On the orientability of shapes

The orientation of a shape is a useful quantity, and has been shown to affect performance of object recognition in the human visual system. Shape orientation has also been used in computer vision to provide a properly oriented frame of reference, which can aid recognition. However, for certain shapes, the standard moment-based method of orientation estimation fails. We introduce as a new shape feature shape orientability, which defines the degree to which a shape has distinct (but not necessarily unique) orientation. A new method is described for measuring shape orientability, and has several desirable properties. In particular, unlike the standard moment-based measure of elongation, it is able to differentiate between the varying levels of orientability of n-fold rotationally symmetric shapes. Moreover, the new orientability measure is simple and efficient to compute (for an n-gon we describe an O(n) algorithm).