Intelligent balloon: a subdivision-based deformable model for surface reconstruction of arbitrary topology

Abstract

In this paper, we develop a novel subdivision-based model—Intelligent Balloon—which is capable of recovering arbitrary, complicated shape geometry as well as its unknown topology simultaneously. Our Intelligent Balloon is a parameterized subdivision surface whose geometry and its deformable behaviors are governed by the principle of energy minimization. Our algorithm starts from a simple seed model (of genus zero) that can be arbitrarily initiated by users within regions of interest. The growing behavior of our model is controlled by a locally defined objective function associated with each vertex. Through the numerical integration of function optimization, our algorithm can adaptively subdivide the model geometry, automatically detect self-collision of the model, properly modify its topology (because of the occurrence of self-collision), correctly evolve the model towards the region boundary and reduce fitting error and improve fitting quality via global subdivision. Commonly used mesh optimization techniques are employed throughout the geometric deformation and topological variation in order to ensure the model both locally smooth and globally well conditioned. We have applied our topologically flexible models to such applications as reverse engineering from range data and surface reconstruction from volumetric image data. Our new models prove to be very powerful and extremely useful for boundary representation of complicated solids of arbitrary topology, shape recovery and segmentation for medical imaging, and iso-surface extraction for visualization.