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 curved shapes. In most of the earlier works, the emphasis had been on the use of second degree implicit polynomials. To describe more complex curves and surfaces, it is necessary that higher degree implicit polynomials be used. In this paper, we have proposed a tensor based approach for obtaining affine and Euclidean invariants from the coefficients of higher degree implicit polynomials. Our approach is more general and computationally efficient than the matrix based approaches for obtaining invariants. For the Euclidean case, the algorithm can be used for both recognition and pose estimation. In this paper, we have demonstrated our approach for obtaining invariants of 2-D shapes using third and fourth degree implicit polynomials.

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