A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A novel method predicts shape development using Riemannian shape spaces.
Geomstats introduces shape module for analyzing shapes of objects.
The paper explores three methods to assign a metric to shape spaces.
Optimizes shapes on non-standard manifolds.
Extended orbit model theory for shape analysis using graded group action framework.
The paper explores metrics and models for analyzing biological shapes.
A new shape space allows optimization of non-smooth shapes in fluid mechanics.
Python tools for 3D shape analysis on Kendall's space.
Space mapping speeds up shape optimization for PDEs.
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations exist, it is sometimes difficult to gain an overview how differential geometry and…
In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds and Lie groups. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull growth data of Book…
The paper classifies and explores isoparametric hypersurfaces in pseudo-Riemannian space forms.
In shape analysis, the concept of shape spaces has always been vague, requiring a case-by-case approach for every new type of shape. In this paper, we give a general definition for an abstract space of shapes in a manifold. This notion encompasses every shape space studied so far in the literature, and offers a rigorou…
This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the prism of Riemannian submersions, with shape space metrics being induced from metrics…
A classical result in Riemannian geometry states that the absolutely continuous curves into a (finite-dimensional) Riemannian manifold form an infinite-dimensional manifold. In the present paper this construction and related results are generalised to absolutely continuous curves with values in a strong Riemannian mani…
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 metrics on this space: so-called outer metrics are metrics that measure shape changes using deformations of the ambient space and they find appli…
The paper derives inequalities for Riemannian maps and submersions involving quaternionic space forms.
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 parametrized or unparametrized curves have several desirable properties not present in lower order metrics, but their discretization is stil…
We create a smooth manifold of triangular meshes with a geodesically complete metric.
A neural network learns efficient parametrizations of product shape spaces.
This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the Riemannian metrics that can be defined thereon, and what is known about the propertie…
New metrics on curve spaces improve shape analysis.
Establish generalized Chen inequalities for Riemannian submersions and Riemannian maps with applications.
This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather than inheriting it from pre-shape space, and using it to formulate a path energ…
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-manifold, which is the notion of shape used here. Endowing shape space with a Riemannian metric opens up the world of Riemannian differential geom…
Introduces intrinsic Riemannian cross-covariance for manifold-valued random objects.
The projective shape of a configuration of k points or "landmarks" in RP(d) consists of the information that is invariant under projective transformations and hence is reconstructable from uncalibrated camera views. Mathematically, the space of projective shapes for these k landmarks can be described as the quotient sp…
The paper explores polyharmonic hypersurfaces in pseudo-Riemannian space forms.
Geometric reduction of the Newtonian planar three-body problem is investigated in the framework of equivariant Riemannian geometry, which reduces the study of trajectories of three-body motions to the study of their moduli curves, that is, curves which record the change of size and shape, in the moduli space of oriente…
Classification theorems for Ricci solitons on Minkowski hypersurfaces.
Characterizes geodesic completeness for landmark spaces.
In this paper we complete the study started in [Pi2] of evolution by inverse mean curvature flow of star-shaped hypersurface in non-compact rank one symmetric spaces. We consider the evolution by inverse mean curvature flow of a closed, mean convex and star-shaped hypersurface in the quaternionic hyperbolic space. We p…
A new method for analyzing shapes and forms using additive models on manifolds.
Paper computes optimal matching between curves on manifolds.
Paper controls shape stability in infinite Riemannian manifolds.
We consider the evolution by inverse mean curvature flow of a closed, mean convex and star-shaped hypersurface in the complex hyperbolic space. We prove that the flow is defined for any positive time, the evolving hypersurface stays star-shaped and mean convex. Moreover the induced metric converges, after rescaling, to…
Rigidity of Wasserstein spaces over Riemannian manifolds
In the elastic shape analysis approach to shape matching and object classification, plane curves are represented as points in an infinite-dimensional Riemannian manifold, wherein shape dissimilarity is measured by geodesic distance. A remarkable result of Younes, Michor, Shah and Mumford says that the space of closed p…
New method for surface analysis using restricted deformation bases.
Unified treatment of elastic metrics for curves in any dimension.
Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their parametrisation. One computationally efficient approach to shape analysis is based on the Sq…
Riemannian first-passage percolation (FPP) is a continuum model, with a distance function arising from a random Riemannian metric in . Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that …
The chapter reviews metrics for comparing curves, focusing on quotient elastic and square root velocity metrics.
Study the isoperimetric problem in Riemannian manifolds with non-trivial conformal vector fields.
New method uses Riemannian geometry to describe molecular shapes.
We consider the results of combining two approaches developed for the design of Riemannian metrics on curves and surfaces, namely parametrization-invariant metrics of the Sobolev type on spaces of immersions, and metrics derived through Riemannian submersions from right-invariant Sobolev metrics on groups of diffeomorp…
The study examines evolving star-shaped hypersurfaces in hyperbolic spaces, influenced by ambient geometry.
Study uses outer metrics for PDE-constrained shape optimization over diffeomorphism group.