Task-Aware 3D Geometric Synthesis
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Date
2024
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University of Toronto
Abstract
This thesis is about the different ways in which three-dimensional shapes come into digital existence inside a computer. Specifically, it argues that this geometric synthesis process should be tuned to the specific end for which an object is modeled or captured, and proposes building algorithms specific to said end. The majority of this thesis is dedicated to how 3D shapes are designed, and introduces changes to this modeling process to incorporate manufacturing constraints (e.g., that an object can physically be built out of a specific material or with a specific machine), precomputed simulation data (e.g., an object’s response to an impact) or specific user inputs (e.g., 3D drawing in Virtual or Augmented Reality). Importantly, these changes include rethinking the ways in which geometry is commonly represented, instead introducing formats that benefit specific applications, as well as efficient algorithms for converting between them. By contrast, the latter part of this thesis concerns itself with the task of capturing real-world 3D surfaces, a process that necessarily involves reconstructing continuous mathematical objects from imperfect, noisy and occluded discrete information. This thesis introduces a novel, stochastic lens from which to study this fundamentally underdetermined process, allowing for the introduction of task-specific priors as well as quantifying the uncertainty of common algorithmic predictions. This perspective is shown to provide critical insights in common 3D scanning paradigms. While geometric capture is the natural first step in which to introduce this statistical perspective, the thesis ends by enumerating other tasks further along the geometric processing pipeline that could benefit from it.
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