An arithmetic overlap value can be two, while a logical intersection is a truth value. They answer different mask questions.
Define the combination operation
Element-wise logical AND is true where both inputs are true. Arithmetic addition instead sums numerical values at corresponding positions. A combined image therefore needs the operation and foreground encoding beside it before an overlap value is interpreted as membership or a count. Primary reference: NumPy element-wise logical AND.
For an original worksheet, retain the two masks and their common coordinate support. Specify numeric conversion when demonstrating sums of binary codes. Do not assume a programming language's boolean addition has the same storage behavior as explicitly summing integer arrays.
Compare fictional aligned masks
Use integer masks A = [1,0,1] and B = [0,1,1], with nonzero meaning foreground. Their logical intersection is [false,false,true], represented as [0,0,1] if converted to these integer codes. Their arithmetic sum is [1,1,2].
The last sum value two records two contributions at one location, not two separate physical objects there. Testing sum greater than zero would describe the union for this defined binary encoding, while testing both foreground conditions describes the intersection. The invented masks provide no actual pack segmentation.
Keep membership and count separate
Prepare an original truth table for each coordinate, recording A, B, logical intersection and integer sum separately. If a later process expects only binary membership, preserve the conversion from a numerical count explicitly. Check that both masks refer to the same spatial frame before combining their values.
This guide claims no HM image-analysis behavior. Its reader decision is whether an overlap calculation represents shared membership, either-source membership or a count of contributions. Those quantities should not inherit one another's meaning merely because the display can make them look similar.
Customer Questions
What is the fictional intersection in integer codes?
[0,0,1].
What is the integer sum?
[1,1,2].
Does sum two identify two physical objects?
No. It records contributions under the defined arithmetic.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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