IEEE Transactions on Pattern Analysis and Machine Intelligence
Design and recovery of 2-D and 3-D shapes using rational Gaussian curves and surfaces
International Journal of Computer Vision
Describing Complicated Objects by 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
A survey of free-form object representation and recognition techniques
Computer Vision and Image Understanding
A survey of methods for recovering quadrics in triangle meshes
ACM Computing Surveys (CSUR)
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Stable Fitting of 2D Curves and 3D Surfaces by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Formulation of Boundary Mesh Segmentation
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Curvature Dependent Polygonization of Implicit Surfaces
SIBGRAPI '04 Proceedings of the Computer Graphics and Image Processing, XVII Brazilian Symposium
Fast Simultaneous Alignment of Multiple Range Images Using Index Images
3DIM '05 Proceedings of the Fifth International Conference on 3-D Digital Imaging and Modeling
Curvature-Based Transfer Functions for Direct Volume Rendering: Methods and Applications
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Fitting Globally Stabilized Algebraic Surfaces to Range Data
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Feature-based similarity search in 3D object databases
ACM Computing Surveys (CSUR)
3D Distance Fields: A Survey of Techniques and Applications
IEEE Transactions on Visualization and Computer Graphics
A model based approach for pose estimation and rotation invariant object matching
Pattern Recognition Letters
A review of recent range image registration methods with accuracy evaluation
Image and Vision Computing
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Improving the stability of algebraic curves for applications
IEEE Transactions on Image Processing
Augmented reality system for visualizing 3-D region of interest in unknown environment
ACCV'10 Proceedings of the 2010 international conference on Computer vision - Volume part II
Multilevel algebraic invariants extraction by incremental fitting scheme
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part I
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When large-scale and complex 3D objects are obtained by range finders, it is often necessary to represent them by algebraic surfaces for such purposes as data compression, multi-resolution, noise elimination, and 3D recognition. Representing the 3D data with algebraic surfaces of an implicit polynomial (IP) has proved to offer the advantages that IP representation is capable of encoding geometric properties easily with desired smoothness, few parameters, algebraic/geometric invariants, and robustness to noise and missing data. Unfortunately, generating a high-degree IP surface for a whole complex 3D shape is impossible because of high computational cost and numerical instability. In this paper we propose a 3D segmentation method based on a cut-and-merge approach. Two cutting procedures adopt low-degree IPs to divide and fit the surface segments simultaneously, while avoiding generating high-curved segments. A merging procedure merges the similar adjacent segments to avoid over-segmentation. To prove the effectiveness of this segmentation method, we open up some new vistas for 3D applications such as 3D matching, recognition, and registration.