MSPA-MCS: Collaborative Research: New Methods for Robust, Feature-Preserving Surface Reconstruction

数字扫描设备能够获得高分辨率的3D模型，并且最近变得负担得起并且商业化。通过扫描真实的物理模型来建模详细的3D形状正变得越来越普遍。目前的扫描仪能够产生大量的原始、密集的点集；因此，最近对处理点集的技术的需求有所增加。当前面临的主要挑战之一是处理所获取数据集固有噪声的表面重建技术的发展。当下伏表面包含尖锐特征时，对噪声的弹性要求尤其具有挑战性，因为噪声和尖锐特征是模糊的，并且大多数现有技术倾向于平滑重要特征甚至放大噪声样本。该项目有助于培养年轻的研究人员在图形、几何和统计学的交叉领域工作，同时使他们能够从事理论上合理、具有深刻实际影响的工作。在这个项目中开发的数据、软件和模型将被传播给其他研究人员用于基准和测试。这项研究涉及生产高效和理论上合理的技术，以实现稳健，保留特征的表面重建。它建立在使用移动最小二乘（MLS）技术从一组点构造流形表面的最新工作的基础上。该项目探索了在基于mls的表面重建中使用由离群值识别产生的稳健统计技术。这种方法与保持特征平滑的最新发展有关，但它定义了一个表面，而不是过滤几何形状。这些技术不仅指向更可靠的MLS投影，而且扩展了底层MLS表面定义的表示能力，使具有尖锐特征的物体能够表示。

Digital scanning devices are capable of acquiring high-resolution 3D models and have recently become affordable and commercially available. Modeling detailed 3D shapes by scanning real physical models is becoming commonplace. Current scanners are able to produce very large amounts of raw, dense point sets; consequently, there has been a recent increase in the need for techniques for processing point sets. One of the principal challenges faced today is the development of surface reconstruction techniques that deal with the inherent noise of the acquired dataset. When the underlying surface contains sharp features, the requirement of being resilient to noise is especially challenging, since noise and sharp features are ambiguous, and most existing techniques tend to smooth important features or even to amplify noisy samples. The project helps to train young researchers to work at the intersection of graphics, geometry, and statistics, while enabling them to pursue theoretically sound work that has deep practical impact. The data, software, and models developed in this project will be disseminated for other researchers to use in benchmarking and testing.This research involves producing efficient and theoretically sound techniques for robust, feature-preserving surface reconstruction. It builds on recent work on the construction of a manifold surface from a set of points by using a moving least-squares (MLS) technique. The project explores the use of robust statistical techniques arising from outlier identification in MLS-based surface reconstruction. The approach is related to recent developments in feature-preserving smoothing, but it defines a surface rather than filtering the geometry. The techniques not only point to more reliable MLS projection but also extend the representation power of the underlying MLS surface definition to enable the representation of objects with sharp features.