THE GARDEN

Image intensity and histograms

Updated 11 Oct 2026

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  Histogram

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    Histogram -> counts pixels by intensity or channel value.

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      Can reveal a narrow range or saturation.

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      Discards spatial arrangement.

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    Histogram equalization -> remaps intensity using the cumulative distribution; may amplify noise.

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      usually used to fix low contrast image

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      main idea is each pixel distributes evenly to available values

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      formua from the course:

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        $$S_k = \frac{n_G - 1}{n} \sum_{i=0}^k n_{r_j}$$
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      dengan

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        $n_G = \text{count of graylevels in the img = L}$

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        $n = \text{pixel count}$

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        $k = (0, 1, \dots, n_G - 1)$

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        $n_{r_j} = \text{count of pixels that have gray degree of } r_j$

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      rounding of $S_k$ must be consistent, but you can do whatever

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      problems -> can be toobright. solution -> separate into blocks (local operation)

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    equalizing a color image, convert it first to something that separates the intensity and colors, then equalize the intensity, then convert back

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    Histogram matching -> maps a distribution toward a reference.

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    contrast -> high variance

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      $s^2 = \sum_i (i - \bar{x})^2 \frac{H \left( i \right)}{N}$

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    dynamic -> in histogram, sparser than contrast

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    full image intensity -> $\bar{x} = \sum_i i \frac{H \left( i \right)}{N}$

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  Point operations

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    Rescaling -> maps an input range to an output range.

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    Image arithmetic / bitwise masks -> combine pixels.

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      Check alignment and data type.

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      Unsigned values may clip or wrap.

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