Learning to optimize for geometry processing

Geometry processing, which focuses on reconstructing and analyzing physical objects and scenes, enjoy a wide range of applications, including medical diagnosis, architecture, bio-imaging, virtual reality, etc. Thanks to the popularity of portable 3D scanning devices and the emergence of big 3D data and exciting progress in artificial intelligence, there is a shift in this field from reconstructing and processing a single model to developing techniques that enable 3D models as a data modality for machine perception. Compared to other data modalities such as images, videos, audios, and natural language descriptions, 3D models provide the most accurate recording of our physical world as they capture the complete geometry of the phyisical objects. As a result, 3D models are critical for applications involving geometric quantities such as distances and orientations, and physical properties such as stability and affordance, etc. However, to enable the 3D model as a data modality for machine perception, we have to develop efficient and robust geometry processing techniques ranging from 3D reconstruction to 3D understanding. This thesis focuses on geometry processing from the perspective of robust optimization, a field that is gaining increasing attention in the era of big data, machine learning, and artificial intelligence, but is under-explored in the field of geometry processing. Important aims include developing robust and efficient optimization procedures with provable guarantees, characterizing the uncertainties of the output distribution, and learning to optimize to adapt to input and output distributions.Computer Science