A family of cubeness measures

Abstract

In this paper we introduce a family of cubeness measures, Cβ(S), as a generalisation of the cubeness measures introduced in Martinez-Ortiz and Zunić (Lecture notes in computer science, vol 5856, pp 716-723, 2009). All measures from the newfamily retain all desirable properties from the original measure: they range over (0, 1] and reach 1 only when the given shape is a cube; they are invariant with respect to rotation, translation, and scaling transformations. The new measures depend on a parameter β which controls the influence that each individual point from the shape considered contributes to the measure computed. This allows us to create a family of descriptors {Cβ(S) | β ε (?3, 0) ? (0,∞)}, such that the behaviour of any measure Cβ(S), from the family, varies depending on the assigned parameter β. Because different cubeness measures produce a different shape rankings, using several cubeness measures Cβ(S) (obtained for different β values) increases the classification efficiency in certain shape classification tasks, as is demonstrated on several examples.