An automatic adaptive surface reconstruction from ellipsoidal skeleton

3D reconstruction is a large area of investigation. The accuracy of the 3D geometry may be dynamically adjusted to constantly provide instantaneous interaction with virtual organs for a given error tolerance. In trying to fulfill those requirements, the authors propose an anlytical approach using the implicit surfaces model. A hierarchical mathematical expression of a 3D solid represented by 3D points including the inner ones is automatically built by progressively positioning implicit primitives within the point cloud (usually acquired from CT-scan or MRI images). Each new primitive addition results in a more precise geometrical approximation of the 3D object, thus generating what is called a semantic level. At last, to reliably conduct the surface-fitting process, the authors propose the tabu metaheuristic that will take any semantic level as initial solution while using an inexpensive surface-to-boundary error measurement. Once those data have been permanently stored, the rendering stage is then performed on the fly using adaptive discretization step, thus producing multiple levels of detail. In this scope, a generic algorithm to guide the polygonization of implicit objects with multiple connected components is also proposed. The analytical model that has been developed is called ellipsoidal skeleton (e-skeleton). Each set of automatically adjusted implicit primitives is converted to a classical Constructive Solid Geometry tree that seamlessly integrates the deformation function and parameters obtained during the surface-fitting proces