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BOM Operation

Arithmetic image operations

Nineteen pixel-wise operations, each giving the result a different meaning

Definition
Each arithmetic operation applies one function to every pixel of one or two input images, giving an output of the same shape. The functions: add, subtract, multiply and divide (image with image or scalar); complement (255 − image at 8 bits; likewise at higher depths); Square and Square root; polynomial (a + b · image^c); Exponential and Logarithm. Most run in the Pre-Processing slotLoading..., before thresholdingLoading... or OtsuLoading....
Supporting
User Interface - Image Viewer + Toolbar
Video · Supporting
Dynamic range - 16bit to 8bit normalization
Video · Supporting
One pattern, nineteen forms
Same per-pixel computation, different math
What arithmetic changes
Brightness, contrast, ratio, dynamic range
Watch the dynamic range
Outputs can exceed the input bit depth
RGB variants work per channel
Three computations and a recombine

Common uses of arithmetic operations

Six cases where reshaping intensity sets up the next step:

Flat-field correction. An illumination gradient across the field shifts the apparent intensity of identical biology from one position to the next. Uneven illumination multiplies the signal, so acquire or estimate a flat-field reference image and divide the sample by it; subtract a background estimate only where the background adds a constant offset. With the per-position bias gone, a single threshold reads the same biology the same way across the field.

Ratiometric measurements. Sometimes the biology is in the ratio of two channels imaged on the same field: a calcium indicator, a FRET donor/acceptor pair, a pH-sensitive dye. Divide images gives a per-pixel ratio map. That map reads out the property the ratio encodes, independent of absolute intensity.

Dynamic-range compression. Microscopy images often span four orders of magnitude, from dim cytoplasm to bright nuclei, and Linear thresholdsLoading... work poorly across that range. Logarithm compresses the high end and expands the low end. Afterward dim and bright sit on comparable footing, and one threshold can address both.

Difference imaging. Image the same field at two time points and subtract images. The static structure cancels, and what changed surfaces.

Inversion for downstream methods that require a bright foreground. Some detection engines require the foreground to be bright. Where it is dark, as in transmitted-light brightfield and certain stains, complement swaps the convention and keeps relative intensity differences intact.

Channel weighting and composition. Add weighted images combines two channels with weights you choose. Use it to synthesize a composite signal, derive a channel from a linear combination, or build a single-channel projection from multichannel data.

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