Computation of Smooth Optical Flow in a Feedback Connected Analog Network

In 1986, Tanner and Mead \cite{Tanner_Mead86} implemented an interesting constraint satisfaction circuit for global motion sensing in aVLSI. We report here a new and improved aVLSI implementation that provides smooth optical flow as well as global motion in a two dimensional visual field. The computation of optical flow is an ill-posed problem, which expresses itself as the aperture problem. However, the optical flow can be estimated by the use of regularization methods, in which additional constraints are introduced in terms of a global energy functional that must be minimized. We show how the algorithmic constraints of Horn and Schunck \cite{Horn_Schunck81} on computing smooth optical flow can be mapped onto the physical constraints of an equivalent electronic network

Full Flow: Optical Flow Estimation By Global Optimization over Regular Grids

We present a global optimization approach to optical flow estimation. The approach optimizes a classical optical flow objective over the full space of mappings between discrete grids. No descriptor matching is used. The highly regular structure of the space of mappings enables optimizations that reduce the computational complexity of the algorithm's inner loop from quadratic to linear and support efficient matching of tens of thousands of nodes to tens of thousands of displacements. We show that one-shot global optimization of a classical Horn-Schunck-type objective over regular grids at a single resolution is sufficient to initialize continuous interpolation and achieve state-of-the-art performance on challenging modern benchmarks.Comment: To be presented at CVPR 201

Optical Flow on Moving Manifolds

Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this article we study a Horn-Schunck type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying image domain. To that end we construct a Riemannian metric that describes the deformation and structure of this evolving surface. The resulting functional can be seen as natural geometric generalization of previous work by Weickert and Schn\"orr (2001) and Lef\`evre and Baillet (2008) for static image domains. In this work we show the existence and wellposedness of the corresponding optical flow problem and derive necessary and sufficient optimality conditions. We demonstrate the functionality of our approach in a series of experiments using both synthetic and real data.Comment: 26 pages, 6 figure

On Universality of Holographic Results for (2+1)-Dimensional CFTs on Curved Spacetimes

The behavior of holographic CFTs is constrained by the existence of a bulk dual geometry. For example, in (2+1)-dimensional holographic CFTs living on a static spacetime with compact spatial slices, the vacuum energy must be nonpositive, certain averaged energy densities must be nonpositive, and the spectrum of scalar operators is bounded from below by the Ricci scalar of the CFT geometry. Are these results special to holographic CFTs? Here we show that for perturbations about appropriate backgrounds, they are in fact universal to all CFTs, as they follow from the universal behavior of two- and three-point correlators of known operators. In the case of vacuum energy, we extend away from the perturbative regime and make global statements about its negativity properties on the space of spatial geometries. Finally, we comment on the implications for dynamics which are dissipative and driven by such a vacuum energy and we remark on similar results for the behavior of the Euclidean partition function on deformations of flat space or the round sphere.Comment: 35+4 pages, 1 figure. v2: corrected discussion of torus to deformed flat space; additional comments adde

Stochastic uncertainty models for the luminance consistency assumption

International audienceIn this paper, a stochastic formulation of the brightness consistency used in many computer vision problems involving dynamic scenes (motion estimation or point tracking for instance) is proposed. Usually, this model which assumes that the luminance of a point is constant along its trajectory is expressed in a differential form through the total derivative of the luminance function. This differential equation links linearly the point velocity to the spatial and temporal gradients of the luminance function. However when dealing with images, the available informations only hold at discrete time and on a discrete grid. In this paper we formalize the image luminance as a continuous function transported by a flow known only up to some uncertainties related to such a discretization process. Relying on stochastic calculus, we define a formulation of the luminance function preservation in which these uncertainties are taken into account. From such a framework, it can be shown that the usual deterministic optical flow constraint equation corresponds to our stochastic evolution under some strong constraints. These constraints can be relaxed by imposing a weaker temporal assumption on the luminance function and also in introducing anisotropic intensity-based uncertainties. We in addition show that these uncertainties can be computed at each point of the image grid from the image data and provide hence meaningful information on the reliability of the motion estimates. To demonstrate the benefit of such a stochastic formulation of the brightness consistency assumption, we have considered a local least squares motion estimator relying on this new constraint. This new motion estimator improves significantly the quality of the results

Highly accurate optic flow computation with theoretically justified warping

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