Higher-Order Nonlinear Priors for Surface Reconstruction

Authors:
T. Tasdizen;R. Whitaker
Affiliations:
-;-
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
2004

Citing 26
Cited 1

On Optimally Combining Pieces of Information, with Application to Estimating 3-D Complex-Object Position from Range Data

IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion

IEEE Transactions on Pattern Analysis and Machine Intelligence
Biased anisotropic diffusion: a unified regularization and diffusion approach to edge detection

Image and Vision Computing - Special issue on the first ECCV 1990
A common framework for image segmentation

International Journal of Computer Vision
Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation

IEEE Transactions on Pattern Analysis and Machine Intelligence
Surface reconstruction from unorganized points

SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Free-form shape design using triangulated surfaces

SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Zippered polygon meshes from range images

SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A signal processing approach to fair surface design

SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A volumetric method for building complex models from range images

SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
A Level-Set Approach to 3D Reconstruction from Range Data

International Journal of Computer Vision
Diffusion of General Data on Non-Flat Manifolds viaHarmonic Maps Theory: The Direction Diffusion Case

International Journal of Computer Vision
Geometric partial differential equations and image analysis

Geometric partial differential equations and image analysis
Anisotropic geometric diffusion in surface processing

Proceedings of the conference on Visualization '00
Variational problems and partial differential equations on implicit surfaces

Journal of Computational Physics
Indoor scene reconstruction from sets of noisy range images

Graphical Models
Geometric surface smoothing via anisotropic diffusion of normals

Proceedings of the conference on Visualization '02
Image Relaxation: Restoration and Feature Extraction

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Maximum-Likelihood Surface Estimator for Dense Range Data

IEEE Transactions on Pattern Analysis and Machine Intelligence
Reliable Surface Reconstructiuon from Multiple Range Images

ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
Generating Fair Meshes with G1 Boundary Conditions

GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Polyhedral Surface Smoothing with Simultaneous Mesh Regularization

GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Adaptive shape evolution using blending

ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Interactive Deformation and Visualization of Level Set Surfaces Using Graphics Hardware

Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Robust anisotropic diffusion

IEEE Transactions on Image Processing
Filling-in by joint interpolation of vector fields and gray levels

IEEE Transactions on Image Processing

Removal of surface artifacts of material volume data with defects

ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part II

Quantified Score

Hi-index	0.14

Visualization

Abstract

For surface reconstruction problems with noisy and incomplete range data, a Bayesian estimation approach can improve the overall quality of the surfaces. The Bayesian approach to surface estimation relies on a likelihood term, which ties the surface estimate to the input data, and the prior, which ensures surface smoothness or continuity. This paper introduces a new high-order, nonlinear prior for surface reconstruction. The proposed prior can smooth complex, noisy surfaces, while preserving sharp, geometric features, and it is a natural generalization of edge-preserving methods in image processing, such as anisotropic diffusion. An exact solution would require solving a fourth-order partial differential equation (PDE), which can be difficult with conventional numerical techniques. Our approach is to solve a cascade system of two second-order PDEs, which resembles the original fourth-order system. This strategy is based on the observation that the generalization of image processing to surfaces entails filtering the surface normals. We solve one PDE for processing the normals and one for refitting the surface to the normals. Furthermore, we implement the associated surface deformations using level sets. Hence, the algorithm can accommodate very complex shapes with arbitrary and changing topologies. This paper gives the mathematical formulation and describes the numerical algorithms. We also show results using range and medical data.