IEEE Transactions on Pattern Analysis and Machine Intelligence
Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations
IBM Journal of Research and Development
Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
A Data-Driven Intermediate Level Feature Extraction Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recovery of Parametric Models from Range Images: The Case for Superquadrics with Global Deformations
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Recognizing and Positioning Curved 3-D Objects from Image Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
On using CAD models to compute the pose of curved 3D objects
CVGIP: Image Understanding - Special issue on directions in CAD-based vision
Recognition and positioning of rigid objects using algebraic and moment invariants
Recognition and positioning of rigid objects using algebraic and moment invariants
Object recognition based on moment (or algebraic) invariants
Geometric invariance in computer vision
An accurate algorithm for rasterizing algebraic curves
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Describing Complicated Objects by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Distance approximations for rasterizing implicit curves
ACM Transactions on Graphics (TOG)
Rasterizing Algebraic Curves and Surfaces
IEEE Computer Graphics and Applications
Projectively Invariant Representations Using Implicit Algebraic Curves
ECCV '90 Proceedings of the First European Conference on Computer Vision
Shape recovery and segmentation with deformable part models
Shape recovery and segmentation with deformable part models
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Distance approximations for rasterizing implicit curves
ACM Transactions on Graphics (TOG)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implicit Simplicial Models for Adaptive Curve Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of VLSI Signal Processing Systems - special issue on applications of neural networks in biomedical image processing
The Determination of Implicit Polynomial Canonical Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fitting Curves and Surfaces With Constrained Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Interactive Object Shape Modeling Using Algebraic Curves
Journal of VLSI Signal Processing Systems - special issue on multimedia signal processing
Error bounded regular algebraic spline curves
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Implicit Polynomials, Orthogonal Distance Regression, and the Closest Point on a Curve
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognizing 3D Objects Using Tactile Sensing and Curve Invariants
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision
The ellipsoidal skeleton in medical applications
Proceedings of the sixth ACM symposium on Solid modeling and applications
Pattern Recognition Letters
Saliency sequential surface organization for free-form object recognition
Computer Vision and Image Understanding
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
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 Technique for Finding the Symmetry Axes of Implicit Polynomial Curves under Perspective Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Motion Recovery by Integrating over the Joint Image Manifold
International Journal of Computer Vision
Computer Aided Geometric Design
Recognising Algebraic Surfaces from Two Outlines
Journal of Mathematical Imaging and Vision
Active Contours Under Topology Control--Genus Preserving Level Sets
International Journal of Computer Vision
Stable Algebraic Surfaces for 3D Object Representation
Journal of Mathematical Imaging and Vision
Technical Section: Variational implicit surface meshing
Computers and Graphics
Surface reconstruction from point clouds by transforming the medial scaffold
Computer Vision and Image Understanding
Computer Aided Geometric Design
A statistical description of the articulating ulna surface for prosthesis design
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Ellipse fitting with hyperaccuracy
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Geometric invariant curve and surface normalization
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part II
A representation of time series based on implicit polynomial curve
Pattern Recognition Letters
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Interest in algebraic curves and surfaces of high degree as geometric models or shape descriptors for different model-based computer vision tasks has increased in recent years, and although their properties make them a natural choice for object recognition and positioning applications, algebraic curve and surface fitting algorithms often suffer from instability problems. One of the main reasons for these problems is that, while the data sets are always bounded, the resulting algebraic curves or surfaces are, in most cases, unbounded. In this paper, the authors propose to constrain the polynomials to a family with bounded zero sets, and use only members of this family in the fitting process. For every even number d the authors introduce a new parameterized family of polynomials of degree d whose level sets are always bounded, in particular, its zero sets. This family has the same number of degrees of freedom as a general polynomial of the same degree. Three methods for fitting members of this polynomial family to measured data points are introduced. Experimental results of fitting curves to sets of points in R/sup 2/ and surfaces to sets of points in R/sup 3/ are presented.