Flipping-based iterative surface reconstruction for unoriented points

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design Pub Date : 2024-04-25 DOI:10.1016/j.cagd.2024.102315

Yueji Ma , Yanzun Meng , Dong Xiao , Zuoqiang Shi , Bin Wang

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Abstract

In this paper, we propose a novel surface reconstruction method for unoriented points by establishing and solving a nonlinear equation system. By treating normals as unknown parameters and imposing the conditions that the implicit field is constant and its gradients parallel to the normals on the input point cloud, we establish a nonlinear equation system involving the oriented normals. To simplify the system, we transform it into a 0-1 integer programming problem solely focusing on orientation by incorporating inconsistent oriented normal information through PCA. We solve the simplified problem using flipping-based iterative algorithms and propose two novel criteria for flipping based on theoretical analysis.

Extensive experiments on renowned datasets demonstrate that our flipping-based method with wavelet surface reconstruction achieves state-of-the-art results in orientation and reconstruction. Furthermore, it exhibits linear computational and storage complexity by leveraging the orthogonality and compact support properties of wavelet bases. The source code is available at https://github.com/mayueji/FISR_code.

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基于翻转的无方向点迭代曲面重构

本文通过建立和求解一个非线性方程系统，提出了一种新颖的无方向点曲面重建方法。通过将法线视为未知参数，并施加隐含场恒定且其梯度与输入点云上的法线平行的条件，我们建立了一个涉及定向法线的非线性方程组。为了简化该系统，我们通过 PCA 将不一致的定向法线信息纳入其中，从而将其转化为只关注定向的 0-1 整数编程问题。我们使用基于翻转的迭代算法来解决简化后的问题，并在理论分析的基础上提出了两个新的翻转标准。在著名数据集上进行的大量实验证明，我们基于翻转的小波曲面重建方法在定向和重建方面取得了最先进的结果。此外，利用小波基的正交性和紧凑支持特性，它还表现出线性计算和存储复杂性。源代码见 https://github.com/mayueji/FISR_code。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Aided Geometric Design 工程技术-计算机：软件工程

CiteScore

3.50

自引率

13.30%

发文量

审稿时长

60 days

期刊介绍： The journal Computer Aided Geometric Design is for researchers, scholars, and software developers dealing with mathematical and computational methods for the description of geometric objects as they arise in areas ranging from CAD/CAM to robotics and scientific visualization. The journal publishes original research papers, survey papers and with quick editorial decisions short communications of at most 3 pages. The primary objects of interest are curves, surfaces, and volumes such as splines (NURBS), meshes, subdivision surfaces as well as algorithms to generate, analyze, and manipulate them. This journal will report on new developments in CAGD and its applications, including but not restricted to the following: -Mathematical and Geometric Foundations- Curve, Surface, and Volume generation- CAGD applications in Numerical Analysis, Computational Geometry, Computer Graphics, or Computer Vision- Industrial, medical, and scientific applications. The aim is to collect and disseminate information on computer aided design in one journal. To provide the user community with methods and algorithms for representing curves and surfaces. To illustrate computer aided geometric design by means of interesting applications. To combine curve and surface methods with computer graphics. To explain scientific phenomena by means of computer graphics. To concentrate on the interaction between theory and application. To expose unsolved problems of the practice. To develop new methods in computer aided geometry.