Abstract
Presents the shape of a sparse point set S in R/sup 2/. A crucial step in finding the shape of a sparse point set is the definition of its boundary. This boundary is a graph indicating a relation among the elements of S. No well defined definition of such a boundary is found in literature. For continuous point sets this problem does not exist as the boundary has a unique definition. The authors pose general criteria a boundary definition should satisfy and show that the alpha -graph satisfies those criteria. The boundary is a function of the scale parameter alpha . The authors further show that the alpha -graph has a strong relation with mathematical morphology. As an application the use of the alpha -graph in the multi-scale recognition of industrial objects is shown. >
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