Spatiotemporal power spectra of motion parallax: the case of cluttered 3D scenes

We examine the spatiotemporal power spectra of image sequences that depict dense motion parallax, namely the parallax seen by an observer moving laterally in a cluttered 3D scene. Previous models of the spatiotemporal power have accounted for effects such as a static 1/f spectrum in each image frame, a spreading of power at high spatial frequencies in the direction of motion, and a bias toward either lower or higher image speeds depending on the 3D density of objects the scene. Here we use computer graphics to generate a parameterized set of image sequences and qualitatively verify the main features of these models. The novel contribution is to discuss how failures of 1/f scaling can occur in cluttered scenes. Such failures have been described for the spatial case, but not for the spatiotemporal case. We find that when objects in the cluttered scene are visible over a wide range of depths, and when the image size of objects is smaller than the image width, failures of 1/f scaling tend to occur at certain critical frequencies, defined by a correspondence between object size and object speed.