Boundary based shape orientation

Abstract

The computation of a shape's orientation is a common task in the area of computer vision and image processing, being used for example to define a local frame of reference and is helpful for recognition and registration, robot manipulation, etc. It is usually an initial step or a part of data preprocessing in many image processing and computer vision tasks. Thus, it is important to have a good solution for shape orientation because an unsuitable solution could lead to a big cumulative error at the end of the computing process. There are several approaches to the problem-most of them could be understood as the 'area based' ones, or at least they do not take into account all the boundary points (if a shape orientation measure is based on its encasing rectangle, only the convex hull points count, for example). Thus, the demand for a pure 'boundary based' method, where the orientation of the shape is dependent on the boundary points seems to be very reasonable. Such a method is presented in this paper. We are initially focused on the shapes having polygonal boundaries. We define the orientation of a polygonal shape by the line that maximises the total sum of squared lengths of all the boundary edge projections onto this line. The advantages and limitations of the new method are analysed. Next, we suggested how the method can be adapted in order to be applicable to a wider class than the initial method is. Finally, we introduced another modification of the method in such a way that the modified method can be applied to shapes with arbitrary boundaries. Several illustrative experiments are provided.