Closed Object Boundaries from Scattered Points

Remco C. Veltkamp (auth.)3540588086, 9783540588085, 0387588086

This monograph is devoted to computational morphology, particularly to the construction of a two-dimensional or a three-dimensional closed object boundary through a set of points in arbitrary position.
By applying techniques from computational geometry and CAGD, new results are developed in four stages of the construction process: (a) the gamma-neighborhood graph for describing the structure of a set of points; (b) an algorithm for constructing a polygonal or polyhedral boundary (based on (a)); (c) the flintstone scheme as a hierarchy for polygonal and polyhedral approximation and localization; (d) and a Bezier-triangle based scheme for the construction of a smooth piecewise cubic boundary.

---

Table of contents :
Introduction….Pages 1-7
Geometric graphs….Pages 9-21
The γ -Neighborhood Graph….Pages 23-36
Boundary construction….Pages 37-44
Boundary from the γ -Graph….Pages 45-62
Approximation and localization….Pages 63-72
The flintstones….Pages 73-91
Smooth curves and surfaces….Pages 93-107
G 1 boundary construction….Pages 109-128
Conclusions….Pages 129-131