Articulation-Invariant Representation of Non-Planar Shapes
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Articulation-Invariant Representation of Non-Planar ShapesRaghuraman Gopalan, Pavan Turaga, and Rama ChellappaCenter for Automation Research, University of Maryland, College Park, MD 20742 USA
Proposed Shape RepresentationFor a unique pair of points (u1k,u2k) Sk, find a distance D s.t.
Approximate convex decomposition (obtain pi)Part-wise affine normalization T(pi)->piInner-distance (ID)  based shape context descriptor D(u1k,u2k)=c, for all Sk M where c is a constant. D(u1k,u2k)=ID(u1k,u2k)+ - affine assumption on articulation of pi, junction deformation, and shape change across 3D object planesApproximate convex decompositionED(u1,um)=ID(u1,um)ID(u1,um)-ED(u1,um) ExperimentsNon-planar articulationsMPEG-7 datasetComparing area-based convexity measures: Top , Bottom - oursReferences Ling, H., and Jacobs, D. Shape classification using inner distance, IEEE TPAMI 29 (2007) 286-299. Belongie, S., Malik, J., and Puzicha, J. Shape matching and object recognition using shape contexts, IEEE TPAMI (24) 2002 509-522. Rahtu, E., Salo, M., and Heikkila, J. A new convexity measure based on the probabolistic interpretation of images. IEEE TPAMI 28 (2006) 1501-1512.R(Sk):0.9999/ 0.99980.5483/ 0.33410.9801/ 0.4655Problem StatementGiven a 2D projection of 3D articulating shape, how to obtain a representation invariant to 3D articulations, under no self-occlusions?Formulation3D Articulating ObjectConvex partsNon-convex junctionsLet A: articulations of X; A(Pi) E(3), A(Qij) ~ deformation, V: view-points.Question: Given a Si M, find a representation R s.t. R(Si)=R(Sk), for all Sk M