A classical morphological technique for shape recognition is by means of the hit-or-miss transform. In essence, there are two structuring elements for each shape, one to fit inside and one to fit outside. These structuring-element pairs are chosen so that there will be a `hit' and a `miss' if and only if the appropriate shape appears. The problem is to design structuring pairs that yield acceptable recognition rates. This can be especially difficult if some shapes are close and the shapes are random (noisy). The present paper analyzes the problem by adopting a shape-noise model that represents both the structures of the individual shapes and edge indeterminacy. For direct application to a given system, the model parameters must be estimated statistically. Optimal shape recognition is characterized in terms of the model. The advantage of the new approach is that it provides an environment for machine design optimal structuring elements for shape recognition.
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