This monograph is an outgrowth of the authors' recent research on the
de- velopment of algorithms for several low-level vision problems using
artificial neural networks. Specific problems considered are static and
motion stereo, computation of optical flow, and deblurring an image.
From a mathematical point of view, these inverse problems are ill-posed
according to Hadamard. Researchers in computer vision have taken the
"regularization" approach to these problems, where one comes up with an
appropriate energy or cost function and finds a minimum. Additional
constraints such as smoothness, integrability of surfaces, and
preservation of discontinuities are added to the cost function
explicitly or implicitly. Depending on the nature of the inver- sion to
be performed and the constraints, the cost function could exhibit
several minima. Optimization of such nonconvex functions can be quite
involved. Although progress has been made in making techniques such as
simulated annealing computationally more reasonable, it is our view that
one can often find satisfactory solutions using deterministic
optimization algorithms.