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This monograph provides a detailed record of the "GRUFF" research project. The goal of the GRUFF project is to develop techniques for robotic vision systems to recognize objects by reasoning about their intended function rather than matching to a pre-defined database of 2-D object appearances or 3-D object shapes. The contributions of this work are: a demonstration of the feasibility of the "form and function" approach to reasoning about 3-D shapes; a demonstration of the concept of using a small number of knowledge primitives as component building blocks in creating a function-based definition of an object category; and an indexing mechanism to make processing for recognition more efficient without any substantial decrease in correctness of classification. Results are given for the analysis of over 500 3-D shape descriptions created with a solid modeling tool and over 200 shape descriptions extracted from real laser range finder images.