Spectral Geometry and Riemannian Manifold Mesh Approximations: Some Autocorrelation Lessons from Spatial Statistics

Abstract

Abstract Awareness of the utility of spectral geometry is permeating the academy today, with special interest in its ability to foster interfaces between a range of analytical disciplines and art, exhibiting popularity in, for example, computer engineering/image processing and GIScience/spatial statistics, among other subject areas. This paper contributes to the emerging literature about such synergies. It more specifically extends the 2-D Graph Moranian operator that dominates spatial statistics/econometrics to the 3-D Riemannian manifold sphere whose analysis the Graph Laplacian operator monopolizes today. One conclusion is that harmonizing the use of these two operators offers a way to expand knowledge and comprehension.