Symmetry Studies in Optics and Vision Science: A Data-Analytic Approach, 1st Edition (Hardback) book cover

Symmetry Studies in Optics and Vision Science

A Data-Analytic Approach, 1st Edition

By Marlos A.G. Viana, Vasudevan Lakshminarayanan

CRC Press

224 pages | 60 B/W Illus.

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Hardback: 9781466583979
pub: 2019-12-30
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This book will present an introduction to the foundations, interpretations, and data-analytic applications of symmetry studies with an emphasis on applications in optical sciences.. Symmetry studies connects algebraic and statistical methods for data summary and inference. In addition, this book demonstrates the usefulness of a unified view of algebra and symmetry studies to address data-analytic questions in optics and vision science. Readers should have an understanding of calculus and linear algebra as well as introductory statistics; The book reviews finite group theory in the introductory chapters. Computational tools used in the text are available for download in the form of Mathmatica® notebooks or R code.

Table of Contents

Symmetry Studies. Experimental Results and Symmetry. Data Reduction under Symmetry Considerations. Symmetry Orbits. Dihedral Analysis. Probability Models and Symmetry Orbits. Inference for Symmetry Orbit Data. Lie Algebraic Treatment of Dioptric Power and Optical Aberrations. Symplectic Optics. The Lie Algebra of Visual Perception. Symmetry Perception Studies. Eye Movement/Tracking Studies. Surface Curvature Estimation and Modeling. Covariance Structure for Extreme-Value Curvature Studies. Retinal Flow Studies. Refraction Power. Visual Field Studies. Dihedral Wavefront Studies. Polarimetry. Eye Imaging Enhancing Studies. Speckle Studies.

About the Authors

Marlos Viana, Ph.D., had his tenure with the faculty of the University of Illinois at Chicago for nearly 30 years where he worked in the area of applications of algebraic methods to the analysis and interpretation of data associated with symmetry conditions, with particular emphases in linear optics, corneal topography, polarimetry, molecular chirality, decompositions of entropy, and short symbolic sequences. Professor Viana has advised, taught, and collaborated with students at all graduate and undergraduate levels in a variety of theoretical and applied fields since 1978 when a faculty member of the Federal University at Rio de Janeiro. His research also includes the development of methods for combined statistical inference, the assessment of screening tests and instrumentation, the covariance structures of dependent order statistics and in applications of Bayesian inference. Professor Viana is a member of several editorial boards and the co-editor of Volumes 287 and 516 of the American Mathematical Society's Contemporary Mathematics series.

Vasudevan Lakhsminarayanan is a professor of vision science, physics, electrical and computer engineering and systems design engineering at the University of Waterloo. He was a "KITP Scholar" at the Kavli Institute for Theoretical Physics at UC Santa Barbara, and has held research and teaching and visiting professorship positions at UC Irvine, UC Berkeley, University of Michigan, the University of Missouri, Indian Institute of Technology, Delhi, Universita degli Studii di Brescia, amongst others. He is a founding member of the UNESCO Active Learning in Optics and Photonics Program and serves on optics advisory board of the International Center for Theoretical Physics (Trieste, Italy). He is a consultant to the ophthalmic medical devices group of the FDA. He is a Fellow of the APS, AAAS, OSA, SPIE, Institute of Physics (UK), Optical Society of India, amongst others. He has published over 300 articles in areas ranging from optical physics and engineering, image processing, cognitive neuroscience, quantum physics, ophthalmology and optometry, biomedical engineering, and history of science as well as science policy. He is the co-author/co-editor of 21 books. His numerous awards include: the SPIE Optics educator award (2011) and the Esther Hoffman Beller medal of OSA (2013).

About the Series

Multidisciplinary and Applied Optics

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Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Physics