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
Dense Estimation of Fluid Flows
IEEE Transactions on Pattern Analysis and Machine Intelligence
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods
SIAM Journal on Numerical Analysis
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing
Journal of Scientific Computing
Image Denoising and Decomposition with Total Variation Minimization and Oscillatory Functions
Journal of Mathematical Imaging and Vision
Dual Norms and Image Decomposition Models
International Journal of Computer Vision
Image Decomposition into a Bounded Variation Component and an Oscillating Component
Journal of Mathematical Imaging and Vision
Variational dense motion estimation using the Helmholtz decomposition
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Discrete orthogonal decomposition and variational fluid flow estimation
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
On a Decomposition Model for Optical Flow
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
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We present a mathematical and computational feasibility study of the variational convex decomposition of 2D vector fields into coherent structures and additively superposed flow textures. Such decompositions are of interest for the analysis of image sequences in experimental fluid dynamics and for highly non-rigid image flows in computer vision. Our work extends current research on image decomposition into structural and textural parts in a twofold way. Firstly, based on Gauss’ integral theorem, we decompose flows into three components related to the flow’s divergence, curl, and the boundary flow. To this end, we use proper operator discretizations that yield exact analogs of the basic continuous relations of vector analysis. Secondly, we decompose simultaneously both the divergence and the curl component into respective structural and textural parts. We show that the variational problem to achieve this decomposition together with necessary compatibility constraints can be reliably solved using a single convex second-order conic program.