팔진트리상에서 산재한 점군으로부터의 음함수 곡면 재구성과 음함수 곡면의 특징 탐지

학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. 강명주.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.1. Introduction 2. Surface Reconstruction Method from Scattered Point Data on Octree 2.1 Previous work 2.1.1 History 2.1.2 Fast sweeping method 2.1.3 Basic finite difference methods on octree 2.1.4 Biconjugate gradient stabilized(BICGSTAB) algorithm 2.2 Mathematical models 2.3 Numerical method 2.3.1 Tree generation and splitting condition 2.3.2 Distance function 2.3.3 Initial guess of signed distance function 2.3.4 Numerical discretization of model (2.2.6) on octree 2.4 Results 2.4.1 Five-leafed clover 2.4.2 Bunny, Dragon, Happy buddha 3 Feature Detection on Implicit Surface 3.1 Related work and background 3.1.1 Segmentation with the level set method 3.1.2 Signed distance function 3.1.3 Nonlocal means filtering 3.2 Corner and sharp edge detection 3.2.1 Corner detection 3.2.2 Sharp edge detection 3.2.3 False feature removal 3.3 Results 4 Conclusion and Further WorkDocto

TVL₁ Planarity Regularization for 3D Shape Approximation

The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within. This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy

TVL₁shape approximation from scattered 3D data

With the emergence in 3D sensors such as laser scanners and 3D reconstruction from cameras, large 3D point clouds can now be sampled from physical objects within a scene. The raw 3D samples delivered by these sensors however, contain only a limited degree of information about the environment the objects exist in, which means that further geometrical high-level modelling is essential. In addition, issues like sparse data measurements, noise, missing samples due to occlusion, and the inherently huge datasets involved in such representations makes this task extremely challenging. This paper addresses these issues by presenting a new 3D shape modelling framework for samples acquired from 3D sensor. Motivated by the success of nonlinear kernel-based approximation techniques in the statistics domain, existing methods using radial basis functions are applied to 3D object shape approximation. The task is framed as an optimization problem and is extended using non-smooth L1 total variation regularization. Appropriate convex energy functionals are constructed and solved by applying the Alternating Direction Method of Multipliers approach, which is then extended using Gauss-Seidel iterations. This significantly lowers the computational complexity involved in generating 3D shape from 3D samples, while both numerical and qualitative analysis confirms the superior shape modelling performance of this new framework compared with existing 3D shape reconstruction techniques

A Semi-Lagrangian Scheme with Radial Basis Approximation for Surface Reconstruction

We propose a Semi-Lagrangian scheme coupled with Radial Basis Function interpolation for approximating a curvature-related level set model, which has been proposed by Zhao et al. in \cite{ZOMK} to reconstruct unknown surfaces from sparse, possibly noisy data sets. The main advantages of the proposed scheme are the possibility to solve the level set method on unstructured grids, as well as to concentrate the reconstruction points in the neighbourhood of the data set, with a consequent reduction of the computational effort. Moreover, the scheme is explicit. Numerical tests show the accuracy and robustness of our approach to reconstruct curves and surfaces from relatively sparse data sets.Comment: 14 pages, 26 figure