Browsing by Author "Guibas, Leonidas J."

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    OptCtrlPoints: Finding the Optimal Control Points for Biharmonic 3D Shape Deformation
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Kim, Kunho; Uy, Mikaela Angelina; Paschalidou, Despoina; Jacobson, Alec; Guibas, Leonidas J.; Sung, Minhyuk; Chaine, Raphaëlle; Deng, Zhigang; Kim, Min H.
    We propose OPTCTRLPOINTS, a data-driven framework designed to identify the optimal sparse set of control points for reproducing target shapes using biharmonic 3D shape deformation. Control-point-based 3D deformation methods are widely utilized for interactive shape editing, and their usability is enhanced when the control points are sparse yet strategically distributed across the shape. With this objective in mind, we introduce a data-driven approach that can determine the most suitable set of control points, assuming that we have a given set of possible shape variations. The challenges associated with this task primarily stem from the computationally demanding nature of the problem. Two main factors contribute to this complexity: solving a large linear system for the biharmonic weight computation and addressing the combinatorial problem of finding the optimal subset of mesh vertices. To overcome these challenges, we propose a reformulation of the biharmonic computation that reduces the matrix size, making it dependent on the number of control points rather than the number of vertices. Additionally, we present an efficient search algorithm that significantly reduces the time complexity while still delivering a nearly optimal solution. Experiments on SMPL, SMAL, and DeformingThings4D datasets demonstrate the efficacy of our method. Our control points achieve better template-to-target fit than FPS, random search, and neural-network-based prediction. We also highlight the significant reduction in computation time from days to approximately 3 minutes.
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    Topology-Aware Surface Reconstruction for Point Clouds
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Brüel-Gabrielsson, Rickard; Ganapathi-Subramanian, Vignesh; Skraba, Primoz; Guibas, Leonidas J.; Jacobson, Alec and Huang, Qixing
    We present an approach to incorporate topological priors in the reconstruction of a surface from a point scan. We base the reconstruction on basis functions which are optimized to provide a good fit to the point scan while satisfying predefined topological constraints. We optimize the parameters of a model to obtain a likelihood function over the reconstruction domain. The topological constraints are captured by persistence diagrams which are incorporated within the optimization algorithm to promote the correct topology. The result is a novel topology-aware technique which can (i) weed out topological noise from point scans, and (ii) capture certain nuanced properties of the underlying shape which could otherwise be lost while performing surface reconstruction. We show results reconstructing shapes with multiple potential topologies, compare to other classical surface construction techniques, and show the completion of real scan data.