A PDE method for patchwise approximation of large polygon meshes

Abstract

Three-dimensional (3D) representations of com- plex geometric shapes, especially when they are recon- structed from magnetic resonance imaging (MRI) and com- puted tomography (CT) data, often result in large polygon meshes which require substantial storage for their handling, and normally have only one fixed level of detail (LOD). This can often be an obstacle for efficient data exchange and interactive work with such objects. We propose to re- place such large polygon meshes with a relatively small set of coefficients of the patchwise partial differential equation (PDE) function representation. With this model, the approx- imations of the original shapes can be rendered with any desired resolution at interactive rates. Our approach can di- rectly work with any common 3D reconstruction pipeline, which we demonstrate by applying it to a large reconstructed medical data set with irregular geometry.