Beschreibung
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.
Autorenportrait
Inhaltsangabe1 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.- 2.3.1 A Discrete Network.- 2.3.2 Decision Rules.- 2.4 Discussion.- 3 Static Stereo.- 3.1 Introduction.- 3.2 Depth from Two Views.- 3.3 Estimation of Intensity Derivatives.- 3.3.1 Fitting Data Using Chebyshev Polynomials.- 3.3.2 Analysis of Filter M(y).- 3.3.3 Computational Consideration for the Natural Images.- 3.4 Matching Using a Network.- 3.5 Experimental Results.- 3.5.1 Random Dot Stereograms.- 3.5.2 Natural Stereo Images.- 3.6 Discussion.- 4 Motion Stereo-Lateral Motion.- 4.1 Introduction.- 4.2 Depth from Lateral Motion.- 4.3 Estimation of Measurement Primitives.- 4.3.1 Estimation of Derivatives.- 4.3.2 Estimation of Chamfer Distance Values.- 4.4 Batch Approach.- 4.4.1 Estimation of Pixel Positions.- 4.4.2 Batch Formulation.- 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.- 5.2.1 General Case: Images Are Nonequally Spaced.- 5.2.2 Special Case: Images Are Equally Spaced.- 5.3 Estimation of the Gabor Features.- 5.3.1 Gabor Correlation Operator.- 5.3.2 Computational Considerations.- 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.- 6.2.1 Estimation of Polynomial Coefficients.- 6.2.2 Computing Principal Curvatures.- 6.2.3 Analysis of Filters.- 6.3 Neural Network Formulation.- 6.3.1 Physiological Considerations.- 6.3.2 Computational Considerations.- 6.3.3 Computing Flow Field.- 6.4 Detection of Motion Discontinuities.- 6.5 Multiple Frame Approaches.- 6.5.1 Batch Approach.- 6.5.2 Recursive Algorithm.- 6.5.3 Detection Rules.- 6.6 Experimental Results.- 6.6.1 Synthetic Image Sequence.- 6.6.2 Natural Image Sequence.- 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.- 7.9.1 Inverse Filter and SVD Pseudoinverse Filter.- 7.9.2 MMSE and Modified MMSE Filters.- 7.10 Optical Implementation.- 7.11 Discussion.- 8 Conclusions and Future Research.- 8.1 Conclusions.- 8.2 Future Research.
