A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
A linear algorithm for motion estimation using straight line correspondences
Computer Vision, Graphics, and Image Processing
On the motion of 3-D curves and its relationship to optical flow
ECCV 90 Proceedings of the first european conference on Computer vision
Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
A theory of the motion fields of curves
International Journal of Computer Vision
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
In Defense of the Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Elementary geometry of algebraic curves: an undergraduate introduction
Elementary geometry of algebraic curves: an undergraduate introduction
Cross-Weighted Moments and Affine Invariants for Image Registration and Matching
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
Regular Article: On the Construction of Complete Sets of Geometric Invariants for Algebraic Curves
Advances in Applied Mathematics
Application of Elliptic Fourier Descriptors to Symmetry Detection Under Parallel Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Feature Based Methods for Structure and Motion Estimation
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
The 3D Line Motion Matrix and Alignment of Line Reconstructions
International Journal of Computer Vision
Efficient Graph-Based Image Segmentation
International Journal of Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Line-Based Structure from Motion for Urban Environments
3DPVT '06 Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06)
Unsupervised Statistical Segmentation of Nonstationary Images Using Triplet Markov Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multilevel thresholding for image segmentation through a fast statistical recursive algorithm
Pattern Recognition Letters
Journal of Mathematical Imaging and Vision
MAC: Magnetostatic Active Contour Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stable Algebraic Surfaces for 3D Object Representation
Journal of Mathematical Imaging and Vision
Visual motion and structure estimation using sliding mode observers
International Journal of Systems Science
Recursive computation of moments of 2D objects represented by elliptic Fourier descriptors
Pattern Recognition Letters
2D shape tracking using algebraic curve spaces
ISCIS'05 Proceedings of the 20th international conference on Computer and Information Sciences
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Moment computation for objects with spline curve boundary
IEEE Transactions on Pattern Analysis and Machine Intelligence
Snakes, shapes, and gradient vector flow
IEEE Transactions on Image Processing
Improving the stability of algebraic curves for applications
IEEE Transactions on Image Processing
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Motivated by problems in vision and robotics, in this paper we are interested in describing the dynamics of planar algebraic curves in rigid and affine motion. A new method is presented for modeling the dynamics of such curves in terms of Riccati equations. It is shown that rigid or affine motion of an algebraic curve can be described using the dynamics of line factors obtained from a unique decomposition of the curve, and each individual line dynamics can be described by a Riccati equation. An estimation algorithm is proposed to estimate rigid or affine motion using line parameters. Importance of data normalization is also investigated in the context of motion estimation. Experiments with simulated data and real images demonstrate that the proposed method can provide satisfactory motion estimation results from perturbed data.