Highly Accurate Optic Flow Computation with Theoretically Justified Warping

Abstract

In this paper, we suggest a variational model for optic flow computation based on non-linearised and higher order constancy assumptions. Besides the common grey value constancy assumption, also gradient constancy, as well as the constancy of the Hessian and the Laplacian are proposed. Since the model strictly refrains from a linearisation of these assumptions, it is also capable to deal with large displacements. For the minimisation of the rather complex energy functional, we present an efficient numerical scheme employing two nested fixed point iterations. Following a coarse-to-fine strategy it turns out that there is a theoretical foundation of so-called warping techniques hitherto justified only on an experimental basis. Since our algorithm consists of the integration of various concepts, ranging from different constancy assumptions to numerical implementation issues, a detailed account of the effect of each of these concepts is included in the experimental section. The superior performance of the proposed method shows up by significantly smaller estimation errors when compared to previous techniques. Further experiments also confirm excellent robustness under noise and insensitivity to parameter variations.

Evaluation of a Nonrigid Motion Compensation Technique Based on Spatiotemporal Features for Small Lesion Detection in Breast MRI

“…Based on the work of Horn and Schunck, a vast variety of research in optical flow estimation has been conducted, most of it on more robust, edge preserving regularity terms, for example [14]. In our work however, we favor the original quadratic formulation, since we explicitly need the filling-in effect of a non-robust regularizer to fill in the information in masked regions.…”

“…In our work however, we favor the original quadratic formulation, since we explicitly need the filling-in effect of a non-robust regularizer to fill in the information in masked regions. To overcome the problem of having a non-convex energy in (5), we use the coarse-to-fine warping scheme detailed in [14], which linearizes the data term as in [12] and computes incremental solutions on different image scales.…”

An Improved Algorithm for TV-L 1 Optical Flow

“…Aubert et al [3] analyze energy functionals for optical flow incorporating an L 1 data fidelity term and a general class of discontinuity preserving regularization forces. Papenberg et al [22] employ a differentiable approximation of the TV (resp. L 1 ) norm and formulate a nested iteration scheme to compute the displacement field.…”

Application of optical flow method for imaging diagnostic in JET

“…The penalizer function Ψ is chosen usually as ( ) [14]. The quantity ε is not an additional parameter, but rather ensures the differentiability of Ψ in s = 0.…”