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Adaptive thresholding uses an image threshold that varies with position, often calculated from a neighborhood around each pixel. It can help separate marks from background when illumination changes across an image. A global image thresholding rule instead uses the same threshold everywhere.^[ref]

For a simple real-arithmetic local-mean model, putwhere ${\overline{I}}_{\mathcal{N}}$ is the neighborhood mean and $C$ a fixed offset. OpenCV documents local-mean and Gaussian-weighted alternatives, with a declared neighborhood size. Its binary comparison assigns the high output value only above the threshold.^[ref]

Consider a three-by-three patch with eight values of $100$ and a central value of $80$. For $C=10$,so the centre receives binary value zero. Adding $60$ to every intensity gives eight values of $160$ and a centre of $140$. Now $T=1330/9\simeq 147.78$, so the centre still receives zero. A fixed threshold of $110$ would classify the two centre values differently, despite their identical contrast with their local backgrounds.

The invariance follows algebraically. If every intensity in a neighborhood increases by the same $b$, its mean and threshold also increase by $b$. Hence $I+b>T+b$ exactly when $I>T$. This proves an additive-shift property of the stated model, assuming no clipping or rounding; it is not a claim about arbitrary spatial gradients or multiplicative brightness changes.

Neighborhood size and offset affect the result. A very small neighborhood can follow noise or include too little background, while a large one can span changing illumination. Integer rounding and image-edge handling must also be specified for an exact implementation comparison. The resulting binary image remains an intensity-based selection; connected-component labeling and semantic interpretation are further steps.

Image thresholding classifies pixels by comparing their intensities with a threshold, often producing a binary image. A global threshold uses the same value throughout the image; adaptive thresholding permits the threshold to depend on position and nearby intensities.^[ref]

For example, defineIntensities $99,100,101$ then become $0,0,1$. The comparison at equality matters: a rule using $I\ge 100$ would instead give $0,1,1$. OpenCV's THRESH_BINARY uses the strict greater-than rule, assigning its chosen maximum output value only above the threshold.^[ref]

Threshold choice affects which distinctions survive. Two different bright intensities can become the same foreground value, while a small change near the boundary can change a pixel's classification. The resulting mask can then feed connected-component labeling, where pixel connectivity separately decides which selected pixels form a region.

A useful motivating experiment keeps one image of dark marks fixed while adding or recording a gradual illumination variation across the background. Compare a global threshold with a declared local-neighborhood rule, inspecting lost strokes and falsely selected background. OpenCV documents local mean and Gaussian-weighted rules with an offset; this addresses varying illumination rather than proving that every resulting region is a meaningful object.^[ref]

A histogram can guide global selection, but intensity statistics alone do not determine semantic identity. Noise and overlapping foreground/background intensities can make every threshold imperfect. Report the input representation, comparison convention and any filtering or local-window settings so that a thresholded result can be reproduced.