A note on 'geometric transforms' of digital sets

  • Authors:

  • Azriel Rosenfeld

  • Affiliations:

  • Computer Vision Laboratory, Computer Science Center, University of Maryland, College Park, MD 20742, USA

  • Venue:
  • Pattern Recognition Letters
  • Year:
  • 1983

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Abstract

We define a 'geometric transform' on the digital plane as a function @? that takes pairs (P, S), where S is a set and P a point of S, into nonnegative integers, and where @?(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 @?(S, P) is the distance from P to S, and 'isovist transforms', where @?(S, P), is the area of the part S visible from P. This note characterizes geometric transforms that have certain simple set-theoretic properties, e.g., such that @?(S@?T,P) = @?(S,P)@?@?(T,P) for all S, T, P. 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.