Quantization effects in applying chaos theory to the detection of motion in image sequences

Recent research has demonstrated that tools from chaos theory can be applied to robustly detect motion and change in image sequences, even in the presence of spatiotemporally varying illumination. One key issue in digital imaging systems, however, is the effect of the quantization. This paper first demonstrates the effects of quantization on the phase space trajectories of pixel amplitudes and then proposes a method for addressing these effects by combining of multi-fractal measures with algebraic curve-based trajectory analysis to identify regions of the phase space with quantized chaotic trajectories. This proposed method is demonstrated in the application of object motion detection in video image sequences, but the results may prove applicable for other digitized information sources which may be produced by non-linear systems or processes.