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
Higher-order interpolation and least-squares approximation using implicit algebraic surfaces
ACM Transactions on Graphics (TOG)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear Programming Fitting of Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fitting Curves and Surfaces With Constrained Implicit Polynomials
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
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hand Recognition Using Implicit Polynomials and Geometric Features
AVBPA '01 Proceedings of the Third International Conference on Audio- and Video-Based Biometric Person Authentication
New, faster, more controlled fitting of implicit polynomial 2D curves and 3D surfaces to data
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Robust Fitting of Implicit Polynomials with Quantized Coefficients to 2D Data
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Boundary Estimation from Intensity/Color Images with Algebraic Curve Models
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 1
Improving the stability of algebraic curves for applications
IEEE Transactions on Image Processing
Training a reciprocal-sigmoid classifier by feature scaling-space
Machine Learning
Hierarchical error-driven approximation of implicit surfaces from polygonal meshes
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
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
Technical Section: Quadratic curve and surface fitting via squared distance minimization
Computers and Graphics
A representation of time series based on implicit polynomial curve
Pattern Recognition Letters
A memetic algorithm for efficient solution of 2D and 3D shape matching problems
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
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This work deals with fitting 2D and 3D implicit polynomials (IPs) to 2D curves and 3D surfaces, respectively. The zero-set of the polynomial is determined by the IP coefficients and describes the data. The polynomial fitting algorithms proposed in this paper aim at reducing the sensitivity of the polynomial to coefficient errors. Errors in coefficient values may be the result of numerical calculations, when solving the fitting problem or due to coefficient quantization. It is demonstrated that the effect of reducing this sensitivity also improves the fitting tightness and stability of the proposed two algorithms in fitting noisy data, as compared to existing algorithms like the well-known 3L and gradient-one algorithms. The development of the proposed algorithms is based on an analysis of the sensitivity of the zero-set to small coefficient changes and on minimizing a bound on the maximal error for one algorithm and minimizing the error variance for the second. Simulation results show that the proposed algorithms provide a significant reduction in fitting errors, particularly when fitting noisy data of complex shapes with high order polynomials, as compared to the performance obtained by the abovementioned existing algorithms.