IRJET -Malignancy Detection using Pattern Recognition and ANNS
Microcalcification Enhancement in Digital Mammogram
1. “The best protection is early detection”
Microcalcification Enhancement
in digital mammogram
Masters -2
Work-progress Presentation #1
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, September 3, 2014
2. Introduction
Breast cancer:
The most devastating and deadly diseases for women.
Steps to control breast cancer:
1) Prevention
2) Detection
3) Diagnosis
4) Treatment
Computerize Breast cancer Detection System:
We will emphasis on :
1) Detection
2) Diagnosis
o Computer aided detection (CADe)
o Computer aided diagnosis (CADx) systems
4. 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 [4].)
3. considered regions of high frequency.
They are caused by a number of reasons:
Aging - The majority of diagnoses are made in women over 50
Genetic - Involving the BRCA1 (breast cancer 1, early onset) and
BRCA2 (breast cancer 2, early onset) genes
5. Mammography
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 :
USE:
Mammography Machine
The early detection of breast cancer
I. Viewing x-ray image
II. Manipulate X-ray image on a computer screen
6. Mammogram
Mammogram:
A mammogram is an x-ray picture of the breast
Use:
To look for changes that are not normal.
Result Archive:
The results are recorded on x-ray film or directly into a computer
Types of mammograms:
I. Screening mammograms-Done for women who have no symptoms of breast
cancer.
II. Diagnostic mammograms -To check for breast cancer after a lump or other
symptom or sign of breast cancer has been found.
III. Digital mammogram-Uses x-rays to produce an image of the breast. The image
is stored directly on a computer.
mdb226.jpg
8. Problem Statement
Main challenge :
QUICKLY AND ACCURATELY overcome the development of breast cancer
Reason behind the problem:
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
9. Problem Statement
The signs of breast cancer are:
Masses
Calcifications
Tumor
Lesion
Lump
Individual Research Areas
A key area of research activity involves :
Developing better ways-
To diagnose and stage breast cancer.
10. GOAL
• Early detection of Breast Cancer.
The Micro-calcification:
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.
• Develop a logistic model:
-Micro-calcification detection
-To determine the likelihood of
CANCEROUS AREA
from the image values of mammograms.
11. Why our work is important?
-Better Cancer Survival Rates(Early Detection ).
-The diagnostic management of breast cancer (a difficult
task)
--Radiologist fails to detect Breast Cancer.
-Computerized decision support systems provide
“second opinion” :
Fast,
Reliable, and
Cost-effective
12. Literature Review
Strickland et.at (1996) :
A biorthogonal filter bank is used
-To compute four dyadic and
-Two cinterpolation scales.
A binary threshold-operator is applied to the six scales.
13. Literature Review
Laine et.al (1994) :
A hexagonal wavelet transform (HWT) is used:
-To obtain multi-scales edges at
orientations of 60, 0 and -60 degrees.
The resulting subbands are enhanced and
The image reconstructed.
14. Literature Review
Wang et.al.(1989):
The mammograms are:
-Decomposed into different frequency subbands.
The low-frequency subband discarded.
The image is reconstructed from the subbands containing only
high frequencies.
15. Literature Review
Heinlein et.al(2003):
For general enhancement of mammograms:
From a model of microcalcifications -
The integrated wavelets are derived
16. 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.
17. 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
18. Literature Review
Daubechies I.(1992):
Wavelets are mainly used :
-Because of their dilation and translation properties
-Suitable for non stationary signals.
19. Main Novelty
- Nonsubsampled Contourlet Transform
- Specific Edge 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
20. Achievement
The proposed method
Outperforms
The current method
Contourlet transformation
(CT)
based on:
Discrete wavelet transform
(DWT)
based on:
Details in upcoming slides
21. Contourlet transformation
Implementation Based On :
• A Laplacian Pyramid decomposition
followed by -
• directional filter banks applied on
each band pass sub-band.
The non-subsampled contourlet transform extracts:
• the geometric information of images.
•which can be used to distinguish noises from weak edges.
Details in upcoming slides
22. Why Contourlet?
•Decompose the mammographic image into well localized and
directional components:
To easily capture the geometry of the image features.
•Accomplished by the 2-D Contourlet Transform (2D-CT) :
Improves the representation scarcity of images over
the Discrete DWT [11], [12],[13], [14].
Target:
Details in upcoming slides
Usefulness of Conterlet :
• This decomposition offers:
-Multiscale and time frequency localization and
-A high degree of directionality and anisotropy.
23. Why Contourlet?
Advantage of using 2D-CT over DWT:
2-D Contourlet Transform (2D-CT) Discrete DWT
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 WT is 1
CT similar as DWT can be
implemented using iterative filter banks.
Details in upcoming slides
25. O/P of Low Pass Filter High Pass Filter = A Band Pass Result
Good temper resolution in high frequencies
Good frequency resolution in low pass band
OBTAION:
Wavelet
A high pass filter
Temper resolution : A vertical high-resolution
Frequency resolution : The sample frequency divided by the number of samples
26. Wavelet
Working with wavelet:
1. Convolve the signal with wavelet filter(h/g)
2. Store the results in coefficients/frequency response
(Result in number is put in the boxes)
3. Coefficients/frequency response:
- The representation of the signal in the new domain.
Properties:
• Maximum frequency depends on the length of the signal.
• Recursive partitioning of the lowest band in subjective to the application.
Details in upcoming slides
27. 1.A length 8 signal
2.Split/divide the signal in two parts
3.Convolve the signal with
the high pass filter
Wavelet
29. Wavelet
First partitioning of lower and higher frequency band
• For perfect low pass filter
• Leave everything intact in 0 (zero)
Spectrodensity of the signal at this point
Unit cell
Unit cell is shrunk by half(1/2)
No information loss due to shrinking
30. Wavelet
Spectrodensity of the signal at this point
For perfect low pass filter For perfect high pass filter
This works even not for perfect high pass/low pass filter
31. Wavelet
Split the signal
And
down-sample by 2
In high frequency
Details at level 1
41. Wavelet
Filter response/Coefficient
of
Practically used wavelet filter
Collect the low frequencies
High frequencies
Wavelet
Behaving
as bandpass
42. Wavelet
Filter response/Coefficient
of
Practically used wavelet filter
Modular square of
These transfer
function
Add up to 1.
To
Prevent
Loosing
signal/energy
Wavelet
Behaving
as bandpass
43. Wavelet
Code Fragments to do the task
% Extract the level 1 coefficients.
a1 = appcoef2(wc,s,wname,1);
h1 = detcoef2('h',wc,s,1);
v1 = detcoef2('v',wc,s,1);
d1 = detcoef2('d',wc,s,1);
% Display the decomposition up to level 1 only.
ncolors = size(map,1); % Number of colors.
sz = size(X);
cod_a1 = wcodemat(a1,ncolors);
cod_a1 = wkeep(cod_a1, sz/2);
cod_h1 = wcodemat(h1,ncolors);
cod_h1 = wkeep(cod_h1, sz/2);
cod_v1 = wcodemat(v1,ncolors);
cod_v1 = wkeep(cod_v1, sz/2);
cod_d1 = wcodemat(d1,ncolors);
cod_d1 = wkeep(cod_d1, sz/2);
image([cod_a1,cod_h1;cod_v1,cod_d1]);
axis image; set(gca,'XTick',[],'YTick',[]);
title('Single stage decomposition')
colormap(map)
pause
% Here are the reconstructed branches
ra2 = wrcoef2('a',wc,s,wname,2);
rh2 = wrcoef2('h',wc,s,wname,2);
rv2 = wrcoef2('v',wc,s,wname,2);
rd2 = wrcoef2('d',wc,s,wname,2);
45. Wavelet
Understand The effect of each this label
Want to understand
The effect of this label
Have to perform
convolution
46. Wavelet
Level 2
details
Graph 01: Transfer functions of the wavelet transforms
Works for Signals more then 8 samples
23= 8, Sample=8, level=3.
Level 1
details
Level 3
details
Level 4
details
Level 5
details
Transfer functions of
Approximation:
The low pass
result
That we keep at
the end
47. Wavelet
Property of wavelet
Level
details
+ approximation= 1
Graph 01: Transfer functions of the wavelet transforms
48. Wavelet
Approximation is a sinc
- A perfect low pass filter
sincA-sincB
A=A frequency
B=A frequency
-A perfect bandpass filter
49. Wavelet
Signal with
more than
eight samples
Scenario:
Temper resolution>
Frequency resolution
Increasing
frequency resolution
Decreases
temporal resolution.
Temper resolution : A vertical high-resolution
Frequency resolution : The sample frequency divided by the number of samples
51. Discrete Wavelet Transform(DWT)
Requires a wavelet ,Ψ(t), such that:
- It scales and shifts
from an orthonormal basis
of the square integral function.
Denote Wavelet
, ( t ) t n
j
(( 2 ) / 2 )
1
2
j
j
j n
Scale Shift
j and n both are integer
nm jl m l n j . , , , j,n (t)To offer an orthonormal basis:
Orthonormal basis: A vector space basis for the space it spans.
.
.
52. Discrete Wavelet Transform(DWT)
Basis Function
Wavelets,Ψ
Scaling Function,Ψ
Basis function : An element of a particular basis for a function space
61. Backward transformation of Wavelets
Opposite of forward transformation
Mirror the forward transformation on the right hand side
Replace the down-sampling by up-sampling.
Signal
Wavelet
transform
of the Signal
Wavelet
transform
of
the Signal
Signal
63. JPEG Compression
Gibbs oscillation
15% lowest
Fourier coefficient=
Lowest 15 frequency
Is used to reconstruct the signal
Low pass version
of the original image
75. 2D Wavelet Transform
Use Separable Transform
Four region:
Blue= Diagonal Details at label 1
Green=Horizontal Details at label 1
Purple=vertical details at label 1
Yellow= Approximation at Label 1
(Low pass in both x and y direction)
76. 2D Wavelet Transform
Use Separable Transform
Doing the above steps recursively:
Take the current approximation
77. 2D Wavelet Transform
Use Separable Transform
Doing the above steps recursively:
1. Take the current approximation
2. And further split it up
78. 2D Wavelet Transform
Use Separable Transform
Doing the above steps recursively:
1. Take the current approximation
2. And further split it up
79. 2D Wavelet Transform
Use Separable Transform
New
approximation
Doing the above steps recursively:
1. Take the current approximation
2. And further split it up
3. Getting new approximation
80. 2D Wavelet Transform
Use Separable Transform
Diagonal Details
Horizontal Details
vertical details
Approximation
(can be further
decomposed)
In summary
81. 2D Wavelet Transform
Use Separable Transform
In summary
Approximation
(can be further
decomposed)
86. 2D Wavelet Transform
Use Separable Transform
Visualization
# of occurrences
Magnitude
of
coefficients
Most
Coefficient
Have values
Close to zero
87. 2D Wavelet Transform
Use Separable Transform
Graph from the histogram
# of occurrences
Magnitude
of
coefficients
Discard
Coefficient
values
Close to zero
88. 2D Wavelet Transform
Use Separable Transform
More
precise
Visualization
Original image:
Gray square on a
Black Background
Horizontal Details
(row by row)
Diagonal Details
Vertical details
(column by column)
96. Experimental Results
1.Original Image
(Benign_mdb252)
2.Decomposition at Label 4
DWT
2.Decomposition at Label 1 3.Decomposition at Label 2 3.Decomposition at Label 3
97. Experimental Results
1.Original Image
(Malignent_mdb253.jpg) 2.Decomposition at Label 4
2.Decomposition at Label 1 3.Decomposition at Label 2 3.Decomposition at Label 3
98. CT vs. DWT
The results obtained by the Contourlet Transformation (CT)
are compared with
The well-known method based on the discrete wavelet transform
DWT Target Goal:
1.Applying a DWT to decompose a digital mammogram into different subbands.
2.The low-pass wavelet band is removed (set to zero) and
the remaining coefficients are enhanced.
3.The inverse wavelet transform is applied to recover
the enhanced mammogram containing microcalcifications [7].
7. Wang T. C and Karayiannis N. B.: Detection of Microcalcifications in Digital Mammograms Using Wavelets, IEEE
Transaction on Medical Imaging, vol. 17, no. 4, (1989) pp. 498-509
99. Plan-of-Action
For microcalcifications enhancement :
We use-
The Nonsubsampled Contourlet Transform(NSCT) [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
100. Plan-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].
This allows finding
• A better set of edges,
• Recovering an enhanced mammogram
with better visual characteristics.
Decompose the
digital mammogram
Using
Contourlet transform
(b) Enhanced image
(mdb238.jpg)
(a) Original image
(mdb238.jpg)
microcalcifications have a very small size
a denoising stage is not implemented
in order to preserve the integrity of the injuries.
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
101. Method
The proposed method is based on the classical approach used in transform
methods for image processing.
1. Input mammogram
2. Forward NSCT
3. Subband Processing
5. Enhanced Mammogram
4. Inverse NSCT
Figure 01: Block diagram of the transform methods for images processing.
102. Method
NSCT is implemented in two stages:
1. Subband decomposition stage
2. Directional decomposition stages.
Details in upcoming slides
103. Method
1. Subband decomposition stage
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.
Details ……..
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
104. Method
1. Subband decomposition stage
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 a Synthesis
flter.
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
105. Method
2.Directional Filter Bank (DFB)
Implemented by using an L-level binary tree decomposition :
Details ……..
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
106. The Contourlet Transform
Decomposes The Image Into Several Directional Subbands And Multiple Scales
The CT is implemented by:
Laplacian pyramid followed by directional filter banks (Fig-01)
The CASCADE STRUCTURE allows:
- Makes possible to:
Decompose each scale into
Input image
Bandpass
Directional
subbands
Bandpass
Directional
subbands
Figure 01
The concept of wavelet:
University of Heidelburg
- The multiscale and
directional decomposition to be
independent
any arbitrary power of two's number of
directions(4,8,16…)
Figure 01: Structure of the Laplacian pyramid together with the directional filter bank
Details ………….
107. The Contourlet Transform
Decomposes The Image Into Several Directional Subbands And Multiple Scales
(a) (b)
Figure 01: (a)Structure of the Laplacian pyramid together with the directional filter bank
(b) frequency partitioning by the contourlet transform
(c) Decomposition levels and directions.
Input
image
Bandpass
Directional
subbands
Bandpass
Directional
subbands
Details….
(c)
Denote
Each subband by yi,j
Where
i =decomposition level and
J=direction
108. The Contourlet Transform
Enhancement of the Directional Subbands
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.
' ( )
yi, j f yi, j ………………..(1)
-After the enhanced subbands are obtained, the inverse
transform is performed to obtain an enhanced image.
Denote
Each subband by yi,j
Where
i =decomposition level and
J=direction Details….
109. The Contourlet Transform
Enhancement of the Directional Subbands
Details….
The directional subbands are enhanced using equation 2.
f (yi, j )
1 , W n n
yi j
( 1, 2)
2 , W n n
yi j
( 1, 2)
If bi,j(n1,n2)=0
If bi,j(n1,n2)=1
………..(2)
Denote
Each subband by yi,j
Where
i =decomposition level and
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
110. The Contourlet Transform
Enhancement of the Directional Subbands
The directional subbands are enhanced using equation 2.
f (yi, j )
1 , W n n
yi j
( 1, 2)
2 , W n n
yi j
( 1, 2)
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
111. The Contourlet Transform
Threshold Selection
Details….
In order to obtain a binary image:
A threshold Ti,j for each subband is calculated.
The threshold calculation is based:
-When mammograms are transformed into the CT domain.
The microcalcifications
appear :
On each subband
Over a very
homogeneous background.
Most of the transform coefficients:
-Are grouped around the mean value of
the subband correspond to the background
-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 .
112. The Contourlet Transform
Weight Selection
Details….
Exhaustive tests:
-Consist on evaluating subjectively a set of 15 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.
A conservative threshold of 3σi;j is selected:
where σi;j is the standard deviation of the corresponding subband y I,j .
113. Metrics
To compare the ability of :
Enhancement achieved by the proposed method.
Why?
Measures used to compare:
1. Distribution Separation Measure (DSM),
2. The Target to Background Contrast enhancement (TBC) and
3. The Target to Background Enhancement Measure based on Entropy (TBCE) [14].
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
114. Metrics
Measures used to compare: 1. Distribution Separation Measure (DSM)
The DSM represents :
How separated are the distributions of each mammogram
DSM = |μucalcE -μtissueE |- |μucalc0 -μtissue0 | …………………………(3)
Defined by:
Where:
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
115. Metrics
2. Target to Background Contrast Enhancement
Measure (TBC). Measures used to compare:
The TBC Quantifies :
The improvement in difference between the background and the target(MC).
…………………………(4)
μucalc
μtissue
E
0
0
0
E
μucalc
μtissue
E
μucalc
μucalc
TCB
Defined by:
Where:
μucalcE
μucalc0
= Standard deviations of the microcalcifications region in the enhanced image
= Standard deviations of the microcalcifications region in the original image
116. Metrics
3.Target to Background Enhancement Measure
Based on Entropy(TBCE) Measures used to compare:
The TBCE Measures :
- An extension of the TBC metric
- Based on the entropy of the regions rather
than in the standard deviations
Defined by:
Where:
…………………………(5)
μucalc
μtissue
E
0
0
0
E
μucalc
μtissue
E
μucalc
μucalc
TCB
= Entropy of the microcalcifications region in the enhanced image
= Entropy of the microcalcifications region in the original image
μucalcE
μucalc0
118. Experimental Results
(a)Original image (b)NSTC method (c)The DWT Method
For visualization purposes :
The ROI in the original mammogram
are marked with a square.
These regions contain :
• Clusters of microcalcifications (target)
• surrounding tissue (background).
120. Experimental Results Analysis
The proposed method gives higher results than the wavelet-based method.
DMS, TBC and TBCE metrics on the enhanced mammograms
1.2
1
0.8
0.6
0.4
0.2
0
TBC
TBC Matrix
Mammogram
NSCT DWT
121. Experimental Results Analysis
The proposed method gives higher results than the wavelet-based method.
DMS, TBC and TBCE metrics on the enhanced mammograms
1.2
1
0.8
0.6
0.4
0.2
0
TBCE
TBCE Matrix
Mammogram
NSCT DWT
122. Experimental Results Analysis
The proposed method gives higher results than the wavelet-based method.
DMS, TBC and TBCE metrics on the enhanced mammograms
1.2
1
0.8
0.6
0.4
0.2
0
DSM
DSM Matrix
Mammogram
NSCT DWT
123. Experimental Results Analysis
Mesh plot of a ROI containing microcalcifications
(a)The original
mammogram
(mdb252.bmp)
(b) The enhanced
mammogram
using NSCT
126. Experimental Results Analysis
More peaks corresponding to microcalcifications are enhanced
The background has a less magnitude with respect to the peaks:
-The microcalcifications are more visible.
Observation:
127.
128. 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)
129. 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
130. Reference
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)
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