Torsten has a tool called symmetry_plane that can be used to find the single plane of symmetry separating the image. The command line options look like this:

> symmetry_plane -h

Compute volume image symmetry plane.
(C) 1997-2007 Torsten Rohlfing  [build 3866M]

Usage: symmetry_plane [options] imagepath

Supported options:

-h, --help	Print this help text.
-v, --verbose	Turn on verbosity mode.

Optimization:
-a, --accuracy	Accuracy (final optimization step size in [mm].
-s, --sampling	Resampled image resolution.
-l, --levels	Number of resolution levels.

Pre-computed symmetry:
--output-only	Give symmetry parameters [Rho Theta Phi] as option, skip search.
--output-only-file	Read symmetry parameters from file, skip search.

Data pre-processing:
--min-value	Force minumum data value.
--max-value	Force maximum data value.

Output:
-c, --cubic	Use cubic rather than trilinear interpolation.
-o, --outfile	File name for symmetry plane parameter output.
-P, --pad-out	Padding value for output images.
--mark-value	Data value to mark (draw) symmetry plane.
--write-marked	File name for output image with marked symmetry plane.
--write-aligned	File name for symmetry plane-aligned output image.
--mark-aligned	Mark symmetry plane in aligned output image.
--write-diff	File name for mirror difference image.
--write-mirror	File name for image mirrored w.r.t. symmetry plane.

As you can see a variety of output options are available. The basic symmetry plane output looks like this:

plane {
        origin 209.6750641 209.6750641 40.5 
        rho 3.400000
        theta -1.091245
        phi 90.000000
        normal 0.9998186339 -0.0190446653 -4.371139e-08 
}

There is a simple function called FindPlaneFromPointAndNormal in my Geometry.R of my R analysis suite to find the standard definition of the equation of a plane from this information.