Abstract: Analytic simulation in computed tomography(CT) generates projection
data for evaluating and improving CT image reconstruction algorithms and has
played an important role in the research and development of x-ray CT. The
simulation is desired to be as realistic as possible while the computation
needs to be efficient and accurate. Early primitive equation-based phantoms
such as Shepp-Logan and FORBILD use only boxes, cylinders, and quadrics to
simulate body parts. The superquadrics have been used in Computer Graphics
since 1980's, and in CT since 1990's. While their more complex shapes make them
more realistic in simulation, the difficulties in solving their equations
increase dramatically, which restricts their use, especially in ray-tracing and
x-ray transform. Zhu et al. developed an algorithm for ray-intersecting the
superellipsoid and used it to build a thorax phantom. No algorithms for
ray-intersecting the supertoroid, however, are known up to now to the best of
our knowledge. In this paper we propose such an algorithm and use it in
computation of x-ray transform. The algorithm was tested by a phantom
consisting of the top portion of vertebrae and a few ribs. Cone-beam data were
produced from the phantom, and then used to reconstruct the phantom.
