An approach to representing and recognizing general 3D curved objects using range data is introduced. A 3D generalized Hough transformation which can be applied to general 3D curved-object recognition and which reduces the computation time and storage requirements is developed. The approach makes use of the relative geometric differences between particular points on the object surface and some virtual points which are prespecified arbitrarily and by task. The method has several advantages, such as a simple knowledge base with less storage requirement, flexibility of the database design according to the tasks to be performed, and the capability of compensating for the uncertainties of position estimation due to noise and quantization error. However, the algorithm may not be suitable for a purely planar object.>