Monica Hernandez Gimenez
Primal-Dual optimization strategies in Huber-L1 optical flow with temporal subspace constraints for non-rigid sequence registration


This web page accompanies the work titled

Primal-Dual optimization strategies in Huber-L1 optical flow with temporal subspace constraints for non-rigid sequence registration

submitted to the Journal of Image and Vision Computing in March 2016.

The author is Monica Hernandez, associate professor at the University of Zaragoza, Spain.




The starting point of this work is the framework proposed by Garg et al. in IJCV 2013 [1]. The authors provided an extended version of improved TV-L1 optical flow algorithm [2] in order to include temporal consistency in the estimation of the flows for non-rigid sequence registration. Detailed information of the proposed framework can be found in the web page:

http://www.eecs.qmul.ac.uk/~lourdes/subspace_flow/

Our work explores different possible combinations of applying Fenchel-Duality to general convex optimization problems and applies them to non-rigid sequence registration with temporal subspace constraints. We have found seven different primal-dual optimization strategies in our application of interest, grouped into five different methods:

- Method 1. Extension of Chambolle and Pock optical flow method [3] to our application of interest
- Method 2. Garg et al. method, hard constraint version [1]
- Method 2 PC. Preconditioned method 2
- Method 3. Garg et al. method, soft constraint gray version [1]
- Method 4. Garg et al. method, soft constraint vector valued version [1]
- Method 4 PC. Preconditioned method 4
- Method 5. Fenchel-Duality extended to the two variational subproblems in method 3

[1] R. Garg, A. Roussos, and L. Agapito, A variational approach to video registration with subspace constraints,Int. J. Comput. Vision, vol. 104(3), pp. 286 - 314, 2013
[2] A. Wedel, T. Pock, C. Zach, H. Bischof, and D. Cremers, An improved algorithm for TV-L1 optical flow, Statistical and Geometrical Approaches to Visual Motion Analysis, Lecture Notes in Computer Science, vol. 5640, pp. 23 - 45, 2009. 
[3]  A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vis., vol. 40(1), pp. 120 - 145, 2011

This web page shows the videos of the results obtained by the five methods in the considered  sequences. For offline comparison, pdf files with the video images can be downloaded in the accompanying links.

- Results on Garg et al. IJCV 2013 sequence


- Results on Hernandez el al. JIVC 2016 sequences

- Results on Garg et al. CVPR 2013 sequence

- Results on Salzmann et al ICCV 2007 sequence