Image Processing Handbook
    Module 0216 min read

    Point Operations and Histograms

    Operations where the output pixel depends only on the input pixel at the same position. Cheap, parallel, and responsible for most of what people call editing.

    A point operation is a function applied independently to every sample. It has no notion of neighbourhood, shape, or edge. That restriction makes it trivially parallel and, for 8-bit data, precomputable into a table of 256 entries.

    Pixel-wise Transformations

    Brightness adds a constant. Contrast scales around a pivot. Inversion subtracts from the maximum. Written as one expression they are the same operation with different coefficients.

    J(x, y) = clamp(a · I(x, y) + b)(2.1)

    a controls contrast, b controls brightness. Clamping is what makes the operation lossy: values pushed past the range do not come back.

    Gamma correction and LUTs

    Gamma correction raises the normalised value to a power. Because the operation depends on nothing but the input value, it collapses into a lookup table built once and applied with a single array read per sample.

    // Build once, apply per pixel.
const lut = new Uint8Array(256);
for (let v = 0; v < 256; v++) {
  lut[v] = Math.round(255 * Math.pow(v / 255, 1 / gamma));
}

for (let i = 0; i < data.length; i += 4) {
  data[i] = lut[data[i]];
  data[i + 1] = lut[data[i + 1]];
  data[i + 2] = lut[data[i + 2]];
}
    Figure 2.1
    A square plot with a diagonal identity line and four transfer curves: an S-curve, a concave and a convex gamma curve, and a descending line
    Transfer curves for several point operations, plotted on a shared input and output axis.
    Image prompt

    Minimal line chart on a transparent background inside a square plotting area with thin grey border and a faint diagonal identity line. Four smooth curves drawn in 1.5px strokes: an S-shaped contrast curve in cyan, a concave gamma curve in grey, a convex inverse-gamma curve in grey, and a descending straight inversion line in light grey. No text, no tick labels, no grid beyond four faint interior guides, flat vector, generous margin around the plot, 16:9.

    Histogram Analysis

    A histogram counts how many pixels fall into each intensity bin. It discards all spatial information and keeps all tonal information, which makes it the right tool for exposure decisions and the wrong tool for anything about shape.

    ShapeReadingUsual response
    Bunched at the leftUnderexposed or very dark subjectLift midtones, check for crushed shadows.
    Bunched at the rightOverexposed, possible clippingNothing recovers clipped highlights.
    Narrow central peakLow contrast, flat sceneStretch, or equalise if detail is hidden.
    Two separated peaksForeground and background differ stronglyA global threshold will work well.

    Global equalisation

    Equalisation redistributes intensities so the cumulative distribution becomes approximately linear. Detail hidden inside a narrow band of values becomes visible. Noise hidden in the same band becomes visible too.

    J(x, y) = round( (L − 1) · cdf( I(x, y) ) )(2.2)

    cdf is the normalised cumulative histogram. The transform is itself a lookup table, so the cost is one pass to build and one pass to apply.

    CLAHE

    Contrast Limited Adaptive Histogram Equalisation runs the same idea on tiles rather than on the whole frame, clips each tile histogram at a ceiling to stop noise amplification, and interpolates between neighbouring tiles to avoid visible seams. It is the version that survives contact with real photographs.

    CLAHECLAHE
    OriginalOriginal
    Local equalisation recovers detail in both the shadow and the highlight regions of a single frame.
    Image prompt

    Two versions of the same photograph for a before and after slider. Subject: a stone archway opening onto a bright courtyard, shot from inside so the interior is deep shadow and the exterior is near clipping. Version A: flat, unprocessed, shadow detail invisible, exterior blown out. Version B: identical framing and colour, with local contrast recovered so the stone texture in shadow and the courtyard detail are both legible. Photographic, neutral colour, no people, no text, identical composition between the two, 16:9.

    Thresholding and Binarisation

    Thresholding reduces an image to two classes. The difficulty is never the comparison, it is choosing the value to compare against.

    MethodHow the threshold is chosenFails when
    FixedSet by hand or by conventionLighting changes between inputs.
    OtsuMaximises between-class variance over the histogramThe histogram is not bimodal.
    Adaptive meanLocal window mean minus a constantThe window is smaller than the features.
    Adaptive GaussianWeighted local meanNoise dominates the window.

    Adaptive methods cost a neighbourhood pass, which strictly speaking makes them spatial filters. They are grouped here because the decision is still per pixel.

    Module 03 lifts the independence restriction. Once a pixel is allowed to consult its neighbours, the entire classical toolkit opens up.