# 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?

## 1 Answer

A precise explanation of the term local histogram is not possible unless someone specifies its mathematical definition. Yet the term local makes the following sense: compute a histogram from a bunch of spatially related pixels, instead of using the whole image.

In addition, the use of a weight further implies that (usually) the closer pixels will have a dominance on the computed histogram statistics. However, it's not clear how this weighting would be translated into the mechanics of the histogram computation.

• By "local histogram" I mean fix a tile in your image and compute that histogram. – user8469759 Jul 20 '18 at 14:13
• yes that's what I mean as local. What do you mean by tile here? a small square within the image or what? – Fat32 Jul 20 '18 at 14:30
• yes. Small square region inside the image. – user8469759 Jul 20 '18 at 14:34
• Hi: the paper may be referring to the histogrammed output of loess, a local smoothing procedure used in statistical applications.. I can't say for sure but it's possible. – mark leeds Jul 21 '18 at 11:17