Past Events

PhD Defense

Shape Modeling of Data with Complex Geometry and Topology


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Tuesday, March 09, 2021, 10:00am - 12:00pm


Speaker: Pengxiang Wu

Location : Remote via Webex


Prof. Dimitris Metaxas (Advisor)

Prof. Konstantinos Michmizos

Prof. Desheng Zhang

Prof. Mingchen Gao (External member; University at Buffalo, SUNY)

Event Type: PhD Defense

Abstract: With the advancement and prevalence of various sensors over the past years, it is increasingly easy to produce and access abundant data with different modalities and properties. These data typically are noisy, and feature complex geometrical and topological structures. Abstracting away the application domains reveals a common thread that such data can be effectively processed from the perspective of shape modeling. Depending on the contexts, shape modeling can be performed at different granularities, from individual data samples to the whole dataset. In this dissertation, we explore the benefits and challenges of shape modeling for such complex data, and offer novel solutions to achieve effective and scalable data processing over different applications. In the first part of this dissertation, we connect data analysis with explicit shape modeling by considering the underlying topological features within data. Based on the theory of algebraic topology, we show that low-dimensional topological structures offer compact global shape information for data analysis, and present provable algorithms to identify these structures. Furthermore, we demonstrate that such topological information not only is rich in individual samples, but also can be discovered from the dataset as a whole. Empirically we show the benefits of harnessing data topology via two specific applications, i.e., cardiac trabeculae restoration from 3D CT images and learning with noisy labels. As the second part of this dissertation, we explore the data-driven paradigms to implicitly model shapes for large-scale data processing. Such implicit strategies are built upon deep neural networks, and typically lead to more robust data descriptions than the explicit ones at the cost of higher sample complexity. We illustrate the machinery behind implicit shape modeling by considering one concrete data modality, i.e., 3D point clouds, which broadly serve as the standard outputs of various sensors. Through developing specialized network architectures, we are able to capture the shape features of point clouds efficiently and effectively, thereby benefiting point cloud-based applications, such as 3D scene segmentation and autonomous driving.


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