Convex analysis and variational problems
Convex analysis and variational problems
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Towards Ultimate Motion Estimation: Combining Highest Accuracy with Real-Time Performance
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Fast Algorithms for Projection on an Ellipsoid
SIAM Journal on Optimization
Highly Accurate Optic Flow Computation with Theoretically Justified Warping
International Journal of Computer Vision
Full-Frame Video Stabilization with Motion Inpainting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Large deformation diffeomorphisms with application to optic flow
Computer Vision and Image Understanding
A duality based approach for realtime TV-L1 optical flow
Proceedings of the 29th DAGM conference on Pattern recognition
A convex approach for variational super-resolution
Proceedings of the 32nd DAGM conference on Pattern recognition
A Database and Evaluation Methodology for Optical Flow
International Journal of Computer Vision
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision
Approximate inference for spatial functional data on massively parallel processors
Computational Statistics & Data Analysis
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The variational TV-L1 framework has become one of the most popular and successful approaches for calculating optical flow. One reason for the popularity is the very appealing properties of the two terms in the energy formulation of the problem, the robust L1-norm of the data fidelity term combined with the total variation (TV) regularization that smoothes the flow, but preserve strong discontinuities such as edges. Specifically the approach of Zach et al. [1] has provided a very clean and efficient algorithm for calculating TV-L1 optical flows between grayscale images. In this paper we propose a generalized algorithm that works on vector valued images, by means of a generalized projection step. We give examples of calculations of flows for a number of multidimensional constancy assumptions, e.g. gradient and RGB, and show how the developed methodology expands to any kind of vector valued images. The resulting algorithms have the same degree of parallelism as the case of one-dimensional images, and we have produced an efficient GPU implementation, that can take vector valued images with vectors of any dimension. Finally we demonstrate how these algorithms generally produce better flows than the original algorithm.