Thresholding of noisy shoeprint images based on pixel context
Pattern Recognition Letters
Staircasing in semidiscrete stabilised inverse linear diffusion algorithms
Journal of Computational and Applied Mathematics
Image Filtering Driven by Level Curves
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
From Local Kernel to Nonlocal Multiple-Model Image Denoising
International Journal of Computer Vision
Adaptive morphological filtering using similarities based on geodesic time
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Generalised Nonlocal Image Smoothing
International Journal of Computer Vision
Self-similarity-based image denoising
Communications of the ACM
Numerical Approximations for a Nonlocal Evolution Equation
SIAM Journal on Numerical Analysis
CUDA optimization strategies for compute- and memory-bound neuroimaging algorithms
Computer Methods and Programs in Biomedicine
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Denoising images can be achieved by a spatial averaging of nearby pixels. However, although this method removes noise it creates blur. Hence, neighborhood filters are usually preferred. These filters perform an average of neighboring pixels, but only under the condition that their grey level is close enough to the one of the pixel in restoration. This very popular method unfortunately creates shocks and staircasing effects. In this paper, we perform an asymptotic analysis of neighborhood filters as the size of the neighborhood shrinks to zero. We prove that these filters are asymptotically equivalent to the Perona–Malik equation, one of the first nonlinear PDE’s proposed for image restoration. As a solution, we propose an extremely simple variant of the neighborhood filter using a linear regression instead of an average. By analyzing its subjacent PDE, we prove that this variant does not create shocks: it is actually related to the mean curvature motion. We extend the study to more general local polynomial estimates of the image in a grey level neighborhood and introduce two new fourth order evolution equations.