Optical Image Registration Research Articles

Multigrid solution of the optical flow system using a combined diffusion‐ and curvature‐based regularizer

AbstractOptical flow techniques are used to compute an approximate motion field in an image sequence. We apply a variational approach for the optical flow using a simple data term but introducing a combined diffusion‐ and curvature‐based regularizer. The same data term arises in image registration problems where a deformation field between two images is computed. For optical flow problems, usually a diffusion‐based regularizer should dominate, whereas for image registration a curvature‐based regularizer is more appropriate. The combined regularizer enables us to handle optical flow and image registration problems with the same solver and it improves the results of each of the two regularizers used on their own. We develop a geometric multigrid method for the solution of the resulting fourth‐order systems of partial differential equations associated with the variational approach for optical flow and image registration problems. The adequacy of using (collective) pointwise smoothers within the multigrid algorithm is demonstrated with the help of local Fourier analysis. Galerkin‐based coarse grid operators are applied for an efficient treatment of jumping coefficients. We show some multigrid convergence rates, timings and investigate the visual quality of the approximated motion or deformation field for synthetic and real‐world images. Copyright © 2008 John Wiley & Sons, Ltd.

Algebraic Topology-Based Image Deformation: A Unified Model

In this paper, a new method for image deformation is presented. It is based upon decomposition of the deformation problem into basic physical laws. Unlike other methods that solve a differential or an energetic formulation of the physical laws involved, we encode the basic laws using computational algebraic topology. Conservative laws are translated into exact global values and constitutive laws are judiciously approximated. In order to illustrate the effectiveness of our model, we deal with both small- and large-scale deformation, utilizing elasticity theory and the viscous fluid model, respectively. The proposed approach is validated through a series of tests on optical flow estimation and image registration.

Human Limb Extraction Based on Motion Estimation Using Optical Flow and Image Registration

We propose a method for extracting human limb regions by the combination of optical flow-based motion segmentation and nonlinear optimization-based image registration. First, rotating limb regions with rough boundaries are extracted and motion parameters are estimated for an approximated model. Then the extracted region and estimated parameters are used as initial values for nonlinear optimization that minimizes residuals of two successive frames and estimates motion parameters. Combining the two steps reduces computational cost and avoids the initial state problem of optimization. According to estimated parameters, the limb region is extracted by a Bayesian classifier to obtain accurate region boundaries. Experimental results on real images are shown.

Image Registration, Optical Flow and Local Rigidity

We address the theoretical problems of optical flow estimation and image registration in a multi-scale framework in any dimension. Much work has been done based on the minimization of a distance between a first image and a second image after applying deformation or motion field. Usually no justification is given about convergence of the algorithm used. We start by showing, in the translation case, that convergence to the global minimum is made easier by applying a low pass filter to the images hence making the energy “convex enough”. In order to keep convergence to the global minimum in the general case, we introduce a local rigidity hypothesis on the unknown deformation. We then deduce a new natural motion constraint equation (MCE) at each scale using the Dirichlet low pass operator. This transforms the problem to solving the energy minimization in a finite dimensional subspace of approximation obtained through Fourier Decomposition. This allows us to derive sufficient conditions for convergence of a new multi-scale and iterative motion estimation/registration scheme towards a global minimum of the usual nonlinear energy instead of a local minimum as did all previous methods. Although some of the sufficient conditions cannot always be fulfilled because of the absence of the necessary a priori knowledge on the motion, we use an implicit approach. We illustrate our method by showing results on synthetic and real examples in dimension 1 (signal matching, Stereo) and 2 (Motion, Registration, Morphing), including large deformation experiments.