Title :
Nonplanar curve and surface estimation in 3-space
Author_Institution :
Brown Univ., Providence, RI, USA
Abstract :
The problem of minimal parameter representation and estimation for complex planar and nonplanar curves, and surfaces is considered. The representation is based on concepts from algebraic geometry: a surface is the set of roots of a polynomial of three variables, and a curve is the intersection of two different surfaces. It is shown that the surfaces of an interesting complex of objects in three-space can be represented by single high degree-polynomials, and a similar statement applies to complex curves in three-space. An approximate expression for the mean-square distance from a set of points to a curve or surface is developed, not only for quadratic surfaces, but also for surfaces and curves defined by polynomials of higher degree. A computationally efficient algorithm is presented to carry out the minimization without using nonlinear optimization techniques
Keywords :
computational complexity; geometry; optimisation; polynomials; algebraic geometry; complex curves; complex planar; minimization; nonplanar curves; optimization; parameter estimation; polynomial; surface estimation; Geometry; Machine vision; Minimization methods; Object recognition; Parameter estimation; Polynomials; Solids; Stereo vision; Surface fitting;
Conference_Titel :
Robotics and Automation, 1988. Proceedings., 1988 IEEE International Conference on
Conference_Location :
Philadelphia, PA
Print_ISBN :
0-8186-0852-8
DOI :
10.1109/ROBOT.1988.12129