Horn–Schunck method

About: Horn–Schunck method is a research topic. Over the lifetime, 88 publications have been published within this topic receiving 14525 citations.

Determining Optical Flow

Abstract: Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.

Performance of optical flow techniques

Abstract: While different optical flow techniques continue to appear, there has been a lack of quantitative evaluation of existing methods. For a common set of real and synthetic image sequences, we report the results of a number of regularly cited optical flow techniques, including instances of differential, matching, energy-based, and phase-based methods. Our comparisons are primarily empirical, and concentrate on the accuracy, reliability, and density of the velocity measurements; they show that performance can differ significantly among the techniques we implemented.

An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences

Abstract: A mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field. In most situations, the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field. Supplementary constraints are necessary, for example the postulate that a displacement vector field varies smoothly as a function of the image position. Taken as a general requirement, this creates difficulties at gray value transitions which correspond to occluding contours. Nagel therefore introduced the ``oriented smoothness'' requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values. This contribution reports results of an investigation about how such an ``oriented smoothness'' constraint may be formulated and evaluated.

Horn-schunck optical flow with a multi-scale strategy

Abstract: The seminal work of Horn and Schunck is the first variational method for optical flow estimation. It introduced a novel framework where the optical flow is computed as the solution of a minimization problem. From the assumption that pixel intensities do not change over time, the optical flow constraint equation is derived. This equation relates the optical flow with the derivatives of the image. There are infinitely many vector fields that satisfy the optical flow constraint, thus the problem is ill-posed. To overcome this problem, Horn and Schunck introduced an additional regularity condition that restricts the possible solutions. Their method minimizes both the optical flow constraint and the magnitude of the variations of the flow field, producing smooth vector fields. One of the limitations of this method is that, typically, it can only estimate small motions. In the presence of large displacements, this method fails when the gradient of the image is not smooth enough. In this work, we describe an implementation of the original Horn and Schunck method and also introduce a multi-scale strategy in order to deal with larger displacements. For this multi-scale strategy, we create a pyramidal structure of downsampled images and change the optical flow constraint equation with a nonlinear formulation. In order to tackle this nonlinear formula, we linearize it and solve the method iteratively in each scale. In this sense, there are two common approaches: one that computes the motion increment in the iterations; or the one we follow, that computes the full flow during the iterations. The solutions are incrementally refined over the scales. This pyramidal structure is a standard tool in many optical flow methods.

Extending the 'Oriented Smoothness Constraint' into the Temporal Domain and the Estimation of Derivatives of Optical Flow

Abstract: Recent experimental results by Schnorr 89 with an approach based on a simplified ‘oriented smoothness constraint’ show considerable improvement at expected discontinuities of the optical flow field. It thus appears justified to study whether the local gray value variation can be exploited in the temporal as well as in the spatial domain in order to achieve further improvements at discontinuities in the optical flow field associated with the image areas of moving objects in image sequences. An extension of the oriented smoothness constraint into the temporal domain is presented. In this context, a local estimation approach for the spatio-temporal partial derivatives of optical flow has been developed. This, in turn, is used to compare two approaches for the definition of optical flow.