An unsupervised scheme for detection of ... - Semantic Scholar

AN UNSUPERVISED SCHEME FOR DETECTION OF MICROCALCIFICATIONSON MAMMOGRAMS Tushar Bhangale, U. B. Desai and Upendra Shama

Department of Electrical Engineering Indian Institute of Tecnology Bombay Bombay, 400076 Email: ubdesai @ ee.iitb.ernet.in ABSTRACT

fine textural patterns in mammograms and thus we are able to develop an unsupervised scheme for detection of microcalcifications that does not make use of any a priori information as opposed to most of the techniques developed in the past.

Clusters of Microcalcifications which appear like small white grains of sand on Mammograms are the earliest signs of Breast Cancer. In this work we employ a Gabor filter bank for texture analysis of mammograms to detect microcalcifications. A subset of the Gabor filter bank with a certain central frequency and different orientations is used to obtain the Gabor-filtered images. The filtered images are then subjected to a histogram based threshold to obtain binary images. Feature vectors are computed using the binary images. A k-means clustering algorithm with a variance scaled Euclidean distance is used for segmentation of the image.

2. REVIEW OF SOME RECENT APPROACHES A number of techniques for detection of microcalcifications have been developed in the past decade. The techniques developed aim at achieving a good true positive detection and at the same time as low a false positive detection rate as is possible. J. Dengler, et a1 [ 13 propose a two-stage algorithm for, detection of microcalcifications and shape extraction. The first step achieves a size-specific and noise-invariant detection of spots using a filtering operation that involves a weighted difference of two Gaussian filters. The second step involves a morphological operation for reconstruction of shape. B. Zheng et a1 [2] have proposed a scheme that uses a neural network with spatial domain features and DCT based features as input and a spectral entropy based decision criteria. The neural algorithm uses Kalman filtering for more efficient detection. Kocur, et a1 [3] use a technique that computes features using Daubechies-4 and biorthogonal wavelets. A back-propagation neural network is used on the extracted features for feature selection. Strickland [4] has developed a wavelet transform-based two-stage scheme for detection of microcalcifications. A large number of techniques for analyzing texture have been described in the past two decades [5] - [8]. The motivation for use of Gabor filters comes from several factors: (i) these are band-pass filters and this property has an important role in texture analysis as distinct textures most often differ significantly in their dominant spatial frequencies, (ii) they can be easily tuned to different center frequencies, dilations and orientations, (iii) it was shown by Zeevi and others that Gabor filters have the ability to capture features even in presence of additive noise [9].

1. INTRODUCTION Breast cancer is the most prevalent cancer and a leading cause of death in women today. About 6% of women develop the disease during their lifetime. Moreover, the incidence is growing worldwide. As the cause of the disease is not clearly understood, primary prevention is not possible. However, since the current methods of treatment are quite effictive against breast cancer in its early stages, early detection through mammograms, is the best way to reduce mortality from breast cancer. Microcalcifications are deposits of calcium that are seen on mammograms or histological examination and are the earliest sign of the disease. Microcalcifications appear as small white spots similar to grains of sand with a diameter of less on 0.5 mm and are grouped closely together to form clusters. They are often extremely difficult to detect since: (i) they are very small in size, (ii) inhomogeneous background, (iii) small calcifications or calcifications located in a dense breast parenchyma typically have a low contrast with the background, (iv) artifacts most often mimic microcalcifications. Our main contribution to the ongoing work in the field is the development of an unsupervised scheme for detecting microcalcifications that uses features extracted using Gabor filtered images. Gabor filters are very effective in detecting

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3. TEXTURE SEGMENTATIONOF MAMMOGRAMS USING GABOR FILTERS Images are often characterized by a band of frequency rather than a single frequency and it is difficult to characterize a given image with a single filter. A set of Gabor filters is therefore necessary. Various schemes have been proposed [lo], [6] for creating a filter bank that almost uniformly covers the spatial-frequency domain in such a way that there is a minimum overlap between the filters while they cover the entire frequency range.

Fig. 1. Original image and the detection results using the preliminary analysis

3.1. Filter Bank Design We employ a scheme proposed by A. K. Jain and E Farrokhnia [lo] for calculation of parameters and filter bank design. A Gabor function is a Gaussian function modulating a sinusoid. The expression for real-valued 2-D Gabor filter is given by :

where N is the width of the image (in this work only square images were used). Br = 0.7 and Bt = n / 4 . s = 1, 2 . . .S, is the number of the scale being used, S being total number of scales used. The following center frequency (F)values were used: l&,

The above center frequencies are 1 octave apart. This choice of center frequencies also guarantees that the passband of the Gabor filter with the highest center frequency ( ( N / 4 ) & ) lies in the size of the image array N . Thus for an image of size 256 x 256, a filter bank can be created with a total of 7 center frequencies.

where F is the center frequency and oxand cy are the variances of the Gaussian envelope along the x and y axes and the spatial-frequency domain representation is given by

where A = 27roXuyand cu = l / ( 2 x o x ) ,ow = 1 / ( 2 n g Y ) and different orientations of filters are obtained via a rotation of x-y coordinate system using

(d, y') = (xcos 8 + y sin 8, --z sin 8 + y cos e)

a h , 4 h , S a . . . . ( N / 4 ) h cyclesperwidth

3.3. Calculation of Feature Vector and Unsupervised Classification The filtering operation is carried out by calculating a circular convolution of the input image I ( s , y) with the selected filter.

(3)

3.2. Selection of Parameters By appropriate selection of parameters, a Gabor filter bank that uniformly covers the spatial-frequencydomain and thus has a minimum amount of overlap between the filters can be obtained. The parameters in this scheme were calculated using:

where m and n represent the scale and orientation respectively and I is the original input image. The filtered images are divided into small non-overlapping blocks and for each block, the mean pmn and the standard deviation rsmn of the pixel intensities are calculated. A feature vector f is constructed using pmn and umnas feature components.

(4)

f = b o o goo pol 001

uz =

-and ay = A 2nou

2na,

. . .pS-lK-l

~S-lK-llT

(8)

where S and K represent the total number of scales and orientations used respectively. We now cluster the feature vectors thus generated using a k-means clustering algorithm for segmentation of microcalcifications. The algorithm is as follows:

(6)

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Step 0: (i) Select number of centers, IC. (ii) Initialize center vectors 3 where, i = 1, 2, .. . . .IC. (iii) Initialize center-spreads 3, where Qi = diag{%} where, 2 is the covariances matrix. Step 1: Assign feature vector f” to winner cluster Ri if the distance, dist = (f”- ~ ) ~ 3 -ci), - between ’ ( f the ” cluster center and the feature vector is the least. Step 2: Compute new centers and center-spreads using, 1 5 = pq &Ri f” and

2=

1

C,,,;(f”

-

-

dT

where, (Rildenotes the cardinality of the cluster. Step 3: Repeat till the centers and the center-spreads do not change.

3.4. Experimental Results The above texture segmentation algorithm was applied to 10 randomly selected unpreprocessed images of size 256 x 256. A filter bank of 56 gabor filters (7 scales and 8 orientations) was created. The detection accuracy obtained was, 78% true positive detection of clusters per image at 3.2 false positive clusters per image. Figure 1 shows an example. The number of categories IC used while implementing the k-means clustering algorithm was 4 in all the cases.

Fig. 2. A ‘difficult-to-diagnosis’ case, Gabor filtered image at orientation 30°, histogram thresholded image and the detected microcalcifications. A feature vector was constructed using the binary image. Images were divided into nonoverlapping blocks of size 6 x 6. The features calculated include: (i) N;mber of non-zero pixels in the window. (ii) Number of non-zero pixels in the neighboring eight blocks of size 6 x 6. Unsupervised classification of the feature vectors was carried out using the k-means clustering algorithm. Figure 2 shows the steps on a ‘difficult-to-diagnose’ case and figure 3 shows some of the detection results on different types of clustered microcalcifications.

4. IMPROVED DETECTION METHOD In order to improve the detection accuracy of the technique and to reduce the computational time, the technique mentioned above is modified. Since Gabor filters are band-pass in nature, and clustered microcalcifications lie in a particular frequency range, we choose only a subset of Gabor filter bank in this technique. Thus the selected filters have a particular center frequency and different orientations. It was shown by Weldon [1I] that the aspect ratio of one works well when the size of the texture element (such as a spot representing microcalcification) is small. Thus, while developing a filter bank we make the following changes to the technique discussed in = 1. section 3 : (i) The aspect ratio was made unity i.e. CY (ii) The filters were complex valued as opposed to the real valued filters in the above scheme (iii) Only a subset of Gabor filter bank that has a particular scale (i. e. fixed center frequency) and different orientations is used. Each Gabor filtered image was subjected to a histogram based thresholding to obtain a binary image. The threshold T is computed from the histogram of the Gabor-filtered image using: T = mean V,where V = variance Ict ( P mode), where P is the value corresponding to the maximum pixel intensity in the filtered image. ICt is a constant.

+

5. RESULTS AND DISCUSSION Two closely inter-related issues involved in any diagnostic investigation are sensitivity and specificity. and the accepted terminology in field of mammography image analysis is ‘true positives’ and ‘false positives’. The detection accuracy of a technique greatly depends upon the dataset used for the study. J. Dengler, et al [1] achieved a true positive detection of 70% using Gaussian Filters and Morphological Filtering based scheme. B. Zheng, et a1 [2] achieved 0.77% false positive clusters/image at a true positive detection rate of 90% on wavelet enhanced images using a neural network with DCT based features as input and a spectral entropy based decision. Kocur, et a1 [3] achieved 88% correct detection on ‘difficult to diagnose’ cases using neural network with wavelet Features as input. Strickland [4] achieved a 3% false positive clusterdimage at 90% true positive detec-

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6. REFERENCES [ 11 J. Dengler, S. Behrens and J. F. Desaga, “Segmentation

of Microcalcifications in Mammograms”, IEEE Transactions on Medical Imaging, vol 12, No 4, pp 634-642. 21 B. Zheng, Wei Quan and Laurence P. Clark, “Digital Mammography: Mixed Feature Neural Network with Spectral Entropy Decision for Detection of Microcalcifications”, IEEE Transactions on Medical Imaging, vol 15, NO5, pp 589-597. 31 Catherine M. Kocur, S. K. Rogers, Myres, Burns, Kabrisky, Hoffmeisler, Baurer and Steppe, “Using Neural Networks to Select Wavelet Features for Breast Cancer Diagnosis”, IEEE Engineering in Medicine and Biology, pp 95-102, October 1996. [4] Robin N. Strickland, “Wavelet Transforms for Detecting Microcalcifications in Mammograms”, IEEE Transactions on Medical Imaging, vol 15, No 2, pp 218-229, April 1996.

Fig. 3. Detected microcalcifications using the proposed method of segmentation.

[5] T. Chang and C. C. J. Kuo, “Texture Analysis and Classification Using Tree-structured Wavelet Transform”, IEEE Transactions on Image Processing, 2(4):429-44 1 , Oct 1993.

tion using a wavelet transform based technique. This work was done on the mammograms form the Nijmegen Database (URL: ftp://figment.csee.usf.edu/pub/mammograms/ nijmegen-images/) on which we testkd our method.

[6] B. S. Manjunath and W. Y. Ma, “Texture Features for Browsing and Retrieval of Image Data”, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol 36, NO7, pp 1169-1179, July 1988.

In this study, true-positive rate is the ratio of the microcalcification clusters correctly detected to the total number of clusters present in the image and false-positiverate is the number of detections in which normal breast parenchyma is classified as a microcalcification cluster.

[7] A. K. Bovik, M. Clark and W. S. Geisler, “Multichannel Texture Analysis Using Localized Spatial Filters”, Pattem Recognition, vol 12, No 1, pp 55-73, Jan 1994. 81 P. Raghu and B. Yegnarayana, “Texture Classification using Probabilistic Neural Networks and Constraint Satisfaction Model”, Proceedings of the Intemational Conference on Neural Networks, vol 1, pp 424-429, June 1996.

The above algorithm was tested on 32 images from the Nijmegen Database. The image size used in this study was 512 x 512. The results were compared with the ground truth provided along with each image by the database which was established by after verification by trained radiologists as well as histology. The value of parameter kt, described in section 4 was varied in order to obtain true positive (tp) detection rates at different false positive (fp) detection rates as described in table 1. tp % 87.54 90.48 93.48 94.54

fP 0.54 0.72 1.09 2.39

91 M. Porat and Y. Y. Zeevi, “Localized Texture Processing in Vision: Analysis and Synthesis in Gaborian Space”, IEEE Transactions on Biomedical Engineering, 36( 1):796-8O4, Nov 1978.

[lo] A. K. Jain and E Farrokhnia, “Unsupervised Texture Segmentation using Gabor Filters”, Pattem Recognition,vol24,No 12,pp 1167-11861991.

kt 1/4 -114 0 -112

[ 113 T. P. Weldon and W. E. Higgins ,“Integrated Approach

to Texture Segmentation Using Multiple Gabor Filters”, In Proceedings of IEEE Conference on Image Processing, Lausanne, Switzerland, September 1996.

Table 1. Overall detection results on the 32 images.

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