Browsing by Author "Panine, Mikhail"

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    Non‐Isometric Shape Matching via Functional Maps on Landmark‐Adapted Bases
    (© 2022 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2022) Panine, Mikhail; Kirgo, Maxime; Ovsjanikov, Maks; Hauser, Helwig and Alliez, Pierre
    We propose a principled approach for non‐isometric landmark‐preserving non‐rigid shape matching. Our method is based on the functional map framework, but rather than promoting isometries we focus on near‐conformal maps that preserve landmarks exactly. We achieve this, first, by introducing a novel landmark‐adapted basis using an intrinsic Dirichlet‐Steklov eigenproblem. Second, we establish the functional decomposition of conformal maps expressed in this basis. Finally, we formulate a conformally‐invariant energy that promotes high‐quality landmark‐preserving maps, and show how it can be optimized via a variant of the recently proposed ZoomOut method that we extend to our setting. Our method is descriptor‐free, efficient and robust to significant mesh variability. We evaluate our approach on a range of benchmark datasets and demonstrate state‐of‐the‐art performance on non‐isometric benchmarks and near state‐of‐the‐art performance on isometric ones.
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    Structured Regularization of Functional Map Computations
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Ren, Jing; Panine, Mikhail; Wonka, Peter; Ovsjanikov, Maks; Bommes, David and Huang, Hui
    We consider the problem of non-rigid shape matching using the functional map framework. Specifically, we analyze a commonly used approach for regularizing functional maps, which consists in penalizing the failure of the unknown map to commute with the Laplace-Beltrami operators on the source and target shapes. We show that this approach has certain undesirable fundamental theoretical limitations, and can be undefined even for trivial maps in the smooth setting. Instead we propose a novel, theoretically well-justified approach for regularizing functional maps, by using the notion of the resolvent of the Laplacian operator. In addition, we provide a natural one-parameter family of regularizers, that can be easily tuned depending on the expected approximate isometry of the input shape pair. We show on a wide range of shape correspondence scenarios that our novel regularization leads to an improvement in the quality of the estimated functional, and ultimately pointwise correspondences before and after commonly-used refinement techniques.