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Given the ever increasing bandwidth of the visual information available tomany intelligent systems, it is becoming essential to endow them with a senseof what is worthwhile their attention and what can be safely disregarded. Thisarticle presents a general mathematical framework to efficiently allocate theavailable computational resources to process the parts of the input that arerelevant to solve a given perceptual problem. By this we mean to find thehypothesis H (i.e., the state of the world) that maximizes a function L(H),representing how well each hypothesis "explains" the input. Given the largebandwidth of the sensory input, fully evaluating L(H) for each hypothesis H iscomputationally infeasible (e.g., because it would imply checking a largenumber of pixels). To address this problem we propose a mathematical frameworkwith two key ingredients. The first one is a Bounding Mechanism (BM) to computelower and upper bounds of L(H), for a given computational budget. These boundsare much cheaper to compute than L(H) itself, can be refined at any time byincreasing the budget allocated to a hypothesis, and are frequently enough todiscard a hypothesis. To compute these bounds, we develop a novel theory ofshapes and shape priors. The second ingredient is a Focus of AttentionMechanism (FoAM) to select which hypothesis' bounds should be refined next,with the goal of discarding non-optimal hypotheses with the least amount ofcomputation. The proposed framework: 1) is very efficient since most hypothesesare discarded with minimal computation; 2) is parallelizable; 3) is guaranteedto find the globally optimal hypothesis; and 4) its running time depends on theproblem at hand, not on the bandwidth of the input. We instantiate the proposedframework for the problem of simultaneously estimating the class, pose, and anoiseless version of a 2D shape in a 2D image.

Hypothesize and Bound: A Computational Focus of Attention Mechanism for  Simultaneous N-D Segmentation, Pose Estimation and Classification Using Shape  Priors