This thesis addresses the problem of constructing virtual representations of surfaces only known as clouds of unstructured points in space. This problem is related to many areas including computer graphics, image processing, computer vision, reverse engineering and geometry studies. Data sets can be acquired from a wide range of sources including Computer Tomography (CT), Magnetic Resonance Imaging (MRI), medical cryosections, laser range scanners, seismic surveys or mathematical models. This thesis will furthermost focus on medical samples acquired through cryosections of bodies.

In this thesis report various computational geometry approaches of surface reconstruction are evaluated in terms of adequateness for scientific uses. Two methods called “γ-regular shapes” and “the Power Crust” are implemented and evaluated. The contribution of this work is the proposal of a new hybrid method of surface reconstruction in three dimensions. The underlying thought of the hybrid solution is to utilize the inverse medial axis transformation, defined by the Power Crust, to recover holes that may appear in the three dimensional γ-regular shapes.