CAREER: Modeling Uncertainties for Geometry Processing

采集设备的进步使得能够生成丰富的3D数据，这些数据可以在从分子到城市环境的全光谱范围内捕获物理对象/场景。与这样的3D信息结合在一起的是几何处理方面令人印象深刻的进步，旨在重建、分析和建模3D几何。随着3D传感器变得更加实惠和普遍，几何处理算法的应用正在从计算机辅助设计和建筑等传统领域扩展到生命科学、自动驾驶汽车和国防中交互和自主系统的集成模块。对于这些新的应用，目前占主导地位的方法是几何处理算法生成单个输出(例如，一个重建的网格)是不够的，因为数据驱动的方法中没有传达诸如输出的精度、其他可信的解决方案和数据不确定性之类的基本信息。这些信息对于关键决策是必不可少的，例如3D重建对于手术计划或桥梁损伤检查是否足够准确，如果不是，则在哪里添加额外的输入以提高重建质量。该项目将建立一个统一的转换框架来对几何处理算法的不确定性进行建模和量化，并将开发具有不确定性输出的新算法，该研究将为几何处理提供第一个系统的不确定性量化研究。为此，该项目将建立一个不确定性量化(UQ)框架，将概率论、统计学和深度生成模型中的工具与几何处理中的核心数据表示和算法无缝集成。在仔细检查输出和各种不确定源(输入、算法和数据)之间的联系的基础上，该框架将包括一个统一的混合模型，用于通过四个推力来编码不确定性，从用于模拟分布的局部形状的代数近似到用于表征混合成分的采样和变分推理。在应用方面，这项工作将研究几何处理管道中的不确定性是如何演变的，从扫描配准和表面重建中的传感器不确定性到结构检测的随机算法，再到数据驱动的几何编辑中的数据不确定性。在算法方面，研究将开发一个统一的框架，输出混合模型，以近似来自不同不确定性来源的输出分布。项目成果的评估将集中在三个行业领域：数字牙科护理、自动驾驶和数字考古。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Advances in acquisition devices have enabled the generation of rich 3D data that captures physical objects/scenes at a full spectrum of scales ranging from molecules to urban environments. Coupled with such 3D information is impressive progress in geometry processing aiming to reconstruct, analyze, and model 3D geometries. As 3D sensors become more affordable and ubiquitous, applications of geometry processing algorithms are expanding from traditional domains such as computer-aided design and architecture to integrative modules of interactive and autonomous systems in the life sciences, self-driving cars, and national defense. For these new applications, the currently dominant approach where geometry processing algorithms generate a single output (e.g., one reconstructed mesh) is not sufficient, because essential information such as the accuracy of the output, other plausible solutions, and data uncertainty in data-driven approaches is not conveyed. Such information is indispensable for critical decision making, such as whether a 3D reconstruction is accurate enough for surgery planning or bridge damage inspection, and if not where to add additional inputs to improve the reconstruction quality. This project will establish a unified and transformative framework to model and quantify uncertainties of geometry processing algorithms, and will develop new algorithms that possess uncertainty outputs.This research will provide the first systematic study of uncertainty quantification for geometry processing. To this end, the project will establish an uncertainty quantification (UQ) framework that seamlessly integrates tools in probability theory, statistics, and deep generative models with core data representations and algorithms in geometry processing. Building upon a careful examination of the connection between the output and various uncertainty sources (input, algorithm, and data), the framework will incorporate a unified mixture model for encoding uncertainties via four thrusts, starting from algebraic approximations for modeling the local shape of a distribution to sampling and variational inference for characterizing mixture components. On the application side, the work will examine how uncertainties evolve in the geometry processing pipeline, starting from sensor uncertainty in scan registration and surface reconstruction to stochastic algorithms for structure detection to data uncertainty in data-driven geometry editing. On the algorithm side, the research will develop a unified framework that outputs mixture models to approximate the output distribution derived from different uncertainty sources. Evaluation of project outcomes will focus on three industrial disciplines: digital dental care, autonomous driving, and digital archaeology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.