Browsing by Author "Cremers, D."

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    Partial Functional Correspondence
    (© 2017 The Eurographics Association and John Wiley & Sons Ltd., 2017) Rodolà, E.; Cosmo, L.; Bronstein, M. M.; Torsello, A.; Cremers, D.; Chen, Min and Zhang, Hao (Richard)
    In this paper, we propose a method for computing partial functional correspondence between non‐rigid shapes. We use perturbation analysis to show how removal of shape parts changes the Laplace–Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Corresponding parts are optimization variables in our problem and are used to weight the functional correspondence; we are looking for the largest and most regular (in the Mumford–Shah sense) parts that minimize correspondence distortion. We show that our approach can cope with very challenging correspondence settings.In this paper, we propose a method for computing partial functional correspondence between non‐rigid shapes. We use perturbation analysis to show how removal of shape parts changes the Laplace‐Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Corresponding parts are optimization variables in our problem and are used to weight the functional correspondence; we are looking for the largest and most regular (in the Mumford‐Shah sense) parts that minimize correspondence distortion. We show that our approach can cope with very challenging correspondence settings.
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    Regularized Pointwise Map Recovery from Functional Correspondence
    (© 2017 The Eurographics Association and John Wiley & Sons Ltd., 2017) Rodolà, E.; Moeller, M.; Cremers, D.; Chen, Min and Zhang, Hao (Richard)
    The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point‐to‐point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly‐isometric, and easily extends to recovering the point‐to‐point correspondence in part‐to‐whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases.The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point‐to‐point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly‐isometric, and easily extends to recovering the point‐to‐point correspondence in part‐to‐whole shape matching problems.
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    Shape Correspondence with Isometric and Non-Isometric Deformations
    (The Eurographics Association, 2019) Dyke, R. M.; Stride, C.; Lai, Y.-K.; Rosin, P. L.; Aubry, M.; Boyarski, A.; Bronstein, A. M.; Bronstein, M. M.; Cremers, D.; Fisher, M.; Groueix, T.; Guo, D.; Kim, V. G.; Kimmel, R.; Lähner, Z.; Li, K.; Litany, O.; Remez, T.; Rodolà, E.; Russell, B. C.; Sahillioglu, Y.; Slossberg, R.; Tam, G. K. L.; Vestner, M.; Wu, Z.; Yang, J.; Biasotti, Silvia and Lavoué, Guillaume and Veltkamp, Remco
    The registration of surfaces with non-rigid deformation, especially non-isometric deformations, is a challenging problem. When applying such techniques to real scans, the problem is compounded by topological and geometric inconsistencies between shapes. In this paper, we capture a benchmark dataset of scanned 3D shapes undergoing various controlled deformations (articulating, bending, stretching and topologically changing), along with ground truth correspondences. With the aid of this tiered benchmark of increasingly challenging real scans, we explore this problem and investigate how robust current state-of- the-art methods perform in different challenging registration and correspondence scenarios. We discover that changes in topology is a challenging problem for some methods and that machine learning-based approaches prove to be more capable of handling non-isometric deformations on shapes that are moderately similar to the training set.