Comparison of Different Approaches for the Calculation of Projective Symmetry or the Axis of a SHGC

Calculating the projective transformation which maps the two sides of a symmetric contour onto each other is an important step in the recognition of objects with symmetric contours, such as planar symmetric objects or surfaces of revolution. Within a more complex recognition system, many such calculations have to be performed as part of the hypotheses generation process, and it is therefore essential that the calculations are both fast as well as accurate. This paper compares different approaches and shows that the method selected can critically influence performance. The discussion trivially extends to finding the axis of a straight homogeneous generalised cylinder, even though its contour will not, in general, exhibit any symmetries.