Optical flow in log-mapped image plane - a new approach

Foveating vision sensors are important in both machine and biological vision. The term space-variant or foveating vision refers to sensor architectures based on smooth variation of resolution across the visual field, like that of the human visual system. Traditional image processing techniques do not hold when applied directly to such an image representation since the translation symmetry and the neighborhood structure in the spatial domain is broken by the space-variant properties of the sensor. Unfortunately, there has been little systematic development of image processing tools that are explicitly designed for foveated vision. The author proposes a novel approach to compute the optical flow directly on log-mapped images. We propose the use of a generalized dynamic image model (GDIM) based method for computing the optical flow as opposed to the brightness constancy model (BCM) based method. We introduce a new notion of "variable window" and use the space-variant form of gradient operator while computing the spatio-temporal gradient in log-mapped images for a better accuracy and to ensure that the local neighborhood is preserved. We emphasize that the proposed method must be numerically accurate, provide a consistent interpretation, and be capable of computing the peripheral motion. Experimental results on both the synthetic and real images have been presented to show the efficacy of the proposed method.