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We present a novel approach for computing a compact and highly discriminant biometric signature for 3D face recognition using linear dimensionality reduction techniques. Initially, a geometry-image representation is used to effectively resample the raw 3D data. Subsequently, a wavelet transform is applied and a biometric signature composed of 7,200 wavelet coefficients is extracted. Finally, we apply a second linear dimensionality reduction step to the wavelet coefficients using Linear Discriminant Analysis and compute a compact biometric signature. Although this biometric signature consists of just 57 coefficients, it is highly discriminant. Our approach, UR3D-C, is experimentally validated using four publicly available databases (FRGC v1, FRGC v2, Bosphorus and BU-3DFE). State-of-the-art performance is reported in all of the above databases.