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Numerous methods have been proposed for the expression-invariant 3D face recognition, but a little attention is given to the local-based representation for the texture of the 3D images. In this paper, we propose an expression-invariant 3D face recognition approach based on the locally extracted moments of the texture when only one exemplar per person is available. We use a geodesic texture transform accompanied by Pseudo Zernike Moments to extract local feature vectors from the texture of a face. An extensive experimental investigation is conducted using publicly available BU-3DFE face databases covering face recognition under expression variations. The performance of the proposed method is compared with the performance of two benchmark approaches. The encouraging experimental results demonstrate that the proposed method can be used for 3D face recognition in single model databases.