Browsing by Author "Kimmel, Ron"

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    Partial Matching of Nonrigid Shapes by Learning Piecewise Smooth Functions
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Bensaid, David; Rotstein, Noam; Goldenstein, Nelson; Kimmel, Ron; Memari, Pooran; Solomon, Justin
    Learning functions defined on non-flat domains, such as outer surfaces of non-rigid shapes, is a central task in computer vision and geometry processing. Recent studies have explored the use of neural fields to represent functions like light reflections in volumetric domains and textures on curved surfaces by operating in the embedding space. Here, we choose a different line of thought and introduce a novel formulation of partial shape matching by learning a piecewise smooth function on a surface. Our method begins with pairing sparse landmarks defined on a full shape and its part, using feature similarity. Next, a neural representation is optimized to fit these landmarks, efficiently interpolating between the matched features that act as anchors. This process results in a function that accurately captures the partiality. Unlike previous methods, the proposed neural model of functions is intrinsically defined on the given curved surface, rather than the classical embedding Euclidean space. This representation is shown to be particularly well-suited for representing piecewise smooth functions. We further extend the proposed framework to the more challenging part-to-part setting, where both shapes exhibit missing parts. Comprehensive experiments highlight that the proposed method effectively addresses partiality in shape matching and significantly outperforms leading state-of-the-art methods in challenging benchmarks. Code is available at https://github.com/davidgip74/ Learning-Partiality-with-Implicit-Intrinsic-Functions
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    Shape Correspondence by Aligning Scale-invariant LBO Eigenfunctions
    (The Eurographics Association, 2020) Bracha, Amit; Halim, Oshri; Kimmel, Ron; Schreck, Tobias and Theoharis, Theoharis and Pratikakis, Ioannis and Spagnuolo, Michela and Veltkamp, Remco C.
    When matching non-rigid shapes, the regular or scale-invariant Laplace-Beltrami Operator (LBO) eigenfunctions could potentially serve as intrinsic descriptors which are invariant to isometric transformations. However, the computed eigenfunctions of two quasi-isometric surfaces could be substantially different. Such discrepancies include sign ambiguities and possible rotations and reflections within subspaces spanned by eigenfunctions that correspond to similar eigenvalues. Thus, without aligning the corresponding eigenspaces it is difficult to use the eigenfunctions as descriptors. Here, we propose to model the relative transformation between the eigenspaces of two quasi-isometric shapes using a band orthogonal matrix, as well as present a framework that aims to estimate this matrix. Estimating this transformation allows us to align the eigenfunctions of one shape with those of the other, that could then be used as intrinsic, consistent, and robust descriptors. To estimate the transformation we use an unsupervised spectral-net framework that uses descriptors given by the eigenfunctions of the scale-invariant version of the LBO. Then, using a spectral training mechanism, we find a band limited orthogonal matrix that aligns the two sets of eigenfunctions.