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Devoted toProf. Dr. Dr.h.c. Herbert Zeitler at the party of his eightieth birthdayProf. Dr. Dr.h.c. Helmut Karzel at the social gathering of his seventy fifth birthdayProf. Dr. Dr.h.c Grozio Stanilov at the celebration of his seventieth birthdayVarna (Bulgaria), September 5-10, 2003

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Committed toProf. Dr. Dr. h. c. Herbert Zeitler at the party of his eightieth birthdayProf. Dr. Dr. h. c. Helmut Karzel at the get together of his seventy fifth birthdayProf. Dr. Dr. h. c Grozio Stanilov at the celebration of his seventieth birthdayVarna (Bulgaria), September 5-10, 2003

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15], this paper focuses on the building of an optimal statistical deformable model from a set of surfaces, whose topological realization is homeomorphic, to a compact 2D manifold with boundary. This is a basic structure of more complicated surfaces [21, 24]. Given a set of partitioned surfaces, the optimal internal correspondence within the training data was identified by MDL objectives on a minimum distortion space. The parameterization of each shape is recursively refined by using hierarchical Piecewise Bilinear Maps (PBM) and tensor product B-spline representation of the surfaces.

The resultant set of displacements was used to update the pose parameters, and the remaining residual displacement of each control point was then rectified by updating the model parameters by following the principal modes of variation. The process is repeated until convergence. 3 Results For this study, we used 38 LV shapes for building the statistical model and a total of 160 LV volumes (inclusive of those used for training) for assessing the accuracy of the segmentation process. With the limited number of shapes used for training, the statistical model may not be able to capture the complete variations.

G. Wolberg. Image morphing: a survey. The Visual Com-puter, 1998, 14(8/9):360– 372. 8. F. Lazarus and A. Verroust. Three-dimensional Metamorpho-sis: a Survey. The Visual Computer, 1998,14(8/9):373–389. 9. D. DeCarlo, J. Gallier, Topological Evolution of Surfaces, Graphic Interface’96, Toronto, Canada, Canadian Human-Computer Communications Society, pp 194– 203. 10. T. Kanai, H. Suzuki and F. Kimura, Metamorphosis of Arbitrary Triangular Meshes, IEEE Computer Graphics and Applications, 20 (2), March/April 2000:62– 75.

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6th International conference on geometry and applications


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