Arithmetic operations rarely show up because someone wants arithmetic. They show up because reshaping intensity is the move that lets the next step in the chain work cleanly. A few representative cases:
Flat-field correction. An illumination gradient across the field shifts the apparent intensity of identical biology in different positions. Acquire (or estimate) a background-only reference image; subtract it from the sample. Per-position bias removed; a single threshold now reads the same biology consistently across the field.
Ratiometric measurements. Two channels imaged of the same field, where the ratio carries the biological signal (a calcium indicator, a FRET donor/acceptor pair, a pH-sensitive dye). Divide images produces a per-pixel ratio map; the result is a quantitative readout of the property the ratio encodes — independent of absolute intensity, which is often the point.
Dynamic-range compression. Microscopy images often span four orders of magnitude in intensity from dim cytoplasm to bright nuclei. Linear thresholdsLoading... struggle with this range. Logarithm compresses the high end and expands the low end; the post-log image presents dim and bright on a more comparable footing, and a single threshold can address both.
Difference imaging. Two acquisitions of the same field at different time points; subtract images highlights what changed. The subtraction makes the static structure cancel; the dynamic structure surfaces.
Inversion for downstream methods that expect bright foreground. Some detection engines assume foreground is bright. For images where the foreground is dark (transmitted light brightfield, certain stains), complement swaps the convention without altering relative intensity differences.
Channel weighting and composition. Add weighted images combines two channels with chosen weights — useful for synthesizing a composite signal, computing a derived channel from a linear combination, or building a single-channel projection from multi-channel data.