We propose a shape matching method that produces dense correspondences tuned to a specific class of shapes and deformations. In a scenario where this class is represented by a small set of example shapes, the proposed method learns a shape descriptor capturing the variability of the deformations in the given class. The approach enables the wave kernel signature to extend the class of recognized deformations from near isometries to the deformations appearing in the example set by means of a random forest classifier. With the help of the introduced spatial regularization, the proposed method achieves significant improvements over the baseline approach and obtains stateof-the-art results while keeping short computation times.

We propose a novel method for computing a geometrically consistent and spatially dense matching between two 3D shapes. Rather than mapping points to points we match infinitesimal surface patches while preserving the geometric structures. In this spirit we consider matchings as diffeomorphisms between the objects' surfaces which are by definition geometrically consistent. Based on the observation that such diffeomorphisms can be represented as closed and continuous surfaces in the product space of the two shapes we are led to a minimal surface problem in this product space. The proposed discrete formulation describes the search space with linear constraints. Computationally, our approach leads to a binary linear program whose relaxed version can be solved efficiently in a globally optimal manner. As cost function for matching, we consider a thin shell energy, measuring the physical energy necessary to deform one shape into the other. Experimental results demonstrate that the proposed LP relaxation allows to compute highquality matchings which reliably put into correspondence articulated 3D shapes. Moreover a quantitative evaluation shows improvements over existing works.

We study an algorithmic framework for computing an elastic orientation-preserving matching of non-rigid 3D shapes. We outline an Integer Linear Programming formulation whose relaxed version can be minimized globally in polynomial time. Because of the high number of optimization variables, the key algorithmic challenge lies in efficiently solving the linear program. We present a performance analysis of several Linear Programming algorithms on our problem. Furthermore, we introduce a multiresolution strategy which allows the matching of higher resolution models.

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