Samoylov,A.
Abstract:
The paper is dedicated to 3D objects matching problem ('matching' here means searching for such a disposition between two objects in 3D space that corresponds to minimal distance between the objects according to given distance function). The author proposes new solution for the particular case of the problem; if the 1st object is piecewise-continuous surface and the 2nd object is a discrete point set which can be significantly sparse (4 points at least). The developed solution is purely based on geometric constructions. It does not require an initial approximation, finds all the possible matches and works also for non-simply connected surfaces, surfaces given by multi-valued functions and surfaces with self-intersections as well. The solution was implemented as a special software, and the test results for several practical cases are presented in the paper. The estimations of computational complexity also are presented. The author also tried to apply the developed solution for matching color 2D images. The corresponding test results are presented.