This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Probabilistic Multiscale Image Segmentation
February 1997 (vol. 19 no. 2)
pp. 109-120

Abstract—A method is presented to segment multidimensional images using a multiscale (hyperstack) approach with probabilistic linking. A hyperstack is a voxel-based multiscale data structure whose levels are constructed by convolving the original image with a Gaussian kernel of increasing width. Between voxels at adjacent scale levels, child-parent linkages are established according to a model-directed linkage scheme. In the resulting tree-like data structure, roots are formed to indicate the most plausible locations in scale space where segments in the original image are represented by a single voxel. The final segmentation is obtained by tracing back the linkages for all roots.

The present paper deals with probabilistic (or multiparent) linking, i.e., a set-up in which a child voxel can be linked to more than one parent voxel. The multiparent linkage structure is translated into a list of probabilities that are indicative of which voxels are partial volume voxels and to which extent. Probability maps are generated to visualize the progress of weak linkages in scale space when going from fine to coarser scale. This is shown to be a valuable tool for the detection of voxels that are difficult to segment properly.

The output of a probabilistic hyperstack can be directly related to the opacities used in volume renderers. Results are shown both for artificial and real world (medical) images. It is demonstrated that probabilistic linking gives a significantly improved segmentation as compared with conventional (single-parent) linking. The improvement is quantitatively supported by an objective evaluation method.

[1] P.J. Burt, T.H. Hong, and A. Rosenfeld, "Segmentation and Estimation of Image Region Properties Through Cooperative Hierarchical Computation," IEEE Trans. Systems, Man, and Cybernetics, vol. 11, no. 12, pp. 802-809, 1981.
[2] C.N. de Graaf, A. Toet, J.J. Koenderink, P. Zuidema, and P.P. Van Rijk, "Some Applications of Hierarchical Image Processing Algorithms," Information Processing in Medical Imaging, F. Deconinck, ed., pp. 343-369,the Hague: Martinus Nijhoff, 1984.
[3] C.N. de Graaf, S.M. Pizer, A. Toet, J.J. Koenderink, P. Zuidema, and P.P. Van Rijk, "Pyramid Segmentation of Medical 3D Images," Proc. Int'l Symp. Computer Graphics, M.L. Rhodes, ed., pp. 71-77, 1984.
[4] P. Meer, S.N. Jiang, E.S. Baugher, and A. Rosenfeld, "Robustness of Image Pyramids Under Structural Perturbations," Computer Vision, Graphics, and Image Processing, vol. 44, pp. 307-331, 1988.
[5] M. Bister, J. Cornelis, and A. Rosenfeld, "A Critical View of Pyramid Segmentation Algorithms," Pattern Recognition Letters, vol. 11, pp. 605-617, 1990.
[6] J.J. Koenderink, "The Structure of Images," Biological Cybernetics, vol. 50, pp. 363-370, 1984.
[7] S.M. Pizer, J.J. Koenderink, L.M. Lifshitz, L. Helmink, and A.D.J. Kaasjager, "An Image Description for Object Definition, Based on Extremal Regions in the Stack," Information Processing in Medical Imaging, S.L. Bacharach, ed., pp. 24-37,Dordrecht: Martinus Nijhoff, 1986.
[8] L.M. Lifshitz and S.M. Pizer, "A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 6, pp. 529-541, June 1990.
[9] A. Grossmann and J. Morlet, "Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape," SIAM J. Math., vol. 15, pp. 723-736, 1984.
[10] I. Daubechies, "Orthonormal Bases of Compactly Supported Wavelets," Comm. Pure Applied Math., vol. 41, pp. 909-996, 1988.
[11] S.G. Mallat,“A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 674-693, 1989.
[12] K.L. Vincken, C.N. de Graaf, A.S.E. Koster, M.A. Viergever, F.J.R. Appelman, and G.R. Timmens, "Multiresolution Segmentation of 3D Images by the Hyperstack," Proc. First Conf. Visualization in Biomedical Computing, pp. 115-122.Los Alamitos: IEEE CS Press, 1990.
[13] C.N. de Graaf, K.L. Vincken, M.A. Viergever, J.J. Koenderink, F.J.R. Appelman, and O. Ying-Lie, "A Hyperstack for the Segmentation of 3D Images," Information Processing in Medical Imaging, D.A. Ortendahl and J. Llacer, eds., pp. 399-413,New York: Wiley-Liss, 1991.
[14] K.L. Vincken, "Probabilistic Multiscale Image Segmentation by the Hyperstack," PhD thesis, Utrecht Univ., The Netherlands, 1995.
[15] K.L. Vincken, A.S.E. Koster, and M.A. Viergever, "Probabilistic Multiscale Image Segmentation—Setup and First Results," Proc. SPIE 1808, Visualization in Biomedical Computing, R.A. Robb, ed., pp. 63-77, 1992.
[16] K.L. Vincken, A.S.E. Koster, and M.A. Viergever, "Probabilistic Hyperstack Segmentation of MR Brain Data," Proc. CVRMed '95 Computer Vision, Virtual Reality and Robotics in Medicine, N. Ayache, ed., vol. 905of lecture notes in computer science, pp. 351-357,Berlin: Springer-Verlag, 1995.
[17] A.P. Witkin, "Scale Space Filtering," Proc. Int'l Joint Conf. Artificial Intelligence, pp. 1,019-1,023, 1983.
[18] T. Lindeberg,“Scale-space for discrete signals,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 3, pp. 234–254, 1990.
[19] L.M.J. Florack, B.M. ter Haar Romeny, J.J. Koenderink, and M.A. Viergever, "Linear Scale-Space," J. Math. Imaging and Vision, vol. 4, no. 4, pp. 325-351, 1994.
[20] K.L. Vincken, W.J. Niessen, and M.A. Viergever, "Blurring Strategies for Image Segmentation Using a Multiscale Linking Model," IEEE Conf. Computer Vision and Pattern Recognition, CVPR '96,San Francisco, Calif., pp. 21-26, IEEE CS Press, 1996.
[21] W.J. Niessen, K.L. Vincken, A.S.E. Koster, and M.A. Viergever, "A Comparison of Multiscale Image Representations for Image Segmentation," IEEE Workshop Math. Methods in Biomedical Image Analysis,San Franciso, Calif., pp. 263-272, 1996.
[22] A.S.E. Koster, "Linking Models for Multiscale Image Segmentation," PhD thesis, Utrecht Univ., The Netherlands, 1995.
[23] A.S.E. Koster, K.L. Vincken, and M.A. Viergever, "Heuristic Linking Models in Multi-Scale Image Segmentation," Computer Vision and Image Understanding, vol. 65, no. 3, Mar. 1997.
[24] H.J. Suermondt and G.F. Cooper, "Probabilistic Inference in Multiply Connected Belief Networks Using Loop Cutsets," Int'l J. Approximate Reasoning, vol. 4, pp. 283-306, 1990.
[25] J. Canny, "A Computational Approach to Edge Detection," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 6, pp. 679-698, June 1986.
[26] R.A. Drebin, L. Carpenter, and P. Hanrahan, "Volume Rendering," Computer Graphics, vol. 22, no. 4, pp. 65-74, 1988.
[27] M. Levoy, “Display of Surfaces from Volume Data,” IEEE Computer Graphics and Applications, vol. 8, no. 3, pp. 29-37, 1988.
[28] K.J. Zuiderveld and M.A. Viergever, "Multi-Modal Volume Visualization Using Object-Oriented Methods," Symp. Volume Visualization, ACM SIGGRAPH,New York, pp. 59-66, 1994.
[29] K.L. Vincken, A.S.E. Koster, and M.A. Viergever, "Probabilistic Segmentation of Partial Volume Voxels," Pattern Recognition Letters, vol. 15, no. 5, pp. 477-484, 1994.
[30] C.N. de Graaf, A.S.E. Koster, K.L. Vincken, and M.A. Viergever, "A Methodology for the Validation of Image Segmentation Methods," Computer-Based Medical Systems, J.N. Brown and P. Santiago, eds., pp. 17-24.Los Alamitos: IEEE CS Press, 1992.
[31] A.S.E. Koster, O.C. Zander, K.L. Vincken, and M.A. Viergever, "Model-Based Evaluation of Image Segmentation Methods," submitted for publication to IEEE Trans. Pattern Analysis and Machine Intelligence.

Index Terms:
Image segmentation, multiscale analysis, scale space, probability maps, partial volume artifact, object definition.
Citation:
Koen L. Vincken, André S.E. Koster, Max A. Viergever, "Probabilistic Multiscale Image Segmentation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19, no. 2, pp. 109-120, Feb. 1997, doi:10.1109/34.574787
Usage of this product signifies your acceptance of the Terms of Use.