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<p><b>Abstract</b>—We address the problem of representing and recognizing 3D free-form objects when 1) the object viewpoint is arbitrary, 2) the objects may vary in shape and complexity, and 3) no restrictive assumptions are made about the types of surfaces on the object. We assume that a range image of a scene is available, containing a view of a rigid 3D object without occlusion. We propose a new and general surface representation scheme for recognizing objects with free-form (sculpted) surfaces. In this scheme, an object is described concisely in terms of maximal surface patches of constant shape index. The maximal patches that represent the object are mapped onto the unit sphere via their orientations, and aggregated via shape spectral functions. Properties such as surface area, curvedness, and connectivity, which are required to capture local and global information, are also built into the representation. The scheme yields a meaningful and rich description useful for object recognition. A novel concept, the <it>shape spectrum</it> of an object is also introduced within the framework of <scp>COSMOS</scp> for object view grouping and matching. We demonstrate the generality and the effectiveness of our scheme using real range images of complex objects.</p>
Free-form objects, sculpted surfaces, arbitrarily curved objects, 3D object representation, shape index, spherical map, shape spectrum, view matching, object recognition.

A. K. Jain and C. Dorai, "COSMOS-A Representation Scheme for 3D Free-Form Objects," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 19, no. , pp. 1115-1130, 1997.
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