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Now showing 1 - 10 of 71
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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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    Incremental Labelling of Voronoi Vertices for Shape Reconstruction
    (© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Peethambaran, J.; Parakkat, A.D.; Tagliasacchi, A.; Wang, R.; Muthuganapathy, R.; Chen, Min and Benes, Bedrich
    We present an incremental Voronoi vertex labelling algorithm for approximating contours, medial axes and dominant points (high curvature points) from 2D point sets. Though there exist many number of algorithms for reconstructing curves, medial axes or dominant points, a unified framework capable of approximating all the three in one place from points is missing in the literature. Our algorithm estimates the normals at each sample point through poles (farthest Voronoi vertices of a sample point) and uses the estimated normals and the corresponding tangents to determine the spatial locations (inner or outer) of the Voronoi vertices with respect to the original curve. The vertex classification helps to construct a piece‐wise linear approximation to the object boundary. We provide a theoretical analysis of the algorithm for points non‐uniformly (ε‐sampling) sampled from simple, closed, concave and smooth curves. The proposed framework has been thoroughly evaluated for its usefulness using various test data. Results indicate that even sparsely and non‐uniformly sampled curves with outliers or collection of curves are faithfully reconstructed by the proposed algorithm.We present an incremental Voronoi vertex labelling algorithm for approximating contours, medial axes and dominant points (high curvature points) from 2D point sets. Though there exist many number of algorithms for reconstructing curves, medial axes or dominant points, a unified framework capable of approximating all the three in one place from points is missing in the literature. Our algorithm estimates the normals at each sample point through poles (farthest Voronoi vertices of a sample point) and uses the estimated normals and the corresponding tangents to determine the spatial locations (inner or outer) of the Voronoi vertices with respect to the original curve. The vertex classification helps to construct a piece‐wise linear approximation to the object boundary. We provide a theoretical analysis of the algorithm for points non‐uniformly (ε‐sampling) sampled from simple, closed, concave and smooth curves.
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    A Variational Approach to Registration with Local Exponential Coordinates
    (© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Paman, Ashish; Rangarajan, Ramsharan; Chen, Min and Benes, Bedrich
    We identify a novel parameterization for the group of finite rotations (SO), consisting of an atlas of exponential maps defined over local tangent planes, for the purpose of computing isometric transformations in registration problems that arise in machine vision applications. Together with a simple representation for translations, the resulting system of coordinates for rigid body motions is proper, free from singularities, is unrestricted in the magnitude of motions that can be represented and poses no difficulties in computer implementations despite their multi‐chart nature. Crucially, such a parameterization helps to admit varied types of data sets, to adopt data‐dependent error functionals for registration, seamlessly bridges correspondence and pose calculations, and inspires systematic variational procedures for computing optimal solutions. As a representative problem, we consider that of registering point clouds onto implicit surfaces without introducing any discretization of the latter. We derive coordinate‐free stationarity conditions, compute consistent linearizations, provide algorithms to compute optimal solutions and examine their performance with detailed examples. The algorithm generalizes naturally to registering curves and surfaces onto implicit manifolds, is directly adaptable to handle the familiar problem of pairwise registration of point clouds and allows for incorporating scale factors during registration.We identify a novel parameterization for the group of finite rotations (SO), consisting of an atlas of exponential maps defined over local tangent planes, for the purpose of computing isometric transformations in registration problems that arise in machine vision applications. Together with a simple representation for translations, the resulting system of coordinates for rigid body motions is proper, free from singularities, is unrestricted in the magnitude of motions that can be represented and poses no difficulties in computer implementations despite their multi‐chart nature. Crucially, such a parameterization helps to admit varied types of data sets, to adopt data‐dependent error functionals for registration, seamlessly bridges correspondence and pose calculations, and inspires systematic variational procedures for computing optimal solutions. As a representative problem, we consider that of registering point clouds onto implicit surfaces without introducing any discretization of the latter. We derive coordinate‐free stationarity conditions, compute consistent linearizations, provide algorithms to compute optimal solutions and examine their performance with detailed examples. The algorithm generalizes naturally to registering curves and surfaces onto implicit manifolds, is directly adaptable to handle the familiar problem of pairwise registration of point clouds and allows for incorporating scale factors during registration.
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    Complex Functional Maps: A Conformal Link Between Tangent Bundles
    (© 2022 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2022) Donati, Nicolas; Corman, Etienne; Melzi, Simone; Ovsjanikov, Maks; Hauser, Helwig and Alliez, Pierre
    In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their . More specifically, we demonstrate that unlike regular functional maps that link of two manifolds, our complex functional maps establish a link between , thus permitting robust and efficient transfer of tangent vector fields. By first endowing and then exploiting the tangent bundle of each shape with a complex structure, the resulting operations become naturally orientation‐aware, thus favouring across shapes, without relying on descriptors or extra regularization. Finally, and perhaps more importantly, we demonstrate how these objects enable several practical applications within the functional map framework. We show that functional maps and their complex counterparts can be estimated jointly to promote orientation preservation, regularizing pipelines that previously suffered from orientation‐reversing symmetry errors.
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    Physically Based Simulation and Rendering of Urban Thermography
    (© 2020 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2020) Aguerre, José Pedro; García‐Nevado, Elena; Acuña Paz y Miño, Jairo; Fernández, Eduardo; Beckers, Benoit; Benes, Bedrich and Hauser, Helwig
    Urban thermography is a non‐invasive measurement technique commonly used for building diagnosis and energy efficiency evaluation. The physical interpretation of thermal images is a challenging task because they do not necessarily depict the real temperature of the surfaces, but one estimated from the measured incoming radiation. In this sense, the computational rendering of a thermal image can be useful to understand the results captured in a measurement campaign. The computer graphics community has proposed techniques for light rendering that are used for its thermal counterpart. In this work, a physically based simulation methodology based on a combination of the finite element method (FEM) and ray tracing is presented. The proposed methods were tested using a highly detailed urban geometry. Directional emissivity models, glossy reflectivity functions and importance sampling were used to render thermal images. The simulation results were compared with a set of measured thermograms, showing good agreement between them.
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    Wavelet‐based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis
    (© 2021 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2021) Kirgo, Maxime; Melzi, Simone; Patanè, Giuseppe; Rodolà, Emanuele; Ovsjanikov, Maks; Benes, Bedrich and Hauser, Helwig
    In this paper, we propose a new construction for the Mexican hat wavelets on shapes with applications to partial shape matching. Our approach takes its main inspiration from the well‐established methodology of diffusion wavelets. This novel construction allows us to rapidly compute a multi‐scale family of Mexican hat wavelet functions, by approximating the derivative of the heat kernel. We demonstrate that this leads to a family of functions that inherit many attractive properties of the heat kernel (e.g. local support, ability to recover isometries from a single point, efficient computation). Due to its natural ability to encode high‐frequency details on a shape, the proposed method reconstructs and transfers ‐functions more accurately than the Laplace‐Beltrami eigenfunction basis and other related bases. Finally, we apply our method to the challenging problems of partial and large‐scale shape matching. An extensive comparison to the state‐of‐the‐art shows that it is comparable in performance, while both simpler and much faster than competing approaches.
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    SiamesePointNet: A Siamese Point Network Architecture for Learning 3D Shape Descriptor
    (© 2020 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2020) Zhou, J.; Wang, M. J.; Mao, W. D.; Gong, M. L.; Liu, X. P.; Benes, Bedrich and Hauser, Helwig
    We present a novel deep learning approach to extract point‐wise descriptors directly on 3D shapes by introducing Siamese Point Networks, which contain a global shape constraint module and a feature transformation operator. Such geometric descriptor can be used in a variety of shape analysis problems such as 3D shape dense correspondence, key point matching and shape‐to‐scan matching. The descriptor is produced by a hierarchical encoder–decoder architecture that is trained to map geometrically and semantically similar points close to one another in descriptor space. Benefiting from the additional shape contrastive constraint and the hierarchical local operator, the learned descriptor is highly aware of both the global context and local context. In addition, a feature transformation operation is introduced in the end of our networks to transform the point features to a compact descriptor space. The feature transformation can make the descriptors extracted by our networks unaffected by geometric differences in shapes. Finally, an N‐tuple loss is used to train all the point descriptors on a complete 3D shape simultaneously to obtain point‐wise descriptors. The proposed Siamese Point Networks are robust to many types of perturbations such as the Gaussian noise and partial scan. In addition, we demonstrate that our approach improves state‐of‐the‐art results on the BHCP benchmark.
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    TexNN: Fast Texture Encoding Using Neural Networks
    (© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Pratapa, S.; Olson, T.; Chalfin, A.; Manocha, D.; Chen, Min and Benes, Bedrich
    We present a novel deep learning‐based method for fast encoding of textures into current texture compression formats. Our approach uses state‐of‐the‐art neural network methods to compute the appropriate encoding configurations for fast compression. A key bottleneck in the current encoding algorithms is the search step, and we reduce that computation to a classification problem. We use a trained neural network approximation to quickly compute the encoding configuration for a given texture. We have evaluated our approach for compressing the textures for the widely used adaptive scalable texture compression format and evaluate the performance for different block sizes corresponding to 4 × 4, 6 × 6 and 8 × 8. Overall, our method (TexNN) speeds up the encoding computation up to an order of magnitude compared to prior compression algorithms with very little or no loss in the visual quality.We present a novel deep learning‐based method for fast encoding of textures into current texture compression formats. Our approach uses state‐of‐the‐art neural network methods to compute the appropriate encoding configurations for fast compression. A key bottleneck in the current encoding algorithms is the search step, and we reduce that computation to a classification problem. We use a trained neural network approximation to quickly compute the encoding configuration for a given texture.We have evaluated our approach for compressing the textures for the widely used adaptive scalable texture compression format and evaluate the performance for different block sizes corresponding to 4 × 4, 6 × 6 and 8 × 8.
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    A Procedural Approach to Modelling Virtual Climbing Plants With Tendrils
    (© 2016 The Eurographics Association and John Wiley & Sons Ltd., 2016) Wong, Sai‐Keung; Chen, Kai‐Chun; Chen, Min and Zhang, Hao (Richard)
    Climbing plants with tendrils show search and coiling behaviour. A tendril searches for a host object and then twines around it. Subsequently, the tendril coils to pull the main stem of the climbing plant close to the host object. Furthermore, the stems may also twine around the host object. In this paper, we propose a procedural approach to incrementally constructing virtual climbing plants with tendrils that mimic such behaviour. We developed several simple rules to guide the construction process. Although our approach is not based on a physical or biological concept, it is fast and efficient in generating climbing plants with tendrils, with acceptable quality. We propose techniques that are useful for enhancing the realism of climbing plants in close‐up view.Climbing plants with tendrils show search and coiling behaviour. A tendril searches for a host object and then twines around it. Subsequently, the tendril coils to pull the main stem of the climbing plant close to the host object. Furthermore, the stems may also twine around the host object. In this paper, we propose a procedural approach to incrementally constructing virtual climbing plants with tendrils that mimic such behaviour. We developed several simple rules to guide the construction process.
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    Efficient Computation of Smoothed Exponential Maps
    (© 2019 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2019) Herholz, Philipp; Alexa, Marc; Chen, Min and Benes, Bedrich
    Many applications in geometry processing require the computation of local parameterizations on a surface mesh at interactive rates. A popular approach is to compute local exponential maps, i.e. parameterizations that preserve distance and angle to the origin of the map. We extend the computation of geodesic distance by heat diffusion to also determine angular information for the geodesic curves. This approach has two important benefits compared to fast approximate as well as exact forward tracing of the distance function: First, it allows generating smoother maps, avoiding discontinuities. Second, exploiting the factorization of the global Laplace–Beltrami operator of the mesh and using recent localized solution techniques, the computation is more efficient even compared to fast approximate solutions based on Dijkstra's algorithm.Many applications in geometry processing require the computation of local parameterizations on a surface mesh at interactive rates. A popular approach is to compute local exponential maps, i.e. parameterizations that preserve distance and angle to the origin of the map. We extend the computation of geodesic distance by heat diffusion to also determine angular information for the geodesic curves. This approach has two important benefits compared to fast approximate as well as exact forward tracing of the distance function: First, it allows generating smoother maps, avoiding discontinuities. Second, exploiting the factorization of the global Laplace–Beltrami operator of the mesh and using recent localized solution techniques, the computation is more efficient even compared to fast approximate solutions based on Dijkstra's algorithm.