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Object classification needs to address not only the changes resulting from various viewpoints but also the different shapes that can be classified into the same category. We present a new framework and its implementation for generic object classification from raw range images, combining structural and functional concepts. The framework addresses low and mid level problems for the decomposition of range images into primitive shape parts, presenting concepts for the classification of shape parts, and calculation of part properties and relations. New concepts are described, addressing the different aspects of generic class descriptions by functional parts. A mapping of functionality (and functional parts) to the primitive shape parts is presented, introducing functional part recognizers. Our approach mainly supports a top-level recognition process in which classes are verified using a verification tree in which functional parts and their realization hypotheses are explored. An algorithm for an effective traversing of the verification tree is presented, in which probabilities of hypotheses and classes are estimated. An experimental system applying our classification concepts to several classes was implemented and tested on a database of real raw range images of objects.