Presentation on theme: "Fast and Accurate Optical Flow Estimation"— Presentation transcript:
1 Fast and Accurate Optical Flow Estimation Primal-Dual Schemes andSecond Order PriorsThomas Pock and Daniel CremersCVPR Group, University of BonnCollaborators: Christopher Zach, Markus Unger, Werner Trobin, and Horst Bischof
2 Variational Optical Flow – Short History 19811993200020042006Horn and SchunckBlack and Anadan, CohenAubertBrox et al.Bruhn et al.
4 Outline Model of Horn and Schunck TV-L1 Model Fast Numerical Scheme Parallel Implementation2nd order Prior
5 The Model of Horn and Schunck  Regularization TermData Term (OFC)+ Convex+ Easy to solve- Does not allow for sharp edges in the solution- Sensitive to outliers violating the OFC Horn and Schunck. Determinig Optical Flow. Artificial Intelligence, 1981
6 Can we do better? Replace quadratic functions by L1 – norms Done by Cohen, Aubert, Brox, Bruhn, ...+Allows for discontinuities in the flow field+Robust to some extent to outliers in the OFC+Still convex- Much harder to solve
7 How can we minimize this functional ? Compute Euler-Lagrange EquationsNon-linear, non-smooth, ...
8 Standard ApproachReplace L1 – norm by regularized variants (Charbonnier function)Example:Small epsilon: Nearly degeneratedLarge espilon: Smears edges
9 Our Approach(1) Introduce auxiliary variables and constraints Quadratic penalty
10 Our Approach(2) What do we gain? We solve a sequence of simpler problems1D ProblemROF Model Algorithm:For fixed (u´,v´), solve for(u,v) using Chambolle‘s algorithmFor fixed (u,v), solve for (u´,v´) using a 1D shrinkage formulaGoto 1. until convergence Rudin, Osher and Fatemi. Nonlinear Total Variation Based Noise Removal Algorithms, 1992 Zach, Pock and Bischof. A Duality Based Algorithm for Realtime TV-L1 Optical Flow, DAGM 2007 Chambolle. An Algorithm for Total Variation Minimization, 2004.
11 Implementation Numerical scheme can be easily parallelized We use state-of-the-art GPUs
12 Performance Evaluation TV-L1 Optical Flow Implemented in CUDA 2.0Computed on Nvidia GeForce GTX 28025 Overall Iterations (5 Chambolle Iterations)Image SizeFrames per Second128x128192256x256108512x51236
13 Results for TV-L1Input Image:Ground Truth:Our Results:
14 2nd order PriorTV regularization favors piecewise constant flow fields (frontoparallel motion)Extension to piecewise affine flow fields?Approach of Cremers et al. Fixed number of regionsApproach of Nir et al. Over-parametrized optical flowOur approach 2nd order derivatives to regularize flow field Cremers and Soatto, Motion Competition: A Variational Framework for Piecwise Parametric Motion Segmentation. Nir, Bruckstein and Kimmel, Over-Parameterized Variational Optical Flow, IJCV 2007 Trobin, Pock, Cremers and Bischof, An Unbiased Second-Order prPior for High-AccuracyMotion Estimation, DAGM 2008
15 2nd-L1 Optical Flow 2nd order derivatives are not orthogonal We use a transformation due to Danielsson OptimizationSimilar strategy to TV-L14th order PDE Danielsson and Lin, Efficient Detection of Second-Degree Variations in 2D and 3D Images, 2001.