ISSN : 1796-2048
Volume : 2    Issue : 2    Date : April 2007

A Chaos Theoretic Analysis of Motion and Illumination in Video Sequences
Michael E. Farmer
Page(s): 53-64
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Accurate and robust image motion detection has been of substantial interest in the image
processing and computer vision communities. Unfortunately, no single motion detection algorithm
has been universally superior, yet biological vision systems are adept at motion detection. Recent
research in neural signals have shown biological neural systems are highly responsive to signals
which appear to be chaotic in nature. In this paper, we exploit these biological results and
hypothesize that motion in images may produce changes in pixel amplitudes that are reminiscent of
chaotic dynamical systems. In particular, we demonstrate that the trajectories of pixel amplitudes in
phase space due to motion result in chaos-like behavior. We likewise demonstrate that the effects
of spatio-temporally varying illumination produces phase space trajectories of the pixel amplitudes
which are clearly non-chaotic. We review the research tying chaotic behavior to the fractal
characteristics of phase space trajectories, and we investigate multi-fractal measures which can be
used to classify the pixels in an image stream based on their fractal behavior in phase space. We
finally apply these measures to the task of motion detection and segmentation and show they are
effective in identifying moving objects while ignoring spatio-temporally varying illumination changes.

Index Terms
Image motion analysis, Image segmentation, Image sequence analysis, Chaos, Nonlinearities.