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.
Unified treatment of elastic metrics for curves in any dimension.
New metrics for surface shapes incorporating curve properties.
The chapter reviews metrics for comparing curves, focusing on quotient elastic and square root velocity metrics.
In the shape analysis approach to computer vision problems, one treats shapes as points in an infinite-dimensional Riemannian manifold, thereby facilitating algorithms for statistical calculations such as geodesic distance between shapes and averaging of a collection of shapes. The performance of these algorithms depen…
In this article we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vector valued one-forms. We provide a numerical framework for the computation of geodesics with respect to these metrics. The family of metrics is invariant …
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…
The paper explores metrics and models for analyzing biological shapes.
New method for surface analysis using restricted deformation bases.
Paper tackles shape graph registration using neural networks.
Improved performance in shape identification tasks using elastic metrics in t-SNE and UMAP.
Paper analyzes shapes of brain arterial networks using statistical methods.
Unsupervised clustering of curves according to their shapes is an important problem with broad scientific applications. The existing model-based clustering techniques either rely on simple probability models (e.g., Gaussian) that are not generally valid for shape analysis or assume the number of clusters. We develop an…
A new method for 3D surface registration using dynamic programming.
Study of red blood cells using elastic surface theory.
The paper studies the free elastic flow of closed curves and finds their asymptotic shape converges to a circle.
Paper develops a new method to analyze 3D tree-like objects.
Optimal thresholds ensure curves remain embedded in flows.
Paper computes optimal matching between curves on manifolds.
Geomstats introduces shape module for analyzing shapes of objects.
Demand variance can result in a mismatch between planned supply and actual demand. Demand shaping strategies such as pricing can be used to shift elastic demand to reduce the imbalance. In this work, we propose to consider elastic demand in the forecasting phase. We present a method to reallocate the historical elastic…
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 are still largely missing. In this paper, we present algorithms to numerically solve the initial and boundary value problems for geodesics. Th…
The aim of this paper is to find an optimal matching between manifold-valued curves, and thereby adequately compare their shapes, seen as equivalent classes with respect to the action of reparameterization. Using a canonical decomposition of a path in a principal bundle, we introduce a simple algorithm that finds an op…
A new algorithm computes elastic shape distances between curves efficiently.
In this paper we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The model and resulting matching algorithm integrate within one common setting both the …
New method weaves paper strips for designing curved surfaces with elasticity.
We introduce elastic geodesic grids for easy-to-fabricate, deployable structures.
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is developed to analytically predict the equilibrium deformed helical shape of an initiall…
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 normal fields and varifold fidelity metrics into a novel framework, which has several potential advantages over previous works. First, our var…
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…
We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoi…
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 discretizations of this infinite-dimensional space are needed, we extend this metric to the space of Lipschitz curves, establish the wellposedness of…
New model for shape graph registration with partial matching constraints.
A new FFT-based method for fast rigid alignment of 2D closed curves.
Sophie Germain's mean curvature deserves recognition as a surface shape measure.
Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape? Motivated by this concern, we first classify, and quantify, the translational, ro…
Study on elastic curves pinned at the boundary, focusing on minimizers and their interaction with obstacles.
We address the geometric Cauchy problem for surfaces associated to the membrane shape equation describing equilibrium configurations of vesicles formed by lipid bilayers. This is the Euler-Lagrange equation of the Canham-Helfrich-Evans elastic curvature energy subject to constraints on the enclosed volume and the surfa…
ES-VAE models skeletal pose trajectories by removing nuisance factors.
Study uniquely determines Riemannian metric derivatives from boundary data.
Stability of hypersurface immersions in Riemannian manifolds proved for perturbations.
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and "shape". We show t…
In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution …
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of bio-membranes, a geometric scheme is proposed to discuss the shape equation of closed…
This work introduces methods to compute optimal Monge maps and learn elastic costs for efficient data mapping.
By introducing a shape manifold as a solution set to solve inverse obstacle scattering problems we allow the reconstruction of general, not necessarily star-shaped curves. The bending energy is used as a stabilizing term in Tikhonov regularization to gain independence of the parametrization. Moreover, we discuss how se…
In this paper, the elastic Dirichlet-to-Neumann map is studied for the stationary elasticity system in a compact Riemannian manifold with smooth boundary . By overcoming methodological difficulties, we explicitly get matrix-valued full symbol for the elastic Dirichlet-to-Neumann map . We …
After a brief introduction to several variational problems in the study of shapes of thin thickness structures, we deal with variational problems on 2-dimensional surface in 3-dimensional Euclidian space by using exterior differential forms. The morphological problems of lipid bilayers and stabilities of cell membranes…
In this article, the clarification to Note 4 (arXiv:1202.0941) for n=8 is considered. In this connection, answers to the following questions are given. 1. How to classify the metric hypercomplex orthogonal group alternative-elastic algebras for n=8? 2. How to associate the metric hypercomplex orthogonal group alternati…