Effectivity of spherical object reconstruction using star-shaped simplex meshes

Three-dimensional objects of an arbitrary shape and topology can be reconstructed using Delingette´s general reconstruction algorithm based on simplex meshes. The method can handle volumetric images as well as three-dimensional range data. The reconstruction is performed in two stages. First, the initialization stage creates a simplex mesh in the vicinity of the input data. Then, an iterative refinement algorithm decreases the distance of the mesh from the data while preserving required shape qualities of the mesh. The general method was adapted to the reconstruction of spherical objects. The basic idea is to consider only star-shaped simplex meshes for the representation of object boundaries and therefore the iterative refinement algorithm is faster and more stable. This paper provides comparison of the effectivity of both methods. The methods were tested on real volumetric images of cell nuclei which were acquired using an optical microscope. The star-shaped method can be used however also for the reconstruction of any object having potato-like shape.