Non-local means is an algorithm in image processing for image denoising. Unlike "local mean" filters, which take the mean value of a group of pixels surrounding a target pixel to smooth the image, non-local means filtering takes a mean of all pixels in the image, weighted by how similar these pixels are to the target pixel. This results in much greater post-filtering clarity, and less loss of detail in the image compared with local mean algorithms.
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If compared with other well-known denoising techniques, such as the Gaussian smoothing model, the anisotropic diffusion model, the total variation denoising, the neighborhood filters and an elegant variant, the Wiener local empirical filter, the translation invariant wavelet thresholding, the non-local means method noise looks more like white noise. Recently non-local means has been extended to other image processing applications such as deinterlacing and view interpolation.
Definition
Suppose
where
Common weighting functions
The purpose of the weighting function,
Gaussian
The Gaussian weighting function sets up a normal distribution with a mean,
where
Discrete algorithm
For an image,
where
Then, for a Gaussian weighting function,
where
where