Implicit Surface Reconstruction from Scattered Point Data on Octree and Feature Detection on the Implicit Surface

Abstract

In this thesis, we are concerned with reverse engineering process using implicit surface represented by level set. We consider two methods. One is to reconstruct implicit surface from scattered point data on octree and the other detects features such as edges and corners on the implicit surface.

Our surface reconstruction method is based on the level set method using octree i.e. a kind of adaptive grid. We start with the surface reconstruction model proposed in Ye's where they considered the surface reconstruction process as an elliptic problem while most previous methods employed the time marching process from an initial surface to point cloud. However, as far as their method is implemented on uniform grid, it exposes inefficiency such as the high cost of memory. We improved it by adapting octree data structure to our problem and by introducing a new redistancing algorithm which is different from the existing one.

We also address feature detection from 3D CT image which is a form of implicit surface. While laser scanner is accurate and has little noise, it can't examine the inside of object. So, CT scanner is recently becoming popular for non-destructive inspection of mechanical part. But for reverse engineering, we should transform 3D image data into B-spline surface data in order to use it on CAD software, that is, change from implicit surface to parametric surface. In that process, we need feature detection for parametrization of surface. But it has more artifacts such as noise and blur than laser scanner. Consequently, preprocess for reducing artifacts is required. We apply some existing denoising algorithms to CT image data and then extract edges and corners with our feature detection method.