Browsing by Author "Ovsjanikov, M."

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    Matching Humans with Different Connectivity
    (The Eurographics Association, 2019) Melzi, S.; Marin, R.; Rodolà, E.; Castellani, U.; Ren, J.; Poulenard, A.; Wonka, P.; Ovsjanikov, M.; Biasotti, Silvia and Lavoué, Guillaume and Veltkamp, Remco
    Objects Matching is a ubiquitous problem in computer science with particular relevance for many applications; property transfer between 3D models and statistical study for learning are just some remarkable examples. The research community spent a lot of effort to address this problem, and a large and increased set of innovative methods has been proposed for its solution. In order to provide a fair comparison among these methods, different benchmarks have been proposed. However, all these benchmarks are domain specific, e.g., real scans coming from the same acquisition pipeline, or synthetic watertight meshes with the same triangulation. To the best of our knowledge, no cross-dataset comparisons have been proposed to date. This track provides the first matching evaluation in terms of large connectivity changes between models that come from totally different modeling methods. We provide a dataset of 44 shapes with dense correspondence as obtained by a highly accurate shape registration method (FARM). Our evaluation proves that connectivity changes lead to Objects Matching difficulties and we hope this will promote further research in matching shapes with wildly different connectivity.
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    On the Stability of Functional Maps and Shape Difference Operators
    (© 2018 The Eurographics Association and John Wiley & Sons Ltd., 2018) Huang, R.; Chazal, F.; Ovsjanikov, M.; Chen, Min and Benes, Bedrich
    In this paper, we provide stability guarantees for two frameworks that are based on the notion of functional maps—the framework of shape difference operators and the one of analyzing and visualizing the deformations between shapes. We consider two types of perturbations in our analysis: one is on the input shapes and the other is on the change in . In theory, we formulate and justify the robustness that has been observed in practical implementations of those frameworks. Inspired by our theoretical results, we propose a pipeline for constructing shape difference operators on point clouds and show numerically that the results are robust and informative. In particular, we show that both the shape difference operators and the derived areas of highest distortion are stable with respect to changes in shape representation and change of scale. Remarkably, this is in contrast with the well‐known instability of the eigenfunctions of the Laplace–Beltrami operator computed on point clouds compared to those obtained on triangle meshes.In this paper, we provide stability guarantees for two frameworks that are based on the notion of functional maps—the shape difference operators introduced in [ROA*13] and the framework of [OBCCG13] which is used to analyse and visualize the deformations between shapes induced by a functional map. We consider two types of perturbations in our analysis: one is on the input shapes and the other is on the change in . In theory, we formulate and justify the robustness that has been observed in practical implementations of those frameworks.