement of pictorial information for human
perception
How can an image/video be made more aesthetically
pleasing
How can an image/video be enhanced to facilitate
extraction of useful information
Processing of data for autonomous machine
perception- Machine Vision
Mammogram(2D)Tomogram(3D)

Micro-calcification
Mammography
Mammogram
Background knowledge

Micro-calcification

Micro-calcification
Micro-calcifications :
- Tiny deposits of calcium
- May be benign or malignant
- A first cue of cancer.
Position:
1. Can be scattered throughout the mammary gland, or
2. Occur in clusters.
(diameters from some µm up to approximately 200 µm.)
3. Considered regions of high frequency.

Micro-calcification
They are caused by a number of reasons:
1. Aging –
The majority of diagnoses are made in women over 50
2. Genetic –
Involving the BRCA1 (breast cancer 1, early onset) and
BRCA2 (breast cancer 2, early onset) genes
Micro-calcifications Pattern Determines :
The future course of the action-
I. Whether it be further investigatory techniques (as part of the triple
assessment), or
II.More regular screening

Mammography
Mammography Machine

Mammography
USE:
I. Viewing x-ray image
II. Manipulate X-ray image on a computer screen
Mammography :
 Process of using low-energy
x-rays to examine the human breast
 Used as a diagnostic and a screening tool.
The goal of mammography :
The early detection of breast cancer
Mammography Machine

Mammogram
mdb226.jpg

Mammogram
Mammogram:
An x-ray picture of the breast
Use:
To look for changes that are
not normal.
Result Archive:
The results are recorded:
1. On x-ray film or
2.Directly into a computer
mdb226.jpg

Wang et.al.(1989):
The mammograms are:
-Decomposed into different frequency subbands.
The low-frequency subband discarded.
Literature Review

Literature Review
Daubechies I.(1992):
Wavelets are mainly used :
-Because of their dilation and translation properties
-Suitable for non stationary signals.

Strickland et.at (1996) :
Used biorthogonal filter bank
-To compute four dyadic and
-Two cinterpolation scales.
Applied binary threshold-operator
-In six scales.
Literature Review

Heinlein et.al(2003):
Goal: Enhancement of mammograms:
Derived The integrated wavelets:
- From a model of microcalcifications
Literature Review

Zhibo et.al.(2007):
A method aimed at minimizing image noise.
Optimize contrast of mammographic image features
Emphasize mammographic features:
A nonlinear mapping function is applied:
-To the set of coefficient from each level.
Use Contourlets:
For more accurate detection of microcalcification clusters
The transformed image is denoised
-using stein's thresholding [18].
The results presented correspond to the enhancement of regions
with large masses only.
Literature Review

Fatemeh et.al.(2007) :
Focus on:
-Analysis of large masses instead of microcalcifications.
- Detect /Classify mammograms:
Normal and Abnormal
Use Contourlets Transform:
For automatic mass classification
Literature Review

Balakumaran et.al.(2010) :
Focus on:
- Microcalcification Detection
Use :
- Wavelet Transform and Fuzzy Shell Clustering
Literature Review

Literature Review
Zhang et.al.(2013) :
Use Hybrid Image Filtering Method:
- Morphological image processing
- Wavelet transform technique
Focus on:
- Presence of microcalcification clusters

Literature Review
Lu et.al.(2013) :
Use Hybrid Image Filtering Method:
- Multiscale regularized reconstruction
Focus on:
- Detecting subtle mass lesions in Digital breast
tomosynthesis (DBT)
- Noise regularization in DBT reconstruction

Literature Review
Leeuw et.al.(2014) :
Use:
- Phase derivative to detect microcalcifications
- A template matching algorithm was designed
Focus on:
- Detect microcalcifications in breast
specimens using MRI
- Noise regularization in image reconstruction

Literature Review
Shankla et.al.(2014) :
Automatic insertion of simulated microcalcification clusters
-in a software breast phantom
Focus on:
-Algorithm developed as part of a virtual clinical trial (VCT) :
-Includes the simulation of breast anatomy,
- Mechanical compression
- Image acquisition
- Image processing, displaying and interpretation.

Reason behind the problem( In real life):
Burdensome Task Of Radiologist :
Eye fatigue:
-Huge volume of images
-Detection accuracy rate tends to decrease
Non-systematic search patterns of humans
Performance gap between :
Specialized breast imagers and
general radiologists
Interpretational Errors:
Similar characteristics:
Abnormal and normal microcalcification
Problem Statement

The signs of breast cancer are:
Masses
Calcifications
Tumor
Lesion
Lump
Individual Research Areas
Problem Statement

Motivation to the Research: Goal
Better Cancer Survival Rates
(Facilitate Early Detection ).
Provide “second opinion” : Computerized decision
support systems
Fast,
Reliable, and
Cost-effective
QUICKLY AND ACCURATELY :
Overcome the development of breast cancer

Develop a logistic model:
Early detection of Breast Cancer.
-Micro-calcification Enhancement
-To determine the likelihood of CANCEROUS AREA
from the image values of mammograms.
Challenge:
Occur in clusters
The clusters may vary in size
from 0.05mm to 1mm in diameter.
Variation in signal intensity and contrast.
May located in dense tissue
Difficult to detect.
Challenges

Gantt Chart
Chart 01: Gantt Chart of this M.Sc thesis
showing the duration of task against the progression of time

Schematic representation of the system

Schematicrepresentation
ofthesystem

Materials and Tools
Matlab 2001a
Database: MIAS

Database: MIAS database
http://skye.icr.ac.uk/miasdb/miasdb.html

Class Of
Abnormality
Severity Of
Abnormality
The Location
Of The
Center Of
The
Abnormality
And Its
Diameter.
1 Calcification
(25)
1.Benign
(Calc-12)
2 Circumscribed
Masses
3 Speculated Masses
4 Ill-defined Masses
5 Architectural
Distortion
2.Malignant
(Cancerous)
(Calc-13)
6 Asymmetry
7
Normal
mdb223.jpg mdb226.jpg
mdb239.jpg mdb249.jpg
Figure01:X-ray image form MIAS database
Database: MIAS Databasehttp://skye.icr.ac.uk/miasdb/miasdb.html
Mammography Image Analysis Society (MIAS)
-An organization of UK research groups

• Consists of 322 images
-- Contains left and right breast images for 161 patients
• Every image is 1024 X 1024 pixels in size
• Represents each pixel with an 8-bit word
MIAS Database
Mammography Image Analysis Society (MIAS)
-An organization of UK research groups
Database: http://skye.icr.ac.uk/miasdb/miasdb.html
http://see.xidian.edu.cn/vipsl/database_Mammo.html

MAIN NOVELTY
Input image
Bandpass
Directional
subbands
Bandpass
Directional
subbands

Main Novelty
-Contourlet Transform
- Specific Edge Filter (Prewitt Filter):
To enhance the directional structures of the image in
the contourlet domain.
- Recover an approximation of the mammogram
(with the microcalcifications enhanced):
Inverse contourlet transform is applied
Details in upcoming slides

Based on the classical approach used in transform methods for image processing.
1. Input mammogram
2. Forward CT
3. Subband Processing
4. Inverse CT
5. Enhanced Mammogram
Schematic representation of the system

Contourlet transformation
Implementation Based On :
• A Laplacian Pyramid decomposition
followed by -
• Directional filter banks applied on
each band pass sub-band.
The Result Extracts:
-Geometric information of images.
Main Novelty

Enhancement of the Directional Subbands
The Contourlet Transform
Laplacian Pyramid: 3 level
Decomposition
Frequency partitioning of a directional filter bank
Decomposition level l=3
The real wedge-shape frequency band is 23=8.
horizontal directions are corresponded by
sub-bands 0-3
Vertical directions are represented by
sub-bands 4-7

Decomposition
Laplacian Pyramid Level-1
8 Direction
4 Direction
4 Direction
(mdb252.jpg)

Decomposition
Wedge-shape frequency band is 23=8.
Horizontal directions are corresponded by
sub-bands 0-3
(1) sub-band 0
(2) sub-band 1
(3) sub-band 2
(4) sub-band 3
Contourlet coefficient at level 4

Decomposition
Contourlet coefficient at level 4
Wedge-shape frequency band is 23=8.
sub-bands 4-7
(5) sub-band 4
(6) sub-band 5
(7) sub-band 6
(8) sub-band 7

Decomposition
(a) Main Image
(mdb252.jpg)
(b) Enhanced Image
(Average in all 8 direction)

(a) Main image
(Toy Image)
Contourlet Transform Example
(b) Horizontal Direction
(c) Vertical Direction
Directional filter banks: Horizontal and Vertical

Directional filter banks
Horizontal directions are corresponded by
sub-bands 0-3
(1) sub-band 0
(2) sub-band 1
(3) sub-band 2
(4) sub-band 3

Directional filter banks
sub-bands 4-7
(5) sub-band 4
(6) sub-band 5
(7) sub-band 6
(8) sub-band 7

Why Contourlet?
•Decompose the mammographic image:
-Into directional components:
To easily capture the geometry of the image features.
Target

• This decomposition offers:
-Multiscale localization(Laplacian Pyramid) and
-A high degree of directionality and anisotropy.
Why Contourlet? Usefulness of Contourlet
Directionality:
Having basis elements
Defined in variety of directions
Anistrophy:
Basis Elements having
Different aspect ration

Contourlet Transform Concept
(a)Wavelet
(Require a lot of dot for fine resolution)
(b)Contourlet
(Requires few different elongated shapes
in a variety of direction following the counter)
3 Different Size of Square Shape brush stroke
(Smallest, Medium, Largest) to provide Multiresolution Image
Example: Painter Scenario

Why Contourlet?
2-D Contourlet Transform (2D-CT) Discrete WT
Handles singularities such as edges in a
more powerful way
Has basis functions at many orientations has basis functions at three
orientations
Basis functions appear a several aspect
ratios
the aspect ratio of DWT is 1
CT similar as DWT can be
implemented using iterative filter banks.
Advantage of using 2D-CT over DWT:

Input image
Bandpass
Directional
subbands
Bandpass
Directional
subbands
Plan-of-Action
For microcalcifications enhancement :
We use-
The Contourlet Transform(CT) [12]
The Prewitt Filter.
12. Da Cunha A. L., Zhou J. and Do M. N,: The Nonsubsampled Contourlet Transform: Theory, Design, and
Applications, IEEE Transactions on Image Processing,vol. 15, (2006) pp. 3089-3101

Art-of-Action
An edge Prewitt
filter to enhance the
directional structures
in the image.
Contourlet transform allows
decomposing the image in
multidirectional
and multiscale subbands[6].
6. Laine A.F., Schuler S., Fan J., Huda W.: Mammographic feature enhancement by multiscale
analysis, IEEE Transactions on Medical Imaging, 1994, vol. 13, no. 4,(1994) pp. 7250-7260
This allows finding
• A better set of edges,
• Recovering an enhanced mammogram
with better visual characteristics.
Microcalcifications have a very small size
a denoising stage is not implemented
in order to preserve the integrity of the injuries.
Decompose the
digital mammogram
Using
Contourlet transform
(b) Enhanced image
(mdb238.jpg)
(a) Original image
(mdb238.jpg)

Method
CT is implemented in two stages:
1. Subband decomposition stage
2. Directional decomposition stages.

Method
For the subband decomposition:
- The Laplacian pyramid is used [13]
Decomposition at each step:
-Generates a sampled low pass version of the original
-The difference between :
The original image and the prediction.
13. Park S.-I., Smith M. J. T., and Mersereau R. M.: A new directional Filter bank for image analysis and classification,
Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '99), vol. 3, (1999) pp.
1417-1420
Details ……..

Method
Details ……..
1. The input image is first low pass filtered
2. Filtered image is then decimated to get a coarse(rough) approximation.
3. The resulting image is interpolated and passed through Synthesis
filter.
4. The obtained image is subtracted from the original image :
To get a bandpass image.
5. The process is then iterated on the coarser version (high resolution)
of the image.
Plan of Action

Method
2.Directional Filter Bank (DFB)
Details ……..
Implemented by using an L-level binary tree decomposition :
resulting in 2L subbands
The desired frequency partitioning is obtained by :
Following a tree expanding rule
- For finer directional subbands [13].
13. Park S.-I., Smith M. J. T., and Mersereau R. M.: A new directional Filter bank for image analysis and classification,
Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '99), vol. 3, (1999) pp.
1417-1420

The CT is implemented by:
Laplacian pyramid followed by directional filter banks (Fig-01)
Input image
Bandpass
Directional
subbands
Bandpass
Directional
subbands
Figure 01: Structure of the Laplacian pyramid together with the directional filter bank
The concept of wavelet:
University of Heidelburg
The CASCADE STRUCTURE allows:
- The multiscale and
directional decomposition to be
independent
- Makes possible to:
Decompose each scale into
any arbitrary power of two's number of
directions(4,8,16…)
Figure 01
Details ………….
Decomposes The Image Into Several Directional Subbands And Multiple Scales

Figure 02: (a)Structure of the Laplacian pyramid together with the directional filter bank
(b) frequency partitioning by the contourlet transform
(c) Decomposition levels and directions.
(a) (b)
Input
image
Bandpass
Directional
subbands
Bandpass
Directional
subbands
Details….
(c)
Denote
Each subband by yi,j
Where
i =decomposition level and
J=direction
Decomposes The Image Into Several Directional Subbands And Multiple Scales

The processing of an image consists on:
-Applying a function to enhance the regions of
interest.
In multiscale analysis:
Calculating function f for each subband :
-To emphasize the features of interest
-In order to get a new set y' of enhanced subbands:
Each of the resulting enhanced subbands can be
expressed using equation 1.
)('
, , jiyfjiy  ………………..(1)
-After the enhanced subbands are obtained, the inverse
transform is performed to obtain an enhanced image.
Denote
Where
J=direction Details….

Details….
The directional subbands are enhanced using equation 2.
)( ,jiyf
)2,1(,1 nnW jiy
)2,1(,2 nnW jiy
If bi,j(n1,n2)=0
If bi,j(n1,n2)=1
………..(2)
Denote
Where
J=direction
W1= weight factors for detecting the surrounding tissue
W2= weight factors for detecting microcalcifications
(n1,n2) are the spatial coordinates.
bi;j = a binary image containing the edges of the subband
Weight and threshold selection techniques are presented on upcoming slides

The directional subbands are enhanced using equation 2.
)( ,jiyf
)2,1(,1 nnW jiy
)2,1(,2 nnW jiy
If bi,j(n1,n2)=0
If bi,j(n1,n2)=1
………..(2)
Binary edge image bi,j is obtained :
-by applying an operator (prewitt edge detector)
-to detect edges on each directional subband.
In order to obtain a binary image:
A threshold Ti,j for each subband is calculated.
Details….
Weight and threshold selection techniques are presented on upcoming slides

Threshold Selection
Details….
The microcalcifications
appear :
On each subband
Over a very
homogeneous background.
Most of the transform coefficients:
-The coefficients corresponding to the
injuries are far from background value.
A conservative threshold of 3σi;j is selected:
where σi;j is the standard deviation of the corresponding subband y I,j .

Weight Selection
Exhaustive tests:
-Consist on evaluating subjectively a set of 322 different mammograms
-With Different combinations of values,
The weights W1, and W2 are determined:
-Selected as W1 = 3 σi;j and W2 = 4 σi;j
These weights are chosen to:
keep the relationship W1 < W2:
-Because the W factor is a gain
-More gain at the edges are wanted.

Applying Contourlet Transformation Benign
Original image Enhanced image
Goal: Microcalcification Enhancement
mdb222.jpg
mdb223.jpg
mdb248.jpg
mdb252.jpg

mdb226.jpg
mdb227.jpg
mdb236.jpg
mdb240.jpg

Original image Enhanced image Original image Enhanced image
mdb218.jpgmdb219.jpg

Applying Contourlet Transformation Malignant
mdb209.jpg
mdb211.jpg
mdb213.jpg
mdb231.jpg

mdb238.jpg
mdb239.jpg
mdb241.jpg
mdb249.jpg

mdb253.jpg
mdb256.jpg

Applying Contourlet Transformation Normal
mdb003.jpg
mdb004.jpg
mdb006.jpg
mdb007.jpg

mdb009.jpg
mdb018.jpg
mdb027.jpg
mdb033.jpg

mdb046.jpg
mdb056.jpg
mdb060.jpg
mdb066.jpg

mdb070.jpg
mdb073.jpg
mdb074.jpg
mdb076.jpg

mdb093.jpg
mdb096.jpg
mdb101.jpg
mdb012.jpg

mdb128.jpg
mdb137.jpg
mdb146.jpg
mdb154.jpg

mdb166.jpg
mdb169.jpg
mdb224.jpg
mdb225.jpg

mdb263.jpg
mdb294.jpg
mdb316.jpg
mdb320.jpg

Use Separable Transform
2D Wavelet Transform
Visualization
Label of
approximation
Horizontal
Details
Horizontal
Details
Vertical
Details
Diagonal
Details
Vertical
Details
Diagonal
Details

Decomposition at
Label 4
Original image
(with diagonal details areas indicated)
Diagonal Details

Vertical Details
Decomposition at
Label 4
Original image
(with Vertical details areas indicated)

Experimental Results
DWT
1.Original Image
(Malignent_mdb238) 2.Decomposition at Label 4
2.Decomposition at Label 1 3.Decomposition at Label 2 3.Decomposition at Label 3

DWT
1.Original Image
(Malignent_mdb238) 2.Decomposition at Label 4

1.Original Image
(Benign_mdb252)
2.Decomposition at Label 4
DWT

1.Original Image
(Malignent_mdb253.jpg) 2.Decomposition at Label 4

Metrics: Quantitive Measurement

Metrics
To compare the ability of :
Enhancement achieved by the proposed method.
Why?
1. Measurement of distributed separation (MDS)
2. Contrast enhancement of background against target (CEBT) and
3. Entropy-based contrast enhancement of background against target (ECEBT) [14].
Measures used to compare:
14. Sameer S. and Keit B.: An Evaluation on Contrast Enhancement Techniques for Mammographic Breast Masses, IEEE
Transactions on Information Technology in Biomedicine, vol. 9, (2005) pp. 109-119

Metrics
1. Measurement of Distributed Separation
(MDS)
The MDS represents :
How separated are the distributions of each mammogram
…………………………(3)MDS = |µucalcE -µtissueE |- |µucalc0 -µtissue0 |
µucalcE = Mean of the microcalcification region of the enhanced image
µucalc0 = Mean of the microcalcification region of the original image
µtissueE = Mean of the surrounding tissue of the enhanced image
µtissue0 = Mean of the surrounding tissue of the enhanced image
Defined by:
Where:

Metrics
2. Contrast enhancement of background against
target (CEBT)
The CEBT Quantifies :
The improvement in difference between the background and the target(MC).
…………………………(4)
0µucalc
Eµucalc
0µtissue
0µucalc
Eµtissue
Eµucalc
CEBT




Defined by:
Where:
Eµucalc
0µucalc
= Standard deviations of the microcalcifications region in the enhanced image
= Standard deviations of the microcalcifications region in the original image

Metrics
3. Entropy-based contrast enhancement of
background against target (ECEBT)
The ECEBT Measures :
- An extension of the TBC metric
- Based on the entropy of the regions rather
than in the standard deviations
Defined by:
Where:
…………………………(5)
0µucalc
Eµucalc
0µtissue
0µucalc
Eµtissue
Eµucalc
ECEBT




= Entropy of the microcalcifications region in the enhanced image
= Entropy of the microcalcifications region in the original image
Eµucalc
0µucalc

MDS, CEBT and ECEBT metrics on the enhanced mammograms
CT Method DWT Method
MDS CEBT ECEBT MDS CEBT ECEBT
0.853 0.477 0.852 0.153 0.078 0.555
0.818 0.330 0.810 0.094 0.052 0.382
1.000 1.000 1.000 0.210 0.092 0.512
0.905 0.322 0.920 1.000 0.077 1.000
0.936 0.380 0.935 0.038 0.074 0.473
0.948 0.293 0.947 0.469 0.075 0.847
0.665 0.410 0.639 0.369 0.082 0.823
0.740 0.352 0.730 0.340 0.074 0.726
0.944 0.469 0.494 0.479 0.095 0.834
0.931 0.691 0.936 0.479 0.000 0.000
0.693 0.500 0.718 0.258 0.081 0.682
0.916 0.395 0.914 0.796 0.079 0.900
Table 1. Decomposition levels and directions.

0
0.2
0.4
0.6
0.8
1
1.2
TBC
Mammogram
MDS Matrix
CT DWT
The proposed method gives higher results than the wavelet-based method.
Experimental Results Analysis

0
0.2
0.4
0.6
0.8
1
1.2
TBCE
Mammogram
CEBT Matrix
CT DWT

0
0.2
0.4
0.6
0.8
1
1.2
DSM
Mammogram
ECEBT Matrix
CT DWT

Mesh plot of a ROI containing microcalcifications
(a)The original
mammogram
(mdb252.bmp)
(b) The enhanced
mammogram
using CT

(a)The original
mammogram
(mdb238.bmp)
(b) The enhanced
mammogram
using CT

(a)The original
mammogram
(mdb253.bmp)
(b) The enhanced
mammogram
using CT

More peaks corresponding to microcalcifications are enhanced
The background has a less magnitude with respect to the peaks:
-The microcalcifications are more visible.
Observation:

(a)Original image (b)CT method (c)The DWT Method
These regions contain :
• Clusters of microcalcifications (target)
• surrounding tissue (background).
For visualization purposes :
The ROI in the original mammogram
are marked with a square.

Plan of action as follows:
1. Segment the microcalcification(MC) from the enhanced image.
2. Find an attribute based on which I can train the machine
2. Based on feature(size/shape), will move on to classification
( benign or malignant)

Reference
1. Alqdah M.; Rahmanramli A. and Mahmud R.: A System of Microcalcifications
Detection and Evaluation of the Radiologist: Comparative Study of the Three Main
Races in Malaysia, Computers in Biology and Medicine, vol. 35, (2005) pp. 905- 914
2. Strickland R.N. and Hahn H.: Wavelet transforms for detecting microcalci¯cations
in mammograms, IEEE Transactions on Medical Imaging, vol. 15, (1996) pp. 218-
229
3. Laine A.F., Schuler S., Fan J., Huda W.: Mammographic feature enhancement by
multiscale analysis, IEEE Transactions on Medical Imaging, 1994, vol. 13, no. 4,
(1994) pp. 7250-7260
4. Wang T. C and Karayiannis N. B.: Detection of Microcalci¯cations in Digital Mam-
mograms Using Wavelets, IEEE Transaction on Medical Imaging, vol. 17, no. 4,
(1989) pp. 498-509

5. Nakayama R., Uchiyama Y., Watanabe R., Katsuragawa S., Namba K. and Doi
K.: Computer-Aided Diagnosis Scheme for Histological Classi¯cation of Clustered
Microcalci¯cations on Magni¯cation Mammograms, Medical Physics, vol. 31, no. 4,
(2004) 786 – 799
6. Heinlein P., Drexl J. and Schneider Wilfried: Integrated Wavelets for Enhance-
ment of Microcalci¯cations in Digital Mammography, IEEE Transactions on Medi-
cal Imaging, Vol. 22, (2003) pp. 402-413
7. Daubechies I.: Ten Lectures on Wavelets, Philadelphia, PA, SIAM, (1992)
8. Zhibo Lu, Tianzi Jiang, Guoen Hu, Xin Wang: Contourlet based mammographic
image enhancement, Proc. of SPIE, vol. 6534, (2007) pp. 65340M-1 - 65340M-8
9. Fatemeh Moayedi, Zohreh Azimifar, Reza Boostani, and Serajodin Katebi:
Contourlet-based mammography mass classi¯cation, ICIAR 2007, LNCS 4633,
(2007) pp. 923-934
Reference

10. Do M. N. and Vetterli M.: The Contourlet Transform: An efficient Directional
Multiresolution Image Representation, IEEE Transactions on Image Processing, vol.
14, (2001) pp. 2091-2106
11. Da Cunha A. L., Zhou J. and Do M. N,: The Nonsubsampled Contourlet Trans-
form: Theory, Design, and Applications, IEEE Transactions on Image Processing,
vol. 15, (2006) pp. 3089-3101
12. Burt P. J. and Adelson E. H.: The Laplacian pyramid as a compact image code,
IEEE Transactions on Communications, vol. 31, no. 4, (1983) pp. 532-540
13. Park S.-I., Smith M. J. T., and Mersereau R. M.: A new directional Filter bank for
image analysis and classification, Proceedings of IEEE International Conference on
Acoustics, Speech, and Signal Processing (ICASSP '99), vol. 3, (1999) pp. 1417-1420
14. Sameer S. and Keit B.: An Evaluation on Contrast Enhancement Techniques for
Mammographic Breast Masses, IEEE Transactions on Information Technology in
Biomedicine, vol. 9, (2005) pp. 109-119
Reference

Published Paper
Available Online:
http://cennser.org/IJCVSP/paper.html

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Paper
Available Online:
http://cennser.org/IJCVSP/paper.html

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M 2 presentation(final)

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M 2 presentation(final)