Symmetry in Optics and Vision Studies: A Data-Analytic Approach [Hardcover]

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 Mathmatica? 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

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.

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 entl#: