Image Histogram

Updated 02 Oct 2026

•
What it is
- •
  counts how many image samples have each intensity or fall within each intensity interval
•
Formula
- •
  for an image with $N$ pixels, $h(k)=\#\{i:f_i=k\}$ .
- •
  normalized histogram: $p(k)=h(k)/N$ , so $\sum_kp(k)=1$ .
- •
  numulative distribution: $F(k)=\sum_{j\le k}p(j)$ .
•
Interpretation
- •
  an 8-bit grayscale image commonly uses $256$ bins for values $0,\ldots,255$ .
- •
  a color image can have a separate histogram for each channel.
- •
  a histogram discards spatial arrangement: different images can have identical histograms.
•
Statistics
- •
  mean intensity: $\mu=\sum_k kp(k)$ .
- •
  population standard deviation: $\sigma=\sqrt{\sum_k(k-\mu)^2p(k)}$ .
- •
  for pixels $0,0,255,255$ , both $\mu$ and $\sigma$ equal $127.5$ .
•
Project clarification
- •
  the statistics endpoint uses grayscale values and np.std with its default population denominator $N$
- •
  standard deviation measures intensity spread and can serve as a global contrast measure; it does not fully describe local contrast or image quality
•
Related

Linked references 4