Mathematical Sciences: Mathematical and Computational Problems in Object Recognition

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The research program focuses on mathematical aspects of object recognition. There are two classes of problems. The first is the recognition of rigid objects positioned in a scene at arbitrary rotations, locations, and scales. A large repertoire of shapes is assumed known in advance, and the problem is to then devise computationally efficient algorithms for recognizing which, if any, of these objects are present in a given scene. Sequential and adaptive strategies will be explored, in which a sequence of image-based observations is made, with the choice of an observation depending upon the results of previous observations. There are close connections to coding theory, sequential design of experiments, multi-armed bandit problems, the game of "twenty questions," and, of course, previous work in machine vision. The second class of problems is the recognition of nonrigid, or deformable, objects. Examples include handwritten numerals and various biological shapes, such as leaves, hands, organelles, etc. Here the issue of shape modeling appears to be central. An approach through deformable templates is proposed. Templates are prototypes which capture global characteristics, whereas deformations are random transformations, satisfying certain regularity constraints, that act upon templates to produce the possible presentations of an object. The proposed shape models suggest certain recognition algorithms, and these will be explored in a variety of application areas.