Minkowski compactness measure

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.Published in: Computational Intelligence (UKCI), 2013, 13th UK Workshop, Guildford UK. Date of Conference: 9-11 Sept. 2013Many 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

Natural Parameterization

The objective of this project has been to develop an approach for imitating physical objects with an underlying stochastic variation. The key assumption is that a set of “natural parameters” can be extracted by a new subdivision algorithm so they reflect what is called the object’s “geometric DNA”. A case study on one hundred wheat grain crosssections (Triticum aestivum) showed that it was possible to extract thirty-six such parameters and to reuse them for Monte Carlo simulation of “new” stochastic phantoms which possessthe same stochastic behavior as the “original” cross-sections