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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.