Measuring conic properties and shape orientations

New methods for computing a shape’s orientation and several shape measures for elongation, linearity, circularity, ellipticity, hyperbolicity, and parabolicity of 2D point sets are outlined. These measures are invariant to rotation, scaling, and translation. They are calculated very quickly as well. Among other things, we discover that the definition of elongation highly correlates with the definition of linearity. All of the shape measures are tested on digital curves and compared with existing methods. All of the methods work in real time. The goal was to find a way of identifying basic shapes in images. The motivation was to be able to use these basic shape descriptors as features in a computer vision system, where more complicated shapes can be seen as collections of basic ones. This way, a computer should one day be able to identify the objects in even the most complicated scenes we deal with in our daily lives.