This Ph.D. dissertation presents the result of research carried out between 1985 and 1992, first at Leiden University as a scientific assistant researcher, and later at CWI (Centre for Mathematics and Computer Science), Amsterdam, as a researcher on the NFI IIICAD project, funded by NWO (Dutch Organization for Scientific Research) under Grant NF-51/62-514.

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.