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I'm glad to have helped.    The question that you posed is extremely interesting.  A solution to it, even if only for a restricted set of circumstances could be useful in many real world situations.  I suspect that there may be papers on such partial solutions in the image processing academic / research literature.  If I get a chance I'll take a look.

If you find anything, come back and let us know by posting in this thread.

Best regards,

Tom M