Measuring Squareness and Orientation of Shapes
Authors: Paul L. Rosin, Joviša Žunić
DOI: 10.1007/s10851-010-0221-7
Abstract:
In this paper we propose a measure which defines the degree to which a shape differs from a square. The new measure is easy to compute and being area based, is robust -e.g., with respect to noise or narrow intrusions. Also, it satisfies the following desirable properties:
- it ranges over (0, 1] and gives the measured squareness equal to 1 if and only if the measured shape is a square;
- it is invariant with respect to translations, rotations and scaling.
In addition, we propose a generalisation of the new measure so that shape squareness can be computed while controlling the impact of the relative position of points inside the shape. Such a generalisation enables a tuning of the behaviour of the squareness measure and makes it applicable to a range of applications. A second generalisation produces a measure, parameterised by δ, that ranges in the interval (0, 1] and equals 1 if and only if the measured shape is a rhombus whose diagonals are in the proportion 1 : δ. The new measures (the initial measure and the generalised ones) are naturally defined and theoretically well founded—consequently, their behaviour can be well understood.
