Investigations of multigrid algorithms for the estimation of optical flow fieldsin image sequences
Computer Vision, Graphics, and Image Processing
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
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 mathematical study of the relaxed optical flow problem in the space BV(&OHgr;)
SIAM Journal on Mathematical Analysis
Ordinary Differential Equations
Ordinary Differential Equations
Optimal Control Formulation for Determining Optical Flow
SIAM Journal on Scientific Computing
High-resolution FEM-TVD schemes based on a fully multidimensional flux limiter
Journal of Computational Physics
Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods
International Journal of Computer Vision
Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (Mps-Siam Series on Optimization 6)
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
An Improved Algorithm for TV-L1 Optical Flow
Statistical and Geometrical Approaches to Visual Motion Analysis
Constraints for the estimation of displacement vector fields from image sequences
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
An Optimal Control Formulation of an Image Registration Problem
Journal of Mathematical Imaging and Vision
Learning PDEs for image restoration via optimal control
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part I
Optical flow guided TV-L1 video interpolation and restoration
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
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The problem of finding an interpolating image between two given images in an image sequence is considered. The problem is formulated as an optimal control problem governed by a transport equation, i.e. we aim at finding a flow field which transports the first image as close as possible to the second image. This approach bears similarities with the Horn and Schunck method for optical flow calculation but in fact the model is quite different. The images are modeled in the space of functions of bounded variation and an analysis of solutions of transport equations in this space is included. Moreover, the existence of optimal controls is proven and necessary conditions are derived. Finally, two algorithms are given and numerical results are compared with existing methods. The new method is competitive with state-of-the-art methods and even outperforms several existing methods.