CAREER: Modeling Uncertainties for Geometry Processing

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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.