Construction of discrete descriptions of biological shapes through curvilinear image meshing

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 curved (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 C1 or C2 smooth boundaries while keeping all elements valid and with good quality as measured by their Jacobians. The technique is illustrated with examples. Experimental results show that the mesh boundaries naturally represent the objects’ shapes, and the accuracy of the representation is improved compared to the corresponding linear mesh.