[IPOL discuss] [IPOL announce] new article: Horn-Schunck Optical Flow with a Multi-Scale Strategy

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A new article is available in IPOL: http://www.ipol.im/pub/art/2013/20/

Horn-Schunck Optical Flow with a Multi-Scale Strategy
by Enric Meinhardt-Llopis, Javier Sánchez Pérez and Daniel Kondermann
Image Processing On Line, vol. 2013, pp. 151–172.
http://dx.doi.org/10.5201/ipol.2013.20

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 approach 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.




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