Line search multilevel optimization as computational methods for dense optical flow

We evaluate the performance of different optimization techniques developed in the context of optical flowcomputation with different variational models. In particular, based on truncated Newton methods (TN) 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 evaluate the performance of a standard unidirectional multilevel algorithm - called multiresolution optimization (MR/OPT), to a bidrectional 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 different image sequences using four models of optical flow computation 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

Multilevel optimization for dense motion estimation

This research has been oriented towards the design of a new technique for fast and reliable dense motion estimation. We used variational models of optical flow computation to estimate the dense motion in a sequence of images.We have been interested in developing a multilevel optimization solver to produce accurate optical flow estimation for real-time applications.To the best of our knowledge, two-ways multilevel optimization techniques are used for the first time in the context of a computer vision problem. We evaluated the performance of different optimization techniques developed in the context of optical flow computation with different variational models.In particular, based on truncated Newton methods (TN) that have been an effective approach for large-scale unconstrained optimization, we developed the use of efficient multilevel schemes for computing the optical flow.More precisely, we evaluated the performance of a standard unidirectional multilevel algorithm - called multiresolution optimization (MR/Opt), to a bidrectional 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 significantly both the TN and MR/Opt algorithms in terms of the computational work and the quality of the optical flow estimation

Retrospective study on phantom for the application of medical image registration in the operating room scenario

This paper presents a phantom study to asses the feasibility of the medical image registration algorithms in the operating room (OR) scenario. The main issues of the registration algorithms in an OR application are, on one hand, the lack of the initial guess of the registration transformation - the images to be registered may be completely independentand, on the other hand, the multimodality of the data. Other requirements to be addressed by the OR registration algorithms are: real-time execution and the necessity of the validation of the results. This work analyzes how, under these requirements, the current state of the art algorithms in medical image registration may be used and shows which direction should be taken when designing a OR navigation system that includes registration as a component

An inexact Newton-Krylov algorithm for constrained diffeomorphic image registration

We propose numerical algorithms for solving large deformation diffeomorphic image registration problems. We formulate the nonrigid image registration problem as a problem of optimal control. This leads to an infinite-dimensional partial differential equation (PDE) constrained optimization problem. The PDE constraint consists, in its simplest form, of a hyperbolic transport equation for the evolution of the image intensity. The control variable is the velocity field. Tikhonov regularization on the control ensures well-posedness. We consider standard smoothness regularization based on $H^1$- or $H^2$-seminorms. We augment this regularization scheme with a constraint on the divergence of the velocity field rendering the deformation incompressible and thus ensuring that the determinant of the deformation gradient is equal to one, up to the numerical error. We use a Fourier pseudospectral discretization in space and a Chebyshev pseudospectral discretization in time. We use a preconditioned, globalized, matrix-free, inexact Newton-Krylov method for numerical optimization. A parameter continuation is designed to estimate an optimal regularization parameter. Regularity is ensured by controlling the geometric properties of the deformation field. Overall, we arrive at a black-box solver. We study spectral properties of the Hessian, grid convergence, numerical accuracy, computational efficiency, and deformation regularity of our scheme. We compare the designed Newton-Krylov methods with a globalized preconditioned gradient descent. We study the influence of a varying number of unknowns in time. The reported results demonstrate excellent numerical accuracy, guaranteed local deformation regularity, and computational efficiency with an optional control on local mass conservation. The Newton-Krylov methods clearly outperform the Picard method if high accuracy of the inversion is required.Comment: 32 pages; 10 figures; 9 table