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Few systems capable of recognizing complex objects with free-form(sculptured) surfaces have been developed. The apparent lack ofsuccess is mainly due to the lack of a competent modelling scheme forrepresenting such complex objects. In this paper, a new form of pointrepresentation for describing 3D free-form surfaces is proposed. Thisrepresentation, which we call the point signature, serves to describe the structural neighbourhood of a point in a more completemanner than just using the 3D coordinates of the point. Beinginvariant to rotation and translation, the point signature can beused directly to hypothesize the correspondence to model points withsimilar signatures. Recognition is achieved by matching thesignatures of data points representing the sensed surface to thesignatures of data points representing the model surface.The use of point signatures is not restricted to the recognition of asingle-object scene to a small library of models. Instead, it can beextended naturally to the recognition of scenes containing multiplepartially-overlapping objects (which may also be juxtaposed with eachother) against a large model library. No preliminary phase ofsegmenting the scene into the component objects is required. Insearching for the appropriate candidate model, recognition need notproceed in a linear order which can become prohibitive for a largemodel library. For a given scene, signatures are extracted atarbitrarily spaced seed points. Each of these signatures is used tovote for models that contain points having similar signatures.Inappropriate models with low votes can be rejected while theremaining candidate models are ordered according to the votes theyreceived. In this way, efficient verification of the hypothesizedcandidates can proceed by testing the most likely model first.Experiments using real data obtained from a range finder have shownfast recognition from a library of fifteen models whose complexitiesvary from that of simple piecewise quadric shapes to complicated facemasks. Results from the recognition of both single-object andmultiple-object scenes are presented.