- Definition
- Common weighting functions Gaussian
- Discrete algorithm
- See also
- References
- External links
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.[2] Recently non-local means has been extended to other image processing applications such as deinterlacing[3], view interpolation[4], and depth maps regularization [5].
Definition
Suppose 
is the area of an image, and 
and 
are two points within the image. Then, the algorithm is:[6]
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.
Gaussian
The Gaussian weighting function sets up a normal distribution with a mean, 
and a variable standard deviation:[7]
where 
is the filtering parameter (i.e., standard deviation) and 
is the local mean value of the image point values surrounding .
Discrete algorithm
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 
.
See also
- Total variation denoising
- Anisotropic diffusion
- Signal Processing
- Digital Image Processing
- Noise reduction
References
2. ^{{cite web|last1=Buades|first1=Antoni|title=On image denoising methods|url=http://123seminarsonly.com/Seminar-Reports/029/42184313-10-1-1-100-81.pdf|website=123 Seminars Only}}
3. ^{{cite web|last1=Dehghannasiri|first1=R.|last2=Shirani|first2=S.|title=A novel de-interlacing method based on locally-adaptive Nonlocal-means|date=2012|url=http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6489324}}
4. ^{{cite web|last1=Dehghannasiri|first1=R.|last2=Shirani|first2=S.|title=A view interpolation method without explicit disparity estimation |date=2013|url=http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6618274}}
5. ^{{cite web |last1=Martinello |first1=Manuel |last2=Favaro |first2=Paolo |title=Depth Estimation From a Video Sequence with Moving and Deformable Objects |url=http://www.manemarty.com/Publications_files/Martinello_DepthSingleVideo.pdf |publisher=IET Image Processing Conference}}
6. ^{{cite web|last1=Buades|first1=Antoni|title=Non-Local Means Denoising|url=http://www.ipol.im/pub/art/2011/bcm_nlm/|website=Image Processing On Line}}
7. ^{{cite web|last1=Buades|first1=Antoni|title=On image denoising methods (page 10)|url=http://123seminarsonly.com/Seminar-Reports/029/42184313-10-1-1-100-81.pdf|website=123 Seminars Only}}
External links
- [https://web.archive.org/web/20111118001653/http://www.stanford.edu/~slansel/tutorial/summary.htm Recent trends in denoising tutorial]
- Non-local image denoising, with code and online demonstration
- Patents citing 2005 IEEE paper where NLM was claimed as a new technique
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