Describing Complicated Objects by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implicit polynomial shape modeling and recognition, and application to image/video databases
Implicit polynomial shape modeling and recognition, and application to image/video databases
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implicitization of Parametric Curves by Matrix Annihilation
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment
Journal of Mathematical Imaging and Vision
Image based visual servoing using algebraic curves applied to shape alignment
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Modeling and Estimation of the Dynamics of Planar Algebraic Curves via Riccati Equations
Journal of Mathematical Imaging and Vision
2D shape tracking using algebraic curve spaces
ISCIS'05 Proceedings of the 20th international conference on Computer and Information Sciences
Geometric invariant curve and surface normalization
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part II
Multilevel algebraic invariants extraction by incremental fitting scheme
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part I
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A new method is presented for identifying and comparing closed, bounded, free-form curves that are defined by even implicit polynomial (IP) equations in the Cartesian coordinates x and y. The method provides a new expression for an IP involving a product of conic factors with unique conic factor centers. The critical points for an IP curve also are defined. The conic factor centers and the critical points are shown to be useful related points that directly map to one another under affine transformations. In particular, the explicit determination of such points implies both a canonical form for the curves and the transformation matrix which relates affine equivalent curves.