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

chapter 1|28 pages

Symmetry Studies

chapter 2|34 pages

Algebraic Aspects

chapter 3|6 pages

Dihedral Decompositions

chapter 4|12 pages


chapter 5|8 pages

Dihedral Polynomials

chapter 6|14 pages

Visual Perception of Symmetry

chapter 7|12 pages

Cyclic Reduction of Symbolic Sequences

chapter 8|34 pages

Symmetrically Dependent Observations

chapter 9|34 pages

Additional Aspects and Applications