Abstract
Tensor fields (matrix valued data sets) have recently attracted increased attention in the fields of image processing, computer vision, visualization and medical imaging. Tensor field segmentation is an important problem in tensor field analysis and has not been addressed adequately in the past. In this paper, we present an effective region-based active contour model for tensor field segmentation and show its application to diffusion tensor magnetic resonance images (MRI) as well as for the texture segmentation problem in computer vision. Specifically, we present a variational principle for an active contour using the Euclidean difference of tensors as a discriminant. The variational formulation is valid for piecewise smooth regions, however, for the sake of simplicity of exposition, we present the piecewise constant region model in detail. This variational principle is a generalization of the region-based active contour to matrix valued functions. It naturally leads to a curve evolution equation for tensor field segmentation, which is subsequently expressed in a level set framework and solved numerically. Synthetic and real data experiments involving the segmentation of diffusion tensor MRI as well as structure tensors obtained from real texture data are shown to depict the performance of the proposed model.
This research was in part funded by the NIH grant RO1-NS42075
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References
Alexander, D., Gee, J.C., Bajcsy, R.: Similarity measure for matching diffusion tensor images. In: British Machine Vision Conference, September 1999, pp. 93–102. University of Nottingham (1999)
Basser, P.J., Mattiello, J., Lebihan, D.: Estimation of the effective self-diffusion tensor from the nmr spin echo. Journal of Magnetic Resonance (103), 247–254 (1994)
Bernd, J.: Digital Image Processing: Concepts, Algorithms, and Scientific Applications with CDROM. Springer, Heidelberg (2001)
Bigün, J., Granlund, G.H., Wiklund, J.: Multidimensional orientation estimation with applications to texture analysis and optical flow. IEEE Trans. on Pattern Analysis and Machine Intelligence 13(2), 775–790 (1991)
Caselles, V., Catte, F., Coll, T., Dibos, F.: A geometric model for active contours in image processing. Numerische Mathematik 66, 1–31 (1993)
Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. In: Fifth International Conference on Computer Vision, pp. 694–699 (1995)
Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. on Image Processing 10(2), 266–277 (2001)
Chan, T.F., Vese, L.A.: A level set algorithm for minimizing the mumford-shah functional in image processing. In: IEEE Workshop on Variational and Level Set Methods, pp. 161–168 (2001)
Haußecker, H., Jähne, B.: A tensor approach for precise computation of dense displacement vector fields. In: Proc. Musterekennung, Berlin, German (1997)
Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., Yezzi, A.: Gradient flows and geometric active contour models. In: Fifth International Conference on Computer Vision, Cambridge, MA (1995)
Kühne, G., Weickert, J., Schuster, O., Richter, S.: A tensor-driven active contour model for moving object segmentation. In: IEEE International Conference on Image Processing, Thessaloniki, Greece, October 2001, pp. 73–76 (2001)
Brox, T., Rousson, M., Deriche, R.: Active unsupervised texture segmentation on a diffusion based feature space non-rigid registration. In: IEEE Conference on Computer Vision and Pattern Recognition, Wisconsin, USA (June 2003)
Malladi, R., Sethian, J.A., Vemuri, B.C.: A topology independent shape modeling scheme. In: SPIE Proc. on Geometric Methods in Computer Vision II, July 1993. SPIE, vol. 2031, pp. 246–256 (1993)
Malladi, R., Sethian, J.A., Vemuri, B.C.: Shape modeling with front propagation: A level set approach. IEEE Trans. Pattern Analysis and Machine Intelligence 17(2), 158–175 (1995)
Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational-problems. Communications on Pure and Applied Mathematics 42, 577–685 (1989)
Rousson, M., Brox, T., Deriche, R.: Active unsupervised texture segmentation on a diffusion based feature space. Technical Report RR-4695, INRIA, France (January 2003)
Tsai Jr., A., Yezzi, A., Willsky, A.S.: Curve evolution implementation of the mumford-shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Trans. on Image Processing 10(8), 1169–1186 (2001)
Zhukov, L., Museth, K., Breen, D., Whitaker, R., Barr, A.: Level set modeling and segmentation of dt-mri brain data. Journal of Electronic Imaging 12(1), 125–133 (2003)
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Wang, Z., Vemuri, B.C. (2004). Tensor Field Segmentation Using Region Based Active Contour Model. In: Pajdla, T., Matas, J. (eds) Computer Vision - ECCV 2004. ECCV 2004. Lecture Notes in Computer Science, vol 3024. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24673-2_25
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DOI: https://doi.org/10.1007/978-3-540-24673-2_25
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