Purpose: We want understand the relationship between the response properties of visual neurons and the statistical structure of natural time-varying images. Beyond the second order statistics (Stringer and Dong 2002 SNF, Dong 2002 SFN), it is interesting to learn the higher order ones. In the previous studies, movies or images form camera or camcorders were used, which at most simulating the periphery inputs. However, it is likely that the statistical structures of time-varying images viewed by real human subjects especially at the center of the gaze are very different from those. Method: Saccadic eye movements provide huge variations in spatio-temporal inputs and the tracking of moving objects keeps the image near the center of the gaze stabilized during fixations and smooth pursuits. These properties make the time-varying images near the center of the gaze different from the periphery. In this study, higher order of statistics of time-varying natural images near the center of the gaze and near the periph...