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E-raamat: Symmetry in Optics and Vision Studies: A Data-Analytic Approach [Taylor & Francis e-raamat]

(University of Waterloo, Ontario, Canada), (University of Illinois, Chicago, USA)
  • Formaat: 192 pages, 19 Tables, black and white; 60 Illustrations, black and white
  • Sari: Multidisciplinary and Applied Optics
  • Ilmumisaeg: 05-Dec-2019
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9780429102394
Teised raamatud teemal:
  • Taylor & Francis e-raamat
  • Hind: 244,66 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Tavahind: 349,51 €
  • Säästad 30%
  • Formaat: 192 pages, 19 Tables, black and white; 60 Illustrations, black and white
  • Sari: Multidisciplinary and Applied Optics
  • Ilmumisaeg: 05-Dec-2019
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9780429102394
Teised raamatud teemal:
This book presents an introduction to the foundations, interpretations, and data-analytic applications of symmetry studies with an emphasis on applications in optical sciences. Symmetry studies connect group theoretic and statistical methods for data summary and inference. 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 Mathmaticaâ notebooks or R scripts. This book:











Demonstrates the usefulness of a unified view of algebra and symmetry studies to address data-analytic questions in optics and vision science





Offers a brief review of finite group theory and elements of multivariate analysis





Includes various examples from diverse areas of optical science
Preface xi
Authors xv
Chapter 1 Symmetry Studies
1(28)
1.1 Introduction
1(1)
1.2 Bilateral Quantities
1(5)
1.3 Sampling
6(5)
1.4 Joint Bilateral Quantities
11(1)
1.5 Covariance Structures
12(2)
1.6 Visual Fields
14(3)
1.7 Snellen Charts
17(3)
1.8 Nystagmus
20(1)
1.9 Corneal Curvature
20(2)
1.10 Refraction
22(2)
1.11 Extreme Values
24(3)
1.12 Summary
27(2)
Chapter 2 Algebraic Aspects
29(34)
2.1 Introduction
29(1)
2.2 Main Definitions
29(12)
2.3 Group Representations
41(9)
2.4 Canonical Projections
50(2)
2.5 Fourier Transforms
52(3)
2.6 Additional Aspects
55(6)
2.7 Summary
61(2)
Chapter 3 Dihedral Decompositions
63(6)
3.1 Introduction
63(1)
3.2 The Stokes Coefficients
63(1)
3.3 The Group Algebra of Compensators
64(1)
3.4 Elementary Optical Instruments
64(1)
3.5 Coherence Matrix Formalism
65(1)
3.6 Data-Analytic Considerations
66(2)
3.7 Summary
68(1)
Chapter 4 Refraction
69(12)
4.1 Introduction
69(1)
4.2 Algebraic Descriptions
70(1)
4.3 Finite Approximations
71(2)
4.4 Conformal Analysis
73(3)
4.5 The Refraction Study
76(3)
4.6 Summary
79(2)
Chapter 5 Dihedral Polynomials
81(8)
5.1 Introduction
81(1)
5.2 Dihedral Polynomials
81(3)
5.3 Between-Class Relations
84(1)
5.4 Applications
85(3)
5.5 Summary
88(1)
Chapter 6 Visual Perception of Symmetry
89(14)
6.1 Introduction
89(2)
6.2 A Symmetry Perception Experiment
91(3)
6.3 The Elementary Orbits
94(4)
6.4 Entropy Invariants
98(3)
6.5 Product Orbit
101(1)
6.6 Summary
102(1)
Chapter 7 Cyclic Reduction of Symbolic Sequences
103(12)
7.1 Introduction
103(1)
7.2 Symbolic Sequences
103(1)
7.3 Injective Sequences
104(1)
7.4 Scalar Quantifications
104(1)
7.5 Orbit Invariance
105(1)
7.6 Invariant Reductions
106(1)
7.7 Entropy Invariants
107(4)
7.8 Dihedral Fourier Analysis
111(2)
7.9 Summary
113(2)
Chapter 8 Symmetrically Dependent Observations
115(34)
8.1 Introduction
115(1)
8.2 Models and Assumptions
116(1)
8.3 The Joint Covariance Structure
116(2)
8.4 Maximum Likelihood and Large-Sample Estimates
118(2)
8.5 Visual Acuity Data Applications
120(3)
8.6 Block-Equicorrelated Observations
123(5)
8.7 Intraocular Pressure Data Applications
128(2)
8.8 Linearizations of Ordered Symmetric Observations
130(7)
8.9 Concomitants of Order Statistics
137(8)
8.10 Bilateral Hemispherical Data Applications
145(3)
8.11 Summary
148(1)
Chapter 9 Additional Aspects and Applications
149(34)
9.1 Chromatic-Spatial Decompositions
149(5)
9.2 Dihedral Summaries of Visual Field Data
154(4)
9.3 Actions on Mappings
158(5)
9.4 Local and Global Symmetries
163(7)
9.5 Entropy and Symmetry
170(3)
9.6 Matrix and Transformation Groups
173(10)
Appendix 183(2)
Bibliography 185(6)
Index 191
Marlos Viana, Ph.D., served on 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 emphasis 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 he first joined the faculty of the Federal University at Rio de Janeiro, Brazil. 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 Societys Contemporary Mathematics series.

Vasudevan Lakshminarayanan 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, 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, among others. He is a founder 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 US FDA (Food and Drug Administration) and is a Fellow of the APS, AAAS, OSA, SPIE, Institute of Physics (United Kingdom), Optical Society of India, among others. He has published over 300 articles in areas ranging from optical physics and engineering, image and signal processing, cognitive neuroscience, quantum physics, ophthalmology, optometry, biomedical engineering, history of science as well as science policy. He is the coauthor/coeditor of 22 books. His numerous awards include the SPIE Optics Educator award (2011) and the Esther Hoffman Beller medal of OSA (2013).