This book discusses mathematical foundations of statistical inference for building a 3-D model of the environment from image and sensor data that contain noise - a central task for autonomous robots guided by video cameras and sensors. A theoretical accuracy bound is derived for the optimization procedure for maximizing the reliability of the estimation based on noisy data, and practical computational schemes that attain that bound are derived. Many synthetic and real data examples are given to demonstrate that conventional methods are not optimal and how accuracy improves if truly optimal methods are employed.

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