We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the segmented objects. Such a-priori information can be expressed in terms of upper a…
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48 results for “level-set method”
Paper presents a robust transfer learning method for active level set estimation.
problem Efficiently identifying regions of a black-box function with limited function evaluations.
method Incorporates prior knowledge from a related function while locally adapting it.
result The method achieves better convergence of level sets compared to standard transfer learning.
New scoring rules for multivariate distributions and level sets.
problem Evaluating forecast accuracy for multivariate distributions and level sets.
method Theoretical framework for scoring rules, decomposition of multivariate scoring functions, numerical algorithm for computation.
result New scoring functions for multivariate distributions and level sets, including density and cumulative distribution level sets.
Deep learning predicts curvature of 2D interfaces in level-set method.
problem Estimating curvature in level-set method for complex interfaces.
method Deep learning using feed-forward neural networks trained on synthetic data.
result Deep learning models approximate curvature with comparable precision to traditional methods.
New method for analyzing elliptic and parabolic equations.
problem Analyzing elliptic and parabolic equations.
method Level set version of partial uniform ellipticity.
result Effective approach to investigate equations.
The level sets of neural networks represent fundamental properties such as decision boundaries of classifiers and are used to model non-linear manifold data such as curves and surfaces. Thus, methods for controlling the neural level sets could find many applications in machine learning. In this paper we present a simpl…
Develops efficient method for nonconvex problems using Regula Falsi.
problem Nonconvex inverse problems with likelihood constraints.
method Regula Falsi root-finding techniques applied to level-set formulations.
result Proves extension of level-set methods to nonconvex problems.
Level sets of harmonic functions on three-dimensional manifolds with nonnegative scalar curvaturemath.DG
Study on harmonic functions on nonnegative curvature 3D manifolds.
problem Analyzing harmonic functions on specific 3D manifolds.
method Inspired by Miao, developed a monotonic quantity for level sets of harmonic functions on with nonnegative scalar curvature.
result Established a rigidity result for the derived monotonic quantity.
In this note we prove that the level-set flow of the topologist's sine curve is a smooth closed curve. In previous work it was shown by the second author that under level-set flow, a locally-connected set in the plane evolves to be smooth, either as a curve or as a positive area region bounded by smooth curves. Here we…
For the minimal graph defined on a convex ring in the space form with nonnegative curvature, we obtain the regularity and the strict convexity about its level sets by the continuity method.
This paper introduces a more efficient method for estimating level sets with a stopping criterion.
problem Efficiently estimating regions where a function exceeds a threshold without exhaustive evaluations.
method Acquisition strategy with a stopping criterion for -accurate level set estimation.
result The method satisfies -accuracy with a confidence level of and guarantees on lower bounds of performance metrics.
Minimal graph level sets are concave if boundary is concave.
problem Understanding curvature of minimal graph level sets.
method Proved an inequality and showed geometric properties.
result Level sets of minimal graphs are concave if boundary is concave.
Bayesian Neural Networks improve high-dimensional level set estimation.
problem Scalability issue in existing LSE methods for high-dimensional inputs.
method Bayesian Neural Networks with information-based acquisition functions.
result Proposed method achieves better results than state-of-the-art approaches.
Stochastic convex optimization problems with expectation constraints (SOECs) are encountered in statistics and machine learning, business, and engineering. In data-rich environments, the SOEC objective and constraints contain expectations defined with respect to large datasets. Therefore, efficient algorithms for solvi…
Study on transnormal functions and their level sets on Finsler manifolds.
problem Understanding transnormal functions and their geometric properties on Finsler manifolds.
method Proving smoothness of focal varieties and regular level sets of transnormal functions.
result Focal varieties of a C2 transnormal function are smooth submanifolds and regular level sets are tubes over these varieties.
New method for high-fidelity shape representations from raw data.
problem Creating accurate shape representations from raw data.
method A simple loss function encouraging neural network to vanish on input point cloud and have unit norm gradient.
result Our method produces high-fidelity, smooth, and natural zero level set surfaces.
A new method optimizes spatial sampling for level set estimation in one dimension.
problem Efficiently localizing regions above/below a threshold function.
method Finite-horizon search procedure balancing estimation error and travel distance.
result Method significantly improves estimation accuracy at lower travel costs.
Families of hypersurfaces that are level-set families of harmonic functions free of critical points are characterized by a local differential-geometric condition. Harmonic functions with a specified level-set family are constructed from geometric data. As a by-product, it is shown that the evolution of the gradient of …
Find conditions for starshapedness of level sets in Heisenberg group.
problem Ensure starshapedness of level sets of -capacitary potentials.
method Examine horizontally -harmonic functions in the Heisenberg group.
result Sharp conditions for strictly starshaped level sets.
Proves a function's locally least gradient property if its level sets are minimal laminations.
problem Understanding the relationship between 1-harmonic functions and minimal laminations.
method Analyzes minimal laminations and their convergence properties, then applies to 1-harmonic functions.
result Proves a function is 1-harmonic if its level sets are minimal laminations.
Proves convexity of level sets of general inverse σ_k equations.
problem Convexity of level sets of general inverse σ_k equations.
method Analyzes level sets of degree n general inverse σ_k equations and uses numerical conditions to verify convexity.
result Proves convexity of level sets of general inverse σ_k equations.
Proves smoothness of conical singularities in mean curvature flow.
problem Resolving singularities in mean curvature flow.
method Analyzes smooth hypersurfaces with isolated conical singularities.
result Smoothness of level set flow through asymptotically conical singularities.
Paper studies generic dynamics of MCFs with spherical singularities.
problem Characterizing the generic behavior of mean curvature flow with spherical singularities.
method Level set formulation of mean curvature flow, analysis of arrival time function.
result Generically, the arrival time function has at most regularity.
In this paper we establish a uniform estimate for level sets of stable solutions to the singularly perturbed Allen-Cahn equation in dimensions (which is optimal). The proof combines two ingredients: one is the infinite dimensional reduction method which enables us to reduce the estimate …
Proves positive mass theorem for 3-manifolds with a boundary.
problem Proving the positive mass theorem for specific 3-manifolds.
method Uses harmonic level set approach.
result Validates the positive mass theorem for new class of manifolds.
The level set tree approach of Hartigan (1975) provides a probabilistically based and highly interpretable encoding of the clustering behavior of a dataset. By representing the hierarchy of data modes as a dendrogram of the level sets of a density estimator, this approach offers many advantages for exploratory analysis…
We introduce novel equations, in the spirit of rough path theory, that parametrize level sets of intrinsically regular maps on the Heisenberg group with values in . These equations can be seen as a sub-Riemannian counterpart to classical ODEs arising from the implicit function theorem. We show that they e…
New method improves transductive learning predictions with multiplicative oracle inequalities.
problem Improving transductive learning predictions with known covariates.
method Median of Level-Set Aggregation (MLSA) for transductive LOO prediction.
result Proved multiplicative oracle inequality for LOO error.
Study approximates unknown function levels with queries.
problem Approximating unknown function levels through sequential queries.
method Introduce Bisect and Approximate algorithms to reduce to local function approximation.
result Rate-optimal sample complexity guarantees for H{ö}lder functions.
Regularity and stability results for the level set flow via the mean curvature flow with surgerymath.DG
In this article we use the mean curvature flow with surgery to derive regularity estimates for the level set flow going past Brakke regularity in certain special conditions allowing for 2-convex regions of high density. We also show a stability result for the plane under the level set flow.
Study shows zero level sets of solutions to Allen-Cahn equation are minimal surfaces with zero mean curvature.
problem Understanding phase transitions through entire solutions of the Allen-Cahn equation.
method Proving minimality of the zero level set with respect to a perimeter functional with density and showing zero mean curvature.
result The zero level set of entire solutions of the Allen-Cahn equation has zero mean curvature and is minimal.
Generative model learns conditional distributions on collective variable levels.
problem Modeling conditional probability distributions on collective variable levels.
method General and efficient learning approach, data enrichment strategy.
result Effective generative models on different level-sets of collective variables.
Estimating the level set of a signal from measurements is a task that arises in a variety of fields, including medical imaging, astronomy, and digital elevation mapping. Motivated by scenarios where accurate and complete measurements of the signal may not available, we examine here a simple procedure for estimating the…
BDMBC clusters data with varying densities using a new PLLS measure.
problem Finding clusters with varying densities in data.
method Bagged -distance with PLLS for mode estimation.
result BDMBC achieves optimal convergence rates for mode and level set estimation.
New method improves level set estimation with theoretical guarantees.
problem Efficiently estimating level sets of expensive-to-evaluate functions.
method Randomized straddle algorithm for level set estimation.
result The method provides theoretical guarantees and better practical performance.
Study lower bounds for connectivity of distance function level sets in convex sets.
problem Understanding connectivity of distance function level sets in convex sets.
method Lower bound calculation using critical points of the distance function.
result Provide a lower bound for the range of connectivity.
The paper studies stability and singularities of a two-convex level set flow.
problem Stability and singularities of a two-convex level set flow.
method Assumes two-convex initial hypersurface and finitely many singular times, then shows the singular set has finitely many connected components.
result Near each connected component of the singular set, the perturbed flow has the same type of singular set.
Level set flow's singularities are type I under 2-convexity, leading to specific curvature blow-up rates.
problem Understanding the nature and behavior of singularities in level set flow.
method Analytical approach using Lojasiewicz inequality and curvature blow-up rates.
result The arrival time is near a critical point if and only if it satisfies a Lojasiewicz inequality.
Optimizes structure topology for ductile and brittle fracture resistance.
problem Minimizing mass while ensuring structural damage and fracture resistance.
method Phase-field approach for modeling fracture, level-set topology optimization.
result Enhanced fracture resistance through two formulations.
The paper characterizes potential functions whose level sets are orbits in mechanical systems.
problem Characterizing smooth potential energy functions on the plane with specific level set properties.
method Analyzing inverse curvature flow and properties of level sets.
result Analytic or functions with totally path-disconnected critical sets must be radial, while every compact convex set is a critical set of a Levi potential.
The paper explores how neural networks make predictions using probabilistic programming.
problem Understanding how neural networks make individual predictions.
method Defining and sampling prediction level sets using probabilistic programming.
result The method can obtain examples that result in specified predictions by neural networks.
New condition for reconstructing Morse functions on 3D manifolds.
problem Reconstructing Morse functions with specific level sets.
method Studied a necessary and sufficient condition for reconstruction.
result New condition strengthens previous sufficient conditions.
New algorithms estimate function levels with near-optimal efficiency.
problem Estimating points where an unknown function exceeds a given threshold.
method Relates to adaptive experimental design methods for linear bandits in RKHS.
result Proves nearly optimal sample complexity bounds for level set estimation.
In this paper, the problem of estimating the level set of a black-box function from noisy and expensive evaluation queries is considered. A new algorithm for this problem in the Bayesian framework with a Gaussian Process (GP) prior is proposed. The proposed algorithm employs a hierarchical sequence of partitions to exp…
The paper connects two clustering methods by showing gradient ascent flow can move up the cluster tree.
problem Establishing a strong correspondence between clustering methods.
method Moving up the cluster tree by following the gradient ascent flow.
result Gradient ascent flow can be used to move up the cluster tree.
The study classifies rational isoparametric functions on Damek-Ricci spaces.
problem Classifying isoparametric functions on Damek-Ricci spaces.
method Using polynomial functions divided by for classification.
result New isoparametric functions discovered and their properties studied.
We analyze the level sets of the norm of the Witten spinor in an asymptotically flat Riemannian spin manifold of positive scalar curvature. Level sets of small area are constructed. We prove curvature estimates which quantify that, if the total mass becomes small, the manifold becomes flat with the exception of a set o…
We prove two new estimates for the level set flow of mean convex domains in Riemannian manifolds. Our estimates give control - exponential in time - for the infimum of the mean curvature, and the ratio between the norm of the second fundamental form and the mean curvature. In particular, the estimates remove a stumblin…