This paper presents a precise definition of the 3-D object recognition problem and discusses the concepts and techniques involved in recognizing three-dimensional objects from range images or depth maps. It reviews the relevant literature and highlights the challenges and requirements of 3-D object recognition, including the need for accurate surface characterization, object reconstruction, and matching algorithms. The paper defines the problem of autonomous single-arbitrary-view 3-D object recognition as a generalized inverse set mapping, where the goal is to determine the possible objects and their parameters that could produce a given depth-map function. The paper also discusses the characteristics of an ideal system for 3-D object recognition, such as handling arbitrary viewing directions, complex objects, and noise, and the importance of surface perception in object recognition. The paper reviews various object and surface representation schemes, including wire-frame, constructive solid geometry, spatial-occupancy, surface boundary, and generalized cone representations, as well as surface representation schemes such as implicit and explicit surface representations. The paper emphasizes the importance of surface characterization and matching algorithms in 3-D object recognition and discusses the challenges of recognizing objects from intensity images versus range images. The paper concludes that a general-purpose 3-D object recognition system must be capable of handling a wide range of objects and situations, and that further research is needed to develop effective algorithms for this task.This paper presents a precise definition of the 3-D object recognition problem and discusses the concepts and techniques involved in recognizing three-dimensional objects from range images or depth maps. It reviews the relevant literature and highlights the challenges and requirements of 3-D object recognition, including the need for accurate surface characterization, object reconstruction, and matching algorithms. The paper defines the problem of autonomous single-arbitrary-view 3-D object recognition as a generalized inverse set mapping, where the goal is to determine the possible objects and their parameters that could produce a given depth-map function. The paper also discusses the characteristics of an ideal system for 3-D object recognition, such as handling arbitrary viewing directions, complex objects, and noise, and the importance of surface perception in object recognition. The paper reviews various object and surface representation schemes, including wire-frame, constructive solid geometry, spatial-occupancy, surface boundary, and generalized cone representations, as well as surface representation schemes such as implicit and explicit surface representations. The paper emphasizes the importance of surface characterization and matching algorithms in 3-D object recognition and discusses the challenges of recognizing objects from intensity images versus range images. The paper concludes that a general-purpose 3-D object recognition system must be capable of handling a wide range of objects and situations, and that further research is needed to develop effective algorithms for this task.