Surface Reconstruction From Unorganized Data In Level Set Method

The technique of surface reconstruction has extending use in surface measuring modification and visualization and such fields. The technique of surface reconstruction from unorganized data, for its universality, is very important both theoretically and practically.This paper first sums up some classical algorithms of surface reconstruction from unorganized data. The author addresses the very popular level set method and reviews some of major applications.Next, after introducing the concepts and thesis of level set method though describing curve evolution, the author solves the shape from shading problem in level set method.It is described formulations and developed fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods in this paper. The data set might consist of points, curves and/or surface patches. In the formulation only distance to the data set is used as the input. Moreover, the distance is computed with optimal speed using a new numerical PDE algorithm (fast sweeping method). The algorithm uses a data processing procedure, obtains more precise distance, and approximates initial surface to data set, reduces the complexity of the algorithm largely. An offset (an exterior contour) of the distance function to the data set is used as initial surface. To find the final shape, the initial surface is continuously deforming following the gradient flow of energy functional. So a minimal surface-like model is constructed. The algorithm uses the level set method in our numerical computation in order to capture the deformation of the initial surface and to find an implicit representation (using the signed distance function) of the final shape on a fixed rectangular grid. The reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density. As is usual with the level set method we can handle complicated topology and deformations, as well as noisy or highly non-uniform data sets easily. The approach is easily scalable for different resolutions and works in any number of space dimensions.According to the improved algorithm provided in this paper, the author presents some numerical examples, achieving a good run, and suggests the future work to do in related research fields.