Anisotropic Foveated Self-Similarity

The foveated patch distance was shown to be a valuable feature for the assessment of nonlocal self-similarity in image filtering. The Foveated NL-means [1], which modifies the classical nonlocal means denoising filter (NL-means) [2] by computing the averaging weights based on the foveated patch distance instead of the conventional windowed patch distance, leads to a consistent improvement in the quality of the restored images according to both objective criteria and visual appearance, particularly due to better contrast and sharpness. The foveated patch distance is measured by means of foveation operators, which transform image patches through a spatially variant blur characterized by point-spread functions (PSFs) whose spread progressively increases with the spatial distance juj from the patch center. Our approach mimics the human visual system (HVS), for which visual acuity is maximal at the fixation point (imaged by the fovea, i.e. the central part of the retina, where the photoreceptor density is highest) and decreases rapidly towards the periphery of the visual field. In particular, in [1] we considered isotropic operators composed of circular-symmetric Gaussian PSFs, like those in Fig. 1(a). Unlike conventional windowing, foveation operator combines at once various multiscale features computed from the local context: the foveated patches embed pixels from fine-scale (the fixation point) to coarse-scale (pixels at the patch periphery) representations of patches.