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Volumetric Segmentation Using Weibull E-SD Fields
July-September 2003 (vol. 9 no. 3)
pp. 320-328

Abstract—This paper presents a coarse-grain approach for segmentation of objects with gray levels appearing in volume data. The input data is on a 3D structured grid of vertices $v(i,j,k) $, each associated with a scalar value. In this paper, we consider a voxel as a $\kappa\times\kappa\times \kappa$ cube and each voxel is assigned two values: expectancy and standard deviation (E-SD). We use the Weibull noise index to estimate the noise in a voxel and to obtain more precise E-SD values for each voxel. We plot the frequency of voxels which have the same E-SD, then 3D segmentation based on the Weibull E-SD field is presented. Our test bed includes synthetic data as well as real volume data from a confocal laser scanning microscope (CLSM). Analysis of these data all show distinct and defining regions in their E-SD fields. Under the guide of the E-SD field, we can efficiently segment the objects embedded in real and simulated 3D data.

[1] A. Razdan, K. Patel, G. Farin, and D.G. Capco, Visualization of Multicolor CLSM Data Set Computers and Graphics, vol. 25, no. 3, pp. 371-382, 2001.
[2] M.B. Jose Dias and M.N. Jose Leitao, “Wall Position and Thickness Estimation from Sequences of Echocardiographis Images,” IEEE Trans. Medical Imaging, vol. 15, pp. 25-38, 1996.
[3] R.A. Hummel and S.W. Zucker, On the Foundations of Relaxation Labeling Processes IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 5, no. 3, pp. 267-287, Mar. 1983.
[4] M.W. Hansen and W.E. Higgins, Relaxation Methods for Supervised Image Segmentation IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 9, pp. 949-962, Sept. 1997.
[5] C. Chesnaud, P. Réfrégier, and V. Boulet, Statistical Region Snake-Based Segmentation Adapted to Different Physical Noise Models IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, pp. 1145-1157, 1999.
[6] M.H. Fox, D.J. Arndt-Jovin, T.M. Jovin, and P.H. Baumann, Robert-Nicoud, M. Spatial and Temporal Distribution of DNA Replication Sites Localized by Immunoflurescence and Confocal Microscopy in Mouse Fibroblast J. Cell Science, vol. 99, pp. 247-253, 1991.
[7] E.M.M. Manders, J. Stap, G.J. Brakenhoff, R. van Driel, and J.A. Aten, Dynamics of Three Dimensional Replication Patterns During the S-Phase, Analyzed by Double Labeling of DNA and Confocal Microscopy J. Cell Science, vol. 103, no. 3, pp. 857-862, 1992.
[8] W.E. Higgins and E.J. Ojard, Interactive Morphological Watershed Analysis for 3D Medical Images Computer Medical Imaging Graphics, special issue on advanced 3D image processing in medicine, vol. 17, nos. 4/5, pp. 387-392, 1993.
[9] C. Garbay, Image Structure Representation and Processing: A Discussion of Some Segmentation Algorithms in Cytology IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8 no. 2, pp. 140-146, Feb. 1986.
[10] P.W. Fung, K.K. Ly, and K. Attikiouzel, "Automatic Segmentation of Biomedical Images," Proc. IEEE Conf. Acoustics, Speech, and Signal Processing, pp. 882-885, Apr. 1988.
[11] A. Rosenfeld, R. Hummel, and S.W. Zucker, Science Labeling by Relaxation Operations IEEE Trans. Systems, Man, and Cybernetics, vol. 6, no. 6, pp. 420-433, 1976.
[12] M. Svensen, F. Kruggel, and D.Y. Cramon, Probabilistic Modeling of Single-Trial fMRI Data IEEE Trans. Medical Imaging, vol. 19, no. 1, pp. 25-35, Jan. 2000.
[13] J. Liu and Y. Tang, Adaptive Image Segmentation with Distributed Behavior-Based Agents IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 6, pp. 544-551, June 1999.
[14] L. Andrews, Special Functions of Mathematics for Engineers, second ed. McGraw-Hill, 1992.
[15] E. Suhir, Applied Probability for Engineering and Science. McGraw-Hill, 1997.
[16] N. Sarkar and B.B. Chaudhuri, An Efficient Differential Box-Counting Approach to Computer the Fractal Dimension of Images IEEE Trans. Systems, Man, and Cybernetics, vol. 24, no. 1, pp. 115-120, Jan. 1994.
[17] M. Kamber, R. Singhal, D. Collins, G. Francis, and A. Evans, “Model-Based 3D Segmentation of Multiple Sclerosis Lesions in Magnetic Resonance Brain Images,” IEEE Trans. Medical Imaging, vol. 4, pp. 442-453, 1995.
[18] B. Chanda, B.B. Chaudhuri, and D.D. Majumde, A Modified Scheme for Segmenting Noisy Images IEEE Trans. Systems, Man, and Cybernetics, vol. 18, no. 3, pp. 458-466, Mar. 1988.
[19] A. Chakraborty and J.S. Duncan, Game-Theoretic Integration for Image Segmentation IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 1, pp. 12-30, Jan. 1999.
[20] T.C.M. Lee, Segmentation Images Corrupted by Correlated Noise IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 5, pp. 481-492, May 1998.
[21] A.D. Lanterman, U. Grenander, and M.I. Miller, Bayesian Segmentation via Asymptotic Partition Functions IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 4, pp. 337-347, Apr. 2000.
[22] J. Berkmann and T. Caelli, Computation of Surface Geometry and Segmentation Using Covariance Techniques IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 11, pp. 1114-1116, Nov. 1994.
[23] G.M. Nielson, M. Gross, H. Hagen, and S.V. Klimenko, Research Issues in Data Modeling for Scientific Visualization IEEE Computer Graphics and Applications, vol. 14, no. 2, pp. 70-73, 1994.

Index Terms:
3D segmentation, Weibull E-SD field, noise index, confocal laser scanning microscope, CLSM.
Citation:
Jiuxiang Hu, Anshuman Razdan, Gregory M. Nielson, Gerald E. Farin, D. Page Baluch, David G. Capco, "Volumetric Segmentation Using Weibull E-SD Fields," IEEE Transactions on Visualization and Computer Graphics, vol. 9, no. 3, pp. 320-328, July-Sept. 2003, doi:10.1109/TVCG.2003.1207440
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