Publication

Measuring shape rectangularity

Dragisa Zunic
2011
Journal Articles

Abstract

A new method for measuring shape rectangularity is introduced. The new shape measure is invariant with respect to similarity transformations, ranges over the interval (0,1] and picks the value 1 if and only if the measured shape is a rectangle. The measure is theoretically well founded and has a clear geometric meaning, i.e. it indicates how the shape considered differs from a rectangle. So, the measure behaviour can be predicted to some extent, which is always an advantage.

Official source

https://infoscience.epfl.ch/entities/publication/4179938a-c616-434c-beca-c3ae19749e8f

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Dragisa Zunic
2011
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/4179938a-c616-434c-beca-c3ae19749e8f

About this result

Related concepts (32)

Outer measure

In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer measures was first introduced by Constantin Carathéodory to provide an abstract basis for the theory of measurable sets and countably additive measures.

Σ-finite measure

In mathematics, a positive (or signed) measure μ defined on a σ-algebra Σ of subsets of a set X is called a finite measure if μ(X) is a finite real number (rather than ∞), and a set A in Σ is of finite measure if μ(A) < ∞. The measure μ is called σ-finite if X is a countable union of measurable sets each with finite measure. A set in a measure space is said to have σ-finite measure if it is a countable union of measurable sets with finite measure. A measure being σ-finite is a weaker condition than being finite, i.

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In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge.

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