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A General Framework for Curve and Surface Comparison and Registration with Oriented Varifolds

Abstract : This paper introduces a general setting for the construction of data fidelity metrics between oriented or non-oriented geometric shapes like curves, curve sets or surfaces. These metrics are based on the representation of shapes as distributions of their local tangent or normal vectors and the definition of reproducing kernels on these spaces. The construction, that combines in one common setting and extends the previous frameworks of currents and varifolds, provides a very large class of kernel metrics which can be easily computed without requiring any kind of parametrization of shapes and which are smooth enough to give robustness to certain imperfections that could result e.g. from bad segmentation. We then give a sense, with synthetic examples, of the versatility and potentialities of such metrics when used in various problems like shape comparison , clustering and diffeomorphic registration.
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Submitted on : Monday, June 18, 2018 - 9:57:51 AM
Last modification on : Friday, August 5, 2022 - 10:51:48 AM
Long-term archiving on: : Wednesday, September 19, 2018 - 4:25:06 PM

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Irène Kaltenmark, Benjamin Charlier, Nicolas Charon. A General Framework for Curve and Surface Comparison and Registration with Oriented Varifolds. 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Jul 2017, Honolulu, United States. ⟨10.1109/CVPR.2017.487⟩. ⟨hal-01817514⟩

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