Supervised hypergraph labeling

Abstract

We address the problem of labeling individual datapoints given some knowledge about (small) subsets or groups of them. The knowledge we have for a group is the likelihood value for each group member to satisfy a certain model. This problem is equivalent to hypergraph labeling problem where each datapoint corresponds to a node and the each subset correspond to a hyperedge with likelihood value as its weight. We propose a novel method to model the label dependence using an Undirected Graphical Model and reduce the problem of hypergraph labeling into an inference problem. This paper describes the structure and necessary components of such model and proposes useful cost functions. We discuss the behavior of proposed algorithm with different forms of the cost functions, identify suitable algorithms for inference and analyze required properties when it is theoretically guaranteed to have exact solution. Examples of several real world problems are shown as applications of the proposed method.

Hypergraph modelling for geometric model fitting

“…Recently, hypergraphs have been introduced to solve some computer vision tasks, e.g., [15][16][17][18][19]. A hypergraph contains higher order similarities instead of pairwise similarities, which can be beneficial to overcome the above-mentioned limitations.…”

“…Obviously, since the number of inliers associated to each structure is different, the degree of each hyperedge is varying. Therefore, we devise a scheme having the following features: the degree of a hyperedge is "data-driven" (hence, varying), and much larger (as close as possible to include all inliers) than the one used in the previous hypergraph based works [15][16][17][18][19].…”

Learning Hypergraph Labeling for Feature Matching

“…We adopt a hypergraph node labeling algorithm proposed in [17]. Given a hypergraph, where the hyperedge weights are computed using a model, this algorithm produces the optimal labeling of the nodes that maximally conforms with the hyperedge weights or likelihood values.…”

“…Given a hypergraph, where the hyperedge weights are computed using a model, this algorithm produces the optimal labeling of the nodes that maximally conforms with the hyperedge weights or likelihood values. Within the framework, the higher order interaction among subsets of datapoints is modeled using a higher order undirected graphical model or the Markov network (see [17] for details). The labels are computed by solving the inference problem on this graphical model where a labeling cost or energy function is minimized to produce the optimal labeling.…”

“…In this paper, we show that the framework of hypergraph node labeling of [17] can be applied for feature matching. In addition, we show how it is possible, and in fact advantageous, to learn (a parametric form of) the)cost function for matching given several labeled examples of feature correspondences.…”