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 strategy of computing geodesics between unparametrized curves. We describe the numerical method used for solving the inexact matching problem, appl…
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169,181 papers · 148 categories
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48 results for “curve matching”
Paper computes optimal matching between curves on manifolds.
problem Matching curves on infinite-dimensional manifolds.
method Geodesic computation using Riemannian metric and quotient structure.
result Algorithm for computing geodesics in shape space.
Paper tackles curve pattern identification from fragmented cultural heritage objects.
problem Identify full design of curve patterns from fragmented cultural heritage objects.
method Two-stage matching algorithm combining template matching and CNN re-ranking.
result Proposed algorithm outperforms traditional methods in identifying curve patterns from fragmented objects.
New method for comparing curves with flexible matching constraints.
problem Comparing plane curves with general elastic metrics.
method Combining transform for elastic metrics with parametrization-invariant fidelity metrics.
result Simple optimization problem for discretized curves.
The process of un-reduction, a sort of reversal of reduction by the Lie group symmetries of a variational problem, is explored in the setting of field theories. This process is applied to the problem of curve matching in the plane, when the curves depend on more than one independent variable. This situation occurs in a…
Paper develops a new method for curve matching using elastic metrics.
problem Matching unparametrized curves with elastic metrics.
method Develops a relaxed variational formulation for curve matching, integrating -metrics and quotienting out similarity groups.
result Proposes a method that avoids optimizing over the reparametrization group and can handle boundary constraints.
Proves curves on surfaces intersect at most once, matching known constructions.
problem Curves on surfaces intersecting at most once.
method Probabilistic argument in graph theory.
result Bound on cardinality of curves on surfaces.
New method for elastic curve and surface matching.
problem Elastic matching of unparametrized curves and surfaces.
method Combines square root normal fields and varifold fidelity metrics.
result Numerical examples demonstrate the approach's effectiveness.
New model for shape graph registration with partial matching constraints.
problem Shape graph registration with topological inconsistencies and partial matching.
method Higher order invariant Sobolev metrics, varifolds, inexact variational formulation, SFISTA algorithm.
result Existence of minimizers for variational problem with TV regularization.
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…
Tropical curves match to special Lagrangian shapes.
problem Connecting tropical geometry to special Lagrangian shapes.
method Gluing construction that matches tropical local models to Lagrangian shapes.
result Locally planar tropical curves can be realized as special Lagrangian limits.
New method for partial matching of shapes with Varifolds.
problem Matching structures with topological or shape differences.
method Varifold shape representation and LDDMM framework.
result Effective partial matching despite topological differences.
New condition prevents hyperbolic spaces from matching curve complexes.
problem Identifying when hyperbolic spaces cannot match curve complexes.
method Analyzing specific hyperbolic complexes and identifying a condition.
result Identified a condition preventing quasi-isometry between hyperbolic spaces and curve complexes.
Automorphisms of fine curve graphs match surface homeomorphisms for planar surfaces.
problem Understanding automorphisms of fine curve graphs on surfaces.
method Analyzing vertices and edges of fine curve graphs to match with surface homeomorphisms.
result Automorphism group of fine curve graphs is naturally isomorphic to the homeomorphism group of boundaryless planar surfaces with at least 7 punctures.
The square root velocity function (SRVF), introduced by Srivastava et al, has proved to be an effective way to compare absolutely continuous curves in modulo reparametrization. Several computational papers have been published based on this method. In this paper, we carefully establish the theoretical foundations …
The paper shows how to rearrange arcs to form closed curves.
problem Creating closed curves from planar arcs.
method Splitting a curve into arcs and rearranging them to form a closed curve.
result Closed curves can be formed by rearranging arcs under weak assumptions.
Any generic closed curve in the plane can be transformed into a simple closed curve by a finite sequence of local transformations called homotopy moves. We prove that simplifying a planar closed curve with self-crossings requires homotopy moves in the worst case. Our algorithm improves the best previou…
A method is proposed to construct spiral curves by inversion of a spiral arc of parabola. The resulting curve is rational of 4-th order. Proper selection of the parabolic arc and parameters of inversion allows to match a wide range of boundary conditions, namely, tangents and curvatures at the endpoints, including thos…
Automorphisms of fine curve graph match surface homeomorphisms.
problem Understanding automorphisms of curve graphs for surfaces.
method Building on previous work, proving isomorphism to surface homeomorphisms.
result The group of automorphisms of the fine curve graph is isomorphic to the extended mapping class group of the surface.
RG-VFM extends VFM to curved manifolds for better material and protein design.
problem Designing materials and proteins on curved manifolds.
method Riemannian Gaussian Variational Flow Matching (RG-VFM) for generative modeling on manifolds.
result RG-VFM more effectively captures manifold structure and improves performance.
Agent-based model simulates market dynamics with real-time order matching.
problem Realistic simulation of market dynamics with realistic price impact.
method Agent-based model with asynchronous, event-time order matching.
result Realistic price impact curves and stylized facts presented.
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.
Unified approach to shape matching using optimal control.
problem Shape registration of curves and surfaces.
method Unified Riemannian metrics, optimal control, chordal distances.
result Unified framework for shape matching.
Flow deforms curves to match an embedded target.
problem Evolve curves to match an embedded target curve.
method Target flow with curve shortening and forcing term.
result Smooth convergence to the target curve.
Automorphism group of nonorientable surface curve graph matches surface homeomorphisms.
problem Identifying automorphisms of nonorientable surface curve graphs.
method Using Bowden, Hensel, and Webb's fine curve graph and Long, Margalit, Pham, Verberne, and Yao's proof as a foundation.
result Automorphism group of nonorientable surface curve graph is isomorphic to the surface's homeomorphism group.
We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations). Given two curves, the distance between them is defined as the infimum of an energy …
Unified framework matches equity and bond yields.
problem Inconsistency in pricing zero-coupon bonds and equity markets.
method Unified term structure of interest rates framework using put-call parity.
result Option-implied yield curves closely match treasury par yield curves.
New algorithm forecasts health indicators for better equipment lifespan prediction.
problem Improving equipment lifespan prediction through health indicator forecasting.
method Generative + scenario matching approach using Gaussian Process.
result Superior performance compared to existing methods.
Study shows K-moduli spaces of curves on quadrics and K3 surfaces match with VGIT quotients.
problem Understanding K-moduli spaces of curves on quadrics and K3 surfaces.
method Using log Fano pairs and VGIT quotients, the study compares K-moduli spaces of curves on and quartic hyperelliptic K3 surfaces.
result K-moduli spaces of curves on quadrics and K3 surfaces form a natural interpolation.
Numerical Solutions of Kahler-Einstein metrics on with conical singularities along a conic curvemath.DG
We solve for the SO(3)-invariant Kahler-Einstein metric on with cone singularities along a smooth conic curve using numerical approach. The numerical results show the sharp range of angles () for the solvability of equations, and the right limit metric space (). These results exactly …
New method uses anisotropic mean curvature flow for contour recognition.
problem Contour recognition in images.
method Coupling anisotropic mean curvature flow with external charges for curve motion.
result Stable numerical approximation for contour recognition.
We study rerouting edges on surfaces without crossings.
problem Reconfiguring edge paths on surfaces without crossing.
method Rerouting one edge at a time, maintaining crossing-free intermediate embeddings.
result Reconfiguration is always possible on the torus and any orientable surface of genus at least one.
This paper establishes an isomorphism between the Bar-Natan skein module of the solid torus with a particular boundary curve system and the homology of the (n,n) Springer variety. The results build on Khovanov's work with crossingless matchings and the cohomology of the (n,n) Springer variety. We also give a formula fo…
New methods predict drug interactions using drug co-medication patterns and graph matching.
problem Predicting adverse drug reactions from drug combinations.
method Developed novel kernels over drug combinations using support vector machines and graph matching to measure similarities.
result Achieved an AUC of 0.912 on a real-world dataset.
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 of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical …
Skeins on Branesmath.SG
Mathematical study connects curve counting to quantum topology.
problem Counting holomorphic curves with Lagrangian boundary in Calabi-Yau 3-folds.
method Organized 1-parameter families of holomorphic curves and matched them to HOMFLYPT skein relations.
result Holomorphic curve counts match HOMFLYPT polynomial coefficients of links in the 3-sphere.
The study examines how the number of noise samples affects diffusion models' performance.
problem Understanding the balance between generalization and memorization in diffusion models.
method Theoretical analysis and empirical experiments with Denoising Score Matching (DSM) using random features.
result Precise expressions for test and train errors under specific conditions reveal the mechanisms of generalization and memorization.
Extends shape analysis to framed space curves using quaternionic arithmetic.
problem Matching and classifying shapes of framed space curves.
method Extends square root transform to framed curves using quaternionic arithmetic and Hopf fibration properties. Describes geodesics in framed curve space explicitly.
result Explicit descriptions of geodesics in framed curve space and averages of collections of curves.
Efficiently models learning curves using Gaussian processes with latent Kronecker structure.
problem Joint modeling of machine learning model performance across hyper-parameters and training progress.
method Imposes latent Kronecker structure to leverage efficient product kernels and handle missing values.
result Matches the performance of a Transformer on a learning curve prediction task.
The paper connects knot invariants to quiver representations via curve counting.
problem Relating knot invariants to quiver representations.
method Combines physics and geometry, using M-theory and curve counting.
result Matches partition functions between quiver theory and curve counting.
Paper introduces k-DTW for robust curve comparison.
problem Robust dissimilarity measure for polygonal curves.
method Introduces k-Dynamic Time Warping (k-DTW) as a novel dissimilarity measure.
result k-DTW is more robust to outliers and has stronger metric properties than DTW.
We develop a multi-curve term structure setup in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to LIBOR swaptions data and show that a rational two-factor lognormal multi-curve model is sufficient to match market data with accuracy. We elucidate the relationship…
Paper tackles shape graph registration using neural networks.
problem Constrained registration of shape graphs with varying nodes and edges.
method Shape-Graph Matching Network (SGM-net) with an elastic shape metric loss function.
result State-of-the-art matching performance and reduced computational cost.
New method identifies vanishing arcs for curve singularities.
problem Characterizing arcs sent to geometric vanishing cycles.
method Introducing geometric variation operator and vanishing arcsets.
result Existence of topological exceptional collections of arcsets.
The un-reduction procedure introduced previously in the context of Mechanics is extended to covariant Field Theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one independent variable (for instance, time and an additional labelling parameter)…
Accelerates pulsar light curve inference with learned representations and optimization.
problem Computational expense of Markov chain Monte Carlo methods for posterior inference.
method Combining U-Net latent representations with local simulator-guided optimization.
result 120x reduction in inference time (24 hours to 12 minutes) with accuracy preserved.
Paper simplifies transforms for elastic metrics on curve shapes.
problem Improving the performance of shape analysis algorithms.
method Extending coordinate transformations to a family of isometries.
result Existence of optimal matchings over the diffeomorphism group.
We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We t…