Geometric modeling of complex anatomical structures based on implicit functions

Abstract

This paper presents a region-aware modeling (RAM) method based on implicit functions for three-dimensional (3D) geometric modeling of complex anatomical structures. The proposed method consists of two major processes. In the reconstruction process, regions composing the anatomical structure are reconstructed from segmented medical images using an implicit surface reconstruction approach, and the set of obtained implicit functions is organized in a vector implicit function (VIF) structure. Then, a meshing process generates quality surface (triangular) meshes and volumetric (tetrahedral) meshes from the VIF structure. Experiments show that using a compact and consistent implicit representation greatly reduces the computer memory requirement. The emphasis of this method is placed on the precision, in terms of geometric quality and low volumetric error necessary for engineering applications.

3D modeling of natural heterogeneous objects: an introduction to methods and algorithms

“…An alternative is to use implicit functions [24]. This is done by isolating each region first, then extracting a cloud of points from each region using the Marching Cubes algorithm, and finally constructing an implicit representation from the point clouds from which the surface can be extracted.…”

“…This is done by isolating each region first, then extracting a cloud of points from each region using the Marching Cubes algorithm, and finally constructing an implicit representation from the point clouds from which the surface can be extracted. The RAM method (Region-aware modeling) described in [24] organizes implicit functions, which represent different regions of the heterogeneous object, into a vector of implicit functions by means of which the computational model is manipulated. This representation allows regions to be considered as a whole instead of isolated parts of the heterogeneous object, for example, in the model of Figure 5-b) liver tumors are modeled as an integral part of a human liver.…”