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