On Variational Curve Smoothing and Reconstruction

Authors:
Yu Wang;Desheng Wang;A. M. Bruckstein
Affiliations:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore;Department of Computer Science, Technion IIT, Haifa, Israel
Venue:
Journal of Mathematical Imaging and Vision
Year:
2010

Citing 25
Cited 3

Efficient implementation of essentially non-oscillatory shock-capturing schemes

Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations

Journal of Computational Physics
A new approach to the maximum-flow problem

Journal of the ACM (JACM)
Nonlinear total variation based noise removal algorithms

Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
A computational approach for corner and vertex detection

International Journal of Computer Vision
Geodesic Active Contours

International Journal of Computer Vision
Global Minimum for Active Contour Models: A Minimal Path Approach

International Journal of Computer Vision
Affine Morphological Multiscale Analysis of Corners andMultiple Junctions

International Journal of Computer Vision
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration

SIAM Journal on Scientific Computing
Heteroscedastic Hough transform (HtHT): an efficient method for robust line fitting in the ‘errors in the variables’ problems

Computer Vision and Image Understanding - Special issue on robusst statistical techniques in image understanding
Implicit and nonparametric shape reconstruction from unorganized data using a variational level set method

Computer Vision and Image Understanding
Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images

IEEE Transactions on Pattern Analysis and Machine Intelligence
Regularized Laplacian Zero Crossings as Optimal Edge Integrators

International Journal of Computer Vision
Matching Distance Functions: A Shape-to-Area Variational Approach for Global-to-Local Registration

ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Computing Geodesics and Minimal Surfaces via Graph Cuts

ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Numerical Geometry of Images: Theory, Algorithms, and Applications

Numerical Geometry of Images: Theory, Algorithms, and Applications
What Energy Functions Can Be Minimizedvia Graph Cuts?

IEEE Transactions on Pattern Analysis and Machine Intelligence
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multilevel Banded Graph Cuts Method for Fast Image Segmentation

ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
What Metrics Can Be Approximated by Geo-Cuts, Or Global Optimization of Length/Area and Flux

ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Robust reconstruction of watertight 3D models from non-uniformly sampled point clouds without normal information

SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Fast Sweeping Methods for Eikonal Equations on Triangular Meshes

SIAM Journal on Numerical Analysis
Adaptive variational curve smoothing based on level set method

Journal of Computational Physics
An edge-weighted centroidal Voronoi tessellation model for image segmentation

IEEE Transactions on Image Processing
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II

Journal of Computational Physics

Constructing 3D motions from curvature and torsion profiles

Computer-Aided Design
Generalized edge-weighted centroidal Voronoi tessellations for geometry processing

Computers & Mathematics with Applications
On the Curve Reconstruction in Riemannian Manifolds

Journal of Mathematical Imaging and Vision

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we discuss and experimentally compare variational methods for curve denoising, curve smoothing and curve reconstruction problems. The methods are based on defining suitable cost functionals to be minimized, the cost being the combination of a fidelity term measuring the "distance" of a curve from the data and a smoothness term measuring the curve's L 1-norm or length.