A Projection Operator for the Restoration of Divergence-Free Vector Fields

Authors:
P. Y. Simard;G. E. Mailloux
Affiliations:
Ecole Polytechnique, Montreal, Que., Canada;Ecole Polytechnique, Montreal, Que., Canada
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1988

Citing 2
Cited 10

Comutations underlying the measuremnt of visual motion.

Artificial Intelligence
Numerical Methods

Numerical Methods

Extracting 3D Vortices in Turbulent Fluid Flow

IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Multiresolution Analysis

IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of Vector Fields in Unconstrained and Inequality Constrained Variational Problems for Segmentation and Registration

Journal of Mathematical Imaging and Vision
Physically-Constrained Diffeomorphic Demons for the Estimation of 3D Myocardium Strain from Cine-MRI

FIMH '09 Proceedings of the 5th International Conference on Functional Imaging and Modeling of the Heart
A divergence-free vector field model for imaging applications

ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Derivation of qualitative information in motion analysis

Image and Vision Computing
Convex set theoretic image recovery: History, current status, and new directions

Journal of Visual Communication and Image Representation
iLogDemons: A Demons-Based Registration Algorithm for Tracking Incompressible Elastic Biological Tissues

International Journal of Computer Vision
An incompressible log-domain demons algorithm for tracking heart tissue

STACOM'11 Proceedings of the Second international conference on Statistical Atlases and Computational Models of the Heart: imaging and modelling challenges
Flow analysis in cardiac chambers combining phase contrast, 3D tagged and cine MRI

FIMH'13 Proceedings of the 7th international conference on Functional Imaging and Modeling of the Heart

Quantified Score

Hi-index	0.14

Visualization

Abstract

The theory of image restoration by projection onto convex sets can also be applied to the restoration of vector fields. These can have properties that restrict them to lie in well-defined closed convex sets. One of the properties, divergence freedom, is considered, and the theory and numerical implementation of its projection operator are presented. The performance of the operator is illustrated by restoring, from partial information, two simulated divergence-free vector fields. This projection operator finds an important application in the restoration of velocity fields or optical flows computed from an image sequence when the real velocity field is known, a priori to be divergence-free.