Foveated Self-Similarity in Nonlocal Image Processing

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 kernels whose spread increases 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.



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Anisotropic Foveated NL-means filternew
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  Alessandro Foi
  Giacomo Boracchi

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  NL-means filter at Matlab Central File Exchange (by J.V. Manjon Herrera & A. Buades)

References References

PDFA. Foi and G. Boracchi, “Foveated nonlocal self-similarity”, Int. J. Computer Vision, vol. 120, no. 1, pp. 78-110, October 2016.  DOI

A. Foi and G. Boracchi, “Nonlocal Foveated Principal Components”, Proc. 2014 IEEE Workshop on Statistical Signal Processing, SSP 2014, pp. 145-148, Gold Coast, Australia, June 29-July 2, 2014.  DOI

PDFA. Foi and G. Boracchi, “Anisotropically Foveated Nonlocal Image Denoising”, Proc. IEEE Int. Conf. Image Process., ICIP 2013, Melbourne, Australia, September 15-18, 2013.

PDFA. Foi and G. Boracchi, “Foveated self-similarity in nonlocal image filtering”, Proc. SPIE Electronic Imaging 2012, Human Vision and Electronic Imaging, 8291-32, Burlingame (CA), USA, January 2012.

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