Convex Hodge Decomposition of Image Flows

Authors:
Jing Yuan;Gabriele Steidl;Christoph Schnörr
Affiliations:
Image and Pattern Analysis Group, Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany;Faculty of Mathematics and Computer Science, University of Mannheim, Germany;Image and Pattern Analysis Group, Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany
Venue:
Proceedings of the 30th DAGM symposium on Pattern Recognition
Year:
2008

Citing 9
Cited 0

Weakly differentiable functions

Weakly differentiable functions
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
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures

Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
An Algorithm for Total Variation Minimization and Applications

Journal of Mathematical Imaging and Vision
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection

International Journal of Computer Vision
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods

Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Fast Global Minimization of the Active Contour/Snake Model

Journal of Mathematical Imaging and Vision
Simultaneous Higher-Order Optical Flow Estimation and Decomposition

SIAM Journal on Scientific Computing
Active contours without edges

IEEE Transactions on Image Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

The total variation (TV) measure is a key concept in the field of variational image analysis. Introduced by Rudin, Osher and Fatemi in connection with image denoising, it also provides the basis for convex structure-texture decompositions of image signals, image inpainting, and for globally optimal binary image segmentation by convex functional minimization. Concerning vector-valued image data, the usual definition of the TV measure extends the scalar case in terms of the L1-norm of the gradients.In this paper, we show for the case of 2D image flows that TV regularization of the basic flow components (divergence, curl) leads to a mathematically more natural extension. This regularization provides a convex decomposition of motion into a richer structure component and texture. The structure component comprises piecewise harmonicfields rather than piecewise constantones. Numerical examples illustrate this fact. Additionally, for the class of piecewise harmonic flows, our regularizer provides a measure for motion boundaries of image flows, as does the TV-measure for contours of scalar-valued piecewise constant images.