Histograms

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The intensity histogram \(h(r_k)\) counts the number of pixels with intensity level \(r_k\):

\[h(r_k) = \sum_{i=0}^{M-1} \sum_{j=0}^{N-1} \delta(f(i,j) - r_k), \quad k = 0, 1, \ldots, L-1\]

Histograms reveal the tonal distribution of an image and are the basis for several enhancement techniques.

Histogram equalization redistributes pixel intensities to achieve a roughly uniform histogram, enhancing global contrast:

\[s_k = (L-1) \sum_{j=0}^{k} p_r(r_j)\]

where \(p_r(r_j) = h(r_j) / (MN)\) is the normalized histogram.

Contrast Limited Adaptive Histogram Equalization (CLAHE) applies equalization locally within tiles and clips the histogram to avoid over-amplifying noise, making it well suited for microscopy images.

See also

• What Is a Digital Image? — bit depth and color spaces, which determine the histogram’s range

• Contrast Enhancement — CLAHE and equalization applied in practice

• Digital Image Processing Basics — every other basics topic