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EFFICIENT GLOBALLY OPTIMAL 2D-TO-3DDEFORMABLE SHAPE MATCHING
Zorah Lähner¹, Emanuele Rodolà1,2, Frank R. Schmidt1,
Michael M. Bronstein2, Daniel Cremers1
Published at CVPR 2016
1 Technical University Munich2 Università della Svizzera Italiana
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THE TASK
Finding a continuous matchingbetween a 2D template shapeand a 3D model that matchespoints which look alike
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RETRIEVAL
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SKETCH-BASED MODELLING
Kraevoy et al., 2009
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INPUTS
NM
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PRODUCT MANIFOLD
n pointsmpoints
x
Each node in the product manifold represents a possible matchbetween a point on the contour and on the model.
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PRODUCT MANIFOLD
x
i j
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PRODUCT MANIFOLD
An edge between (i, j) and (k, l) exists ifboth i, k and j, l are the same orneighbors on the original shapes.
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ENERGY FORMULATION
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ENERGY FORMULATION
x
i jx
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SLICED PRODUCT MANIFOLD
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SLICED PRODUCT MANIFOLD
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RUNTIME
Given a 2D template shape M and a 3D model shape N, discretized at m and nvertices, respectively, we can find a minimizer inO(mn2 log(n)) time.If n = O(m2), this leads to the subcubic runtime of O(n2.5 log(n)).
m vertices n vertices
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FEATURES
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SPECTRAL FEATURES
Purely based on intrinsic properties and therefore invariant toisometric deformations
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SPECTRAL FEATURES
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SPECTRAL FEATURES
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RESULTS
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RESULTS
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RETRIEVAL RESULTS
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CLASSIFICATION
Embedding of all Tosca Shapes into 2D
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CONCLUSION
● Fully automated Matching● Provable subcubic time, even faster in normal cases● Globally optimal solution● Continuous solution● Comparable 2D-to-3D Features
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Thank you for your attention!Questions?