Affiliations: School of Systems Engineering, University of Reading,
Whiteknights, Reading RG6 6AY, UK | Visiting professor, concurrently at various UK
universities
Abstract: This paper describes a method for reconstructing 3D frontier points,
contour generators and surfaces of anatomical objects or smooth surfaces from a
small number, e.g. 10, of conventional 2D X-ray images. The X-ray images are
taken at different viewing directions with full prior knowledge of the X-ray
source and sensor configurations. Unlike previous works, we empirically
demonstrate that if the viewing directions are uniformly distributed around the
object's viewing sphere, then the reconstructed 3D points automatically cluster
closely on a highly curved part of the surface and are widely spread on smooth
or flat parts. The advantage of this property is that the reconstructed points
along a surface or a contour generator are not under-sampled or
under-represented because surfaces or contours should be sampled or represented
with more densely points where their curvatures are high. The more complex the
contour's shape, the greater is the number of points required, but the greater
the number of points is automatically generated by the proposed method. Given
that the number of viewing directions is fixed and the viewing directions are
uniformly distributed, the number and distribution of the reconstructed points
depend on the shape or the curvature of the surface regardless of the size of
the surface or the size of the object. The technique may be used not only in
medicine but also in industrial applications.
Keywords: 3D reconstruction, apparent contour, contour generator, epipolar, frontier point, multiview, space curve, surface points, surface reconstruction, X-ray
