| 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
A family of pixel-wise arithmetic operations — add, subtract, multiply, divide, log, exp, polynomial, complement, square, and square root — for combining images, correcting intensities, and transforming pixel value distributions.
19 Operations
Image-to-image and image-to-scalar arithmetic
Point-Wise Processing
Each pixel processed independently
Dynamic Range Management
Log compresses, exp expands, polynomial remaps
Overflow/Underflow Clamping
Results clamped to valid bit-depth range
Operations Reference
Simplified
The arithmetic operations do basic math on pixels: add or subtract a value to brighten/darken, multiply to adjust contrast, divide by a reference for normalization. Logarithms compress the range of bright values (useful for 16-bit data). Complement inverts bright↔dark. All operations work pixel by pixel.
When to Use Which
Common arithmetic workflows in tissue image processing:
Background Correction
Subtract images or Divide images — Subtract a background estimate from the signal, or divide by a flat-field reference for illumination normalization. Division is preferred when the artifact is multiplicative (uneven illumination); subtraction when it's additive (constant offset).
Channel Combination
Add weighted images — Combine signals from multiple channels with user-defined weights. Useful for creating virtual channels from partially overlapping fluorophores.
Inversion
Complement — Inverts the image so that bright becomes dark and vice versa. Essential for converting brightfield hematoxylin (dark nuclei on light background) to fluorescence-like representation (bright nuclei on dark background) for detection engines that expect fluorescence-style input.
Dynamic Range
Logarithm — Compresses the wide dynamic range of 16-bit fluorescence images. Also the basis of the OD transform (see Optical Density Conversion).
Polynomial — General-purpose intensity remapping when log/exp/sqrt aren't the right curve shape.
Simplified
Use Subtract to remove background. Use Divide to correct uneven illumination. Use Complement to invert hematoxylin for detection. Use Log to compress 16-bit dynamic range. Use Add weighted to blend channels. Most pipelines use just 2–3 of these operations.