Logical Operations | StrataQuest Glossary

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Definition

Logical Operations apply AND, OR, NOT and XOR to binary or grayscale images, one pixel position at a time. Each result is a new mask or composite image, ready for the next step of a BOM pipeline.

Four Boolean Operations

AND, OR, NOT, XOR for spatial set logic

Binary Mask Algebra

Combine spatial regions with set operations

Grayscale Bitwise

Operations work on integer bit representations

Pipeline Logic Building Blocks

Create complex spatial conditions from simple masks

Operations Reference

Operation	Inputs	Set Operation	Truth Table
And	Image A, Image B	Intersection (A ∩ B)	1 only where both inputs are 1
And (with value)	Image, Value	Bitwise AND of every pixel with one number	Each bit is 1 only where the pixel and Value both have 1
Or	Image A, Image B	Union (A ∪ B)	1 where either input is 1
Or (with value)	Image, Value	Bitwise OR of every pixel with one number	Each bit is 0 only where the pixel and Value both have 0
Not	Image A	Complement (Aᶜ)	Inverts: 0→1, 1→0
Xor	Image A, Image B	Symmetric Difference (A △ B)	1 where inputs differ
Xor (with value)	Image, Value	Bitwise XOR of every pixel with one number	Each bit is 1 where the pixel and Value differ

On binary masks, compound expressions build on these. Three come up often:

A AND NOT B: region A without region B (set difference)
NOT (A OR B): everything outside both regions
(A OR B) AND NOT (A AND B): the same as XOR (exclusive regions)

Simplified

AND keeps the pixels that are white in both images, the overlap. OR keeps pixels white in either. NOT flips black and white. XOR keeps pixels that differ.

Combine masks this way, and 'tumor AND positive-staining' gives you only the overlap.

When to Use Which

Region Intersection (AND)

AND is the most common: it restricts analysis to where two conditions both hold, as in tumor tissue AND positive staining, tissue mask AND ROI mask, or channel-A-positive AND channel-B-positive (co-expression).

Region Combination (OR)

OR combines areas from several sources: tissue masks from different detection methods, several ROI selections, or all the stain-positive areas across channels.

Exclusion (NOT)

NOT makes the inverse mask. NOT tissue is the glass, or background, and NOT tumor is stroma, normal tissue and necrosis. Paired with AND, NOT excludes: tissue AND NOT necrosis is the viable tissue.

Mutual Exclusion (XOR)

XOR finds the regions unique to each mask. Marker-A-positive XOR marker-B-positive marks cells that express one marker but not both, which separates exclusive from co-expressing populations in their spatial context.

Simplified

Use AND to find where two masks overlap; it is the most common. Use OR to combine masks, NOT to invert one, and XOR to find areas that belong to one mask but not both. Chain them for conditions like 'tumor AND stain-positive AND NOT necrosis.'

Connected Terms

Threshold & Compare Category Related
Arithmetic Operations Category Related
Tissue Detection Related
Classifier Related
Morphological Operations Category
Optical Density Conversion Category
Sobel Filter Category
Median Filter Category

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