Foveated Nonlocal Self-Similarity

When we gaze a scene, our visual acuity is maximal at the fixation point (imaged by the fovea, the central part of the retina) and decreases rapidly towards the periphery of the visual field. This phenomenon is known as foveation. We investigate the role of foveation in nonlocal image filtering, installing a different form of self-similarity: the foveated self-similarity. We consider the image denoising problem as a simple means of assessing the effectiveness of descriptive models for natural images and we show that, in nonlocal image filtering, the foveated self-similarity is far more effective than the conventional windowed self-similarity. To facilitate the use of foveation in nonlocal imaging algorithms, we develop a general framework for designing foveation operators for patches by means of spatially variant blur. Within this framework, we construct several parametrized families of operators, including anisotropic ones. Strikingly, the foveation operators enabling the best denoising performance are the radial ones, in complete agreement with the orientation preference of the human visual system.