  The estimation of correspondences between two images resp. point sets is a
core problem in computer vision. One way to formulate the problem is graph
matching leading to the quadratic assignment problem which is NP-hard. Several
so called second order methods have been proposed to solve this problem. In
recent years hypergraph matching leading to a third order problem became
popular as it allows for better integration of geometric information. For most
of these third order algorithms no theoretical guarantees are known. In this
paper we propose a general framework for tensor block coordinate ascent methods
for hypergraph matching. We propose two algorithms which both come along with
the guarantee of monotonic ascent in the matching score on the set of discrete
assignment matrices. In the experiments we show that our new algorithms
outperform previous work both in terms of achieving better matching scores and
matching accuracy. This holds in particular for very challenging settings where
one has a high number of outliers and other forms of noise.
