Title :
Computing invariants using elimination methods
Author :
Kapur, Deepak ; Lakshman, Y.N. ; Saxena, Tushar
Author_Institution :
Inst. of Programming & Logics, State Univ. of New York, Albany, NY, USA
Abstract :
Geometric invariants appear to play an important role in object recognition as an aid to building model libraries of objects. Useful invariants are often found by extensive experience and they are based on geometric invariant properties studied by algebraists over many years. Given a geometric configuration, there is however a need to systematically generate and search for its invariants. In this paper we give a complete solution, in principle, to computing a single invariant for a geometric configuration, if it exists. The algorithm works in three steps: (i) the problem formulation step in which algebraic relations are established between object parameters and image parameters (or equivalently, parameters of two different images) using an imaging transformation, (ii) elimination of transformation parameters resulting in an invariant relation between object and image parameters, and (iii) finally, extraction of a single invariant from the algebraic relation. The main contribution of the paper is to give a complete solution for the third step, called the separability problem. It is shown that there is a simple and efficient solution to the separability problem provided the resultant obtained from the second step is explicitly known. The efficiency of the algorithm is linked to the efficiency of computing the resultant. Dixon´s method is proposed to be used for computing the resultant
Keywords :
image matching; object recognition; algebraic relations; elimination methods; geometric configuration; geometric invariants; image parameters; imaging transformation; invariants computing; object parameters; object recognition; separability problem; Concrete; Equations; Humans; Image recognition; Libraries; Logic programming; Object recognition; Solid modeling; Transforms;
Conference_Titel :
Computer Vision, 1995. Proceedings., International Symposium on
Conference_Location :
Coral Gables, FL
Print_ISBN :
0-8186-7190-4
DOI :
10.1109/ISCV.1995.476984