Machine perception requires the digitization of physically-sensed signals. During the last ten years, digital range images have become available from a variety of sensors. This book is devoted to the problem of range image understanding with computers. Its aims are to develop a theoretical framework, devise appropriate algorithms, and demonstrate a software implementation of those algorithms that will confirm the usefulness of surfaces in range image understanding. It will be of interest to the researcher studying the theoretical concepts of image understanding, as well as the engineer who wants to implement these concepts in practical applications.Machine perception requires the digitization of physically-sensed signals. During the last ten years, digital range images have become available from a variety of sensors. This book is devoted to the problem of range image understanding with computers. Its aims are to develop a theoretical framework, devise appropriate algorithms, and demonstrate a software implementation of those algorithms that will confirm the usefulness of surfaces in range image understanding. It will be of interest to the researcher studying the theoretical concepts of image understanding, as well as the engineer who wants to implement these concepts in practical applications.1 Introduction.- 1.1 Perception, Surfaces, and Range Images.- 1.2 Low-Level vs. High-Level Processing.- 1.3 Data-Driven Range Image Analysis.- 1.4 Qualitative Algorithm Description.- 1.5 Overview.- 1.6 Literature Review.- 2 Object Recognition and Segmentation.- 2.1 Three-Dimensional Object Recognition.- 2.2 Mathematical Recognition Problem.- 2.3 Recognition System Components.- 2.4 Capabilities of an Ideal System.- 2.5 Segmentation into Surface Primitives.- 2.6 Mathematical Segmentation Problem.- 2.7 Segmentation Errors.- 2.8 Range Image Segmentation and Recognition.- 2.9 Summary.- 3 Surface Curvature Characteristics.- 3.1 Visible Invariance.- 3.2 Differential Geometry Review.- lÓ$