Click the card below to follow the " CVer " official account
AI/CV heavy dry goods, delivered in the first time
Click to enter —>【Computer Vision】WeChat Exchange Group
Reprinted from: Heart of the Machine
On July 7, 2023, the results of the Best Paper Awards for ACM SIGGRAPH 2023, the top computer graphics conference, will be announced. Among them, the academic paper "Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field" published by the research team of the Interdisciplinary Research Center (IRC) of the School of Computer Science and Technology of Shandong University was rated as one of the five best papers. This is the first time that a domestic scientific research team has won the award since the establishment of the Best Paper Award by SIGGRAPH (NA).
The first author of the paper is Xu Rui, a second-year master's student at Shandong University, and his advisors are Professor Tu Changhe and Associate Professor Xin Shiqing from the Interdisciplinary Research Center of Shandong University. Collaborators also include doctoral student Dou Zhiyang from the University of Hong Kong, doctoral student Wang Ningna from the University of Texas at Dallas, associate professor Chen Shuangmin from Qingdao University of Science and Technology, professor Jiang Mingyan from Shandong University, professor Guo Xiaohu from the University of Texas at Dallas, and professor Wang Wenping from Texas A&M University.
Thesis project home page: https://xrvitd.github.io/Projects/GCNO/index.html
Code: https://github.com/Xrvitd/GCNO
Introduction video
The research topic of this paper is the problem of point cloud normal orientation. Considering that the traditional method fails to make full use of the global shape prior (manifold, watertight, orientable), the author uses the strong coupling relationship between the globally consistent normal and the canonical winding number field (Winding Number Field) to propose a smooth optimization function to obtain orientation information that can reflect the underlying shape.
Point cloud data can be considered as a set of sampling points falling on an orientable watertight manifold surface. The estimation method is an important step in the task of 3D reconstruction and provides the necessary information support for many geometry processing tasks. Specifically, the estimation of the normal direction can be subdivided into the problem of orientation consistency and the problem of normal direction accuracy. However, the original point cloud may have various imperfections (noise, sparseness, inhomogeneity, missing, etc.), and the underlying shape may be very complex (thin plates, thin tubes, sharp edges and corners, high genus), which further exacerbates the difficulty of normal estimation. This paper observes that the problem of orientation consistency and the problem of normal accuracy are not two independent problems, so they are considered together, aiming at the inability to directly restore the normal information with accuracy and consistency to the point cloud.
Traditional directional algorithms are mostly based on the paradigm of propagation, spreading outward layer by layer from near to far. However, this procedural algorithm has the inherent defect of "wrong step, wrong step". In the final analysis, how to make full use of the shape global prior to overcome the ambiguity of point cloud data is the key to solving this difficult problem. The author observed that the correct orientation can produce a canonical winding number field (either 0 or 1), so using the "winding number field encoding global shape information" as a tool, a new idea based on the normalized winding number field was proposed. As shown in Figure 1, when the normal of the point cloud is completely random, the winding number field of the point cloud is almost zero everywhere; and when the normal of the point cloud is completely correct, the winding number field of the point cloud is either 0 or 1, and the model is 0 outside and 1 inside.
Figure 1. The left side is the winding number field generated by the random normal direction, and the right side is the winding number field generated by the correct normal direction
As shown in Figure 2, in order to force the winding number to be "either 0 or 1", the author uses the double potential well function in physics to encourage the winding number to evolve towards 0 or 1. At the same time, in order to prevent all-zero winding numbers, this paper adds a correction term to the double potential well function to further increase the tendency to take a value of 1. Its corresponding function is:
Figure 2. Ordinary double potential well function and the modified function image
The authors observe that there is a correlation between the orientation consistency problem and the normal accuracy problem, although they reflect global and local geometry, respectively. Studies have shown that the spatial Voronoi diagram can describe the local geometric structure and has advantages in accurate normal estimation. Therefore, this paper first solves the Voronoi diagram in three-dimensional space, and then takes the Voronoi vertices as observation points to define the global consistency and local accuracy of the normal. Assuming there are M Voronoi vertices, the normality of the winding number field can be described as:
Figure 3. The Voronoi cell of each point, the top picture is the Voronoi vertex, and the bottom picture is the pole (farthest point)
In the case of relatively dense sampling, the Voronoi cell part of each sampling point is inside and part outside. The outer Voronoi vertex corresponds to a winding number of 0, and the inner Voronoi vertex corresponds to a winding number of 1. In order to suppress the "all 0" or "all 1" situation, ensure that the potential surface divides the three-dimensional space into two parts, the inner and outer parts, and introduce a balance item:
As shown in Figure 3, for a Voronoi cell, there is an inner vertex farthest from the site and an outer vertex farthest from the site, which are called poles. It has been shown that poles provide a geometric basis for the accuracy of normal orientation. Therefore, the paper also introduces an alignment item to describe whether the direction of the normal is consistent with the orientation of the pole:
Figure 4. Iterative optimization process
Ultimately, the consistency and accuracy requirements are described as an objective function consisting of three energy terms whose minimum values reflect consistency and accuracy:
where n is the normal direction of the point cloud to be sought. The authors rigorously prove that there is a non-trivial optimal solution to this objective function. The optimization process is shown in Figure 4. Even for challenging models such as thin plates and thin tubes, neat normal information can be obtained regardless of random normal initialization or spherical normal initialization.
Figure 5. Comparison of normal consistency results (red points are prediction errors)
Figure 6. Sparse point cloud Poisson reconstruction results
This paper compares existing normal estimation algorithms (Fig. 5) and conducts black-box testing using Poisson Reconstruction (Fig. 6), which fully demonstrates the effectiveness of the method. Even on sparse, noisy, complex (Fig. 7) or even wireframe-only (Fig. 8) models, the algorithm can still obtain high-quality normal information and reconstruction results.
Figure 7. Complex model reconstruction results
Figure 8. Wireframe point cloud normal estimation and reconstruction results
To summarize, this paper proposes a method to obtain globally consistent normals by normalizing the wrapping field. The method takes the winding number field to be either 0 or 1 as the basic requirement, and simultaneously considers the accuracy (alignment with Voronoi poles) and internal and external separability (0-1 balance), and transforms the normal orientation problem into a minimization problem. In this paper, extensive experiments on point clouds with various defects and challenges, such as noise, sparsity, gaps, thin plates, and highly complex geometries/topologies, demonstrate the superiority of the proposed method. This technology is expected to be applied in reverse engineering, intelligent manufacturing, 3D imaging, unmanned driving, human-computer interaction, digital city, movie entertainment and other fields. It is worth mentioning that the video related to the paper was also selected into the SIGGRAPH 2023 technical paper promotional video, highlighting its importance and innovation.
The Interdisciplinary Research Center (IRC) of Shandong University was established in September 2013, focusing on the development and application of emerging technologies in the fields of visual perception and interaction. Since its inception, the center has focused on the country's major needs in intelligent manufacturing, virtual reality and augmented reality, big data visualization, and intelligent robots, and has established three directions: computer graphics, computer vision, visualization and visual analysis.
Click to enter —>【Computer Vision】WeChat Exchange Group
ICCV/CVPR 2023 Paper and Code Download
Background reply: CVPR2023, you can download the collection of CVPR 2023 papers and code open source papers
后台回复：ICCV2023，即可下载ICCV 2023论文和代码开源的论文合集目标检测和Transformer交流群成立
扫描下方二维码，或者添加微信：CVer333，即可添加CVer小助手微信，便可申请加入CVer-目标检测或者Transformer 微信交流群。另外其他垂直方向已涵盖：目标检测、图像分割、目标跟踪、人脸检测&识别、OCR、姿态估计、超分辨率、SLAM、医疗影像、Re-ID、GAN、NAS、深度估计、自动驾驶、强化学习、车道线检测、模型剪枝&压缩、去噪、去雾、去雨、风格迁移、遥感图像、行为识别、视频理解、图像融合、图像检索、论文投稿&交流、PyTorch、TensorFlow和Transformer等。
一定要备注：研究方向+地点+学校/公司+昵称（如目标检测或者Transformer+上海+上交+卡卡），根据格式备注，可更快被通过且邀请进群
▲扫码或加微信号: CVer333，进交流群
CVer计算机视觉（知识星球）来了！想要了解最新最快最好的CV/DL/AI论文速递、优质实战项目、AI行业前沿、从入门到精通学习教程等资料，欢迎扫描下方二维码，加入CVer计算机视觉，已汇集数千人！
▲扫码进星球
▲点击上方卡片，关注CVer公众号It's not easy to organize, please like and watch