Algorithmic Research On Implicit Surface Reconstruction Based On Normal Constraints

Many application fields want to get computer 3D models of real-word objects. The surface of the object is first digitized into a set of unorganized sample points, and then a surface reconstruction technique is applied to precisely build a continuous surface representation function. Because of so many good properties of implicit surface,it gained a wide range of researchers'attention in surface reconstruction field. This paper introduces an algorithm based on normal constrains, that was designed to creating surfaces from large collections of unorganized points.This algorithm uses normal constrains to rapidly approximating local implicit basis. The algorithm accepts a 3D point cloud with normal. The reconstruction starts with a bounding box and creates an adaptive octree-based subdivision. Each octan cell has a spherical support region of some radius. In the support region, a local implicit basis is fitting through interpolatory constrains and normal constrains. This algorithm uses a general quadric as local implicit basis. The unknown coefficients of the general quadric can be found by solving a least square problem and transformed into a linear equation system. If the local approximation error is greater than a given tolerance, then the octree node is subdivided into eight new nodes and recursively the same procedure until the desired fitting accuracy is achieved. In the end, these local implicit bases are combined by use of smooth blending function to get a global implicit function, and then obtain the reconstructed surface by extracting an appropriate isosurface.The experimental results varied that the introduced algorithm meets the requirement of large scale unorganized point cloud rapid reconstruction with a controlled error, and the algorithm is conceptually simple, easy to implement.