Components of the Shape Revisited

There are multiple and even interacting dimensions along which shape representation schemes may be compared and contrasted. In this paper, we focus on the following question. Are the building blocks in a compositional model localized in space (e.g. as in part based representations) or are they holistic simplifications (e.g. as in spectral representations)? Existing shape representation schemes prefer one or the other. We propose a new shape representation paradigm that encompasses both choices.

[1]  Niklas Peinecke,et al.  Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids , 2006, Comput. Aided Des..

[2]  Sibel Tari,et al.  Extracting Parts of 2D Shapes Using Local and Global Interactions Simultaneously , 2011, ArXiv.

[3]  Xin Li,et al.  2D Shape Decomposition Based on Combined Skeleton-Boundary Features , 2008, ISVC.

[4]  George Stiny,et al.  Shape: Talking about Seeing and Doing , 2006 .

[5]  Michael Batty,et al.  Environment and Planning B , 1982 .

[6]  Ronen Basri,et al.  Shape representation and classification using the Poisson equation , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[7]  J. Shah,et al.  A computationally efficient shape analysis via level sets , 1996, Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis.

[8]  Jitendra Malik,et al.  Parts, objects and scenes: computational models and psychophysics , 2003 .

[9]  I. Biederman Recognition-by-components: a theory of human image understanding. , 1987, Psychological review.

[10]  Jayant Shah,et al.  Extraction of Shape Skeletons from Grayscale Images , 1997, Comput. Vis. Image Underst..

[11]  J. Koenderink,et al.  The Shape of Smooth Objects and the Way Contours End , 1982, Perception.

[12]  George Stiny,et al.  Shape Grammars and the Generative Specification of Painting and Sculpture , 1971, IFIP Congress.

[13]  D. Marr,et al.  Representation and recognition of the spatial organization of three-dimensional shapes , 1978, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[14]  R. Basri,et al.  Shape representation and classification using the Poisson equation , 2004, CVPR 2004.

[15]  Petros Maragos,et al.  Pattern Spectrum and Multiscale Shape Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  B. S. Manjunath,et al.  Drums and Curve Descriptors , 2004, BMVC.

[17]  Sibel Tari,et al.  Hierarchical Shape Decomposition via Level Sets , 2009, ISMM.

[18]  D. Navon Forest before trees: The precedence of global features in visual perception , 1977, Cognitive Psychology.

[19]  Sibel Tari,et al.  Embedding Shapes without Predefined Parts , 2010 .