127 citations · 595 across the 29 of their papers we have counts for
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Riemannian geometry on spaces of submanifolds induced by the diffeomorphism group
Martins Bruveris
The space of embedded submanifolds plays an important role in applications such as computational anatomy and shape analysis. We can define two different classes on Riemannian metri…
Varifold-based matching of curves via Sobolev-type Riemannian metrics
Martins Bauer, Martins Bruveris, Nicolas Charon +1
Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifold-based inexact matching to explore a new strateg…
Completeness of Length-Weighted Sobolev Metrics on the Space of Curves
Martins Bruveris, Jakob Møller-Andersen
In this article we prove completeness results for Sobolev metrics with nonconstant coefficients on the space of immersed curves and on the space of unparametrized curves. We provid…
Fractional Sobolev metrics on spaces of immersed curves
Martin Bauer, Martins Bruveris, Boris Kolev
Motivated by applications in the field of shape analysis, we study reparametrization invariant, fractional order Sobolev-type metrics on the space of smooth regular curves $\operat…
Soliton solutions for the elastic metric on spaces of curves
Martin Bauer, Martins Bruveris, Philipp Harms +1
In this article we investigate a first order reparametrization-invariant Sobolev metric on the space of immersed curves. Motivated by applications in shape analysis where discretiz…