# Extraction of surface parameters from depth maps viewing planes and quadrics of revolution

## Abstract

This paper presents a first step in the definition and construction of a vision system to recognize three-dimensional objects whose surface are composed of planar patches and patches of quadrics of revolution. A large portion of man-made objects can be either modeled exactly, or at least well approximated by a number of patches of such surfaces. The problems addressed in this paper are three-dimensional surface recognition and parameter extraction from noisy depth maps viewing one surface. The basis for the surface recognition and parameter estimation is the curvature information that can be extracted from polynomial approximations to the range data. The curvature properties are derived directly from the Weingarten map, a well-known concept from classical differential geometry. The actual process of recognition and parameter extraction is framed as a set of stacked parameter space transforms that compute measures of confidence in an iterative refinement, or multi-level relaxation, scheme. This scheme resulted from experiments with connectionist visual recognition systems. The measure of confidence associates a measure with a hypothesis that a parameterization (corresponding to a surface) actually exists in the scene. © 1987 SPIE.