Please look here:
http://en.wikipedia.org/wiki/Ambiguous_image[
^].
Perhaps, for you these ideas are trivial, but this page clearly illustrates: the problem is not resolvable in the comment sense of the word "solution". This is so-called
ill-posed problem.
Please read on the concept of
ill-posed problem. The classical Tikhonov's theory of ill-posed problems introduces the criteria for a
well-posed problem of a wide class. For ill-posed problems, the concept of
quasi-solution is introduced. The problem you are dealing with belongs to the class of those ill-posed problems. You probably understand that each set of 2-dimensional image, strictly speaking, allows for infinite number of solutions. The software should seek for "most likely" or "simplest" one, which is also hard to defined and cannot be defined in all cases.
Please see:
http://en.wikipedia.org/wiki/Well-posed_problem[
^],
http://en.wikipedia.org/wiki/Tikhonov_regularization[
^].
I just mean to explain that the problem is extremely difficult; so you should not expect too good results, no matter what you use. There are many cases (some of them are artificially designed), when even a human being makes mistakes.
—SA