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 he used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper, we provide efkient 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 such as those that 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 image.

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The Joint Bi-level Image Experts Group jbig, an international study group a liated with iso iec and itut, is in the process of drafting a new standard for lossy and lossless compression of bi-level images. The new standard, informally referred to as jbig2, will support model-based coding for text and halftones to permit compression ratios up to three times those of existing standards for lossless compression. jbig2 will also permit lossy preprocessing without specifying how it is to be done. In this case compression ratios up to eight times those of existing standards may beobtained with imperceptible loss of quality. It is expected that jbig2 will become an International Standard by 2000.

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