A multi-resolution technique for comparing images using the Hausdorff distance

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. An efficient method of computing this distance is developed, based on a multi-resolution tessellation of the space is possible transformations of the model set. One of the key ideas is that entire cells in this tessellation can be ruled out quickly, without actually computing the Hausdorff distance for many of them. Emphasis is placed on the case in which the model is allowed to translate and scale (independently in x and y) with respect to the image. This four-dimensional transformation space is searched rapidly while guaranteeing that no match will be missed. Some examples of identifying an object in a cluttered scene are presented, including cases where the object is partially hidden from view