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

Irène Kaltenmark (1) , Benjamin Charlier (2) , Nicolas Charon (3)

1 INT - Institut de Neurosciences de la Timone
2 IMAG - Institut Montpelliérain Alexander Grothendieck
3 CMLA - Centre de Mathématiques et de Leurs Applications

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.

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Machine Learning [stat.ML]

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⟩