Attribute Openings, Thinnings, and Granulometries

In this paper we establish an attribute-based approach to openings and closings and provide an efficient algorithm for their implementation on gray-scale images. Attribute openings are similar to openings by reconstruction since they are connected component transformations. However, attribute openings are more general because they can describe generalized shape features and openings that have no shape-bias. This work is then extended to gray-scale granuolmetries and to include gray-scale thinnings, which are nonincreasing filters. The use of nonincreasing gray-scale thinnings is seen as an important generalization because it allows the use of nonincreasing shape descriptors such as compactness and eccentricity to be applied to filter gray-scale images. Applications are then given to illustrate the performance of the filters proposed.

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