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arXiv · 1601.06070

Efficient Globally Optimal 2D-to-3D Deformable Shape Matching

Zorah Lähner·Emanuele Rodolà·Frank R. Schmidt·Michael M. Bronstein·Daniel Cremers
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Abstract

We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a 2D shape represented as a planar curve and a 3D shape represented as a surface; the output is a continuous curve on the surface. We cast the problem as finding the shortest circular path on the product 3-manifold of the surface and the curve. We prove that the optimal matching can be computed in polynomial time with a (worst-case) complexity of $O(mn^2\log(n))$, where $m$ and $n$ denote the number of vertices on the template curve and the 3D shape respectively. We also demonstrate that in practice the runtime is essentially linear in $m\!\cdot\! n$ making it an efficient method for shape analysis and shape retrieval. Quantitative evaluation confirms that the method provides excellent results for sketch-based deformable 3D shape retrieval.

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Zorah Lähner, Emanuele Rodolà, Frank R. Schmidt, Michael M. Bronstein, Daniel Cremers. 2016-01-22. Efficient Globally Optimal 2D-to-3D Deformable Shape Matching. https://arxiv.org/abs/1601.06070

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