| Operation | Formula | Use Case |
|---|---|---|
| Add images | A + B | Combine signals from two channels |
| Add value / Add value (RGB) | A + c | Brighten image by constant offset |
| Add weighted images | w₁·A + w₂·B | Weighted blend of two channels |
| Subtract images | A − B | Background subtraction, change detection |
| Subtract value / (RGB) | A − c | Remove constant background offset |
| Multiply images | A × B | Masking (multiply by binary mask) |
| Multiply with value / (RGB) | A × c | Contrast scaling, gain adjustment |
| Divide images | A / B | Ratio imaging, flat-field correction |
| Divide by value / (RGB) | A / c | Normalize intensity range |
| Complement | max − A | Invert image (e.g., hematoxylin → fluorescence-like) |
| Logarithm (Ln) | ln(A) | Dynamic range compression, OD-related transforms |
| Exponential (Exp) | exp(A) | Reverse log transform |
| Polynomial | a + b·A^c | Flexible intensity curve remapping |
| Square (Sqr) | A² | Enhance high intensities, energy computation |
| Square root (Sqrt) | √A | Moderate dynamic range compression |
BOM Group
Arithmetic Operations
Point-wise math on image pixel values
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Definition
Subtract a background image from a signal image, and each output pixel is the signal there minus the background there. Every operation in this group follows that pattern, for combining images, adjusting intensities and reshaping value distributions: add, subtract, multiply, divide, log, exp, polynomial, complement, square and square root.
19 operations
Image-to-image and image-to-scalar arithmetic
Point-wise processing
Each pixel processed independently
Reshaping the dynamic range
Log compresses, exp expands, polynomial remaps
Keeping results in range
Scaling factor multiplies results by 2^value
Operations Reference
Simplified
These operations do simple math on each pixel. Add or subtract a value to brighten or darken; multiply to adjust contrast; divide by a reference to normalize. Logarithm compresses bright values, which helps with 16-bit data, and Complement swaps bright and dark.
When to Use Which
Common arithmetic workflows in tissue image processing:
Background Correction
Subtract images or Divide images. Subtract a background estimate when the background adds a constant offset to the signal. Divide by a flat-field reference when uneven illumination multiplies it.
Channel Combination
Add weighted images combines two images with weights you set (Weight 1 and Weight 2, both default 0; a negative weight subtracts). It can build a virtual channel from partially overlapping fluorophores.
Inversion
Complement swaps bright and dark. Brightfield hematoxylin shows dark nuclei on a light background; complemented, it shows bright nuclei on a dark one. That is the fluorescence-style input some detection engines require.
Dynamic Range
Logarithm compresses the wide dynamic range of 16-bit fluorescence images. It is also the basis of the OD transform (see Optical Density Conversion).
Polynomial remaps intensity when log, exp or sqrt isn't the curve shape you need.
Simplified
Subtract a background; Divide by a reference to even out illumination; Complement hematoxylin for detection; Log to compress 16-bit range; Add weighted to blend channels. Most pipelines use only two or three of these.