Human and Computer Vision -- Neuronal Pathways of Vision -- Color -- Linear Tools of Vision -- Discrete Images and Hilbert Spaces -- Continuous Functions and Hilbert Spaces -- Finite Extension or Periodic Functions—Fourier Coefficients -- Fourier Transform—Infinite Extension Functions -- Properties of the Fourier Transform -- Reconstruction and Approximation -- Scales and Frequency Channels -- Vision of Single Direction -- Direction in 2D -- Direction in Curvilinear Coordinates -- Direction in ND, Motion as Direction -- World Geometry by Direction in N Dimensions -- Vision in Multiple Directions -- Group Direction and N-Folded Symmetry -- Grouping, Segmentation, and Region Description -- Reducing the Dimension of Features -- Grouping and Unsupervised Region Segregation -- Region and Boundary Descriptors -- Concluding Remarks.

This introductory textbook presents the modern signal processing concepts used in computer vision and image analysis in a systematic and mathematically coherent way. For the first time in a textbook on image processing, single direction, group direction, corners and edges, Hough transform, and motion estimation are developed in a principled way using direction tensors as the unifying concept. The topics presented include Hilbert spaces, the Fourier transform, scale analysis, direction fields, structure tensors, motion tensors, the Hough transform, grouping, and segmentation. Directional signal processing, an increasingly crucial element of computer vision for which neural circuits exist in human vision, is dealt with in depth by use of tensors. All chapters are richly illustrated, with color graphics from cover to cover; applications are studied in various fields, including biometric person authentication, texture analysis, optical character recognition, and motion estimation and tracking; and exercises help the sudent verify progress. Developed out of courses given by the author, this introductory textbook addresses advanced undergarduates as well as master and PhD students in computer science, engineering, mathematics, and in other disciplines where techniques from computer vision, image processing, visual computation and signal analysis are applied.