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.