Since the pioneering work of Terzopoulos etal. [19,35] in 1987, deformable models have achieved great success in the areas of computer visionand pattern recognition. In general, deformable models can be divided into two categories: explicit models and implicit models. Explicit models include parametric representations such as the dynamic superquadrics proposed by Metaxas etal. [29] and discrete representations such as the dynamic polygonal model developed by Miller etal. [30]. Implicit models were recently proposed by Malladi et al. [25] and Caselles etal. [8] with the ability to handle topology changes. Their schemes are based on the modeling of propagating fronts, which are the level set of some scalar function. More recently, researchers have proposed topologically adaptive explicit models, for example the topologically adaptive snake proposed by McInerney andTerzopoulos [26,28] and the discrete triangle model of Lachaud et al. [23]. For a detailed review, please refer to the survey paper by [27].
The aforementioned deformable models were proposed mainly for the purpose of shape reconstruction from volumetric data and for medical image segmentation. For shape reconstruction from point clouds, existing work is mostly on static methods. They are either explicit methods using Voronoi Diagram and DelaunayTriangulation such as the Alpha-shape proposed by Edelsbrunner et al. [13] or the Crust algorithm developed by Amenta etal. [3], or implicit methods such as the method proposed by Hoppe et al. [17] and methods based on the radial basis function(RBF) [7,11]. A previous attempt to recover shape as well as topology from range data used super-quadratic blended deformable models [10]. Recently Zhao et al. [16] proposed a fast level-set approach for shape reconstruction from point clouds.