Unsupervised Learning of Graph and Hypergraph Matching

Abstract

Graph and hypergraph matching are fundamental problems in computer vision, which have been receiving a steadily growing attention in the last two decades due to the recent modern algorithms and models that are both fast and accurate. Graph and hypergraph matching are successful in tackling many real-world tasks that require 2D and 3D feature matching and alignment. Matching is a general problem in vision and graphs have always been quintessential for modeling information that has both local and longer range connections. Therefore, graph matching will continue to influence computer vision and robotics research, crossing over many different mathematical and computational models, including Bayesian networks, conditional and Markov random fields, spectral graph models, and, more recently, deep neural networks. While graph matching is limited to using pairwise relationships, hypergraph matching permits the use of relationships between sets of features of any order. Consequently, it carries the promise to make matching more robust to changes in scale, deformations, and outliers. In this chapter, we present several key ideas, computational models, and optimization methods that introduced in the literature the possibility to learn graph and hypergraph matching in a semi-supervised or even completely unsupervised fashion. We start by describing two methods for solving graph and hypergraph matching based on spectral matching and integer projected fixed point methods, introduced in Chap. 1. Then, based on the same intuition (also discussed in Chap. 1) that correct assignments form a strong cluster of agreements, we follow up by introducing the main approach to learning as it applies to graph and hypergraph matching, as well as the more general Maximum A Posteriori (MAP) inference problem in probabilistic graphical models (MRFs and CRFs). In the last part of the chapter, we demonstrate experimentally the effectiveness of the algorithms presented and, whenever possible, provide extensive comparisons to other top published methods. Moreover, we show that our learning approach is general and can significantly boost the performance of different state-of-the-art matching algorithms in the literature.