Orientation and anisotropy of multi-component shapes from boundary information

We define a method for computing the orientation of compound shapes based on boundary information. The orientation of a given compound shape S   is taken as the direction αα that maximises the integral of the squared length of projections, of all the straight line segments whose end points belong to particular boundaries of components of S   to a line that has the slope αα. Just as the concept of orientation can be extended from single component shapes to multiple components, elongation can also be applied to multiple components, and we will see that it effectively produces a measure of anisotropy since it is maximised when all components are aligned in the same direction. The presented method enables a closed formula for an easy computation of both orientation and anisotropy.

Research highlights► A method is defined for computing the orientation of multiple component shapes. ► A measure of anisotropy is defined for multiple component shapes. ► The proposed orientation and anisotropy values can be computed efficiently in closed form.