Line Search Multilevel Optimization as Computational Methods for Dense Optical Flow

Abstract

Abstract. We evaluate the performance of different optimization techniques developed in the context of optical flow computation with different variational models. In particular, based on truncated Newton (TN) methods that have been an effective approach for large-scale unconstrained optimization, we develop the use of efficient multilevel schemes for computing the optical flow. More precisely, we compare the performance of a standard unidirectional multilevel algorithm-called multiresolution optimization (MR/Opt)-with that of a bidirectional multilevel algorithm-called full multigrid optimization (FMG/Opt). The FMG/Opt algorithm treats the coarse grid correction as an optimization search direction and eventually scales it using a line search. Experimental results on three image sequences using four models of optical flow with different computational efforts show that the FMG/Opt algorithm outperforms both the TN and MR/Opt algorithms in terms of the computational work and the quality of the optical flow estimation.

Optical flow modeling and computation: A survey

“…Due to the large scale of the problem, Newton methods requiring the inversion of the Hessian of the energy are not applicable, and only quasi-Newton methods are computationally tractable. A few works have explored this direction, with Truncated Newton [134,135] or L-BFGS [75].…”

Trust Region versus Line Search for Computing the Optical Flow

“…Our purpose is to compare their numerical performance with the corresponding line search versions previously studied in [9]: LSTN (unilevel) and MR/LSTN (multiresolution), respectively. For that issue we use three sequences of synthetic images that consist of scenes of various complexity; namely, the translating tree, the diverging tree and the Yosemite sequences.…”

“…In the context of our paper, the process to find the step s k is called inner iterations while the process to update w k using the computed s k is called outer iterations. For the line search truncated Newton method (LSTN), the inner (Algorithm 1) and outer (Algorithm 2) iterations are recalled from [9].…”

“…The image gradient I x 2 and I y 2 is computed as explained in [9]. Note that the function and gradient evaluation requires the evaluation of the image and gradient at noninteger points.…”

“…As in various computer vision works, the line search strategy has been the focus of our previous paper [9] in the context of optical flow. However, recent interest is shown to the use of the trust region techniques in vision applications due to their strong convergence properties.…”