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 th...

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Bibliographic Details
Published in:Pattern recognition 1998-03, Vol.31 (3), p.301-313
Main Authors: Kaveti, Satish, Khwang Teoh, Eam, Wang, Han
Format: Article
Language:English
Subjects:
Algebraic invariants
Algorithmics. Computability. Computer arithmetics
Applied sciences
Artificial intelligence
Computer science
control theory
systems
Exact sciences and technology
Free form objects
Implicit polynomials
Pattern recognition. Digital image processing. Computational geometry
Pose estimation
Recognition
Theoretical computing
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Summary: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.
ISSN:0031-3203
1873-5142
DOI:10.1016/S0031-3203(97)00047-2