EFFICIENT ALGORITHMS FOR OBTAINING ALGEBRAIC INVARIANTS FROM HIGHER DEGREE IMPLICIT POLYNOMIALS FOR RECOGNITION OF CURVED OBJECTS

Implicit polynomials can be used for describing a large variety of cur ved shapes. In most of the earlier works, the emphasis had been on the use of second degree implicit polynomials. To describe more complex c urves and surfaces, it is necessary that higher degree implicit polyno mials be used. In this paper, we have proposed a tensor based approach for obtaining affine and Euclidean invariants from the coefficients o f higher degree implicit polynomials. Our approach is more general and computationally efficient than the matrix based approaches for obtain ing invariants. For the Euclidean case, the algorithm can be used for both recognition and pose estimation. In this paper, we have demonstra ted our approach for obtaining invariants of 2-D shapes using third an d fourth degree implicit polynomials. (C) 1997 Pattern Recognition Soc iety. Published by Elsevier Science Ltd.