Assembling virtual pots from 3D measurements of their fragments
Proceedings of the 2001 conference on Virtual reality, archeology, and cultural heritage
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Robust Estimation Algorithms for Tracking Explicit Curves
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Hand Recognition Using Implicit Polynomials and Geometric Features
AVBPA '01 Proceedings of the Third International Conference on Audio- and Video-Based Biometric Person Authentication
Implicitization of Parametric Curves by Matrix Annihilation
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Combining implicit polynomials and geometric features for hand recognition
Pattern Recognition Letters - Special issue: Audio- and video-based biometric person authentication (AVBPA 2001)
Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment
Journal of Mathematical Imaging and Vision
Topologically Faithful Fitting of Simple Closed Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stable Fitting of 2D Curves and 3D Surfaces by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
A model based approach for pose estimation and rotation invariant object matching
Pattern Recognition Letters
Hierarchical error-driven approximation of implicit surfaces from polygonal meshes
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Kernel PCA for similarity invariant shape recognition
Neurocomputing
Stable Algebraic Surfaces for 3D Object Representation
Journal of Mathematical Imaging and Vision
3D Model Segmentation and Representation with Implicit Polynomials
IEICE - Transactions on Information and Systems
Adaptively determining degrees of implicit polynomial curves and surfaces
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
Modeling and Estimation of the Dynamics of Planar Algebraic Curves via Riccati Equations
Journal of Mathematical Imaging and Vision
Multilevel algebraic invariants extraction by incremental fitting scheme
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part I
A representation of time series based on implicit polynomial curve
Pattern Recognition Letters
Efficient detection of symmetries of polynomially parametrized curves
Journal of Computational and Applied Mathematics
A coarse-to-fine IP-driven registration for pose estimation from single ultrasound image
Computer Vision and Image Understanding
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An algebraic curve is defined as the zero set of a polynomial in two variables. Algebraic curves are practical for modeling shapes much more complicated than conics or superquadrics. The main drawback in representing shapes by algebraic curves has been the lack of repeatability in fitting algebraic curves to data. Usually, arguments against using algebraic curves involve references to mathematicians Wilkinson (and Runge). The first goal of this article is to understand the stability issue of algebraic curve fitting. Then a fitting method based on ridge regression and restricting the representation to well behaved subsets of polynomials is proposed, and its properties are investigated. The fitting algorithm is of sufficient stability for very fast position-invariant shape recognition, position estimation, and shape tracking, based on invariants and new representations. Among appropriate applications are shape-based indexing into image databases