On the Use of Functionals on Boundaries
in Hierarchical Models of Object Recognition
1:00 p.m., Friday, July 28, 2000
12th floor conference room, 719 Broadway
Object recognition is a central problem in computer vision. Typically it is assumed to follow a sequential model in which successively more specific hypotheses are generated about the image. This is a rather simplistic model, allowing as it does no margin for error at any point. We follow a more general approach in which the various representations involved are allowed to influence one another from the outset. As a guide and ultimate goal, we study the problem of finding the region occupied by human beings in images, and the separation of the region into arms, legs and head. We approach the problem as that of defining a functional on the space of boundaries in images whose minimum specifies the region occupied by the human figure. Previous work that uses such functionals suffers from a number of difficulties. These include an uncontrollable dependence on scale, an inability to find the global minimum for boundaries in polynomial time, and the inability to include region as well as boundary information. We present a new form of functional on boundaries in a manifold that solves these problems, and is also the unique form of functional in a specific class that possesses a non-trivial, efficiently computable global minimum. We describe applications of the model to single images and to the extraction of boundaries from stereo pairs and motion sequences. In addition, the functionals used in previous work could not include information about the shape of the region sought. We develop a model for the part structures of boundaries that extends previous work to the case of real images, thus including shape information in the functional framework. We show that such part structures are hyperpaths in a hypergraph. An `optimal hyperpath' algorithm is developed that globally minimizes the functional under some conditions. We show how to use exemplars of a shape to construct a functional that includes specific information about the topology of the part structure sought. An algorithm is developed that globally minimizes such functionals in the case of a fixed boundary. The behaviour of the functional mimics an aspect of human shape comparison.