Kenichi Kanatani Knihy

This text for graduate students discusses the mathematical foundations of statistical inference for building three-dimensional models from image and sensor data that contain noise--a task involving autonomous robots guided by video cameras and sensors.The text employs a theoretical accuracy for the optimization procedure, which maximizes the reliability of estimations based on noise data. The numerous mathematical prerequisites for developing the theories are explained systematically in separate chapters. These methods range from linear algebra, optimization, and geometry to a detailed statistical theory of geometric patterns, fitting estimates, and model selection. In addition, examples drawn from both synthetic and real data demonstrate the insufficiencies of conventional procedures and the improvements in accuracy that result from the use of optimal methods.

Focusing on the foundational mathematics of Hamilton, Grassmann, and Clifford, this book uniquely presents geometric algebra by first detailing individual algebras before illustrating their integration. It includes historical context and exercises to deepen understanding of the mathematical theories essential for complex geometric computations. Additionally, it offers practical applications for 3D modeling in computer graphics and computer vision, making it valuable for both theoretical insights and practical skills.

Focusing on geometric interpretations, this book bridges linear algebra with pattern information processing, particularly in analyzing high-dimensional data relevant to computer vision and graphics. It covers essential concepts like projection, spectral decomposition, and singular value decomposition, illustrating their applications in least-squares solutions and covariance matrices. The text emphasizes visualizing abstract spaces and includes practical examples, such as reconstructing 3D locations from camera views, to enhance understanding of linear algebra's role in data analysis amidst noise.

The book delves into the computational analysis of 3D rotation, emphasizing its crucial role in various applications such as 3D sensing with cameras and sensors, modeling for computer vision and graphics, and robot motion control and simulation. By prioritizing computational techniques over traditional motion analysis, it offers a focused exploration of how 3D rotation impacts these fields, making it a valuable resource for professionals and researchers interested in advanced 3D applications.

This classroom-tested and easy-to-understand textbook/reference describes the state of the art in 3D reconstruction from multiple images, taking into consideration all aspects of programming and implementation. Unlike other computer vision textbooks, this guide takes a unique approach in which the initial focus is on practical application and the procedures necessary to actually build a computer vision system. The theoretical background is then briefly explained afterwards, highlighting how one can quickly and simply obtain the desired result without knowing the derivation of the mathematical detail. Features: reviews the fundamental algorithms underlying computer vision; describes the latest techniques for 3D reconstruction from multiple images; summarizes the mathematical theory behind statistical error analysis for general geometric estimation problems; presents derivations at the end of each chapter, with solutions supplied at the end of the book; provides additional material at anassociated website.