Partial differential equations for 3D Data compression and Reconstruction

This paper describes a Partial Differential Equation (PDE) based method for 3D reconstruction of surface patches. The PDE method is exploited using data obtained from standard 3D scanners. First the original surface data are sparsely re-meshed by a number of cutting planes whose intersection points on the mesh are represented by Fourier coefficients in each plane. Information on the number of vertices and scale of the surface are defined and, together, these efficiently define the compressed data. The PDE method is then applied at the reconstruction stage by defining PDE surface patches between the sparse cutting planes recovering thus, the vertex density of the original mesh. Results show that compression rates over 96% are achieved while preserving the quality of the 3D mesh. The paper discusses the suitability of the method to a number of applications and general issues in 3D compression and reconstruction.