Smooth Foveal vision with Gaussian receptive fields

Despite the huge amount of information, the human brain is able to perceive and interpret visual signals in real time. One of reasons is that visual information is selectively sampled in the retina providing higher acuity in the center (where usually the most important information is) than in periphery. Humanoids vision can benefit from such space-variant representations of the visual field with utility not only in image data reduction but also in others applications as vergence, active tracking, as demonstrated in the last decades' research. However, classical methods model foveation processes with non-smooth receptive fields with are a weak match to the human physiology. Instead we propose an alternative representation using Gaussian kernels. While increasing redundancy, Gaussian receptive fields provide a smoother representation of Foveal images and model certain properties of data acquisition in human vision. In addition, we propose an algebraic approach for the analysis, synthesis and processing of Foveal images, using simple matrix computations and operator theory. We show how to derive the equivalent Foveal operators to common Cartesian domain linear processing routines such as image geometrical transformations and filtering operations. We present experiments illustrating the performance of the proposed methodology in comparison to classical approaches for space-variant image processing both in image reconstruction and in motion estimation/tracking tasks.