The image retrieval problem is to assist somebody in searching for a particular image in a large database. In one common scenario, the "user" has no technical knowledge about images and responds to a sequence of machine queries by declaring which of two (or more) displayed images is ``closest'' to his target. The answers are inevitably subjective and the interaction then has an inherently random component. To complicate matters, the images are usually not characterized by their semantic content since automatic indexing of this nature is currently an unsolved problem; instead, images are identified with "low-level" feature vectors.

I will discuss a general stochastic feedback model. The responses of the user are based on a sequence of independent random metrics in feature space whose distribution may depend on both the displayed images and the target. Each new query (pair of displayed images) is chosen to minimize the expected conditional entropy of the distribution over targets given the previous responses; this distribution then evolves according to the new response. The resulting algorithm is demonstrated for shape and image retrieval and its performance compared with theoretical bounds and other models. Time permitting, I will also indicate how one might incorporate available textual cues, such as keywords, in order to accelerate the search.

Donald Geman received the B.A. degree in English Literature from the University of Illinois in 1965 and the Ph.D. degree in Mathematics from Northwestern University in 1970. Since 1970 he has been a member of the Department of Mathematics and Statistics at the University of Massachusetts, Amherst. He also holds appointments at Ecole Polytechnique and ENS-Cachan in Paris. His research is a blend of statistics, information theory and computer vision. Current themes include i) visual selection and object recognition based on coarse-to-fine templates; ii) image retrieval based on stochastic feedback and stepwise entropy reduction; iii) analyzing brain lesions based on MRI and hierarchical random fields; and iv) mathematical foundations of "twenty questions" and inductive learning.