An Alternative to Medial Axis for the 3D Reconstruction of Unorganized Set of Points Using Implicit Surfaces

Abstract

Rebuilding three-dimensional objects represented by a set of points is a classical problem in computer graphics. Multiple applications like medical imaging or industrial techniques require finding shape from scattered data. Therefore, the reconstruction of a set of points that represents a shape has been widely studied, depending on data source and reconstruction’s objectives. This purpose of this paper is to provide an automatic reconstruction from an unorganized cloud describing an unknown shape in order to provide a solution that will allow to compute the object’s volume and to deform it with constant volume. The main idea in this paper consists in filling the object’s interior with an equipotential surface resulting of the fusion of potential field primitives also called metaballs or blobs. Nevertheless, contrary to most of usual rebuilding methods based on implicit primitives blending, we do not compute any medial axis to set the primary objects. Indeed, a fast voxelization is used to find a summary contour from the discrete shape and to determine interior areas. Then, the positioning of implicit primitives rely on a multilayer system. Finally, a controlled fusion of the isosurfaces guarantees the lack of any holes and a respectful contour of the original object, such that we obtain a complete shape filling.