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LOCAL NORM.
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ImageJ's plugin
The local normalization tends to uniformize the mean and variance of an image around a local neighborhood. This is especially useful for correct uneven illumination or shading artifacts. Thanks to our fact implementation of the Gaussian filtering, the Local Normalization is running very fast.
D. Sage, M. Unser, Easy Java Programming for Teaching Image Processing Proceedings of the IEEE International Conference on Image Processing (ICIP'01), Thessaloniki, Hellenic Republic, 2001.
@INPROCEEDINGS(http://bigwww.epfl.ch/publications/sage0101.html, AUTHOR="Sage, D. and Unser, M.", TITLE="Easy {J}ava Programming for Teaching Image Processing", BOOKTITLE="Proceedings of the 2001 {IEEE} International Conference on Image Processing ({ICIP'01})", YEAR="2001", editor="", volume="{III}", series="", pages="298301", address="{$\mathit{\Theta}$}{$\varepsilon$}{$\sigma$}{$\sigma$}{$\alpha$}{$\lambda$}{$o$}{$\nu$}{$\acute{\iota}$}{$\kappa$}{$\eta$} (Thessaloniki), {$E$}{$\lambda$}{$\lambda$}{$\eta$}{$\nu$}{$\iota$}{$\kappa$}{$\acute{\eta}$} {$\Delta$}{$\eta$}{$\mu$}{$o$}{$\kappa$}{$\rho$}{$\alpha$}{$\tau$}{$\acute{\iota}$}{$\alpha$} (Hellenic Republic)", month="October 710,", organization="", publisher="", note="")
The local normalization of f(x,y) is computed as follows:
where:

The estimation of the local mean and variance is performed through local spatial smoothing. In this implementation, we use fast recursive Gaussian filters. The parameters of the algorithm are the sizes of the smoothing windows, σ_{1}, and, σ_{2}, which control the estimation of the local mean and local variance, respectively. Often σ_{2} should be larger than σ_{1}.
The software provided here is a plugin for ImageJ, a general purpose imageprocessing and imageanalysis package. It runs also on the imageprocessing package Fiji. ImageJ has a public domain licence; it runs on several plateforms: Unix, Linux, Windows, and Mac OS X. It doesn't take more than a couple of minutes to install.
Download Local_Norm.jar [Version 17.01.2017].
The plugin consists in one single JAR file; place it into the "plugins" folder of ImageJ.
Do not unzip the JAR file.
After restarting ImageJ, you have a new entrie in the Plugin » Filters of ImageJ, which is Local_Normalization.
Matlab version of the Local Normalization, by Guanglei Xiong, 17 Aug 2005 (Updated 07 Sep 2005)
We have also a demonstration of this algorithm running on any browser.
Input image 
Output image 
daniel.sage@epfl.ch • 20.12.2020