Foveated self-similarity in nonlocal image filtering

Nonlocal image filters suppress noise and other distortions by searching for similar patches at different locations within the image, thus exploiting the self-similarity present in natural images. This similarity is typically assessed by a windowed distance of the patches pixels. Inspired by the human visual system, we introduce a patch foveation operator and measure patch similarity through a foveated distance, where each patch is blurred with spatially variant point-spread functions having standard deviation increasing with the spatial distance from the patch center. In this way, we install a different form of self-similarity in images: the foveated self-similarity. We consider the Nonlocal Means algorithm (NL-means) for the removal of additive white Gaussian noise as a simple prototype of nonlocal image filtering and derive an explicit construction of its corresponding foveation operator, thus yielding the Foveated NL-means algorithm. Our analysis and experimental study show that, to the purpose of image denoising, the foveated self-similarity can be a far more effective regularity assumption than the conventional windowed self-similarity. In the comparison with NL-means, the proposed foveated algorithm achieves a substantial improvement in denoising quality, according to both objective criteria and visual appearance, particularly due to better contrast and sharpness. Moreover, foveation is introduced at a negligible cost in terms of computational complexity.