Seeing structure through chaos

Abstract

Research in motion perception has concentrated on recognizing regularities in images due to rigid motion. However, rigid motion is only one type of motion that occurs in our world. There is also elastic motion, fluid motion, and turbulent flow. Examples of turbulent flow include clouds, waves, boiling water, rustling leaves, or flags fluttering in the wind. Fully developed turbulent flow is completely chaotic and incoherent motion. Yet, it has a regular statistical structure underlying the apparent chaos. These regularities are due to the coherence of the physical process which generates turbulence. By using image data to characterize the parameters of this process we can make useful predictions and inferences: solid/fluid, viscosity, mean flow velocity. This paper develops a fractal-based model of turbulent flow, demonstrates that turbulence can be recognized visually, and suggests how the model can be used to make inferences about the flowing fluid. The model is implemented by testing for a fractal scale-invariant regularity across space and time using linear spatiotemporal bandpass filters. These filters can also be used to measure optical flow and are similar to receptive fields in the visual cortex.