Browsing by Author "Liu, Hsueh-Ti Derek"

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    Algorithms for Data-Driven Geometric Stylization & Acceleration
    (University of Toronto, 2022-09-29) Liu, Hsueh-Ti Derek
    In this thesis, we investigate computer algorithms for creating stylized 3D digital content and numerical tools for processing high-resolution geometric data. This thesis first addresses the problem of geometric stylization. Existing 3D content creation tools lack support for creating stylized 3D assets. They often require years of professional training and are tedious for creating complex geometries. One goal of this thesis is to address such a difficulty by presenting a novel suite of easy-to-use stylization algorithms. This involves a differentiable rendering technique to generalize image filters to filter 3D objects and a machine learning approach to renovate classic modeling operations. In addition, we address the problem by proposing an optimization framework for stylizing 3D shapes. We demonstrate how these new modeling tools can lower the difficulties of stylizing 3D geometric objects. The second part of the thesis focuses on scalability. Most geometric algorithms suffer from expensive computation costs when scaling up to high-resolution meshes. The computation bottleneck of these algorithms often lies in fundamental numerical operations, such as solving systems of linear equations. In this thesis, we present two directions to overcome such challenges. We first show that it is possible to coarsen a geometry and enjoy the efficiency of working on coarsened representation without sacrificing the quality of solutions. This is achieved by simplifying a mesh while preserving its spectral properties, such as eigenvalues and eigenvectors of a differential operator. Instead of coarsening the domain, we also present a scalable geometric multigrid solver for curved surfaces. We show that this can serve as a drop-in replacement of existing linear solvers to accelerate several geometric applications, such as shape deformation and physics simulation. The resulting algorithms in this thesis can be used to develop data-driven 3D stylization tools for inexperienced users and for scaling up existing geometry processing pipelines.
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    Normal-Driven Spherical Shape Analogies
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Liu, Hsueh-Ti Derek; Jacobson, Alec; Digne, Julie and Crane, Keenan
    This paper introduces a new method to stylize 3D geometry. The key observation is that the surface normal is an effective instrument to capture different geometric styles. Centered around this observation, we cast stylization as a shape analogy problem, where the analogy relationship is defined on the surface normal. This formulation can deform a 3D shape into different styles within a single framework. One can plug-and-play different target styles by providing an exemplar shape or an energy-based style description (e.g., developable surfaces). Our surface stylization methodology enables Normal Captures as a geometric counterpart to material captures (MatCaps) used in rendering, and the prototypical concept of Spherical Shape Analogies as a geometric counterpart to image analogies in image processing.
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    Spectral Mesh Simplification
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Lescoat, Thibault; Liu, Hsueh-Ti Derek; Thiery, Jean-Marc; Jacobson, Alec; Boubekeur, Tamy; Ovsjanikov, Maks; Panozzo, Daniele and Assarsson, Ulf
    The spectrum of the Laplace-Beltrami operator is instrumental for a number of geometric modeling applications, from processing to analysis. Recently, multiple methods were developed to retrieve an approximation of a shape that preserves its eigenvectors as much as possible, but these techniques output a subset of input points with no connectivity, which limits their potential applications. Furthermore, the obtained Laplacian results from an optimization procedure, implying its storage alongside the selected points. Focusing on keeping a mesh instead of an operator would allow to retrieve the latter using the standard cotangent formulation, enabling easier processing afterwards. Instead, we propose to simplify the input mesh using a spectrum-preserving mesh decimation scheme, so that the Laplacian computed on the simplified mesh is spectrally close to the one of the input mesh. We illustrate the benefit of our approach for quickly approximating spectral distances and functional maps on low resolution proxies of potentially high resolution input meshes.