Date of Original Version



Conference Proceeding

Rights Management

Copyright 1995 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited

Abstract or Description

We define the notions of strong convexity and strong visibility. These notions generalize standard convexity and visibility, as well as several types of nontraditional convexity, such as iso-oriented rectangles and C-oriented polygons. We explore the properties of strong convexity and strong visibility in two and three dimensions. In particular, we establish analogs of the following properties of standard convex sets: (1) Every two points of a convex set are visible to each other. (2) The intersection of convex sets is a convex set. (3) For every point in the boundary of a convex set, there exists a supporting plane through this point. (4) A closed convex set in three dimensions is the intersection of all halfspaces that contain it.



Published In

Proceedings of the Vision Geometry IV Conference, 61-72.