Browsing by Author "Chien, Edward"

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    Singularity-Free Frame Fields for Line Drawing Vectorization
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Guțan, Olga; Hegde, Shreya; Berumen, Erick Jimenez; Bessmeltsev, Mikhail; Chien, Edward; Memari, Pooran; Solomon, Justin
    State-of-the-art methods for line drawing vectorization rely on generated frame fields for robust direction disambiguation, with each of the two axes aligning to different intersecting curve tangents around junctions. However, a common source of topological error for such methods are frame field singularities. To remedy this, we introduce the first frame field optimization framework guaranteed to produce singularity-free fields aligned to a line drawing. We first perform a convex solve for a roughly-aligned orthogonal frame field (cross field), and then comb away its internal singularities with an optimal transport–based matching. The resulting topology of the field is strictly maintained with the machinery of discrete trivial connections in a final, non-convex optimization that allows non-orthogonality of the field, improving smoothness and tangent alignment. Our frame fields can serve as a drop-in replacement for frame field optimizations used in previous work, improving the quality of the final vectorizations.
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    A Subspace Method for Fast Locally Injective Harmonic Mapping
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Hefetz, Eden Fedida; Chien, Edward; Weber, Ofir; Alliez, Pierre and Pellacini, Fabio
    We present a fast algorithm for low-distortion locally injective harmonic mappings of genus 0 triangle meshes with and without cone singularities. The algorithm consists of two portions, a linear subspace analysis and construction, and a nonlinear nonconvex optimization for determination of a mapping within the reduced subspace. The subspace is the space of solutions to the Harmonic Global Parametrization (HGP) linear system [BCW17], and only vertex positions near cones are utilized, decoupling the variable count from the mesh density. A key insight shows how to construct the linear subspace at a cost comparable to that of a linear solve, extracting a very small set of elements from the inverse of the matrix without explicitly calculating it. With a variable count on the order of the number of cones, a tangential alternating projection method [HCW17] and a subsequent Newton optimization [CW17] are used to quickly find a low-distortion locally injective mapping. This mapping determination is typically much faster than the subspace construction. Experiments demonstrating its speed and efficacy are shown, and we find it to be an order of magnitude faster than HGP and other alternatives.