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Blended Deformable Models
April 1996 (vol. 18 no. 4)
pp. 443-448

Abstract—This paper develops a new class of parameterized models based on the linear interpolation of two parameterized shapes along their main axes, using a blending function. This blending function specifies the relative contribution of each component shape on the resulting blended shape. The resulting blended shape can have aspects of each of the component shapes. Using a small number of additional parameters, blending extends the coverage of shape primitives while also providing abstraction of shape. In particular, it offers the ability to construct shapes whose genus can change. Blended models are incorporated into a physics-based shape estimation framework which uses dynamic deformable models. Finally, we present experiments involving the extraction of complex shapes from range data including examples of dynamic genus change.

[1] A. Barr, "Superquadrics and angle-preserving transformations," IEEE Computer Graphics and Applications, vol. 1, no. 1, pp. 11-23, 1981.
[2] I. Biederman, "Recognition-by-components: A theory of human image understanding," Psychological Review, vol. 94, pp. 115-147, Apr. 1987.
[3] T. Binford, "Visual perception by computer," Proc. IEEE Conf. Systems and Control, Dec. 1971.
[4] D. DeCarlo and D. Metaxas, "Blended Deformable Models," Computer Vision and Pattern Recognition '94, pp. 566-572, 1994.
[5] G. Farin, Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide. Academic Press, 1993.
[6] A.J. Hanson,“Hyperquadrics: Smoothly deformable shapes with convex polyhedral bounds,” Computer Vision, Graphics, and Image Processing, vol. 44, pp. 191-210, 1988.
[7] C.M. Hoffmann and J. Hopcroft, "The geometry of projective blending surfaces," Artificial Intelligence, vol. 37, pp. 357-376, 1988.
[8] J. Koënderink, Solid Shape. Cambridge, Mass.: MIT Press, 1991.
[9] R. Malladi, J. Sethian, and B.C. Vemuri, "Shape Modeling with Front Propagation: A Level Set Approach," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, pp. 158-175, 1995.
[10] D. Marr and K. Nishihara, "Representation and recognition of the spatial organization of three-dimensional shapes," Proc. Royal Soc. London, vol. 200, pp. 269-294, 1978.
[11] D. Metaxas, "Physics-based modeling of nonrigid objects for vision and graphics," PhD thesis, Dept. of Computer Science, Univ. of Toronto, 1992.
[12] D. Metaxas and D. Terzopoulos, "Dynamic deformation of solid primitives with constraints," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 6, pp. 569-579, June 1993.
[13] S. Muraki,“Volumetric shape description of range data using’blobby model’,” Proc. SIGGRAPH’91 (Las Vegas, Nevada, July 29-Aug. 2, 1991). In Computer Graphics, vol. 25, no. 4, pp. 227-235, 1991.
[14] T. O'Donnell, T. Boult, X. Fang, and A. Gupta, "The Extruded Generalized Cylinder: A Deformable Model for Object Recovery," Computer Vision and Pattern Recognition '94, pp. 174-181, 1994.
[15] A. Pentland,“Perceptual organization and the representation of natural form,” Artificial Intelligence, vol. 28, pp. 293-331, 1986.
[16] A. Pentland and S. Sclaroff, "Closed-Form Solutions for Physically-Based Shape Modeling and Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp. 715-729, July 1991.
[17] J.M. Snyder, Generative Modeling for Computer Graphics and CAD. Academic Press, 1992.
[18] F. Solina and R. Bajcsy,“Recovery of parametric models from range images: The case for superquadrics with global deformations,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, pp. 131-147, Feb. 1990.
[19] R. Szeliski, D. Tonnesen, and D. Terzopoulos, "Modeling Surfaces of Arbitrary Topology with Dynamic Particles," Proc. IEEE Computer Vision and Pattern Recognition, pp. 82-85,New York, NY, June 1993.
[20] G. Taubin, "An improved algorithm for algebraic curve and surface fitting," Proc. Fourth Int'l Conf. Computer Vision, pp. 658-665,Berlin, Germany, May 1993.
[21] D. Terzopoulos and D. Metaxas, “Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp. 703-714, July 1991.
[22] D. Terzopolous, A. Witkin, and M. Kass, "Constraints on deformable models: Recovering 3D shape and nonrigid motion, AI, no. 36, pp. 91-123, 1988.
[23] B.C. Vemuri and A. Radisavljevic, “Multiresolution Stochastic Hybrid Shape Models with Fractal Priors,” ACM Trans. Graphics, vol. 13, no. 2, pp. 177-207, Apr. 1994.

Index Terms:
Shape representation, shape blending, shape abstraction, shape estimation, physics-based modeling.
Douglas DeCarlo, Dimitri Metaxas, "Blended Deformable Models," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 4, pp. 443-448, April 1996, doi:10.1109/34.491626
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