Mendable Consistent Orientation of Point Clouds Jian Liu a , Junjie Cao a,∗ , Xiuping Liu a , Jun Wang b , Xiaochao Wang a , Xiquan Shi c a School of Mathematical Sciences, Dalian University of Technology, China b College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, China c Department of Mathematical Sciences, Delaware State University, USA Abstract Consistent normal orientation is challenging in the presence of noise, non-uniformities and thin sharp features. None of any existing local or global methods is capable of orienting all point cloud models consistently, and none of them offers a mechanism to rectify the inconsistent normals. In this paper, we present a new normal orientation method based on the multi-source propagation technique with two insights: faithful normals respecting sharp features tend to cause incorrect orientation propagation, and propagation orientation just using one source is problematic. It includes a novel orientation-benefit normal estimation algorithm for reducing wrong normal propagation near sharp features, and a multi-source orientation propagation algorithm for orientation improvement. The results of any orientation methods can be corrected by adding more credible sources, interactively or automatically, then propagating. To alleviate the manual work of interactive orientation, we devise an automatic propagation sources extraction method by visibility voting. It can be applied directly to find multiple credible sources, combing with our orientation-benefit normals and multi-source propagation technique, to generate a consistent orientation, or to rectify an inconsistent orientation. The experimental results show that our methods generate consistent orientation more or as faithful as those global methods with far less computational cost. Hence it is more pragmatic and suitable to handle large point cloud models. Keywords: point cloud, orientation, surface reconstruction 1. Introduction Surface reconstruction from raw points is a funda- mental problem in computer vision and computer graphics [1, 2, 3, 4, 5, 6, 7, 8]. Consistently oriented normals are critical for surface reconstruction. The state-of-the-art reconstruction algorithms [1, 9, 2, 10] may produce poor quality results without consistent orientation [11, 12]. Although some advanced 3D scan- ning devices are capable of generating some additional properties, such as color and normal, when acquiring point positions, more general digitizing devices and computer vision algorithms do not provide such prop- erties. Hence consistent orientation of raw points has drawn increasing attention recently [13, 14, 11, 12, 15, 16, 17]. As pointed out in [4, 7], robust orientation is as diffi- cult as reconstructing the whole surface itself. Further- more the acquired point sets are inevitably ridden with noise, outliers, non-uniformities and holes [7], which ∗ Corresponding author. Telephone: 86-15041171529 Email address: jjcao1231@gmail.com (Junjie Cao) challenges the traditional local orientation methods. Hence, more attentions are paid to global approaches [15, 16, 17], since they are robust to these defects. In addition, sharp features also bring changes to both local approaches (see (b) and (d) of Fig. 1) and global approaches (see (c) of Fig. 1). Many feature-preserving methods, such as [19], generate faithful normals which benefit consistent orientation. However, normals preserving features may lead to incorrect orientation as illustrated in Fig. 2. Thus we design an orientation- benefit normal estimation algorithm for reducing wrong normal propagation across sharp features. Finally, as far as we know, none of any local, even global methods is capable of achieving consistent orientation for all point clouds and none of them offers a mechanism or strategy to identify and make right the inconsistent normals. The inconsistent orientation is hard to detect just from the surface itself, because they tend to be surrounded by sharp features and satisfy the geometry constraints of the algorithm generating them. To address the above issues, we present an mendable local orientation propagation method, since it gener- Preprint submitted to Elsevier May 21, 2014