Texture Classication of Mouse Liver Cell Nuclei. Using Invariant Moments of Consistent Regions. 1 Introduction

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1 Texture Classication of Mouse Liver Cell Nuclei Using Invariant Moments of Consistent Regions Fritz Albregtsen, Helene Schulerud, and Luren Yang Image Processing Laboratory, Department of Informatics, University of Oslo P. O. Box 1080 Blindern, N-0316 Oslo, Norway Abstract. A new texture analysis approach is applied to the problem of classication of pathological states from electron microscopy images of mouse liver cell nuclei. For each pixel in the image, a region of consistent connected neighbouring pixels is extracted, forming a local texel of pixels belonging to the same gray level population. The geometric properties of each texel is described by invariant moment-based features. A recently developed method for fast and exact computation of Cartesian geometric moments is utilized. Each cell nucleus is characterized by a feature vector, giving the average feature values of both the bright and the dark structures. A leave-one-out classication is performed, using 4 dierent classes of cells (normal, proliferating, precancer and cancer). The results demonstrate that using gray level connected neighbour structures as texels gives us important information about the chromatin texture of the cell nuclei and thus the pathological state of the cell. Several pairs of radiometric and geometric moment features of the texels gave a 90% correct classication. 1 Introduction Statistical texture analysis consists of a large variety of methods, and in a few cases the Cartesian geometric moments have also been used [10]. A structural texture description, on the other hand, is given by a set of texture primitives (texels) and placement rules that govern the stochastic spatial relations between them. Bigun and du Buf [2] extracted geometric primitives by complex moments in Gabor space and applied this to texture segmentation. We present a new texture analysis approach that for each pixel in the image uses concepts from adaptive ltering to nd the neighbouring pixels that belong to the local texel, and concepts from pattern recognition to characterize each texel as an object. Finding the neighbouring pixels that belong to the same population as a current pixel, for all pixel positions throughout the image, the locally selected pixels may be seen as a small object, with specic radiometric and geometric properties. The geometric properties may be characterized by the orientation of the object and by its geometric moments, or using the invariant moment combinations of Hu [5].

2 2 Connected Consistent Neighbours A number of adaptive ltering methods are available to select pixels that in some aspect belong to the same population as the center pixel of a window. However, as we are interested in selecting pixels that belong to the same gray level population and that are geometrically connected (4- or 8-neighbours) to the center pixel, we have used a modication of the K Nearest Connected Neighbour (KNCN) concept of L nnestad [7]. Using a xed value of K, the algorithm would in some cases include pixels that dier very much from the center pixel, and hence do not belong to the local texel. Therefore, we use K max as the maximum number of pixels to include in a neighbourhood. Starting with the K min = 5 nearest connected neighbours, the local mean and standard deviation, (; ), are calculated. Selecting pixels for moment computation stops at n < K max, if the next candidate pixel deviates from the current value of by more than 2. The values of (; ) are updated as new pixels are selected. The value of is not allowed to fall below a lower limit, otherwise the region would not grow, in strictly homogeneous areas. Using a maximum value K max (here 200), one avoids the problem of very large structures. 3 Cartesian Geometric Moments Cartesian geometric moments (for short moments) have been widely used in shape analysis and pattern recognition. The (p + q)'th order central moment of a discrete image g(x; y) is dened as pq = X x X y (x? x) p (y? y) q g(x; y); x = m 10 m 00 ; y = m 01 m 00 (1) Scaling invariant central moments are obtained by the normalization pq = pq ( 00 ) ; = p + q + 1; p + q 2: (2) Invariant Moment Features A number of techniques have been used to derive invariant features from moments for object representation and recognition (see Belkasim et al. [1] and Prokop and Reeves [8] for a survey and comparison). The set of seven moment combinations by Hu [5] is representative of nonlinear combinations of low-order two-dimensional Cartesian moments. The radius of gyration of an object is dened as the radius of a circle where we could concentrate all the mass of the object without altering the moment of inertia about its center of mass [8]. This feature is inherently invariant to image orientation, and is therefore a simple and useful rotationally invariant feature for shape analysis. In terms of second order central moments, it is given by R = r (3)

3 The object ellipse is also a simple, invariant object feature. The object ellipse is dened as the ellipse whose least and greatest moments of inertia equal those of the object. The lengths of the semiaxes and the numerical eccentricity of the ellipse are given by (a; b) = vu u t h p ( 20? 02 ) Fast Computation of Moments 00 ; = i s a 2? b 2 a 2 (4) Using contour following and Green's theorem, Li and Shen [6] proposed a fast algorithm to compute the moments of binary objects. The method is fast but not accurate, since Li and Shen's formula is obtained by a discrete approximation of Green's theorem. Yang and Albregtsen [11] presented a method that is as fast as the method of Li and Shen, giving correct results for all types of objects. Yang and Albregtsen [12] proposed two new methods for fast computation of moments by using a discrete version of Green's theorem. One of them is used to compute moments from binary images; the other to compute moments of regions in gray level images. 3.3 List of features used For each input image, using the scheme outlined above, we generate a multi-band feature image. The list of features extracted from the connected neighbours of each pixel in the input image includes: the mean and standard deviation (; ) of the intensity of the region found by the modied KNCN algorithm, the area of the region (A), the radius of gyration ( R), the two semiaxes of the object ellipse (a; b), the eccentricity (), and the logarithm (base 10) of the seven invariant moment combinations of Hu ( 1 ; :::; 7 ). Thus, 14 feature images are extracted from the region of interest (ROI) of the original image. In the general case it would also be natural to include the orientation. However, in the present context there is no reason to believe that the structures are systematically oriented. 4 Liver Cell Images The biological test material is taken from biopsies of normal liver and hepatocellular carcinomas taken from (C3H/Hej) male mice after treatment with the carcinogen diethylnitrosamine. All specimens were treated for ultrathin sectioning, and then Feulgen stained, before being studied in a transmission electron microscope at a primary magnication of The cell images were recorded on Kodak 4489 EM photographic lm and were digitized using a Grundig FA76 video camera [3]. There are four dierent classes of cell nuclei in the present study: normal, proliferating (or regenerating), precancer (or noduli) and cancer. We have used

4 cell nuclei from 20 animals, 5 animals from each of the 4 classes, and 20 cell nuclei from each animal. Thus, 400 dierent cell nuclei were used in this study. Images of cell nuclei were randomly chosen from each animal. The digitized images used here were bits, and the resolution is 39 nm per pixel. Figure 1 shows four samples of cell nuclei. The intensely stained particles (excluding nucleoli) in each nucleus are dened as heterochromatin and the lightly stained background as euchromatin. Fig. 1. Four samples from the liver cell data base, showing normal (left), regenerating (middle-left), precancerous (middle-right) and cancerous nuclei (right). 4.1 Preprocessing The original data may contain some noise. It is well established that the results of an image segmentation or classication based on texture improve if random noise is removed from the input data. However, a careful balance has to be struck between the desired noise removal and the unwanted altering of the local texture. In the present context we have used a 3 3 median lter for the pre-processing of the images. As we are primarily interested in the texture within the cell nuclei, we have created an ROI by manually outlining the cell nucleus for each cell image. Systematic variations in slice thickness, staining, illumination or variations in the photographic processes could possibly bias rst order statistical parameters such as the mean and standard deviation. All segmented images have therefore been linearly scaled to the same mean (127.5) and standard deviation (50.0). 5 Classication Histograms of the cell nuclei are generally bimodal. To characterize each individual cell nucleus we therefore compute two average values for each feature, using a gray level threshold of 127. Thus, for each cell we obtain 28 features, characterizing both the dark heterochromatin and the lightly stained euchromatin. The 20 cells from each animal are taken from a liver with known condition, i.e. normal, regenerating, precancerous, or cancerous. However, some of the 20 cells from a given liver may belong to a dierent class, e.g. the liver of an animal that is in the precancerous state may also contain normal cells. We assume that the majority of the cells from each liver belong to the correct cell type, and thus the mean feature vector has been used to represent the condition of each liver.

5 As the data set was relatively small, we did not use separate training and test sets, but used crossvalidation of the Bayesian classication, assuming multinormally distributed features. We used a pooled covariance matrix, and equal a priori probabilities. We performed the classication for all single features, and selected the features that gave the highest correct classication rate. In the present context, we have found the optimal feature set of reduced dimension by an exhaustive combinatorial search for the optimal feature pair. Feature pairs having the same Correct Classication Rate (CCR) are evaluated and ranked by the estimated Posteriori Probability Error (PPE)[4]. 6 Results We found thathe best single feature is the sixth Hu moment of the bright structures which gave a correct classication rate of 80%. The second best feature is the standard deviation of the gray levels in the bright structures which gave a correct classication rate of 75%. The feature pair which gave the lowest Posteriori Probability Error estimate is a combination of the standard deviation of the gray levels in the bright structures and the numerical eccentricity of the dark structures which gave a correct classication rate of 90%, see Figure 2. Two animals from the normal group are misclessied as regenerating. The second best feature pair was the second and sixth Hu moment of the dark structures. In this case one animal from the normal group is classied as premalignant and one animal from the cancer group is classied as regenerating. These misclassications are more serious than the errors made by the best feature pair. A list of the best single features and feature pairs is given in Table 1, giving the correct classication rate for each of the four classes, together with the overall correct classication rate (CCR). 7 Discussion Previous work [14],[9] on the same data set have tested rst, second and higher order statistical texture features to discriminate the four classes. Both achieved a correct classication rate of 95% with two features. In a study of changes in chromatin organization during experimental liver carcinogenesis in mice, Danielsen et al. [3] interactively excluded all nucleoli as well as chromatin particles smaller than 5 pixels. The exclusion of small particles is performed automatically in our modied KNCN-scheme, but the nucleoli are not excluded, as they are fragmented into a number of small, dark structures. Thus, some deviations may be expected between our results and those of Danielsen et al. [3]. Local geometrical moments as texture features has been used earlier by Tuceryan [10]. He computed the six low order central moments (p + q 2) within small local windows W i;j of size L L around each pixel (i; j) in the image. Texture feature images F k corresponding to moment images M k with

6 Features N R P C CCR PPE 6 b b d d d Eccentricity of the dark structures Standard deviation of the bright structures b; d d; d d ; 6 d b; d Tab.1. Correct classication rate in percent for some of the best single features and feature pairs. N=normal, R=regenerating, P=precancer and C=cancer. CCR = overall correct classication rate. PPE = Posteriori Probability Error Estimate. Fig. 2. Graylevel standard deviation of bright structures (y = b), versus numerical eccentricity of dark structures (x = d), o = Normal, = Regenerating, = Precancer and + = Cancer. mean value M were then obtained by a nonlinear transform, using a hyperbolic tangent function. A weak point in Tuceryan's approach is the global, xed window. However, the scheme for selecting pixels that belong to the same gray level population, as described above, makes the method adaptive to any texel size and shape. As the features of Tuceryan are mixing contrast, scale and rotation, and possibly also treating several texels at the same time, it is also dicult to interpret them in terms of physical properties of the individual texels. In the present approach we have used concepts from adaptive ltering to nd the neighbouring pixels that belong to the local texel, and moment based features to characterize the gray level texel as an object. The results described above seem to indicate that the present approach is indeed fruitful. We note that the scheme is completely adaptive, i.e. we do not specify any window size or scale parameters. The method is also applicable to 3D data. 8 Conclusion We have presented a new texture analysis approach that for each pixel in the image uses an adaptive ltering concepts to nd connected neighbouring pixels that belong to the same gray level population, and thus constitute a texel. We then use concepts from pattern recognition to characterize the radiometric and geometric properties of the texel. For this purpose, a new method for fast and exact computation of geometric moments is very useful, as it gives exact values even for small and complex objects. The results demonstrate that using gray level connected neighbour structures as texels gives us important information about the chromatin texture of the cell nuclei and thus the pathological state of the cell.

7 Acknowledgements The authors would like to thank dr. H vard E. Danielsen of the Department of Pathology, the Norwegian Radium Hospital for making the liver cell images available for this study, and Ruth Puntervold and the late Barbara Schuler for their skillful technical assistance. References 1. S. O. Belkasim, M. Shridhar, and M. Ahmadi, Pattern recognition with moment invariants: a comparative study and new results, Pattern Recogn. 24(12), (1991). 2. J. Bigun, and J. M. H. du Buf, Geometric image primitives by complex moments in Gabor space and the application to texture segmentation, Proc. CVPR, pp (1992). 3. H. E. Danielsen, G. E. Farrants and A. Reith, Characterization of chromatin structure by image analysis - A method for assessment of changes in cromatin organization, Scanning Microscopy Suppl., 3, (1988). 4. N. Glick, Additive estimators for probabilities of correct classication, Pattern Recognition, 10, (1978). 5. M.-K. Hu, Visual pattern recognition by moment invariants, IRE Trans. Information Theory 8, (1962). 6. B.-C. Li, and J. Shen, Fast computation of moment invariants, Pattern Recogn. 24(8), (1991). 7. T. L nnestad, Connected lters for noise removal, Proc. 9thICPR, pp , Rome (1988). 8. R. J. Prokop, and A. P. Reeves, A survey of moment-based techniques for unoccluded object representation and recognition, CVGPR: Graphical Models and Image Processing 54(5), (1992). 9. H. Schulerud and J.M. Carstensen, Multiresolution Texture Analysis of four classes of Mice Liver cells using dierent cell cluster representations, Proceedings, 9th SCIA, Uppsala, Sweden (1995). 10. M. Tuceryan, Moment based texture segmentation, Pattern Recogn. Letters 15, (1994). 11. L. Yang, and F. Albregtsen, Fast computation of invariant geometric moments: A new method giving correct results, Proc. 12thICPR, Vol. A, pp , (1994). 12. L. Yang, and F. Albregtsen, Fast and exact computation of cartesian geometric moments using discrete Green's theorem, submitted to Pattern Recognition, (1994). 13. K. Yogesan, F. Albregtsen, A. Reith, and H. E. Danielsen, Cooccurrence and run length-based texture analysis of experimental liver carcinogenesis in mice, Proc. of 8th Scandinavian Conference on Image Analysis, pp (1993). 14. K. Yogesan, F. Albregtsen, J.M. Nesland, and H.E. Danielsen, Chromatin texture analysis of normal, regenerating, premalignant and malignant liver cells, Ultrastructural Pathology (In Press).

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