Browsing by Author "Ovsjanikov, Maks"

Now showing 1 - 7 of 7
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    Discrete Optimization for Shape Matching
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Ren, Jing; Melzi, Simone; Wonka, Peter; Ovsjanikov, Maks; Digne, Julie and Crane, Keenan
    We propose a novel discrete solver for optimizing functional map-based energies, including descriptor preservation and promoting structural properties such as area-preservation, bijectivity and Laplacian commutativity among others. Unlike the commonly-used continuous optimization methods, our approach enforces the functional map to be associated with a pointwise correspondence as a hard constraint, which provides a stronger link between optimized properties of functional and point-topoint maps. Under this hard constraint, our solver obtains functional maps with lower energy values compared to the standard continuous strategies. Perhaps more importantly, the recovered pointwise maps from our discrete solver preserve the optimized for functional properties and are thus of higher overall quality. We demonstrate the advantages of our discrete solver on a range of energies and shape categories, compared to existing techniques for promoting pointwise maps within the functional map framework. Finally, with this solver in hand, we introduce a novel Effective Functional Map Refinement (EFMR) method which achieves the state-of-the-art accuracy on the SHREC'19 benchmark.
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    Inverse Computational Spectral Geometry
    (The Eurographics Association, 2022) Rodolà, Emanuele; Cosmo, Luca; Ovsjanikov, Maks; Rampini, Arianna; Melzi, Simone; Bronstein, Michael; Marin, Riccardo; Hahmann, Stefanie; Patow, Gustavo A.
    In the last decades, geometry processing has attracted a growing interest thanks to the wide availability of new devices and software that make 3D digital data available and manipulable to everyone. Typical issues faced by geometry processing algorithms include the variety of discrete representations for 3D data (point clouds, polygonal or tet-meshes and voxels), or the type of deformation this data may undergo. Powerful approaches to address these issues come from looking at the spectral decomposition of canonical differential operators, such as the Laplacian, which provides a rich, informative, robust, and invariant representation of the 3D objects. The focus of this tutorial is on computational spectral geometry. We will offer a different perspective on spectral geometric techniques, supported by recent successful methods in the graphics and 3D vision communities and older but notoriously overlooked results. We will discuss both the “forward” path typical of spectral geometry pipelines (e.g. computing Laplacian eigenvalues and eigenvectors of a given shape) with its widespread applicative relevance, and the inverse path (e.g. recovering a shape from given Laplacian eigenvalues, like in the classical “hearing the shape of the drum” problem) with its ill-posed nature and the benefits showcased on several challenging tasks in graphics and geometry processing.
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    Limit Shapes - A Tool for Understanding Shape Differences and Variability in 3D Model Collections
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Huang, Ruqi; Achlioptas, Panos; Guibas, Leonidas; Ovsjanikov, Maks; Bommes, David and Huang, Hui
    We propose a novel construction for extracting a central or limit shape in a shape collection, connected via a functional map network. Our approach is based on enriching the latent space induced by a functional map network with an additional natural metric structure. We call this shape-like dual object the limit shape and show that its construction avoids many of the biases introduced by selecting a fixed base shape or template. We also show that shape differences between real shapes and the limit shape can be computed and characterize the unique properties of each shape in a collection - leading to a compact and rich shape representation. We demonstrate the utility of this representation in a range of shape analysis tasks, including improving functional maps in difficult situations through the mediation of limit shapes, understanding and visualizing the variability within and across different shape classes, and several others. In this way, our analysis sheds light on the missing geometric structure in previously used latent functional spaces, demonstrates how these can be addressed and finally enables a compact and meaningful shape representation useful in a variety of practical applications.
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    Orthogonalized Fourier Polynomials for Signal Approximation and Transfer
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Maggioli, Filippo; Melzi, Simone; Ovsjanikov, Maks; Bronstein, Michael M.; Rodolà, Emanuele; Mitra, Niloy and Viola, Ivan
    We propose a novel approach for the approximation and transfer of signals across 3D shapes. The proposed solution is based on taking pointwise polynomials of the Fourier-like Laplacian eigenbasis, which provides a compact and expressive representation for general signals defined on the surface. Key to our approach is the construction of a new orthonormal basis upon the set of these linearly dependent polynomials. We analyze the properties of this representation, and further provide a complete analysis of the involved parameters. Our technique results in accurate approximation and transfer of various families of signals between near-isometric and non-isometric shapes, even under poor initialization. Our experiments, showcased on a selection of downstream tasks such as filtering and detail transfer, show that our method is more robust to discretization artifacts, deformation and noise as compared to alternative approaches.
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    PointCleanNet: Learning to Denoise and Remove Outliers from Dense Point Clouds
    (© 2020 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2020) Rakotosaona, Marie‐Julie; La Barbera, Vittorio; Guerrero, Paul; Mitra, Niloy J.; Ovsjanikov, Maks; Benes, Bedrich and Hauser, Helwig
    Point clouds obtained with 3D scanners or by image‐based reconstruction techniques are often corrupted with significant amount of noise and outliers. Traditional methods for point cloud denoising largely rely on local surface fitting (e.g. jets or MLS surfaces), local or non‐local averaging or on statistical assumptions about the underlying noise model. In contrast, we develop a simple data‐driven method for removing outliers and reducing noise in unordered point clouds. We base our approach on a deep learning architecture adapted from PCPNet, which was recently proposed for estimating local 3D shape properties in point clouds. Our method first classifies and discards outlier samples, and then estimates correction vectors that project noisy points onto the original clean surfaces. The approach is efficient and robust to varying amounts of noise and outliers, while being able to handle large densely sampled point clouds. In our extensive evaluation, both on synthetic and real data, we show an increased robustness to strong noise levels compared to various state‐of‐the‐art methods, enabling accurate surface reconstruction from extremely noisy real data obtained by range scans. Finally, the simplicity and universality of our approach makes it very easy to integrate in any existing geometry processing pipeline. Both the code and pre‐trained networks can be found on the project page ().
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    Robust Structure‐Based Shape Correspondence
    (© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Kleiman, Yanir; Ovsjanikov, Maks; Chen, Min and Benes, Bedrich
    We present a robust method to find region‐level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the shapes, and devise an adapted graph‐matching technique, from which we infer correspondences between shape regions. The simplified shape graphs are designed to primarily capture the overall structure of the shapes, without reflecting precise information about the geometry of each region, which enables us to find correspondences between shapes that might have significant geometric differences. Moreover, due to the special care we take to ensure the robustness of each part of our pipeline, our method can find correspondences between shapes with different representations, such as triangular meshes and point clouds. We demonstrate that the region‐wise matching that we obtain can be used to find correspondences between feature points, reveal the intrinsic self‐similarities of each shape and even construct point‐to‐point maps across shapes. Our method is both time and space efficient, leading to a pipeline that is significantly faster than comparable approaches. We demonstrate the performance of our approach through an extensive quantitative and qualitative evaluation on several benchmarks where we achieve comparable or superior performance to existing methods.We present a robust method to find region‐level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the shapes, and devise an adapted graph‐matching technique, from which we infer correspondences between shape regions. The simplified shape graphs are designed to primarily capture the overall structure of the shapes, without reflecting precise information about the geometry of each region, which enables us to find correspondences between shapes that might have significant geometric differences. Moreover, due to the special care we take to ensure the robustness of each part of our pipeline, our method can find correspondences between shapes with different representations, such as triangular meshes and point clouds.
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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.