On the Stability of Functional Maps and Shape Difference Operators

dc.contributor.authorHuang, R.en_US
dc.contributor.authorChazal, F.en_US
dc.contributor.authorOvsjanikov, M.en_US
dc.contributor.editorChen, Min and Benes, Bedrichen_US
dc.date.accessioned2018-04-05T12:48:38Z
dc.date.available2018-04-05T12:48:38Z
dc.date.issued2018
dc.description.abstractIn 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.en_US
dc.description.number1
dc.description.sectionheadersArticles
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume37
dc.identifier.doi10.1111/cgf.13238
dc.identifier.issn1467-8659
dc.identifier.pages145-158
dc.identifier.urihttps://doi.org/10.1111/cgf.13238
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13238
dc.publisher© 2018 The Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectdigital geometry processing
dc.subjectmodelling
dc.subjectI.3.3 [Computer Graphics]: Shape Analysis
dc.titleOn the Stability of Functional Maps and Shape Difference Operatorsen_US
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