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We approach the problem of labeling a set of objects from a quantitative standpoint. We define a world model in terms of transition probabilities and propose a definition of a class of global criteria that combine both ambiguity and consistency. A projected gradient algorithm is developed to minimize the criterion. We show that the minimization procedure can be implemented in a highly parallel manner. Results are shown on several examples and comparisons are made with relaxation labeling techniques.

This paper describes an algorithm which builds a ``Peano scanning,'' i.e., the reciprocal mapping, from [0, 1]n to [0, 1], of the well-known ``Peano curve.'' This Peano scanning is applied to a set of points in [0, 1]n and gives a one-dimensional image of it. Several applications of this technique have already been developed and are presented in this paper.