Abstract: An isometric integral invariant is proposed,which is suitable for recognizing 3D faces with expressions.The invariant is obtained by multiple integrals of invariant kernels on multi-level regions around the nose tip.The invariant kernel is constructed by invariant geometric primitives on surfaces,which fully depends on the intrinsic properties of surfaces,and has an intuitive geometric meaning.Experimental results show that this approach is less sensitive to noise and leads to higher accuracy than Laplace-Beltrami operator.