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The estimation of correspondences between two images resp. point sets is acore problem in computer vision. One way to formulate the problem is graphmatching leading to the quadratic assignment problem which is NP-hard. Severalso called second order methods have been proposed to solve this problem. Inrecent years hypergraph matching leading to a third order problem becamepopular as it allows for better integration of geometric information. For mostof these third order algorithms no theoretical guarantees are known. In thispaper we propose a general framework for tensor block coordinate ascent methodsfor hypergraph matching. We propose two algorithms which both come along withthe guarantee of monotonic ascent in the matching score on the set of discreteassignment matrices. In the experiments we show that our new algorithmsoutperform previous work both in terms of achieving better matching scores andmatching accuracy. This holds in particular for very challenging settings whereone has a high number of outliers and other forms of noise.

A Flexible Tensor Block Coordinate Ascent Scheme for Hypergraph Matching