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
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