The Combinatorics of Object Recognition in Cluttered Environments Using Constrained Search

Abstract

When clustering techniques such as the Hough transform are used to isolate likely subspaces of the search space, empirical performance in cluttered scenes improves considerably. In this paper we establish formal bounds on the combinatorics of this approach. Under some simple assumptions, we show that the expected complexity of recognizing isolated objects is quadratic in the number of model and sensory fragments, but that the expected complexity of recognizing objects in cluttered environments is exponential in the size of the correct interpretation. We also provide formal bounds on the efficacy of using the Hough transform to preselect likely subspaces, showing that the problem remains exponential, but that in practical terms, the size of the problem is significantly decreased.