[IPOL announce] new article: Horn-Schunck Optical Flow with a Multi-Scale Strategy
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Sat Jul 20 16:03:35 CEST 2013
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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