Symmetry in Optics and Vision Studies A Data-Analytic Approach Multidisciplinary and Applied Optics Series
Auteurs : Viana Marlos A.G., Lakshminarayanan Vasudevan
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
1. Symmetry Studies 2. Algebraic Aspects 3. Dihedral Decompositions 4. Refraction 5. Dihedral Polynomials 6. Visual Perception of Symmetry 7. Cyclic Reduction of Symbolic Sequences 8. Symmetrically Dependent Observations 9. Additional Aspects and Applications
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 Society’s 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 publ
Date de parution : 12-2019
15.6x23.4 cm
Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).
Prix indicatif 184,47 €
Ajouter au panierMots-clés :
Group Algebra; Dihedral Group; Speckle Studies; Canonical Projections; Eye Imaging; Symmetry Studies; Polarimetry; Canonical Space; Dihedral Wavefront; Irreducible Representation; Visual Field Studies; Frequency Counts; Refraction Power; Vision Screening Program; Retinal Flow; Cyclic Orbits; Extreme-Value Curvature; Refraction Contour; Covariance Structure; Orbit Invariants; Surface Curvature Modeling; Protocol II; Surface Curvature Estimation; Symmetry Perception; Eye Tracking; Canonical Polynomials; Eye Movement; Coherence Matrix; Baker's Models; Visual Perception; Structural Biology; Lie Algebra; Cyclic Sets; Symplectic Optics; Group Theoretical Methods; Optical Aberrations; Posterior Densities; Dioptric Power; Canonical Axes; Symmetry Orbit Data; Toric Surface; Probability Models; Canonical Decomposition; Dihedral Analysis; Oxford County; Symmetry Orbits; Monochromatic Plane Waves; Symmetry Considerations; Symmetry in Physics; Vision Studies; Optical Symmetry; Data-analytic applications; Optical sciences; Multivariate analysis