On the Sensitivity of the Hough Transform for Object Recognition

Abstract

Object recognition from sensory data involves, in part, determining the pose of a model with respect to a scene. A common method for finding an object's pose is the generalized Hough transform, which accumulates evidence for possible coordinate transformations in a parameter space whose axes are the quantized transformation parameters. Large clusters of similar transformations in that space are taken as evidence of a correct match. This article provides a theoretical analysis of the behavior of such methods. The authors derive bounds on the set of tranformations consistent with each pairing of data and model features, in the presence of noise and occlusion in the image. They also provide bounds on the likelihood of false peaks in the parameter space, as a function of noise, occlusion, and tessellation effects. It is argued that blithely applying such methods to complex recognition tasks is a risky proposition, as the probability of false positives can be very high. Keywords: Two dimensional noise analysis.

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