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We present a novel local surface description technique for automatic three dimensional (3D) object recognition. In the proposed approach, highly repeatable keypoints are first detected by computing the divergence of the vector field at each point of the surface. Being a differential invariant of curves and surfaces, the divergence captures significant information about the surface variations at each point. The detected keypoints are pruned to only retain the keypoints which are associated with high divergence values. A keypoint saliency measure is proposed to rank these keypoints and select the best ones. A novel integral invariant local surface descriptor, called 3D-Vor, is built around each keypoint by exploiting the vorticity of the vector field at each point of the local surface. The proposed descriptor combines the strengths of signature-based methods and integral invariants to provide robust local surface description. The performance of the proposed fully automatic 3D object recognition technique was rigorously tested on three publicly available datasets. Our proposed technique is shown to exhibit superior performance compared to state-of-the-art techniques. Our keypoint detector and descriptor based algorithm achieves recognition rates of 100%, 99.35% and 96.2% respectively, when tested on the Bologna, UWA and Ca' Foscari Venezia datasets. (C) 2015 Elsevier B.V. All rights reserved.