Before revision:  To this end, in this paper, we propose a novel mathematical formulation to extend CNNs onto two-dimensional (2D) manifold domains. More specifically, we approximate a tensor field defined over a manifold using orthogonal basis functions, called Zernike polynomials, on local tangent spaces. We prove that the convolution of two functions can be represented as a simple dot product between Zernike polynomial coefficients .
After revision:  To this end, in this paper, we prove that the convolution of two functions can be represented as a simple dot product between Zernike polynomial coefficients .