A Chaos Theoretic Analysis of Motion and Illumination in Video Sequences

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.