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Page 1: Articulation-Invariant Representation of Non-Planar Shapes

Articulation-Invariant Representation of Non-Planar ShapesRaghuraman Gopalan, Pavan Turaga, and Rama Chellappa

Center for Automation Research, University of Maryland, College Park, MD 20742 USA

Proposed Shape RepresentationFor a unique pair of points (u1k,u2k) ϵ Sk, find a distance D s.t.

Approximate convex decomposition (obtain pi)

Part-wise affine normalization T(pi)->p’i

Inner-distance (ID) [1] based shape context descriptor [2]

D(u1k,u2k)=c, for all Sk ϵ M where c is a constant.

D(u1k,u2k)=ID(u’1k,u’2k)+η

η - affine assumption on articulation of pi, junction deformation, and shape change across 3D object planes

Approximate convex decomposition

ED(u1,um)=ID(u1,um)

ID(u1,um)-ED(u1,um) ↑

Experiments

Non-planar articulations

MPEG-7 dataset

Comparing area-based convexity measures: Top [3], Bottom - ours

References[1] Ling, H., and Jacobs, D. Shape classification using inner distance, IEEE TPAMI 29 (2007) 286-299.

[2] Belongie, S., Malik, J., and Puzicha, J. Shape matching and object recognition using shape contexts, IEEE TPAMI (24) 2002 509-522.

[3] 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):

3D articulations Viewpoint variation

0.9999/ 0.9998

0.5483/ 0.3341

0.9801/ 0.4655

Problem StatementGiven a 2D projection of 3D articulating shape, how to obtain a representation invariant to 3D articulations, under no self-occlusions?

Formulation ij

njiij

n

ii QPX

,,11

}{}{

3D Articulating Object

Convex parts

Non-convex junctions

Let A: articulations of X; A(Pi) ϵ E(3), A(Qij) ~ deformation, V: view-points.

ij

njiij

n

ii

DtoD qpSVAM

,,11

23 }{}{

Question: Given a Si ϵ M, find a representation R s.t. R(Si)=R(Sk), for all Sk ϵ M