Filling holes of 3D point clouds based on bezier curve interpolation

Abstract

Geometric modeling is a branch of computational geometry and applied mathematics that research methods and algorithms for mathematical description of shapes to represent an object in multi-dimensional space Surface reconstruction of a 3D model has been widely studied in the field of geometric modeling. These methods consist of many steps, such as simplification, subdivision, hole filling and surface refining. While the methods for filling the holes of a triangular mesh has been researched and developed. They are introduced to process and fill in the holes of a mesh based on the neighborhood information of boundary triangles. However, the method for filling holes of 3D point clouds is still a challenge to researchers. In this thesis, we base on the Bezier curve computation, the reverse engineering of building a Bezier curve to determine missing points on the curve. They are also the points that need to be inserted into the holes of 3D point cloud. The method consists of three steps. In the first step, we extract the exterior boundary of the surface based on the neighborhood relationship between the 3D points and our particular definition of these points. In the second step, we detect the hole boundary and its extended boundary by using a growth function on the interior boundary of the surface. In the third step, we fill the hole based on the reverse computation of Bezier curves and surface patch to find and insert missing points into the hole. We also represent the result with some experimental results, respectively. Key word: Geometric models, reconstruction surface, 3D point clouds, filling the holes, Bezier curve.