This book investigates the mathematical foundations of statistical inference for constructing accurate 3-D environmental models from noisy sensor and image data. It addresses the central task for autonomous robots relying on video cameras and sensors, deriving a theoretical accuracy bound for optimization procedures to maximize reliability from noisy inputs. Practical computational schemes that achieve this bound are then presented, supported by numerous synthetic and real data examples. The work demonstrates the sub-optimality of conventional methods and the benefits of employing truly optimal approaches.

The book is positioned as a valuable resource for academic and industrial institutions involved in computer science, robotics, and advanced technology. Its focus on theoretical accuracy bounds and practical computational schemes suggests a rigorous approach to solving complex problems in 3D reconstruction from noisy data. The inclusion of numerous examples indicates a commitment to demonstrating the practical implications and advantages of the proposed statistical optimization methods over conventional techniques.