81 citations · 344 across the 24 of their papers we have counts for
28 papers
Long-time existence of Brownian motion on configurations of two landmarks
Karen Habermann, Philipp Harms, Stefan Sommer
We study Brownian motion on the space of distinct landmarks in , considered as a homogeneous space with a Riemannian metric inherited from a right-invariant metric on…
Regularity and completeness of half-Lie groups
Martin Bauer, Philipp Harms, Peter W. Michor
Half Lie groups exist only in infinite dimensions: They are smooth manifolds and topological groups such that right translations are smooth, but left translations are merely requir…
Cylindrical stochastic integration and applications to financial term structure modeling
Johannes Assefa, Philipp Harms
We develop a novel - cylindrical - solution concept for stochastic evolution equations. Our motivation is to establish a Heath-Jarrow-Morton framework capable of analysing financia…
Geometry of Sample Spaces
Philipp Harms, Peter W. Michor, Xavier Pennec +1
In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of the…
A numerical framework for elastic surface matching, comparison, and interpolation
Martin Bauer, Nicolas Charon, Philipp Harms +1
Surface comparison and matching is a challenging problem in computer vision. While reparametrization-invariant Sobolev metrics provide meaningful elastic distances and point corres…
Fractional Sobolev metrics on spaces of immersions
Martin Bauer, Philipp Harms, Peter W. Michor
We prove that the geodesic equations of all Sobolev metrics of fractional order one and higher on spaces of diffeomorphisms and, more generally, immersions are locally well posed.…
Approximation of Riemannian Distances and Applications to Distance-Based Learning on Manifolds
Philipp Harms, Elodie Maignant, Stefan Schlager
Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute,…
Inexact elastic shape matching in the square root normal field framework
Martin Bauer, Nicolas Charon, Philipp Harms
This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root no…
Math in the Black Forest: Workshop on New Directions in Shape Analysis
Martin Bauer, Nicolas Charon, Philipp Harms +9
These are the proceedings of the workshop "Math in the Black Forest", which brought together researchers in shape analysis to discuss promising new directions. Shape analysis is an…
Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics
Martin Bauer, Martins Bruveris, Philipp Harms +1
We show for a certain class of operators and holomorphic functions that the functional calculus is holomorphic. Using this result we are able to prove that…
Vanishing distance phenomena and the geometric approach to SQG
Martin Bauer, Philipp Harms, Stephen C. Preston
In this article we study the induced geodesic distance of fractional order Sobolev metrics on the groups of (volume preserving) diffeomorphisms and symplectomorphisms. The interest…
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…
A Numerical Framework for Sobolev Metrics on the Space of Curves
Martin Bauer, Martins Bruveris, Philipp Harms +1
Statistical shape analysis can be done in a Riemannian framework by endowing the set of shapes with a Riemannian metric. Sobolev metrics of order two and higher on shape spaces of…
Metrics with prescribed horizontal bundle on spaces of curve
Martin Bauer, Philipp Harms
We study metrics on the shape space of curves that induce a prescribed splitting of the tangent bundle. More specifically, we consider reparametrization invariant metrics on th…
Hörmander's condition for normal bundles on spaces of immersions
Martin Bauer, Philipp Harms
Several representations of geometric shapes involve quotients of mapping spaces. The projection onto the quotient space defines two sub-bundles of the tangent bundle, called the ho…
Second order elastic metrics on the shape space of curves
Martin Bauer, Martins Bruveris, Philipp Harms +1
Second order Sobolev metrics on the space of regular unparametrized planar curves have several desirable completeness properties not present in lower order metrics, but numerics ar…
Curve Matching with Applications in Medical Imaging
Martin Bauer, Martins Bruveris, Philipp Harms +1
In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization…
Metrics on Spaces of Immersions where Horizontality Equals Normality
Martin Bauer, Philipp Harms
We study metrics on shape space of immersions that have a particularly simple horizontal bundle. More specifically, we consider reparametrization invariant Sobolev metrics on t…
The Poincaré Lemma in Subriemannian Geometry
Philipp Harms
This work is a short, self-contained introduction to subriemannian geometry with special emphasis on Chow's Theorem. As an application, a regularity result for the Poincaré Lemma i…
Sobolev metrics on shape space of surfaces
Philipp Harms
Many procedures in science, engineering and medicine produce data in the form of geometric shapes. Mathematically, a shape can be modeled as an un-parameterized immersed sub-manifo…
Geodesics in infinite dimensional Stiefel and Grassmann manifolds
Philipp Harms, Andrea C. G. Mennucci
Let be a separable Hilbert space, possibly infinite dimensional. Let $\St(p,V)$ be the Stiefel manifold of orthonormal frames of vectors in , and let $\Gr(p,V)$ be the G…
Sobolev Metrics on Shape Space, II: Weighted Sobolev Metrics and Almost Local Metrics
Martin Bauer, Philipp Harms, Peter W. Michor
In continuation of [3] we discuss metrics of the form $$ G^P_f(h,k)=\int_M \sum_{i=0}^pΦ_i(\Vol(f)) \g((P_i)_fh,k) \vol(f^*\g) $$ on the space of immersions $\Imm(M,N)$ and on shap…
Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group
Martin Bauer, Martins Bruveris, Philipp Harms +1
We study Sobolev-type metrics of fractional order on the group $\Diff_c(M)$ of compactly supported diffeomorphisms of a manifold . We show that for the important specia…
Curvature weighted metrics on shape space of hypersurfaces in -space
Martin Bauer, Philipp Harms, Peter W. Michor
Let be a compact connected oriented dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from to $\mathbb R^n…