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
IEEE Transactions on Pattern Analysis and Machine Intelligence
Smoothing polyhedra using implicit algebraic splines
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Implicit Curves and Surfaces in CAGD
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Describing Complicated Objects by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
3L Fitting of Higher Degree Implicit Polynomials
WACV '96 Proceedings of the 3rd IEEE Workshop on Applications of Computer Vision (WACV '96)
Computationally fast Bayesian recognition of complex objects based on mutual algebraic invariants
ICIP '95 Proceedings of the 1995 International Conference on Image Processing (Vol.2)-Volume 2 - Volume 2
PIMs and Invariant Parts for Shape Recognition
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Assembling virtual pots from 3D measurements of their fragments
Proceedings of the 2001 conference on Virtual reality, archeology, and cultural heritage
Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Guest Editorial: Computational Vision at Brown
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
The Medial Scaffold of 3D Unorganized Point Clouds
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hierarchical error-driven approximation of implicit surfaces from polygonal meshes
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
International Journal of Intelligent Systems Technologies and Applications
Stable Algebraic Surfaces for 3D Object Representation
Journal of Mathematical Imaging and Vision
Implicit Surface Reconstruction with an Analogy of Polar Field Model
PSIVT '09 Proceedings of the 3rd Pacific Rim Symposium on Advances in Image and Video Technology
3D Model Segmentation and Representation with Implicit Polynomials
IEICE - Transactions on Information and Systems
A system for reconstruction of solid models from large point clouds
Machine Graphics & Vision International Journal
Adaptively determining degrees of implicit polynomial curves and surfaces
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
Modeling and Estimation of the Dynamics of Planar Algebraic Curves via Riccati Equations
Journal of Mathematical Imaging and Vision
Multilevel algebraic invariants extraction by incremental fitting scheme
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part I
A representation of time series based on implicit polynomial curve
Pattern Recognition Letters
A coarse-to-fine IP-driven registration for pose estimation from single ultrasound image
Computer Vision and Image Understanding
Hi-index | 0.14 |
In this paper, we introduce a completely new approach to fitting implicit polynomial geometric shape models to data and to studying these polynomials. The power of these models is in their ability to represent nonstar complex shapes in two- (2D) and three-dimensional (3D) data to permit fast, repeatable fitting to unorganized data which may not be uniformly sampled and which may contain gaps, to permit position-invariant shape recognition based on new complete sets of Euclidean and affine invariants and to permit fast, stable single-computation pose estimation. The algorithm represents a significant advancement of implicit polynomial technology for four important reasons. First, it is orders of magnitude faster than existing fitting methods for implicit polynomial 2D curves and 3D surfaces, and the algorithms for 2D and 3D are essentially the same. Second, it has significantly better repeatability, numerical stability, and robustness than current methods in dealing with noisy, deformed, or missing data. Third, it can easily fit polynomials of high, such as 14th or 16th, degree. Fourth, additional linear constraints can be easily incorporated into the fitting process, and general linear vector space concepts apply.