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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.
List of contents
1 Introduction.- 1.1 Neural Methods.- 1.2 Plan of the Book.- 2 Computational Neural Networks.- 2.1 Introduction.- 2.2 Amari and Hopfield Networks.- 2.3 A Discrete Neural Network for Vision.- 2.4 Discussion.- 3 Static Stereo.- 3.1 Introduction.- 3.2 Depth from Two Views.- 3.3 Estimation of Intensity Derivatives.- 3.4 Matching Using a Network.- 3.5 Experimental Results.- 3.6 Discussion.- 4 Motion Stereo-Lateral Motion.- 4.1 Introduction.- 4.2 Depth from Lateral Motion.- 4.3 Estimation of Measurement Primitives.- 4.4 Batch Approach.- 4.5 Recursive Approach.- 4.6 Matching Error.- 4.7 Detection of Occluding Pixels.- 4.8 Experimental Results.- 4.9 Discussion.- 5 Motion Stereo-Longitudinal Motion.- 5.1 Introduction.- 5.2 Depth from Forward Motion.- 5.3 Estimation of the Gabor Features.- 5.4 Neural Network Formulation.- 5.5 Experimental Results.- 5.6 Discussion.- 6 Computation of Optical Flow.- 6.1 Introduction.- 6.2 Estimation of Intensity Values and Principal Curvatures.- 6.3 Neural Network Formulation.- 6.4 Detection of Motion Discontinuities.- 6.5 Multiple Frame Approaches.- 6.6 Experimental Results.- 6.7 Discussion.- 7 Image Restoration.- 7.1 Introduction.- 7.2 An Image Degradation Model.- 7.3 Image Representation.- 7.4 Estimation of Model Parameters.- 7.5 Restoration.- 7.6 A Practical Algorithm.- 7.7 Computer Simulations.- 7.8 Choosing Boundary Values.- 7.9 Comparisons to Other Restoration Methods.- 7.10 Optical Implementation.- 7.11 Discussion.- 8 Conclusions and Future Research.- 8.1 Conclusions.- 8.2 Future Research.
