A New Graph-Theoretic Approach to Clustering, with Applications to Computer Vision

This work applies cluster analysis as a unified approach for a wide range of vision applications, thereby combining the research domain of computer vision and that of machine learning. Cluster analysis is the formal study of algorithms and methods for recovering the inherent structure within a given dataset. Many problems of computer vision have precisely this goal, namely to find which visual entities belong to an inherent structure, e.g. in an image or in a database of images. For example, a meaningful structure in the context of image segmentation is a set of pixels which correspond to the same object in a scene. Clustering algorithms can be used to partition the pixels of an image into meaningful parts, which may correspond to different objects. In this work we focus on the problems of image segmentation and image database organization. The visual entities to consider are pixels and images, respectively. Our first contribution in this work is a novel partitional (flat) clustering algorithm. The algorithm uses pairwise representation, where the visual objects (pixels, images) are mapped to the nodes of an undirected edge-weighted graph, with edge weights representing pairwise similarity relations. The clustering problem is formulated as a graph partitioning problem, namely a meaningful partitioning of the nodes into clusters is thought. Our clustering algorithm is centered around the notion of a dominant set, a novel combinatorial concept which arises from the study of a continuous formulation of the maximum clique problem. Our proposal seems to be a plausible generalization of the notion of a maximal clique in the context of edge-weighted graphs since, in the unweighted case, dominant sets turn out to be equivalent to (strictly) maximal cliques. Formal properties, intuitive arguments, and empirical findings make dominant sets reasonable candidates for a new