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What is the unit of compactness of a region?

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What is the unit of compactness of a region?

(a) Meter

(b) Meter2

(c) No units

(d) Meter-1

This question was addressed to me by my college director while I was bunking the class.

This intriguing question comes from Regional Descriptors topic in division Representation and Description of Digital Image Processing

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Right answer is (c) No units

For explanation I would say: The compactness of a region is defined as (perimeter)2/area. Thus, the compactness of a region is a dimensionless quantity.

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