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.
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.