Statistical Optimization for Geometric Computation
Kenichi Kanatani
ISBN 10: 0486443086 ISBN 13: 9780486443089
Editore: Dover Publications Inc., US, 2005
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Codice articolo LU-9780486443089
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This text for graduate students discusses the mathematical foundations of statistical inference for building three-dimensional models from image and sensor data that contain noise--a task involving autonomous robots guided by video cameras and sensors.
The text employs a theoretical accuracy for the optimization procedure, which maximizes the reliability of estimations based on noise data. The numerous mathematical prerequisites for developing the theories are explained systematically in separate chapters. These methods range from linear algebra, optimization, and geometry to a detailed statistical theory of geometric patterns, fitting estimates, and model selection. In addition, examples drawn from both synthetic and real data demonstrate the insufficiencies of conventional procedures and the improvements in accuracy that result from the use of optimal methods.
The text employs a theoretical accuracy for the optimization procedure, which maximizes the reliability of estimations based on noise data. The numerous mathematical prerequisites for developing the theories are explained systematically in separate chapters. These methods range from linear algebra, optimization, and geometry to a detailed statistical theory of geometric patterns, fitting estimates, and model selection. In addition, examples drawn from both synthetic and real data demonstrate the insufficiencies of conventional procedures and the improvements in accuracy that result from the use of optimal methods.
Contenuti: 1. Introduction 2. Fundamentals of Linear Algebra 3. Probabilities and Statistical Estimation 4. Representation of Geometric Objects 5. Geometric Correction 6. 3-D Computation by Stereo Vision 7. Parametric Fitting 8. Optimal Filter 9. Renormalization 10. Applications of Geometric Estimation 11. 3-D Motion Analysis 12. 3-D Interpretation of Optical Flow 13. Information Criterion for Model Selection 14. General Theory of Geometric Estimation References Index
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Titolo: Statistical Optimization for Geometric ...
Casa editrice: Dover Publications Inc., US
Data di pubblicazione: 2005
Legatura: Paperback
Condizione: New