A Graph-Rewriting Paradigm for Discrete Relaxation

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Abstract
In image analysis, recognition of the primitives plays an important role. Subsequent analysis is used to interpret the arrangement of primitives. This subsequent analysis must make allowance for errors or ambiguities in the recognition of primitives. In this paper, we assume that the primitive recognizer produces a set of possible interpretations for each primitive. To reduce this primitive-recognition ambiguity, we use contextual information in the image, and apply constraints from the image domain. This process is variously termed constraint satisfaction, labeling or discrete relaxation. Existing methods for discrete relaxation are limited in that they assume a priori knowledge of the neighborhood model: before relaxation begins, the system is told (or can determine) which sets of primitives are related by constraints. These methods do not apply to image domains in which complex analysis is necessary to determine which primitives are related by constraints. For example, in music notation, we must recognize which notes belong to one measure, before it is possible to apply the constraint that the number of beats in the measure should match the time signature. Such constraints can be handled by our graph-rewriting paradigm for discrete relaxation: here neighborhood-construction is interleaved with constraint-application. In applying this approach to the recognition of simple music notation, we use approximately 180 graph-rewriting rules to express notational constraints and semantic-interpretation rules for music notation. The graph rewriting rules express both binary and higher-order notational constraints. As image-interpretation proceeds, increasingly abstract levels of interpretation are assigned to (groups of) primitives. This allows application of higher-level constraints, which can be formulated only after partial interpretation of the image.

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