Spherical object reconstruction using star-shaped simplex meshes

Abstract

Spherical object reconstruction is of great importance, especially in the field of cell biology, since cells as well as cell nuclei mostly have the shape of a deformed sphere. Fast, reliable and precise procedure is needed for automatic measuring of topographical parameters of the large number of cells or cell nuclei. This paper presents a new method for spherical object reconstruction. The method springs from Delingette general object reconstruction algorithm which is based on the deformation of simplex meshes. However, the unknown surface is searched only within the subclass of simplex meshes, which have the shape of a star. Star-shaped simplex meshes are suitable for modelling of spherical or ellipsoidal objects. In our approach, the law of motion was altered so that it preserves the star-shape during deformation. The proposed method is easier than the general method and therefore faster. In addition, it uses more computationally stable expressions than a method strictly implemented according to Delingette’s paper. It is also shown how to partly avoid the occasional instability of the Delingette method. The accuracy of both methods is comparable. The star-shaped method achieves a stable state more often.