Curvilinear Triangular Discretization of Biomedical Images

Mesh generation is a useful tool for obtaining discrete descriptors of biological objects represented by images. The generation of meshes with straight sided elements has been fairly well understood. However, in order to match curved shapes that are ubiquitous in nature, meshes with high-order elements are required. Moreover, for the processing of large data sets, automatic meshing procedures are needed. In this work we present a new technique that allows for the automatic construction of high-order curvilinear meshes. This technique allows for a transformation of straight-sided meshes to curvilinear meshes with C-2 smooth boundaries while keeping all elements valid as measured by their Jacobians. The technique is demonstrated with examples.