Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fitting affine invariant conics to curves
Geometric invariance in computer vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Describing Complicated Objects by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Machine vision
Representation of 3D Surfaces by Two-Variable Fourier Descriptors
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fitting Curves and Surfaces With Constrained Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implicit Polynomials, Orthogonal Distance Regression, and the Closest Point on a Curve
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
Proceedings of the sixth ACM symposium on Solid modeling and applications
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Topologically Faithful Fitting of Simple Closed Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
CGIV '04 Proceedings of the International Conference on Computer Graphics, Imaging and Visualization
Fitting Globally Stabilized Algebraic Surfaces to Range Data
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Affine-invariant B-spline moments for curve matching
IEEE Transactions on Image Processing
Improving the stability of algebraic curves for applications
IEEE Transactions on Image Processing
Modeling and Estimation of the Dynamics of Planar Algebraic Curves via Riccati Equations
Journal of Mathematical Imaging and Vision
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Linear fitting techniques by implicit algebraic models usually suffer from global stability problems. Ridge regression regularization can be used to improve the stability of algebraic surface fits. In this paper a Euclidean Invariant 3D ridge regression matrix is developed and applied to a particular linear algebraic surface fitting method. Utilization of such a regularization in fitting process makes it possible to globally stabilize 3D object fits with surfaces of any degree. Robustness to noise and moderate levels of occlusion has also been enhanced significantly. Experimental results are presented to verify the improvements in global stability and robustness of the resulting fits.