Abstract
This thesis describes an efficient method for automatic reconstruction of closed, piecewise smooth and seamless surfaces from accurate and dense 3D points based on variational implicit surface. The problem of surface reconstruction arises in a diversity of applications in scientific and engineering domains such as computer graphics, animation, CAD, scientific visualization and medical imaging etc. Traditionally, a variational implicit surface uses a single implicit function formulated as a sum of weighted radial basis functions to describe the unknown surface. However, the global support nature and exponential growth of the complexity of RBFs makes it infeasible for modeling data sets with more than only a few thousand points. The piecewise representation of implicit surfaces outlined in this thesis provides an algorithmic solution to the difficulties in handling large data sets faced by traditional approaches. The basic principle of our method is to partition the input data points into a set of clusters and apply the traditional method to them separately. The decomposed local implicit patches are then joined together to form the complete surface. The reconstruction method has two major parts: 1) partitioning of the implicit surfaces and 2) progressive reconstruction. A key component in part 2 and another main contribution of this thesis is the introduction of a novel iterative refinement algorithm based on the Schur complement formula. The effectiveness of the proposed method is demonstrated by a number of experimental results of reconstructed surfaces from real-world scanning data.