A General Framework for Curve and Surface Comparison and Registration with Oriented Varifolds
Year: 2017
Type: conference-paper
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.
Institutions: Université Paris-Saclay, Institut de Neurosciences de la Timone, Center for MathematicaL studies and their Applications, Centre National de la Recherche Scientifique, Université de Montpellier, Institut Montpelliérain Alexander Grothendieck, Université Montpellier 2, École Normale Supérieure Paris-Saclay, Johns Hopkins University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2741275949