A method for recognition of partially occluded and overlapping objects in composite scenes is presented. The objects to be recognized belong to a large database of model objects which are known in advance. A geometric hashing technique which is an improvement of a previous technique due to J. T. Schwartz and M. Sharir (1987) is proposed. The algorithm's complexity is linear in the number of sample points on the boundary of the composite scene. Experimental results from large databases are presented, including results that could not be obtained by the previous technique.