Averaging histograms

An image histogram is the number of each pixel value, which is displayed in the graph.

x axis of the graph is pixel value, range from 0 to 255;

y axis of the graph is the number of this pixel value;

An example of an standard image together with its luminance and RGB histograms

1.How to averaging histograms?

Our goal is to generate a new image with a more even histogram distribution.

The accumulated value of the histogram is equal to the image resolution.

So we get an equation:

 q             
 ∑  hist(k） = H*W 
k=0

The cumulative value of target histogram is equal to the one of original historam.

So we got:

 q              p
 ∑  hist(k） =  ∑ target_hist(k)
k=0            k=0

We want to average the histogram, so we make the number of each pixel value approximately equal to the average number of pixel in the image:

target_hist(k) = H*W/256

Here target_hist(k) means the average number of k, then we can get:

p
∑ target_hist(k) =  (p+1) * target_hist(k) = (p+1)(H*W/256)
k=0

then

q             
 ∑  hist(k） = (p+1)(H*W/256)
k=0

we got

    q
p = ∑ (hist(k)/(H*W) * 256) - 1
    k=0

TAG: 直方图均值化,

REFERENCE:

「点个赞」