REDUCE: Software for algebraic computation
REDUCE: Software for algebraic computation
Geometric invariance in computer vision
Geometric invariance in computer vision
Implicit Curves and Surfaces in CAGD
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Geometric invariants and object recognition
International Journal of Computer Vision
Algorithms in invariant theory
Algorithms in invariant theory
Theory of algebraic invariants
Theory of algebraic invariants
3D motion recovery via affine epipolar geometry
International Journal of Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Symbolic Computation to Find Algebraic Invariants
IEEE Transactions on Pattern Analysis and Machine Intelligence
2D shape tracking using algebraic curve spaces
ISCIS'05 Proceedings of the 20th international conference on Computer and Information Sciences
Planar shape representation and matching under projective transformation
Computer Vision and Image Understanding
| Hi-index | 0.00 |
Combining implicit polynomials and algebraic invariants for representing and recognizing complicated objects proves to be a powerful technique. In this paper, we explore the findings of the classical theory of invariants for the calculation of algebraic invariants of implicit curves and surfaces, a theory largely disregarded in the computer vision community by a shadow of skepticism. Here, the symbolic method of the classical theory is described, and its results are extended and implemented as an algorithm for computing algebraic invariants of projective, affine, and Euclidean transformations. A list of some affine invariants of 4th degree implicit polynomials generated by the proposed algorithm is presented along with the corresponding symbolic representations, and their use in recognizing objects represented by implicit polynomials is illustrated through experiments. An affine invariant fitting algorithm is also proposed and the performance is studied.