 ### Proceedings Paper

New measure for the rectilinearity of polygons
Author(s): Jovisa Zunic; Paul L. Rosin
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Paper Abstract

A polygon Pis said to be rectilinear if all interior angles of P belong to the set {π/2, 3π/2}. In this paper we establish the mapping R(P)=(π/(π-2x√2))⊗(maxα∈[0,2π] ((P1(P,α)/√2⊗P2(P))-((2√2)/π)) where P is an arbitrary polygon, P2(P) denotes the Euclidean perimeter of P, while P1(P,α) is the perimeter in the sense of l1 metrics of the polygon obtained by the rotation of P by angle α with the origin as the center of the applied rotation. It turns out that R(P) can be used as an estimate for the rectilinearity of P. Precisely, R(P) has the following desirable properties: - any polygon P has the estimated rectilinearity R(P) which is a number from [0,1]; - R(P)=1 if and only if P is a rectilinear polygon; - infp∈II R(P) = 0, where II denotes the set of all polygons - a polygon's rectilinearity measure is invariant under similarity transformations. The proposed rectilinearity measure can be an alternative for the recently described measure R1(P)1. Those rectilinearity measures are essentially different since there is no monotonic function f, such that f(R1(P))= R(P), that holds for all P ∈ II. A simple procedure for computing R(P) for a given polygon P is described as well.

Paper Details

Date Published: 24 November 2002
PDF: 11 pages
Proc. SPIE 4794, Vision Geometry XI, (24 November 2002); doi: 10.1117/12.453591
Show Author Affiliations
Jovisa Zunic, Cardiff Univ. (United Kingdom)
Paul L. Rosin, Cardiff Univ. (United Kingdom)

Published in SPIE Proceedings Vol. 4794:
Vision Geometry XI
Longin Jan Latecki; David M. Mount; Angela Y. Wu, Editor(s)

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