Surface reconstruction from three-dimensional segmentations using implicit functions

Real-world object modeling is a crucial part of computer graphics, with findings of great importance for many applications in areas of computer assisted design, manufacturing and engineering. However, geometric modeling of such objects proves quite challenging, especially when complex volumetric structures are involved as in the case of biological anatomy. In this paper, we present a method for the 3-D modeling of human organs based on an implicit representation approach. The principal idea consists of sampling the region of interest from three-dimensional labeled images and implicitly reconstructing its surface using an algorithm based on the Poisson surface reconstruction method. From there, either a surface mesh or a 3-D mesh is adjusted to the implicit surface, which is given by the zero level set of a function f(x) = 0. This is done to allow not only the visualization but physically-based simulations. As far as assessment of the new method is concerned, we used the Dice Similarity Coefficient, and the Hausdorff Distance to evaluate accuracy.