university computervision week1 theory
Histograms
Source:
Idea
A histogram summarizes an image by counting how many pixel values fall inside each value interval or bin.
For a grayscale image, this describes the distribution of luminance values.
Univariate histogram
For bins with edges e_i, the lecture gives:
So each bin count tells you how many pixels have values in that interval.
Choosing bins
Main tradeoff from the lecture:
- too many bins: many empty bins, noisy high-frequency detail
- too few bins: the distribution is oversmoothed and important structure disappears
The slides mention Sturges’ rule:
where k is the number of bins and n is the number of pixels.
Cumulative histogram
The cumulative histogram H_f(u) counts how many pixels satisfy:
This is the discrete analogue of a cumulative distribution function.
Color histograms
For color images, the lecture discusses:
- three separate 1D histograms, one per channel
- one 3D histogram over the joint color values
The 3D histogram keeps channel correlations, which separate 1D histograms lose.
Why histograms matter
They are useful for:
- summarizing image brightness distributions
- detecting low contrast
- thresholding
- contrast stretching
- histogram equalization