Boundary based orientation of polygonal shapes

The computation of a shape's orientation is a common task in many areas of computer vision and image processing applications. It is usually an initial step or a part of data preprocessing. There are several approaches to the problem - most of them could be understood as the 'area based' ones. In spite of many unavoidable problems where working with shape boundaries in discrete space, the demand for a pure 'boundary based' method, seems to be very reasonable. Such a method for shapes having polygonal boundaries is presented in this paper. We define the shape orientation by the line that maximises the total sum of squared lengths of projections of all the shape boundary edges onto this line. Advantages and disadvantages of the method are discussed.