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Minkowski Difference


The Minkowski difference of sets A and B is used in two related senses. The pointwise difference is

 A-B={a-b:a in A, b in B}=A+(-B),

where the last operation is a Minkowski sum. The geometric or morphological difference is

 A circleminus B={x:x+B subset= A}.

The latter operation is also called erosion. Neither operation is generally an inverse of Minkowski addition.


See also

Minkowski Sum, Set Difference

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References

Schneider, R. Convex Bodies: The Brunn-Minkowski Theory. Cambridge, England: Cambridge University Press, 1993.

Cite this as:

Weisstein, Eric W. "Minkowski Difference." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MinkowskiDifference.html

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