# What Is a Weighted Local Histogram?

I'm reading through a couple of academic papers, and this terms often comes up "local weighted histogram". An example of quote is the following:

First, cumulative histograms are built for every pixel from its neighborhood, using Gaussian-neighborhood weighting

I would be able to construct a local histogram, I'm not sure what this weighting is about.

Say the central pixel is at $p_0 = (y_0,x_0)$, and we have two pixels of same gray scale value $r$ at coordinates $p_1 = (y_1,x_1)$ and $p_2 = (y_1,x_1)$, but such that $d(p_0,p_1) < d(p_0,p_2)$. A normal histogram would count that value $r$ twice. With a Gaussian weighting for example how would we count such pixel value in the histogram construction?

A weighted local histogram would mean filtering the image $$I(x,y)$$ with a localised filter $$H(x,y)$$ (gaussian in this example). The resultant image is the 2D convolution $$Y(x,y) = I(x,y)*H(x,y)$$. The normal histogram of $$Y(x,y)$$ is the localised histogram of $$I(x,y)$$. It is used to view certain specific characteristics of an image depending on the filter used