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.
If compared with other well-known denoising techniques, non-local means adds "method noise" (i.e. error in the denoising process) which looks more like white noise, which is desirable because it is typically less disturbing in the denoised product. Recently non-local means has been extended to other image processing applications such as deinterlacing and view interpolation.
Suppose is the area of an image, and and are two points within the image. Then, the algorithm is:
where is the filtered value of the image at point , is the unfiltered value of the image at point , is the weighting function, and the integral is evaluated over .
is a normalizing factor, given by:
Common weighting functions
The purpose of the weighting function, , is to determine how closely related the image at the point is to the image at the point . It can take many forms.
where is the filtering parameter (i.e., standard deviation) and is the local mean value of the image point values surrounding .
For an image, , with discrete pixels, a discrete algorithm is required.
where is given by:
Then, for a Gaussian weighting function,
where is given by:
where and is a square region of pixels surrounding and is the number of pixels in the region .
- Total variation denoising
- Anisotropic diffusion
- Signal Processing
- Digital Image Processing
- Noise reduction
- Buades, Antoni (20–25 June 2005). "A non-local algorithm for image denoising". Computer Vision and Pattern Recognition, 2005. 2: 60–65. doi:10.1109/CVPR.2005.38.
- Buades, Antoni. "On image denoising methods" (PDF). 123 Seminars Only.
- Dehghannasiri, R.; Shirani, S. (2012). "A novel de-interlacing method based on locally-adaptive Nonlocal-means".
- Dehghannasiri, R.; Shirani, S. (2013). "A view interpolation method without explicit disparity estimation".
- Buades, Antoni. "Non-Local Means Denoising". Image Processing On Line.
- Buades, Antoni. "On image denoising methods (page 10)" (PDF). 123 Seminars Only.