I am working on NL means for denoising and other segmentation based results. I am confused as to why it is called non parametric. It does have parameters which are definite with regards to patch size, window size and few other factors but the parameters are finite and remain the same. Why exactly is it called non-parametric?
2026-03-26 09:38:45.1774517925
Why is Non-local means non parametric?
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NL means is called non-parametric in the sense that it does not estimate any parameter of an assumed model for an input image.
More precisely, the term - non-parametric comes from the inherent nature of the NL means which is non-parametric regression on the input image.
The patch-size, window-size, etc. that you are thinking of as parameters are somehow optimally guessed through a rigorous study of the nature of an ensemble of a particular type of images (e.g. for natural images, an optimal value of the patch-size is $7\times7$). These factors are not estimated from or for a particular input image.
References:
Buades, A., B. Coll, and J-M. Morel. "A non-local algorithm for image denoising." 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05). Vol. 2. IEEE, 2005.
Milanfar, Peyman. "A tour of modern image filtering: New insights and methods, both practical and theoretical." IEEE Signal Processing Magazine 30.1 (2013): 106-128.
Haque, S. M., G. P. Pai, and V. M. Govindu. "Symmetric smoothing filters from global consistency constraints." IEEE Transactions on Image Processing 24.5 (2015): 1536-1548.