Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1992 · 99 citations · 0 references
Natural SciencesComputer ScienceMathematicsComputational GeometryGeometryTopologyGeometric MeasurementMetric GeometryShape AnalysisShape DeformationShape FunctionsShape MetricsDeformationGeometric Measure TheoryObject Size EstimationProperties Of ShapesSizeSize - Distance RelationshipSize Measurement
Size functions map the real plane to natural numbers to describe the shape of submanifolds in Euclidean space, while deformation distance quantifies shape differences between manifolds. The paper defines size functions and deformation distance between manifolds, and highlights their interrelation. We provide two computational techniques for size functions and illustrate them with examples.
We define the concept of size functions. They are functions from the real plane to the natural numbers which describe the `shape of the objects' (seen as submanifolds of a Euclidean space). We give two different techniques of computation of size functions and some actual examples of computation. Moreover, we present the concept of deformation distance between manifolds (i.e., curves, surfaces, etc.). It is a distance which measures the `difference in shape' of two manifolds. Finally we point out the link between deformation distances and size functions.