The Hausdorff distance measures the extent to which each point of a "model" set lies near some point of an "image" set and vice versa. In this paper we describe an efficient method of computing this distance, based on a multi-resolution tessallation of the space of possible transformations of the model set. We focus on the case in which the model is allowed to translate and scale with respect to the image. This four-dimensional transformation space (two translation and two scale dimensions) is searched rapidly, while guaranteeing that no match will be missed. We present some examples of identifying an object in a cluttered scene, including cases where the object is partially hidden from view.