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International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 5



          Case study of CAD Based Mammographic Lesions using Wavelet
                                 Decomposition
                                       Elayabharathi.T1, Dr.Nagappan.A2
   1
       is a research Scholar in the Department of computer science &engineering at the Vinayaka mission research foundation
                                           deemed university, Salem, Tamilnadu, India.



Abstract – This paper describes the efforts by study of the characteristics of true masses compared to the falsely detected
masses is carried out using wavelet decomposition transform. According to the cancer statistics, the breast cancer incidence rate
is increased almost every year since 1980, the death rate is shown a substantial decrease. Both trends may be attributed, in large
part to mammography which is widely recognized as the most sensitive technique for breast cancer detection

Index terms –Lesions, Wavelet, contourlet, Mammogram, CAD

1. Introduction                                                     difficulty in maximizing both sensitivity to tumoral
          Conventional mammography is a film based x-ray            growths and specificity in identifying their nature.
Technique referred as a screen-film mammography. Full               X-ray mammography is the best current method for early
field digital mammography is a new technology in which a            detection of breast cancer, with an accuracy of between
solid state detector is used instead of film for the generation     85% and 95%[3]. Identifying abnormalities such as
of the breast image. Modern applications, including                 calcifications and masses often requires the eye of a
computer aided detection and computer aided diagnosis,              trained radiologist. As a result, some anomalies may be
computer display and interpretation, digital image and              missed due to human error as a result of fatigue, etc.
transmission and storage, require a digital format of the           The development of CAD systems that assist the
mammogram                                                           radiologist has thus become of prime interest, the aim
1.1 Objective                                                       being not to replace the radiologist but to offer a second
          The purpose of our study was to retrospectively           opinion. Eventually, the state-of-the-art could advance to
evaluate the impact on recall rates and cancer detection            the point where such systems effectively substitute for
when converting from film-screen to digital mammography             trained radiologists, an eventuality that is desirable for
in a small community-based radiology practice.                      small outfits that cannot afford to have an expert
Digital mammography offers considerable advantages over             radiologist at their continuous disposal. For example, a
film-screen mammography [1-3]. Despite advantages, it has           CAD system could scan a mammogram and draw red
been slow to be adopted. This reluctance is due to many             circles around suspicious areas. Later, a radiologist can
factors, including the high initial capital expenditure and the     examine these areas and determine whether they are
question of whether the added expense results in a better           true lesions or whether they are artifacts of the scanning
mammography “product” [4-7]. The reluctance to upgrade              process, such as shadows.
to digital mammography is especially true of small
community-based imaging centers, where capital is less              To our knowledge, no prior study has compared cancer
prevalent and patient volumes are lower than in larger              detection and recall rates at a single center before and after
metropolitan locations.                                             the installation of a digital mammography system, keeping
1.2 statistics and discussions                                      the interpreting radiologists constant. Such a study would
      Breast cancer ranks first in the causes of cancer             limit the number of uncontrolled variables, allowing
deaths among women and is second only to cervical                   potential outcomes to be mediated only by the introduction
cancer in developing countries[8]. The best way to                  of the technology and the variability in the women
reduce death rates due to this disease is to treat it at an         undergoing screening.
early stage. Early diagnosis of breast cancer requires an           2. Background
effective procedure to allow physicians to differentiate                Considerable effort has been expended to develop
between benign tumors               from malignant ones.            CAD systems to aid the trained radiologist identify
Developing computer-aided diagnosis (CAD) systems to                areas with possible pathology on an image. Most of
help with this task is a non-trivial problem, and current           these efforts have concentrated on X-ray mammography
methods employed in pursuit of this goal illustrate the             and chest radiography. A number of CAD schemes

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International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 5



have been investigated in literature. These include:              3. Methods
                                                                     By careful consideration of the design of various
•   Subtraction techniques that identify anomalies by             CAD schemes, it is possible to categorize the techniques
    comparison with normal tissue                                 employed under three broad headings:
•   Topographic techniques that perform feature
    extraction and analysis to identify anomalies                 •     Data reduction - the image is examined in order
•   Filtering techniques that use digital signal                        to identify the ROIs.
    processing filters, often developed especially to             •     Image enhancement - the ROIs are subjected to
    augment anomalies for easy detection                                processes that enhance or augment the visibility of
•   staged expert systems that perform rule-based                       pathological anomalies, such as microcalcifications
    analysis of image data in an attempt to provide a                   and lesions.
    correct diagnosis
                                                                  •     Diagnosis - the ROIs are subjected to one or more
          The majority of CAD systems attempt to                        of the broad categories of procedures mentioned in
identify anomalies by either looking for image                          Section 2 in order to arrive at a diagnosis, most
differences based on comparison with known normal                       commonly in the form of “benign” or “malignant”
tissue (subtraction techniques)[4] or by image feature
identification and extraction of features that correlate               These categories are extremely broad, and there
with pathological anomalies, such as in texture analysis          may exist CAD systems           that subject images to
(topographic techniques)[11, 4, 6, 36]. Most systems              techniques that do not fall under one of them. However,
proceed in stages, first examining the image data and             most of the CAD systems employ methods that can be
extracting pre-determined features, then localizing               classified under one or more of them.
regions of interest or ROIs which can be examined
further     for potential anomalies.     High degrees of          3.1      Data Reduction
sensitivity have been achieved using several of these                      Data reduction is the process by which an image
techniques, but many have been hampered by high                   is decomposed into a collection of regions that appear to
false-positive rates and hence low specificity. The               contain anomalies that differ from the surrounding
problem of false positives is compounded further by               tissue. These regions are usually a strict subset of the
the fact that false positive rates are reported per               original image and are subregions of the original image
image, not per case.            Since many radiological           that may contain ROIs. By doing this, the CAD system
examinations i n c l u d e more than one image, the actual        need only process those subregions identified by the data
number of false positives may be a multiple of those              reduction step, rather than the entire input image. Data
reported.                                                         reduction           accomplishes       two      objectives
      A number of different approaches have been                  simultaneously[34]:
employed in an effort to reduce false positive rates, many
of them focusing on the use of artificial neural                  •    An increase in throughput v i a a reduction in input
networks (ANNs). A common metric used for evaluating                   data
the performance of CAD systems, the receiver operating            • A reduction in false positives by limiting the scope
curve or ROC (see Appendix A), is commonly used to                     of the detection algorithms in the rest of the CAD
evaluate a CAD scheme’s degree of tradeoff between                     system to the ROIs only. With less of the original
sensitivity and specificity. The area under this curve,                image to worry about, the CAD system gains
Az , is a measure of overall performance, with a value of              specificity since less image means less false-
Az closer to 1 indicating better performance. Since                    positives in general, assuming that the detection
                                                                       algorithms work as intended.
sensitivity in most techniques is quite high, specificity
                                                                            It is clear that the most obvious way to perform
often becomes the limiting factor, with techniques                data reduction is to have a trained radiologist identify
displaying higher specificity performing at higher Az             the ROIs for the CAD system.                This can be
values.                                                           accomplished through a graphical interface to the CAD
          This study decomposes several techniques and            system that allows the radiologist to specify suspicious
identifies their salient features and characteristics w i t h     regions. It should be noted that some CAD systems do
respect to performance.        The extent of the array o f        not require this step at all due to the nature of their
techniques e x a m i n e d herein is by no means all-             diagnostic process, such as that those that employ
inclusive; rather, a number of techniques are described           subtraction techniques.
and their performance evaluated.

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International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 5



                                                                   can then be used by a radiologist; however, the CAD
                                                                   scheme proposed in
                                                                   [2] uses pseudo-color mapping[10] to convert the
                                                                   grayscale to a color image. This is done since human
                                                                   vision can only discern a limited number of grayscale
                                                                   levels. The end results is a pseudo-color breast map in
                                                                   which the lesions have been highlighted in different
                                                                   colors and confirmed by visual inspection by a trained
                                                                   radiologist. Anguh et al[2] claim that this multiscale
                                                                   segmentation       and enhancement method            detects
                                                                   virtually all lesions identified by an expert radiologist in
                                                                   the process of visual inspection in initial tests on 25
                                                                   mammograms.

                                                                   4. Wavelet-Based Enhancement
                                                                            Koren et al[18]         developed a contrast
 Figure 1: overview of front-end data reduction module with        enhancement method based on the adaptation           of
                           images                                  specific     enhancement      schemes     for  distinct
                                                                   mammographic features, which were then used to
3.2 Image Enhancement                                              combine the set of processed images into an enhanced
     Mammographic image enhancement methods are                    image. In their scheme, the mammo- graphic image is
typically aimed at either improvement of the overall               first processed for enhancement of microcalcifications,
visibility of features or enhancement of a specific sign           masses and stellate lesions.       From the resulting
of malignancy. Various schemes for doing this exist,               enhanced image, the final enhanced image is
with most of them          based in signal processing              synthesized by means of image fusion[20]. Specifically,
techniques used either in their original form (such as             their algorithm consisted of two major steps:
simple histogram equalization) or adapted for specific
use in mammography.                                                1. the image is first subjected to a redundant B-spline
     A number of generic image enhancement methods                     wavelet transform decomposition[18]
exist.     Histogram equalization and fuzzy image                      from which a set of wavelet coefficients is obtained
enhancement[35] are just two examples. Though a                    2. the wavelet coefficients are modified distinctly for
whole slew of image enhancement techniques exist in the                each type of malignancy (microcal- cifications,
general domain, very few are specifically targeted at the              stellate lesions or circumscribed masses).
enhancement of mammographic         images. Section 4              3. the multiple sets of coefficients thus obtained are
describes one of them.                                                 fused into a single set from which the reconstruction
3.3 Statistical Techniques                                             is computed The algorithm is illustrated in Figure
                                                                       2, as applied to a digitized mammogram that they
     Anguh et al[2] propose a multiscale method for                    obtained from the University of Florida database.
segmenting and enhancing lesions of various sizes in                   The theoretical treatment for the mathematics
mammograms.       The first stage applies a multiscale                 involved in this scheme is beyond the scope of this
automatic threshold esti- mator based on histogram                     study. However, it is interesting to note that the
moments to segment the mammogram at multilevels.                       enhance image produced by this scheme is “more
The second stage then converts the segmented image                     easily interpreted by a radi- ologist compared to
using pseudo-color mapping to produce a color                          images      produced     via    global  enhancement
image[2]. The final result is analogous to a breast map                techniques”[18].      It is yet to be seen what
which provides an adequate basis for radiological breast               improvement this enhancement scheme can
tissue differentiation      and analysis in digital                    contribute t o existing CAD schemes.
mammography. Their paper provides a treatment on the
mathematical theory of moments before present an
algorithm for the multiscale thresholding        of the
mammogram. The result of this thresholding technique
is a mammographic map or breast map based on
various thresholds with varying object sizes. This map

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International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 5




                                                                   where 0 ≤ u ≤ 1.




 Figure 2. Overview of the image fusion algorithm based
             on B-Spline Wavelet Transform

5. Classification
         Apply B´zier splines[17] to both lesion
                    e
detection and characterization, where lesion detection
is achieved      by segmentation       using a threshold
computed from the B´zier smoothed histogram and
                         e
lesion characterization is achieved by means of fitness
between Gaussian and B´zier histograms of data
                              e
projected on principal components of the segmented                 Figure 7. System overview of the B´zier spline-based
                                                                                                        e
lesions. The most interesting component of their                   thresholding and segmentation algorithm.
systems in the use of the B´zier splines as a basis of
                                e
thresholding of the mammographic image - the overall               6. Results
performance of their classification scheme is significantly            The database used for this work comes from
worse than that seen from, for example, the ANN-based              vina yaka mis sio ns hospital and is a set of 43 digitalized
scheme used by Chen et al[2],                                      mammographic images, 25 of them corresponding to benign
     B´zier splines are a spline approximation method,
      e                                                            pathologies and 18 to breast cancer. Due to the good
developed by the French engineer Pierre B´zier for use
                                              e                    performance of the detection stage, only few
in the design of Renault automobile bodies. Since a                microcalcifications are not detected. Detection of the
B´zier curve lies within the convex hull of the control
  e                                                                maximum possible number of microcalcificactions is very
points on which it is fitted, applying it to the                   important for the success of the system, being very critical
histogram of the original image produces a smoothed                the correct adjustment of noise thresholds in the contourlet
histogram from which a threshold can be easily chosen              pre-processing stage.
by simply finding the largest minimum or the
rightmost inflection point, which is where the highest
                                                                   7. Conclusions
brightness level is located. As a rule, a B´zier curve
                                                e
                                                                            The proposed system combines several state of the
is a polynomial of degree one less than the number of
                                                                   art image processing techniques, namely contourlet
control points used. Since a typicalgrayscale image
                                                                   transforms for the noise removal of the mammographic
consists of 256 brightness levels, the histogram values of
                                                                   images and border detection with the wavelet transform
these levels can be used as the control points for a B´zier
                                                      e
                                                                   modulus maxima lines. The tested wavelet based
curve polynomial of degree 255. If the histogram levels
                                                                   compression method proved to be an accurate approach
are denoted by pk = (xk , yk ), where both k and xk
                                                                   for digitized mammography.
vary from 0 to 255, then these coordinate
points can be blended to produce a position vector P
(u) which describes the path of an approximating                   References
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International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 5 - Case study of CAD Based Mammographic Lesions using Wavelet Decomposition

  • 1. International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 5 Case study of CAD Based Mammographic Lesions using Wavelet Decomposition Elayabharathi.T1, Dr.Nagappan.A2 1 is a research Scholar in the Department of computer science &engineering at the Vinayaka mission research foundation deemed university, Salem, Tamilnadu, India. Abstract – This paper describes the efforts by study of the characteristics of true masses compared to the falsely detected masses is carried out using wavelet decomposition transform. According to the cancer statistics, the breast cancer incidence rate is increased almost every year since 1980, the death rate is shown a substantial decrease. Both trends may be attributed, in large part to mammography which is widely recognized as the most sensitive technique for breast cancer detection Index terms –Lesions, Wavelet, contourlet, Mammogram, CAD 1. Introduction difficulty in maximizing both sensitivity to tumoral Conventional mammography is a film based x-ray growths and specificity in identifying their nature. Technique referred as a screen-film mammography. Full X-ray mammography is the best current method for early field digital mammography is a new technology in which a detection of breast cancer, with an accuracy of between solid state detector is used instead of film for the generation 85% and 95%[3]. Identifying abnormalities such as of the breast image. Modern applications, including calcifications and masses often requires the eye of a computer aided detection and computer aided diagnosis, trained radiologist. As a result, some anomalies may be computer display and interpretation, digital image and missed due to human error as a result of fatigue, etc. transmission and storage, require a digital format of the The development of CAD systems that assist the mammogram radiologist has thus become of prime interest, the aim 1.1 Objective being not to replace the radiologist but to offer a second The purpose of our study was to retrospectively opinion. Eventually, the state-of-the-art could advance to evaluate the impact on recall rates and cancer detection the point where such systems effectively substitute for when converting from film-screen to digital mammography trained radiologists, an eventuality that is desirable for in a small community-based radiology practice. small outfits that cannot afford to have an expert Digital mammography offers considerable advantages over radiologist at their continuous disposal. For example, a film-screen mammography [1-3]. Despite advantages, it has CAD system could scan a mammogram and draw red been slow to be adopted. This reluctance is due to many circles around suspicious areas. Later, a radiologist can factors, including the high initial capital expenditure and the examine these areas and determine whether they are question of whether the added expense results in a better true lesions or whether they are artifacts of the scanning mammography “product” [4-7]. The reluctance to upgrade process, such as shadows. to digital mammography is especially true of small community-based imaging centers, where capital is less To our knowledge, no prior study has compared cancer prevalent and patient volumes are lower than in larger detection and recall rates at a single center before and after metropolitan locations. the installation of a digital mammography system, keeping 1.2 statistics and discussions the interpreting radiologists constant. Such a study would Breast cancer ranks first in the causes of cancer limit the number of uncontrolled variables, allowing deaths among women and is second only to cervical potential outcomes to be mediated only by the introduction cancer in developing countries[8]. The best way to of the technology and the variability in the women reduce death rates due to this disease is to treat it at an undergoing screening. early stage. Early diagnosis of breast cancer requires an 2. Background effective procedure to allow physicians to differentiate Considerable effort has been expended to develop between benign tumors from malignant ones. CAD systems to aid the trained radiologist identify Developing computer-aided diagnosis (CAD) systems to areas with possible pathology on an image. Most of help with this task is a non-trivial problem, and current these efforts have concentrated on X-ray mammography methods employed in pursuit of this goal illustrate the and chest radiography. A number of CAD schemes Issn 2250-3005(online) September| 2012 Pag1318
  • 2. International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 5 have been investigated in literature. These include: 3. Methods By careful consideration of the design of various • Subtraction techniques that identify anomalies by CAD schemes, it is possible to categorize the techniques comparison with normal tissue employed under three broad headings: • Topographic techniques that perform feature extraction and analysis to identify anomalies • Data reduction - the image is examined in order • Filtering techniques that use digital signal to identify the ROIs. processing filters, often developed especially to • Image enhancement - the ROIs are subjected to augment anomalies for easy detection processes that enhance or augment the visibility of • staged expert systems that perform rule-based pathological anomalies, such as microcalcifications analysis of image data in an attempt to provide a and lesions. correct diagnosis • Diagnosis - the ROIs are subjected to one or more The majority of CAD systems attempt to of the broad categories of procedures mentioned in identify anomalies by either looking for image Section 2 in order to arrive at a diagnosis, most differences based on comparison with known normal commonly in the form of “benign” or “malignant” tissue (subtraction techniques)[4] or by image feature identification and extraction of features that correlate These categories are extremely broad, and there with pathological anomalies, such as in texture analysis may exist CAD systems that subject images to (topographic techniques)[11, 4, 6, 36]. Most systems techniques that do not fall under one of them. However, proceed in stages, first examining the image data and most of the CAD systems employ methods that can be extracting pre-determined features, then localizing classified under one or more of them. regions of interest or ROIs which can be examined further for potential anomalies. High degrees of 3.1 Data Reduction sensitivity have been achieved using several of these Data reduction is the process by which an image techniques, but many have been hampered by high is decomposed into a collection of regions that appear to false-positive rates and hence low specificity. The contain anomalies that differ from the surrounding problem of false positives is compounded further by tissue. These regions are usually a strict subset of the the fact that false positive rates are reported per original image and are subregions of the original image image, not per case. Since many radiological that may contain ROIs. By doing this, the CAD system examinations i n c l u d e more than one image, the actual need only process those subregions identified by the data number of false positives may be a multiple of those reduction step, rather than the entire input image. Data reported. reduction accomplishes two objectives A number of different approaches have been simultaneously[34]: employed in an effort to reduce false positive rates, many of them focusing on the use of artificial neural • An increase in throughput v i a a reduction in input networks (ANNs). A common metric used for evaluating data the performance of CAD systems, the receiver operating • A reduction in false positives by limiting the scope curve or ROC (see Appendix A), is commonly used to of the detection algorithms in the rest of the CAD evaluate a CAD scheme’s degree of tradeoff between system to the ROIs only. With less of the original sensitivity and specificity. The area under this curve, image to worry about, the CAD system gains Az , is a measure of overall performance, with a value of specificity since less image means less false- Az closer to 1 indicating better performance. Since positives in general, assuming that the detection algorithms work as intended. sensitivity in most techniques is quite high, specificity It is clear that the most obvious way to perform often becomes the limiting factor, with techniques data reduction is to have a trained radiologist identify displaying higher specificity performing at higher Az the ROIs for the CAD system. This can be values. accomplished through a graphical interface to the CAD This study decomposes several techniques and system that allows the radiologist to specify suspicious identifies their salient features and characteristics w i t h regions. It should be noted that some CAD systems do respect to performance. The extent of the array o f not require this step at all due to the nature of their techniques e x a m i n e d herein is by no means all- diagnostic process, such as that those that employ inclusive; rather, a number of techniques are described subtraction techniques. and their performance evaluated. Issn 2250-3005(online) September| 2012 Pag1319
  • 3. International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 5 can then be used by a radiologist; however, the CAD scheme proposed in [2] uses pseudo-color mapping[10] to convert the grayscale to a color image. This is done since human vision can only discern a limited number of grayscale levels. The end results is a pseudo-color breast map in which the lesions have been highlighted in different colors and confirmed by visual inspection by a trained radiologist. Anguh et al[2] claim that this multiscale segmentation and enhancement method detects virtually all lesions identified by an expert radiologist in the process of visual inspection in initial tests on 25 mammograms. 4. Wavelet-Based Enhancement Koren et al[18] developed a contrast Figure 1: overview of front-end data reduction module with enhancement method based on the adaptation of images specific enhancement schemes for distinct mammographic features, which were then used to 3.2 Image Enhancement combine the set of processed images into an enhanced Mammographic image enhancement methods are image. In their scheme, the mammo- graphic image is typically aimed at either improvement of the overall first processed for enhancement of microcalcifications, visibility of features or enhancement of a specific sign masses and stellate lesions. From the resulting of malignancy. Various schemes for doing this exist, enhanced image, the final enhanced image is with most of them based in signal processing synthesized by means of image fusion[20]. Specifically, techniques used either in their original form (such as their algorithm consisted of two major steps: simple histogram equalization) or adapted for specific use in mammography. 1. the image is first subjected to a redundant B-spline A number of generic image enhancement methods wavelet transform decomposition[18] exist. Histogram equalization and fuzzy image from which a set of wavelet coefficients is obtained enhancement[35] are just two examples. Though a 2. the wavelet coefficients are modified distinctly for whole slew of image enhancement techniques exist in the each type of malignancy (microcal- cifications, general domain, very few are specifically targeted at the stellate lesions or circumscribed masses). enhancement of mammographic images. Section 4 3. the multiple sets of coefficients thus obtained are describes one of them. fused into a single set from which the reconstruction 3.3 Statistical Techniques is computed The algorithm is illustrated in Figure 2, as applied to a digitized mammogram that they Anguh et al[2] propose a multiscale method for obtained from the University of Florida database. segmenting and enhancing lesions of various sizes in The theoretical treatment for the mathematics mammograms. The first stage applies a multiscale involved in this scheme is beyond the scope of this automatic threshold esti- mator based on histogram study. However, it is interesting to note that the moments to segment the mammogram at multilevels. enhance image produced by this scheme is “more The second stage then converts the segmented image easily interpreted by a radi- ologist compared to using pseudo-color mapping to produce a color images produced via global enhancement image[2]. The final result is analogous to a breast map techniques”[18]. It is yet to be seen what which provides an adequate basis for radiological breast improvement this enhancement scheme can tissue differentiation and analysis in digital contribute t o existing CAD schemes. mammography. Their paper provides a treatment on the mathematical theory of moments before present an algorithm for the multiscale thresholding of the mammogram. The result of this thresholding technique is a mammographic map or breast map based on various thresholds with varying object sizes. This map Issn 2250-3005(online) September| 2012 Pag1320
  • 4. International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 5 where 0 ≤ u ≤ 1. Figure 2. Overview of the image fusion algorithm based on B-Spline Wavelet Transform 5. Classification Apply B´zier splines[17] to both lesion e detection and characterization, where lesion detection is achieved by segmentation using a threshold computed from the B´zier smoothed histogram and e lesion characterization is achieved by means of fitness between Gaussian and B´zier histograms of data e projected on principal components of the segmented Figure 7. System overview of the B´zier spline-based e lesions. The most interesting component of their thresholding and segmentation algorithm. systems in the use of the B´zier splines as a basis of e thresholding of the mammographic image - the overall 6. Results performance of their classification scheme is significantly The database used for this work comes from worse than that seen from, for example, the ANN-based vina yaka mis sio ns hospital and is a set of 43 digitalized scheme used by Chen et al[2], mammographic images, 25 of them corresponding to benign B´zier splines are a spline approximation method, e pathologies and 18 to breast cancer. Due to the good developed by the French engineer Pierre B´zier for use e performance of the detection stage, only few in the design of Renault automobile bodies. Since a microcalcifications are not detected. Detection of the B´zier curve lies within the convex hull of the control e maximum possible number of microcalcificactions is very points on which it is fitted, applying it to the important for the success of the system, being very critical histogram of the original image produces a smoothed the correct adjustment of noise thresholds in the contourlet histogram from which a threshold can be easily chosen pre-processing stage. by simply finding the largest minimum or the rightmost inflection point, which is where the highest 7. Conclusions brightness level is located. As a rule, a B´zier curve e The proposed system combines several state of the is a polynomial of degree one less than the number of art image processing techniques, namely contourlet control points used. Since a typicalgrayscale image transforms for the noise removal of the mammographic consists of 256 brightness levels, the histogram values of images and border detection with the wavelet transform these levels can be used as the control points for a B´zier e modulus maxima lines. The tested wavelet based curve polynomial of degree 255. If the histogram levels compression method proved to be an accurate approach are denoted by pk = (xk , yk ), where both k and xk for digitized mammography. vary from 0 to 255, then these coordinate points can be blended to produce a position vector P (u) which describes the path of an approximating References B´zier polynomial between p 0 and p255 : e [1] Predrag Baki’c And. Application of neural networks in computer aided diagnosis of breast cancer. http://citeseer.nj.nec.com/404677.html. [2] M.M. Anguh and A.C. Silva. Multiscale segmentation and enhancement in mammo- grams. Issn 2250-3005(online) September| 2012 Pag1321
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