Compactness measure for 3D shapes

In this paper we propose a new compactness measure which defines the degree to which a 3D shape differs from a perfect sphere. The new measure is easy to compute and satisfies the following desirable properties: - it ranges over (0, 1] and gives the measured compactness equal to 1 if and only if the measured shape is a sphere; - it is invariant with respect to translations, rotations and scaling. Compared with a naive 3D compactness measure, which consider the relation between the shape volume and surface area, the new measure performs better in the case of shapes with deep intrusions and in case of compound shapes. In contrast to such a compactness measure, the new measure depends on the mutual position of the components inside a compound shape. Several experimental results are provided in order to illustrate the behaviour of the new measure.