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Enhancement of Mammographic Images using Morphology and Wavelet
Transform Harish Kumar.N1 Amutha. S2 Dr. Ramesh Babu .D. R3
1Lecturer, Dept. of CSE, Dayananda Sagar College of Engineering, Bangalore, India 2Assistant Professor, Dept of CSE, Dayananda Sagar College of Engineering, Bangalore, India
3Professor, Dept. of CSE, Dayananda Sagar College of Engineering, Bangalore, India
[email protected] [email protected]
Abstract
Mammography is the effective technology for early detection
of breast cancer and breast tumour analysis. In
mammography, low dose x-ray is used for imaging. Due to
the low dose X-ray the images obtained from mammography
are poor in contrast and are contaminated by noise. Hence it
is difficult for the radiologist to screen the mammograms for
any abnormalities like microcalcifications and masses. This
ensures the need for image enhancement to aid radiologist
for interpretation. This paper introduces a new enhancement
method for digital mammographic images based on modified
mathematical morphology and biorthogonal wavelet
transform. In the proposed method we adopted a level
dependent threshold for thresholding the detail coefficients of
wavelet transform. To evaluate the performance of the
proposed method, Contrast Improvement Index (CII) and
Edge Preservation Index (EPI) are used. Experimental results
and performance analysis indicate that the proposed method
consistently outperforms existing techniques.
1. Introduction Breast cancer is the most common cancer among
women in the United States [1]. It is the leading cause
for death of women between the ages 35 and 54. Early
detection is the most successful method of dealing with
breast cancer. Currently the best method available for
early detection of breast cancer is mammography.
Other techniques, such as computed tomography (CT),
magnetic resonance imaging (MRI), ultrasound and
transillumination have been investigated, but
mammography remains the proven technique. A
mammogram is a picture of breast taken with a safe,
low dose X-ray machine. Generally, mammograms are
poor in contrast and features that indicate the breast
cancer are very minute. Digitally enhancing the
mammograms will provide us confident interpretation
of critical cases, as well as allowing quicker diagnosis.
It is very difficult to interpret the x-ray mammograms
because of small differences in image density of
various breast tissues in particular for dense breasts [2].
When the radiologists screen the mammograms with
low dose X-ray the images obtained are poor in
contrast.
In low-contrast mammograms, it is difficult to
interpret between the normal tissue and malignant
tissue. In general while screening the mammograms,
due to imperfect machines, the obtained mammograms
are contaminated by noise. Image enhancement
techniques have been widely used in the field of
radiology where the subjective quality of images is
important for human interpretation and diagnosis.
Numerous algorithms are available in literature for
enhancement of medical images such as histogram
equalization, unsharp masking, median filter, Gaussian
filters, and morphological filters [3, 4]. Conventional
image enhancement techniques do not perform well on
mammographic images. Recently multiscale techniques
have evolved and sparked the interest of researchers for
contrast enhancement of mammographic images.
Nowadays wavelet domain has gained more popularity
in image denoising rather than conventional spatial
domain techniques such as average, median, min-max
filters. In wavelet domain each noisy coefficient is
modified according to certain threshold calculated. The
threshold is applied to each noisy coefficient to obtain
better performance. However, soft thresholding is most
widely used in the literature [5].
The organization of the rest of the paper is as
follows: Section 2 presents review of recent literature.
Section 3, describes the proposed Enhancement
method. Section 4 highlights the results of extensive
experimentation conducted on some mammographic
images. Finally conclusion is discussed.
Harish Kumar N et al,Int.J.Computer Techology & Applications,Vol 3 (1),192-198
IJCTA | JAN-FEB 2012 Available [email protected]
192
ISSN:2229-6093
2. Review of Literature Some work has been done in the past for the
enhancement of mammograms. Dhawan et al. [6]
proposed an optimal adaptive neighborhood processing
algorithm with a set of contrast enhancement functions
to enhance the mammographic features. The method
was the improvement of the earlier work developed by
Gordon and Ranagayyan [6].The method can enhance
the desired, but unseen or barely seen features of an
image with little enhancement of the noise and other
background variations. Tomklav StojiC et.al. [7]
Proposed a new algorithm for both local contrast
enhancement and background texture suppression in
digital Mammographic images. The algorithm was
based on mathematical morphology applied to gray-
scale image processing. The algorithm was not efficient
in enhancing the micro calcifications in digital
mammograms. Yajie Sun et.al. [8] developed an
adaptive-neighborhood contrast enhancement algorithm
(ANCE) for skin-line extraction. ANCE is used to
enhance the parenchyma of the breast and suppress the
background noise. Suppression of the background noise
can improve skin-line extraction and skin line
extraction is an important step in CAD. The method
can enhance only the skin-line rather than the whole
image. Heinlein et al. [9] proposed an algorithm for
enhancing microcalcifications in mammograms based
on filter banks derived from continuous wavelet
transformation, which were called integrated wavelets.
The major disadvantage of the method was that it
required an empirical selection of appropriate
thresholds for image denoising, as well as the
specification of an appropriate size range for the
structures to be enhanced [10]. Sakellaropoulos et al.
[10] developed a method to enhance contrast with
redundant dyadic wavelet transform. The method can
enhance the contrast of the mammograms and depress
the image noise. Jiang et al. [11] developed a method to
enhance possible microcalcifications combining fuzzy
logic and structure tensor. In the method, a structure
tensor operator was first produced and was then applied
to each pixel of the mammographic image, which
resulted in an eigenimage. The eigenimage was used to
combine with the fuzzy image which was obtained by a
fuzzy transform from the original image to enhance the
contrast. This method can suppress non-MCs regions
while enhancing the MC’s regions. The method is
complex in nature due to fuzziness and combination of
two different domains need expertise. Scharcanski et al.
[12] developed a wavelet transform based adaptive
method for contrast enhancement and noise reduction
in mammographic images. In this method, the images
were first pre-processed to improve the local contrast
and subtle details, then the pre-processed images were
transformed into wavelet domain for noise reduction
and edge enhancement. Although the method gave
good enhancement results the complexity of the
algorithm is more due to the wavelet domain. . Hence a
method with better results for improvement in contrast
as well as denoising of mammogram images is
necessary.
3. Proposed Method The basic enhancement needed in mammography is
the increase in contrast and denoising, especially for
dense breasts. The enhancement model takes
mammographic image I(x, y) as input. The image I(x,
y) is separated into low frequency and high frequency
components by using Gaussian low pass filter to get a
higher degree of control over dynamic range. For the
low pass filtered image L(x,y), modified mathematical
morphology is applied. The high pass filtered image
H(x,y) contains the edge information and the noise.
Edge Enhancement algorithm is applied to the high
pass filtered image to enhance the edge information and
to attenuate the noise. Then morphologically processed
image M(x,y) and Edge Enhanced image EE(x,y) are
added to get the contrast enhanced Image C(x,y). To
remove the noise wavelet transform is applied. Wavelet
transform consists of three operations: wavelet
decomposition, thresholding detail coefficients and
wavelet reconstruction. Approximation and detail
coefficients are obtained by decomposition. For the
detail coefficients level dependent threshold is applied.
Finally the decomposed image is reconstructed by the
approximation and the modified detail coefficients
E(x,y).In the following subsections the methods used
for enhancement of mammographic images are
discussed in detail.
3.1 Modified Mathematical Morphology
Mathematical morphology originated in set theory
and finds its place in any disciplines when it is
necessary to establish the relationship between the
geometry of physical system and some of its property.
As such, morphology offers a unified and powerful
approach to different image processing problems [15],
[16]. Two simple morphological operations: Erosion
and Dilation are fundamental to morphological
processing. By combining them one can derive
different image processing algorithms.
The dilation of a gray-scale digital image I(x,y) by a
structural element S(i,j) is defined as:
I⨁S m, n = max I m − i, n − j + s i, j (1) (3.1)
The gray-scale erosion is given by Eqn. (3.2):
Harish Kumar N et al,Int.J.Computer Techology & Applications,Vol 3 (1),192-198
IJCTA | JAN-FEB 2012 Available [email protected]
193
ISSN:2229-6093
I⨂S m, n = min I m + i, n + j − S i, j (2) (3.2)
The opening of image I(x,y) by structuring element
S is defined as erosion followed by dilation and is
expressed as Eqn. (3.3). The closing of image I(x,y) is
defined as dilation followed by erosion and is given by
Eqn. 3 and Eqn. 4:
I ∘ S = I⨂S ⨁S (3) (3.3)
I S = I⨁S ⨂S (4)
Gray-scale opening can remove light details smaller
than the structuring element. Similarly gray-scale
closing removes dark details smaller than structuring
element.
The top-hat by opening is defined as the difference
between the original image and its gray scale opening
using structuring element S and it is defined as Eqn. 5:
TO = I − I ∘ S (5)
Similarly dual bottom-hat by closing is the
difference between the gray-scale closing image and
original image is represented by Eqn. 6:
BC = I S − I (6) (3.6)
Top-hat by opening yields an image that contains all
residual features removed by opening. Adding these
features back to original image has the effect of
attenuating the high intensity structures. The dual
residual obtained by using bottom-hat by closing is
then subtracted from resulting image to attenuate low
intensity structures:
C x, y = I x, y + TO − BC (7)
The mathematical morphological approach is shown
in Figure 2.
3.2 Edge Enhancement Algorithm
High-pass filtered image H(x,y) is mainly composed
of edge information and noise. The high-pass filtered
image is obtained by subtracting the low-pass filtered
image L(x,y) of the given input image from the original
input image I(x,y). Usually the edge information pixels
have small values where as the noisy pixels have high
values. The edge information has to be enhanced mean
while the noisy pixels are to be attenuated. To
accomplish this we adopt two gain parameters namely
g1 and g2. The first gain parameter is used to enhance
the edge information while the other gain parameter is
used to attenuate the noise. These gain parameters are
applied based on selecting an arbitrary pixel value such
that, the pixel values below the arbitrary pixel selected
are assumed to be the edge pixels and the pixels above
the arbitrary pixel value are noisy pixels. The arbitrary
pixel in this context is selected by taking min and max
pixel value in the high-pass filtered image and taking
the average of both. The Edge Enhancement Algorithm
is given below:
Step1: Select an arbitrary pixel a(x, y) from the high-
pass filtered image and gains G1 and G2.
Step 2: If the pixel in the image is less than a(x, y), go
to step 3. Else go to step 4.
Step 3: Multiply the pixel in image with gain G1.
Step 4: Multiply the pixel in image with gain G2,
where G2<G1.
Step 5: Add the resulting images.
3.3 Wavelet Denoising
Wavelets are mathematical functions that cut up data
into different frequency components and then study
each component with a resolution matched to its scale.
They have advantages over traditional Fourier methods
in analyzing physical situations where the signal
contains discontinuities and sharp spikes. The wavelet
denoising is accomplished in the following three steps
namely Wavelet Decomposition, Threshold Detail
Coefficients, Wavelet Reconstruction.
In this proposed method bi-orthogonal wavelet is
used for decomposition. The input image I(x,y) is
decomposed at two levels. After decomposition the
given image is realized by one approximation
coefficient and 6 detail coefficients. Bi-orthogonal
wavelet representation has many advantages compared
to orthogonal. The subband images are invariant under
translation and do not have aliasing. Smooth
symmetrical or anti symmetrical wavelet functions are
used for alleviation of boundary effects via mirror
extension of the signal. The detail coefficients obtained
after decomposition are horizontal, vertical, and
diagonal coefficients. These detail coefficients are
mainly composed of noisy details so they have to be
denoised using appropriate threshold value.
In the proposed method soft-thresholding is
employed. The level dependent threshold is calculated
at each level. The threshold is given by equation as
shown below.
T = j/2 max(dj) (8)
Where, j is level at which threshold T is computed. In
this step we perform wavelet reconstruction using the
last approximation coefficients and the modified detail
coefficients after thresholding from level N to 1. The
resulting image E(x,y) will be a contrast enhanced
denoised image which is clearer than the original image
Harish Kumar N et al,Int.J.Computer Techology & Applications,Vol 3 (1),192-198
IJCTA | JAN-FEB 2012 Available [email protected]
194
ISSN:2229-6093
and it will aid the radiologist to mark any abnormalities
like lesions, microcalcifications, and masses.
Figure 1. Enhancement Model
Figure 2. Modified Mathematical Morphology
Figure 3. Edge Enhancement Algorithm Figure3. Shows the flow chart of Edge Enhancement
algorithm. Finally the resulting image will be an edge
Low pass filtered Image
Morphologically Contrast
Enhanced Image
Tophat by opening
Erosion
Dilation
Bottom hat by
closing
Dilation
Erosion
C(x,y)
I(x,y)
G(x,y)
L(x,y)
H(x,y)
EE(x,y) M(x,y)
W(x,y)
E(x,y)
Apply Gaussian Low Pass
Filter
Modified
Mathematical
Morphology
Input mammographic
image
Low frequency components
High frequency
components
Edge Enhancement
Algorithm
Contrast Enhanced
Image
Wavelet Denoising
Enhanced Image
High frequency
component image f(x, y)
Select an Arbitrary pixel a(x, y)
a(x,y)=(min f(x,y)+max f(x,y))/2
If a(x, y)
< f(x, y)
These are edge
pixels and multiply by
gain G1
These are noisy
pixels and multiply by
gain G2 (G2<G1)
Edge Enhanced
image
Harish Kumar N et al,Int.J.Computer Techology & Applications,Vol 3 (1),192-198
IJCTA | JAN-FEB 2012 Available [email protected]
195
ISSN:2229-6093
enhanced image. The edge enhanced image and the
morphologically enhanced image of the both high-pass
and low-pass filtered images respectively, are added to
give contrast enhanced edge preserved image. Mean
while the noise content may also be enhanced due to
morphological operations and edge enhancement.
4. Experimental Results
The proposed method has been applied to more than
40 mammographic images from the standard Database,
Mammographic Image Analysis Society (MIAS) [17].
To measure the quantitative performance analysis of
the proposed method, parameters such as Contrast
Improvement Index (CII) and Edge Preservation Index
(EPI) are employed.
4.1 Contrast Improvement Index (CII)
A quantitative measure of contrast improvement can
be defined by a contrast improvement index. The
contrast improvement index is defined as follows [13]:
CII =Cprocessed
Coriginal (10)
Where, CProcessed and COriginal are the contrasts for the
processed and original images, respectively. The
contrast C of an image is defined by the following
form:
C =f−b
f+b (11)
Where, f and b denote the mean gray-level value of
the foreground and the background, respectively. The
local contrast at each pixel is measured within its 5x5
pixel neighbourhood. More the value of CII, better
improvement in contrast.
4.2 Edge Preservation Index (EPI)
The edge preservation index [14] is defined as
follows:
EPI = Ip i,j −Ip i+1,j +|Ip i,j −Ip i,j+1 |
Io i,j −Io i+1,j +|I0 i,j −I0 i,j+1 | (12) (4.2)
Where Io(i,j) is an original image pixel intensity
value for the pixel location (x,y), Ip(i, j) is the processed
image pixel intensity value for the pixel location (x,y).
The greater value of EPI gives a much better indication
of image quality.
Table 1. CII Values of enhanced mammograms at the second wavelet decomposition levels
Table 2. EPI Values of enhanced mammograms at the second wavelet decomposition level
The proposed method achieved highest CII and EPI
values as shown in Table 1and Table 2 respectively.
Figure 4 shows the resulting output for some existing
methods took for comparison with the proposed
approach.
5. CONCLUSION
In this paper a new method for enhancement of
mammograms for early detection and diagnosis of
breast cancer has been introduced. It is based on
modified mathematical morphology and Bi-orthogonal
wavelet transform. The algorithm has been applied to
more than 40 mammographic images from the standard
Database MIAS. For performance evaluation of the
proposed method, Contrast Improvement Index (CII)
and Edge Preservation Index (EPI) are adopted.
Experimental results show that the proposed method
yields significantly better image quality when
compared with other contemporary methods.
Image ID VisuShrink Bayes shrink
SURE Shrink
Proposed
Mdb 057 0.8571 0.7963 1.0793 1.49
Mdb 147 0.8566 0.8192 1.1421 1.4977
Mdb 148 0.8579 0.8322 1.1258 1.5639
Mdb 186 0.8387 0.8038 1.1342 1.660
Image ID VisuShrink Bayes shrink
SURE Shrink
Proposed
Mdb 057
0.8596 0.8618 1.1641 2.5615
Mdb 147
0.8419 0.8247 1.0093 2.2926
Mdb 148
0.8328 0.8087 1.2617 2.3573
Mdb 186
0.9537 0.9970 1.1941 2.1739
Harish Kumar N et al,Int.J.Computer Techology & Applications,Vol 3 (1),192-198
IJCTA | JAN-FEB 2012 Available [email protected]
196
ISSN:2229-6093
6. References
1] Canadian Cancer Society, Facts on Breast Cancer,
Apr.1989.
[2] P.C. Johns, M.J. Yaffe,“X-ray characterization of normal
and neoplastic breast tissues,” Physics Medical and Biology, Vol.32, no. 6, 1987, pp. 675-695.
[3]K.Thangavel, M.Karan, R.Sivakum-ar, A. Kaja Mohideen,
“Automatic detection of microcalcification in
mammograms: a review,” ICGST-GVIP Journal, Volume (5), Issue (5), May 2005.
[4]Issac N. Bankman, “Handbook of medical imaging,”
Academic Press, 2000.
[5]D. L. Donoho, “Denoising by soft-thresholding,” IEEE Transaction on Information Theory, vol. 41, May 1995.
[6] A. P. Dhawan, G. Buellon, and R. Gordon, “Enhancement
of mammographic feature by optimal adaptive neighborhood
image processing,” IEEE Trans. Med. Imag., vol. MI-6, no. 1, 1986, pp. 82–83.
[7]Tomklav StojiC, Irini Reljin, Branimir Reljin, “Local
contrast enhancement in digital mammography by using
mathematical morphology,” IEEE Transactions, 2005. [8]Yajie Sun, Jasjit Suri, Zhen Ye, Rangaraj M. Rangayyan,
Roman Janer, “Effect of adaptive neighborhood contrast
enhancement on the extraction of the breast skin line in
mammograms,” Proceedings of the IEEE , Engineering in Medicine and Biology 27th Annual Conference , Shanghai,
China, September 1-4, 2005.
[9] P. Heinlein et al., “Integrated wavelets for enhancement
of microcalcifications in digital mammography,” IEEE Transactions on Medical Imaging, vol. 22, no. 3, 2003, pp.
402–413.
[10] P. Sakellaropoulos etal,“A wavelet-based spatially
adaptive method for mammographic contrast enhancement,” Phys. Med. Biol., vol. 48, no. 6, 2003, pp. 787–803.
[11] J. Jiang et al., “Integration of fuzzy logic and structure
tensor towards mammogram contrast enhancement,”
Computer Medical Imaging and Graphics, vol. 29, no. 1, 2005, pp. 83–90.
[12] J. Scharcanski and C. R. Jung, “Denoising and
enhancing digital mammographic images for visual
screening,” Computer Medical Imaging and Graphics, vol. 30, no. 4, 2006, pp. 243–254.
[13] W. M. Morrow, R. B. Paranjape, R. M. Rangayyan, and
J. E. L. Desautels, “Region-based contrast enhancement of
mammograms,” IEEE Trans. Med. Imag., vol. 11, no. 3, pp. 392–406, 1992.
[14] M H Xie and Z M Wang, “The partial Differential
Equation Method for Image resolution Enhancement”,
Journal of Remote Sensing, Vol. 9, No. 6, 2005, pp. 673-679. [15] Gonzalez R. C and Woods R. B., Digital Image
Processing, Pearson Education, Asia, 2001.
[16] J Sara, “Image analysis and mathematical morphology,”
Academic Press, London (UK), 1982. [17]http://www.wiau.man.ac.uk/services/MIASIMIA-
mini.htm: The Mammographic Image Analysis Society: Mini
Mammography Database, 2008.
a b
c d
e
Mdb148
b
c d
e
a
Mdb147
Mdb057
Harish Kumar N et al,Int.J.Computer Techology & Applications,Vol 3 (1),192-198
IJCTA | JAN-FEB 2012 Available [email protected]
197
ISSN:2229-6093
Figure 4. (a) Original image (b) VisuShrink
(c) Bayesshrink (d) Sureshrink (e) Proposed
a b
c d
e
Mdb 186
Harish Kumar N et al,Int.J.Computer Techology & Applications,Vol 3 (1),192-198
IJCTA | JAN-FEB 2012 Available [email protected]
198
ISSN:2229-6093
Harish Kumar N et al,Int.J.Computer Techology & Applications,Vol 3 (1),192-198
IJCTA | JAN-FEB 2012 Available [email protected]
199
ISSN:2229-6093