Models for near-rigid shape matching are typically based on distance-related features, in order to infer matches that are consistent with the isometric assumption. However, real shapes from image datasets, even when expected to be related by almost isometric" transformations, are actually subject not only to noise but also, to some limited degree, to variations in appearance and scale. In this paper, we introduce a graphical model that parameterises appearance, distance, and angle features and we learn all of the involved parameters via structured prediction. The outcome is a model for near-rigid shape matching which is robust in the sense that it is able to capture the possibly limited but still important scale and appearance variations. Our experimental results reveal substantial improvements upon recent successful models, while maintaining similar running times."

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data.

We present a method for learning max-weight matching predictors in bipartite graphs. The method consists of performing maximum a posteriori estimation in exponential families with sufficient statistics that encode permutations and data features. Although inference is in general hard, we show that for one very relevant application - document ranking - exact inference is efficient. For general model instances, an appropriate sampler is readily available. Contrary to existing max-margin matching models, our approach is statistically consistent and, in addition, experiments with increasing sample sizes indicate superior improvement over such models. We apply the method to graph matching in computer vision as well as to a standard benchmark dataset for learning document ranking, in which we obtain state-of-the-art results, in particular improving on max-margin variants. The drawback of this method with respect to max-margin alternatives is its runtime for large graphs, which is high comparatively.