Hypergraph Based Visual Segmentation and Retrieval

This chapter explores original techniques for the construction of hypergraph models for computer vision applications. A hypergraph is a generalization of a pairwise simple graph, where an edge can connect any number of vertices. The expressive power of the hypergraph models places a special emphasis on the relationship among three or more objects, which has made hypergraphs better models of choice in a lot of problems. This is in sharp contrast with the more conventional graph representation of visual patterns where only pairwise connectivity between objects is described. This chapter draws up from three aspects to carry the discussion of hypergraph based methods in computer vision: (i) The advantage of the hypergraph neighborhood structure is analyzed. The author argues that the summarized local grouping information contained in hypergraphs causes an ‘averaging’ effect which is beneficial to the clustering problems; (ii)The chapter discusses how to build hypergraph incidence structures and how to solve the related unsupervised and semi-supervised problems for two different computer vision scenarios: video object segmentation and image retrieval; (iii) For the application of image retrieval, the chapter introduces a novel hypergraph model — probabilistic hypergraph to exploit the structure of the data manifold by considering not only the local grouping information, but also the similarities between vertices in hyperedges.