A Narrow‐Band Approach for Approximating the Laplace‐Beltrami Spectrum of 3D Shapes

The spectrum of the Laplace‐Beltrami operator is a useful tool for various shape analysis problems as it provides an intrinsic, Fourier‐like characterization of 3D shapes. The numerical computation of the Laplace‐Beltrami spectrum is typically based on a triangular mesh representation of the 3D surface, which makes its robustness dependent upon the quality of triangulation. In this paper, we propose an alternative approach by approximating the Laplace‐Beltrami spectrum with the Laplacian spectrum of a narrow band composed of regular cubes with the Neumann boundary condition, thus mesh quality is not an issue in our method. We validate our method by computing the spectrum of real anatomical shapes and comparing with the mesh‐based method.