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Thought this may be of interest to some.
Don't know if anyone here is playing with tomography (ala CAT or CT scans).
A friend is starting to and this is his first result. Interesting how much
quicker he gets than real iron of a few years ago by using some intelligence
and a modernish processor.


regards


      Russell McMahon
_____________________________



> Russell,
>
> Thought you might like to see my first tomographic reconstruction using
> filtered back-projection.
>
> The original object slice was a 16x16 array with a 4x4 black/white
> checkerboard pattern.  It was scanned at 128 angles (equally spaced over a
> range of 180 degrees) using 16 parallel beams, and reconstructed as a
64x64
> array.  Note that the reconstructed image looks best when viewed at 25% of
> actual size since this is the size of the original slice data (the
> interpolation to 64x64 adds no image information).
>
> Reconstruction takes about 3.4 seconds on my 450 MHz PIII using 6-byte
reals
> and 1.4 seconds using floats native to the 8087.  With native 8087 floats
> and runtime range-checking off it takes 0.44 seconds.
>
> In 1995 the original implementation in Matlab took over 12 minutes on a
Sun
> Sparc 10, 2.74 seconds on an Intel Paragon (16x i860's running parallel
> Fortran) and 3.29 seconds on a Connection Machine Model CM5 (512
processors
> running parallel Fortran).
>
> The reason that I seem to have done so much better is that the original
> implementations were coded "naively" with all processing done in the inner
> of three nested loops:
>
>     for x_index = 1 to 64
>         for y_index = 1 to 64
>             for angle_index = 1 to 128
>                 evaluate f (x_index, y_index)
>
> In my implementation, I have moved as much processing involved in the
> evaluation of f (x,y) to the outermost loop possible, and used
> pre-calculated trig functions stored in look-up tables.  With a bit of
extra
> effort I'm sure I could do better still.
>
> I am slowly coming to terms with the maths (its not as simple as the toy
> demo on the web might suggest) and believe it should also be possible to
do
> better in terms of the quality of the reconstructed image.
>
> Regards,
>
>     Ken

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