Stable Evaluation of 3D Zernike Moments for Surface Meshes

The 3D Zernike polynomials form an orthonormal basis of the unit ball. associated moments have been successfully applied for shape recognition; they are popular in structural biology comparing protein structures and properties. Many algorithms proposed computing those moments, starting from a voxel-based representation or surface based geometric mesh shape. As order increases, however, suffer decrease computational efficiency more importantly numerical accuracy. In this paper, new to compute homogeneous defined by unstructured triangulation its that remove inaccuracies. These rely on analytical integration tetrahedra triangles central point set novel recurrent relationships between corresponding integrals. mathematical implementation details presented their stability is evaluated.