Describing Complicated Objects by Implicit Polynomials

Authors:
Daniel Keren;David Cooper;Jayashree Subrahmonia
Affiliations:
-;-;-
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1994

Citing 8
Cited 46

Direct least-squares fitting of algebraic surfaces

SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
On Recognizing and Positioning Curved 3-D Objects from Image Contours

IEEE Transactions on Pattern Analysis and Machine Intelligence
On Three-Dimensional Surface Reconstruction Methods

IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation

IEEE Transactions on Pattern Analysis and Machine Intelligence
Invariant Descriptors for 3D Object Recognition and Pose

IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
From Uncertainty to Visual Exploration

IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
Recognition and positioning of rigid objects using algebraic and moment invariants

Recognition and positioning of rigid objects using algebraic and moment invariants
Projectively Invariant Representations Using Implicit Algebraic Curves

ECCV '90 Proceedings of the First European Conference on Computer Vision

Localization vs. identification of semi-algebraic sets

COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Local Invariants For Recognition

IEEE Transactions on Pattern Analysis and Machine Intelligence
Determining Pose of 3D Objects With Curved Surfaces

IEEE Transactions on Pattern Analysis and Machine Intelligence
Practical Reliable Bayesian Recognition of 2D and 3D Objects Using Implicit Polynomials and Algebraic Invariants

IEEE Transactions on Pattern Analysis and Machine Intelligence
COSMOS-A Representation Scheme for 3D Free-Form Objects

IEEE Transactions on Pattern Analysis and Machine Intelligence
VideoQ: an automated content based video search system using visual cues

MULTIMEDIA '97 Proceedings of the fifth ACM international conference on Multimedia
Parametric Model Fitting: From Inlier Characterization to Outlier Detection

IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear Programming Fitting of Implicit Polynomials

IEEE Transactions on Pattern Analysis and Machine Intelligence
3-D Heart Modeling and Motion EstimationBased on Continuous Distance Transform Neural Networks andAffine Transform

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
Localization vs. Identification of Semi-Algebraic Sets

Machine Learning
On Interactive Object Shape Modeling Using Algebraic Curves

Journal of VLSI Signal Processing Systems - special issue on multimedia signal processing
VC-Dimension Analysis of Object Recognition Tasks

Journal of Mathematical Imaging and Vision
Embedding Gestalt Laws in Markov Random Fields

IEEE Transactions on Pattern Analysis and Machine Intelligence
The 3L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data

IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognizing 3D Objects Using Tactile Sensing and Curve Invariants

Journal of Mathematical Imaging and Vision
A Bayesian Method for Fitting Parametric and Nonparametric Models to Noisy Data

IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of Error in Curvature Computation on Multi-Scale Free-Form Surfaces

International Journal of Computer Vision
3D object recognition: Representation and matching

Statistics and Computing
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting

IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Symbolic Computation to Find Algebraic Invariants

IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonparametric Segmentation of Curves into Various Representations

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Maximum-Likelihood Surface Estimator for Dense Range Data

IEEE Transactions on Pattern Analysis and Machine Intelligence
A note on conic fitting by the gradient weighted least-squares estimation: refined eigenvector solution

Pattern Recognition Letters
Hand Recognition Using Implicit Polynomials and Geometric Features

AVBPA '01 Proceedings of the Third International Conference on Audio- and Video-Based Biometric Person Authentication
Harmonic Shape Images: A Representation for 3D Free-Form Surfaces Based on Energy Minimization

EMMCVPR '99 Proceedings of the Second International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
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
A Similarity-Based Aspect-Graph Approach to 3D Object Recognition

International Journal of Computer Vision
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
Constructive implicit fitting

Computer Aided Geometric Design
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
Constructive implicit fitting

Computer Aided Geometric Design
3-D shape approximation using parametric geons

Image and Vision Computing
Hand tracking in a natural conversational environment by the interacting multiple model and probabilistic data association (IMM-PDA) algorithm

Pattern Recognition
Adaptively determining degrees of implicit polynomial curves and surfaces

ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
Experimental analysis of harmonic shape images

3DIM'99 Proceedings of the 2nd international conference on 3-D digital imaging and modeling
Automatic registration for 3D shapes using hybrid dimensionality-reduction shape descriptions

Pattern Recognition
Ellipse fitting with hyperaccuracy

ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Rigid 3D geometry matching for grasping of known objects in cluttered scenes

International Journal of Robotics Research
ElliFit: An unconstrained, non-iterative, least squares based geometric Ellipse Fitting method

Pattern Recognition

Quantified Score

Hi-index	0.16

Visualization

Abstract

This paper introduces and focuses on two problems. First is the representation power of closed implicit polynomials of modest degree for curves in 2-D images and surfaces in 3-D range data. Super quadrics are a small subset of object boundaries that are well fitted by these polynomials. The second problem is the stable computationally efficient fitting of noisy data by closed implicit polynomial curves and surfaces. The attractive features of these polynomials for Vision is discussed.