Fast image transforms using Diophantine methods

Many image transformations in computer vision involve a pipeline when
an initial integer image is processed with floating point computations
for purposes of symbolic information.  Traditionally, in the interests
of time, the floating point computation is approximated by integer
computation where the integerization process requires a guess of a
integer.  Examples of this phenomenon include the discretization
interval of $\rho$ and $\theta$ in the accumulator array in classical
Hough transform and in geometric manipulation of images
(e.g. rotation, where a new grid is overlaid on the image).

The result of incorrect discretization is either a poor quality visual
image necessitating a ``kludge'' to cleanup, or worse, hampers
measurements of critical parameters such as density or length in high
fidelity machine vision.  In this paper, we present a method that uses
the theory of basis reduction in Diophantine approximations; the
method outperforms prior integer based computation {\em without}
sacrificing accuracy (subject to machine epsilon).