A new method for 3D surface registration using dynamic programming.
problem Elastic shape registration of 3D surfaces.
method Optimization over a subset of reparametrizations using dynamic programming.
result Proposes an algorithm that produces a solution closer to optimal than gradient-based methods.
A new numerical framework simplifies elastic surface matching and comparison.
problem Challenging problem in surface comparison and matching in computer vision.
method Relaxing the geodesic boundary constraint using a varifold fidelity metric.
result Flexibility to deal with arbitrary topologies and sampling patterns, scalability to large meshes.
We study a class of elastic energy functionals for maps between planar domains (among them the so-called squared distance functional) whose critical points (elastic maps) allow a far more complete theory than one would expect from general elasticity theory. For some of these functionals elastic maps even admit a "Weier…
Paper develops multivariate time series similarity and distance measures.
problem Compensating for misalignments in multivariate time series data.
method Adapted Independent and Dependent DTW strategies to seven elastic similarity and distance measures.
result Each measure achieves highest accuracy on at least one dataset, supporting their value.
Study of elastic models in non-Euclidean spaces via Γ-convergence.
problem Elasticity in non-Euclidean ambient spaces with incompatible local rest distances.
method Γ-convergence to derive a limit elastic model, relating minimum energy to curvature discrepancy.
result Linearized version of a conjecture in elasticity confirmed, linking energy to curvature.
A new algorithm computes elastic shape distances between curves efficiently.
problem Computing elastic shape distances between curves in high dimensions.
method Dynamic Programming for optimal diffeomorphisms and Kabsch-Umeyama algorithm for optimal rotation matrices.
result Efficient computation of elastic shape distances with improved efficiency for closed curves.
The chapter reviews metrics for comparing curves, focusing on quotient elastic and square root velocity metrics.
problem Comparing and analyzing shapes of curves.
method Construction and theoretical properties of quotient elastic metrics, special case of square root velocity metric, numerical approaches for estimation.
result Simplified expression for the square root velocity metric distance.
We derive a continuum model for incompatible elasticity as a variational limit of a family of discrete nearest-neighbor elastic models. The discrete models are based on discretizations of a smooth Riemannian manifold (M,g), endowed with a flat, symmetric connection ∇. The metric g deter…
Study spherical curves with curvature dependent on distance to a great circle.
problem Understanding spherical curves with curvature dependent on distance to a great circle.
method Introducing spherical angular momentum, characterizing known curves, finding new families, and obtaining arc length parametrizations.
result New families of spherical curves with intrinsic equations in elementary or Jacobi elliptic functions.
Classifies soap film surfaces with vertical potentials.
problem Classifying soap film surfaces with vertical potentials.
method Variational characterization of n-elastic curves. result Obtains a full description of n-elastic curves. Unified treatment of elastic metrics for curves in any dimension.
problem Defining metrics on spaces of Euclidean curves for statistical analysis.
method Developing a unified approach to elastic metrics, extending results on existence of solutions and algorithms for computing distances and geodesics.
result Unified treatment of elastic metrics for all parameter choices, extending previous work.
This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves. Our approach combines the general simplifying transform for first-order elastic metrics that was recently introduced by Kurtek and Needham, together with a relaxatio…
A new FFT-based method for fast rigid alignment of 2D closed curves.
problem Rigid alignment of 2D closed curves with application to shape analysis.
method FFT-based algorithm for optimal rigid alignment of closed curves with O(N log N) complexity.
result Order of magnitude speed-up in curve alignment compared to previous methods.
We provide an easy approach to the geodesic distance on the general linear group GL(n) for left-invariant Riemannian metrics which are also right-O(n)-invariant. The parametrization of geodesic curves and the global existence of length minimizing geodesics are deduced using simple methods based on the calculus of varia…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a configuration of a body in classical elasticity is the sum of local contributions …
We prove that the boundary distance map of a smooth compact Finsler manifold with smooth boundary determines its topological and differentiable structures. We construct the optimal fiberwise open subset of its tangent bundle and show that the boundary distance map determines the Finsler function in this set but not in …
For a given family of smooth closed curves γ1,...,γα⊂R3 we consider the problem of finding an elastic \emph{connected} compact surface M with boundary γ=γ1∪...∪γα. This is realized by minimizing the Willmore energy W on a suitable class of competitors. While the direct minimi…
This work introduces methods to compute optimal Monge maps and learn elastic costs for efficient data mapping.
problem Efficiently mapping one probability distribution to another using elastic costs.
method Proposes numerical methods to compute optimal Monge maps and a learning loss for parameterized regularizers.
result Proves the optimality of computed Monge maps and learns the parameters of elastic costs.
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…
We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic regression, the bias due to outliers always causes the parameter vector to implode, t…
Analyzes properties of stiffness tensors for elastic wave imaging.
problem Characterizing stiffness tensor fields for elastic wave imaging.
method Finsler-geometric methods applied to anisotropic stiffness tensor fields.
result Conditions for Finsler-geometric methods to be applicable.
This paper introduces an elasticity reconstruction method based on local displacement observations of elastic bodies. Sparse reconstruction theory is applied to formulate the underdetermined inverse problems of elasticity reconstruction including unobserved areas. An online local clustering scheme called a superelement…
Elastic Cash adjusts money supply to stabilize interest rates.
problem Stabilizing interest rates in a decentralized system.
method Modifies supply to keep interest rate fixed by public market.
result Improves elasticity of US Dollar and new cryptocurrencies.
Characterizes null Lagrangians in Cosserat elasticity.
problem Understanding null Lagrangians in micropolar elasticity.
method Applying Olver and Sivaloganathan's theorem to characterize null Lagrangians.
result Complete characterization of null Lagrangians for three-dimensional bodies and shells.
Approximate 3D elastic curves with exact constraints
problem Designing and approximating 3D elastic curves
method Numerically stable method for recovering 11 parameters
result Fast and stable approximation of arbitrary curves
The paper studies rigidity and continuity in nonlinear elasticity on manifolds and hypersurfaces.
problem Rigidity and continuity properties of elastic bodies in non-Euclidean settings.
method Geometric rigidity estimates, asymptotic rigidity of elastic membranes, simplified geometric proof of continuous dependence.
result Established geometric rigidity estimate and proved asymptotic rigidity of elastic membranes.
Study preserves planar and graphical properties of curves under elastic flow.
problem Maintaining planar and graphical properties of non-compact curves under elastic flow.
method Extended recent work on adapted elastic energy to derive thresholds for planar and graphical embeddedness.
result Derived new Li--Yau type inequality for complete planar curves.
The paper studies the free elastic flow of closed curves and finds their asymptotic shape converges to a circle.
problem Challenges in studying the asymptotic behavior of the free elastic flow for closed curves.
method Analysis of the free elastic flow as an L2-gradient flow for Euler's elastic energy. result An appropriate rescaling of initial curves geometrically close to circles converges to a unique round circle.
Motivated by the problem of finding an explicit description of a developable narrow Moebius strip of minimal bending energy, which was first formulated by M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently E.L. Starostin and G.H.M. van der Heijden found a numerical description for an elastic Mo…
Study on migrating elastic flows of curves across half-planes.
problem Migrating elastic flows of curves from upper to lower half-planes.
method Analytical and numerical construction of migrating elastic flows.
result Construction of various migrating elastic flows.
Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.
problem Recover stiffness tensor and density from Dirichlet-to-Neumann map.
method Analyze invariance under coordinate transformations and gauge freedoms.
result Present gauge freedoms in the Dirichlet-to-Neumann map for Riemannian elastic wave equation.
Solves curve migration problem with elastic flows.
problem Curve migration problem with natural boundary conditions.
method Constructing migrating elastic flows.
result Extends previous work to purely local flow.
New insights into stability of special curves on spheres.
problem Stability of closed p-elastic curves on spheres. method Analytical proof and construction of curves.
result All closed spherical p-elastic curves for p∈(0,1) are unstable. Due to the advantage of achieving a better performance under weak regularization, elastic net has attracted wide attention in statistics, machine learning, bioinformatics, and other fields. In particular, a variation of the elastic net, adaptive elastic net (AEN), integrates the adaptive grouping effect. In this paper,…
Symmetric elastic knots are found for certain classes with dihedral symmetry.
problem Finding elastic knots with specific symmetries.
method Minimizing bending energy under dihedral symmetry constraints.
result Existence of dihedral symmetric elastic knots, including a figure-eight union for the trefoil.
New discrete curves defined in space forms with geometric properties.
problem Defining discrete elastic and constrained elastic curves in space forms.
method Extending discrete Euclidean curvature to space forms and using Bäcklund transformations.
result Discrete elastic and constrained elastic curves are elements of a curve hierarchy.
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…
The elastic flow, which is the L2-gradient flow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elastic flow in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples in…
Lipid-bilayers are the fundamental constituents of the walls of most living cells and lipid vesicles, giving them shape and compartment. The formation and growing of pores in a lipid bilayer have attracted considerable attention from an energetic point of view in recent years. Such pores permit targeted delivery of dru…
Unified survey of elastic flow for curves and networks.
problem Understanding the evolution of curves and networks under elastic forces.
method Unified presentation and proof of global existence and convergence for closed curves.
result Global existence and smooth convergence to critical points for closed curves in R^2.
Study on elastic curves with variable stiffness, derived from bending energy.
problem Modeling elastic wires with varying thickness.
method Derive Euler-Lagrange equations for curves with variable bending stiffness.
result Characterizations of elastic curves with variable stiffness.
Study on closed p-elastic curves in hyperbolic and de Sitter planes.
problem Existence of closed p-elastic curves with nonconstant curvature. method Analysis of p-elastic curves in hyperbolic and de Sitter planes. result Existence of closed p-elastic curves in hyperbolic plane for p>1; in de Sitter plane for p<0. Paper develops a new method to analyze 3D tree-like objects.
problem Analyzing complex geometrical and topological variations in 3D tree-like objects.
method Extended SRVF representation and new metric for tree-shaped 3D objects.
result Captures full elasticity and topological variations of branches.
In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, Rk. We prove the Γ-convergence of elastic energies for configurations of a converging sequence, Mn→M, of body manifolds. This convergence result …
Study on Transfer Elastic Net error bounds and grouping effect.
problem Estimation error and grouping effect in Transfer Elastic Net.
method Derives non-asymptotic error bound and examines grouping effect scenarios.
result Effective error bounds and grouping effect observed in Transfer Elastic Net.
Study shows global invertibility in nonlinear elasticity with vanishing self-repulsion term.
problem Global invertibility in nonlinear elasticity with a vanishing nonlocal self-repulsion term.
method Proves global invertibility in the Γ-limit of elastic energy with a vanishing nonlocal self-repulsion term. result Global invertibility can be obtained in the Γ-limit of the elastic energy with a vanishing nonlocal self-repulsion term. Study on spectral asymptotics in elasticity on smooth manifolds.
problem Analyzing spectral asymptotics in linear elasticity on smooth manifolds.
method Established two-term spectral asymptotics for boundary value problems in linear elasticity.
result Corrected erroneous results in previous studies.
We provide a new angle and obtain new results on a class of metrics on length-normalized curves in d dimensions, represented by their unit tangents expressed as a function of arc-length, which are functions from the unit interval to the (d−1)-dimensional unit sphere. These metrics are derived from the combined acti…