Minkowski compactness measure
Martinez-Ortiz, C; Everson, R
Date: 31 October 2013
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Publisher DOI
Abstract
Many compactness measures are available in the
literature. In this paper we present a generalised compactness
measure Cq(S) which unifies previously existing definitions of
compactness. The new measure is based on Minkowski distances
and incorporates a parameter q which modifies the behaviour of
the compactness measure. Different ...
Many compactness measures are available in the
literature. In this paper we present a generalised compactness
measure Cq(S) which unifies previously existing definitions of
compactness. The new measure is based on Minkowski distances
and incorporates a parameter q which modifies the behaviour of
the compactness measure. Different shapes are considered to be
most compact depending on the value of q: for q = 2, the most
compact shape in 2D (3D) is a circle (a sphere); for q → ∞,
the most compact shape is a square (a cube); and for q = 1, the
most compact shape is a square (a octahedron).
For a given shape S, measure Cq(S) can be understood as a
function of q and as such it is possible to calculate a spectum of
Cq(S) for a range of q. This produces a particular compactness
signature for the shape S, which provides additional shape
information.
The experiments section of this paper provides illustrative
examples where measure Cq(S) is applied to various shapes and
describes how measure and its spectrum can be used for image
processing applications.
Computer Science
Faculty of Environment, Science and Economy
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