# Analyzing the Probability of a False Alarm for the Hausdorff Distance Under Translation

W. Eric L. Grimson

Daniel P. Huttenlocher

MIT AI Lab

Cambridge, MA 02139

Cornell Computer Science Dept.

Ithaca, NY 14853

Here is a postscript version of this paper. [181 Kb]

## ABSTRACT

In order for model-based recognition and geometric shape comparison methods to
be more useful in practice, we need accurate models for predicting their
performance. Over the last several years a number of formal models have been
developed for estimating the probability of a false match for model-based
recognition methods that are based on geometric feature correspondences.
These models can be used to set the parameters of such methods automatically,
so as to limit the probability of a randomly occurring match to some
pre-specified level. This paper considers the related problem of developing a
formal model for the probability of a false match when using the generalized
Hausdorff measure. The model enables the parameters of Hausdorff methods (the
distance and fraction) to be set so as to produce a desired level of false
positive matches.