An Alternative Approach to Computing Shape Orientation with an Application to Compound Shapes

We consider the method that computes the shape orientation as the direction α that maximises the integral of the length of projections, taken to the power of 2N, of all the straight line segments whose end points belong to the shape, to a line that has the slope α. We show that for N=1 such a definition of shape orientation is consistent with the shape orientation defined by the axis of the least second moment of inertia. For N>1 this is not the case, and consequently our new method can produce different results. As an additional benefit our approach leads to a new method for computation of the orientation of compound objects.