A Multigrid Platform for Real-Time Motion Computation with Discontinuity-Preserving Variational Methods |
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Authors: | Andrés Bruhn Joachim Weickert Timo Kohlberger Christoph Schnörr |
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Affiliation: | (1) Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E1 1, 66041 Saarbrücken, Germany;(2) Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer Science, University of Mannheim, 68131 Mannheim, Germany |
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Abstract: | Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and
can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise
and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive
in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order
to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance.
In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods
for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby,
our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of
five classical and two recent variational techniques that real-time performance is possible in all cases—even for very complex
optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image
sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup
of two to four orders of magnitude. |
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Keywords: | partial differential equations variational methods optic flow multigrid methods |
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