A Note on 'Geometric Transforms' of Digital Sets.
MARYLAND UNIV COLLEGE PARK COMPUTER VISION LAB
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Document defines a geometric transform on the digital plane as a function f that takes pairs P,S, where S is a set and P a point of S, into nonnegative integers, and where f S,P depends only on the positions of the points of S relative to P. Transforms of this type are useful for segmenting and describing S. Two examples are distance transforms, for which f S,P is the distance from P to S, and isovist transforms, where f S,P is e.g. the area of the part of S visible from P. This ncte characterizes geometric transforms that have certain simple set-theoretic properties. It is shown that a geometric transform has this intersection property if and only if it is defined in a special way in terms of a neighborhood base the class of such neighborhood transforms is a generalization of the class of distance transforms.
- Theoretical Mathematics