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. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model. We focus primarily on the case in which the model is only allowed to translate with respect to the image. Then we consider how to extend the techniques to rigid motion (translation and rotation). The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors as occur with edge detectors and other feature extraction methods. Moreover, we show how the method extends naturally to the problem of comparing a portion of a model against an i...