Pixel Club: Analysis of Non-Rigid 3D Shapes

Speaker:
Zorah Lähnerand & Matthias Vestner (TU Munich)
Date:
Wednesday, 29.3.2017, 14:30
Place:
Room 337 Taub Bld.

Zorah Lähner and Matthias Vestner are PhD students from the group of Daniel Cremers at TU Munich. Both are working in the Analysis of Non-Rigid 3D Shapes and in particular consider the (dense) correspondence problem between instances of those. Z.L. will present (an extended version of) her CVPR 2016 paper "Efficient Globally Optimal 2D-to-3D Deformable Shape Matching" (2D-3D), M.V. will present (an extended version of) his CVPR 2017 paper "Product Manifold Filter: Non-Rigid Shape Correspondence via Kernel Density Estimation in the Product Space" (PMF).

Abstract Product Manifold Filter:
Finding a dense correspondence between two Non-Rigid shapes is still an open problem. Most existing approaches either make restrictive assumptions on the considered shapes (such as isometry) and/or produce matchings that are neither surjective nor continuous as they rely on some type of nearest neighbor search in a descriptor space - in case of functional maps those descriptors are eg. aligned harmonics. I will present an iterative method that guarantees bijections with increasing continuity at each iteration without any isometry assumptions. If you have already attended a presentation about the PMF, (or even read the paper) you will still see something new: Extension to settings where the optimal solution is not a bijection (partiality, different sampling). Relation of the PMF to quadratic assignment problems (such as discretizations of Gromov-Wasserstein distances).

Abstract 2D-to-3D:
Finding correspondences between different dimensional objects casts many additional problems. Common descriptors only work on the same dimension and even defining the optimal solution is not always trivial. This setting can, for example, be used to search large collections of 3D shapes based on sketches given by a user. In this talk I will present a method to find correspondences between a 2D silhouette of an object represented by a closed curve - possibly drawn by a human - and a 3D shape. I show retrieval results on a collection of shapes in which both of the inputs are allowed to undergo non-rigid pose deformations. The obtained correspondences are continuous and can be chosen to be either globally optimal or an epsilon-approximation of it (with similar retrieval rates but improved runtime). The talk will include descriptors which are comparable between 2D and 3D but can still handle non-rigid deformations.

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