We introduce an algorithm to locate contours of functions that are expensive to evaluate. The problem of locating contours arises in many applications, including classification, constrained optimization, and performance analysis of mechanical and dynamical systems (reliability, probability of failure, stability, etc.).…
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48 results for “contour functions”
Describing shapes by suitable measures in object segmentation, as proposed in [24], allows to combine the advantages of the representations as parametrized contours and indicator functions. The pseudo-Riemannian structure of optimal transport can be used to model shapes in ways similar as with contours, while the Kanto…
Metrics stabilize persistent homology in data analysis.
problem Stabilizing invariants for characterizing connectivity structures in data.
method Using contour functions to define metrics for rank invariants.
result Optimal contours provide robust descriptors of spatial patterns.
In this paper we consider planar sections and visual contours of co-dimension one affine immersions. The main theorem says that the third order Taylor expansion of the difference between the visual contour and planar section functions is exactly the cubic form. We also consider parameterizations on two dimensional affi…
Defines surfaces with specific contour patterns.
problem Characterizing surfaces with concentric or parallel -contours.
method Presented examples and characterization given.
result Characterization of surfaces with concentric or parallel -contours.
A new method for analyzing shapes using FDA techniques.
problem Statistical shape analysis of deformed contours.
method Functional Data Analysis (FDA) with basis expansion and principal component analysis.
result Successfully identifies deformation parameters and captures contour distributions.
Investigate the local geometry of smooth surfaces in 4-space via contact with 2-planes and apparent contours.
problem Local geometry of smooth surfaces in 4-space
method Contact with 2-planes and apparent contour
result Prove connections between singularities of parallel projections, orthogonal projections, and height functions.
ICSGLD improves efficiency in posterior sampling for big data.
problem Efficient posterior sampling for large datasets.
method Embarrassingly parallel multiple-chain CSGLD with efficient interactions.
result ICSGLD is more efficient than a single-chain CSGLD.
The paper finds surfaces closest to being flat that span a given contour.
problem Finding surfaces in that are as flat as possible while spanning a given contour.
method The approach involves minimizing the total Gaussian curvature squared and solving a system of PDEs.
result The optimal surface is shown to be controlled by a biharmonic equation with specific boundary conditions.
The paper tightens bounds on distances between Reeb graphs.
problem Certifying quasi-universality of distances between Reeb graphs.
method Establishes tight bi-Lipschitz bounds for various distances.
result Proves strict universality of the functional contortion distance for contour trees and coincides with interleaving distance for merge trees.
Optimizes learning Hilbert-Schmidt operators between Sobolev spaces.
problem Statistical limits of learning mappings between infinite-dimensional function spaces.
method Minimax optimal regularization and multilevel training.
result Multilevel kernel operator learning achieves optimal learning rate.
A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., to appear] for integrating semi-discrete advection-diffusion PDEs, is extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parame…
Paper proposes a new Wasserstein distance for mixtures of radially contoured distributions.
problem Generalization of Wasserstein distance to non-elliptically contoured distributions.
method Relaxed formulation for mixtures of radially contoured distributions without marginal consistency.
result The new distance yields more stable error and better color distribution in image transfer tasks.
We develop mask iterative hard thresholding algorithms (mask IHT and mask DORE) for sparse image reconstruction of objects with known contour. The measurements follow a noisy underdetermined linear model common in the compressive sampling literature. Assuming that the contour of the object that we wish to reconstruct i…
Machine learning models have been shown vulnerable to adversarial attacks launched by adversarial examples which are carefully crafted by attacker to defeat classifiers. Deep learning models cannot escape the attack either. Most of adversarial attack methods are focused on success rate or perturbations size, while we a…
Properly immersed curves in arbitrary surfaces via apparent contours on spines of traversing flowsmath.GT
The paper studies curves in surfaces using flow-spines and apparent contours.
problem Understanding curves in arbitrary surfaces using flow-spines and apparent contours.
method By considering generic curves and their apparent contours relative to a traversing flow, the paper reconstructs curves and allows them to vary up to homotopy.
result A finite set of local moves on decorated graphs allows for the reconstruction and variation of curves within a fixed generic flow.
The fundamental frequency (F0) contour of speech is a key aspect to represent speech prosody that finds use in speech and spoken language analysis such as voice conversion and speech synthesis as well as speaker and language identification. This work proposes new methods to estimate the F0 contour of speech using deep …
IrisNet tracks tongue contours in ultrasound videos using deep learning.
problem Automatic and real-time tracking of tongue contours in ultrasound videos.
method Convolutional neural network mimicking peripheral vision.
result Outstanding generalization on various ultrasound tongue datasets.
The contour map of estimation error of Expected Shortfall (ES) is constructed. It allows one to quantitatively determine the sample size (the length of the time series) required by the optimization under ES of large institutional portfolios for a given size of the portfolio, at a given confidence level and a given esti…
We present a new implementation of anisotropic mean curvature flow for contour recognition. Our procedure couples the mean curvature flow of planar closed smooth curves, with an external field from a potential of point-wise charges. This coupling constrains the motion when the curve matches a picture placed as backgrou…
We explore a connection between the Finslerian area functional and well-investigated Cartan functionals to prove new Bernstein theorems, uniqueness and removability results for Finsler-minimal graphs, as well as enclosure theorems and isoperimetric inequalities for minimal immersions in Finsler spaces. In addition, we …
Wilson loops in supersymmetric Yang-Mills theory correspond at strong coupling to extremal surfaces in . We study a class of extremal surfaces known as special Legendrian submanifolds. The "hemisphere" corresponding to the circular Wilson loop is an example of a special Legendrian submanifold, and w…
Completeness of the eigenfunctions of a quantum mechanical system is crucial for its probability interpretation. By using the method of contour integral we give properly normalized eigenfunctions for both discrete and continuum spectrum of the Morse potential, and explicitly prove the completeness relation. As an appli…
Proposes a new network to improve nuclei segmentation in histopathology images.
problem Challenges in separating overlapped nuclei in histopathology images.
method Introduces a bending loss regularized network to minimize contour points with large curvatures.
result Outperforms six state-of-the-art approaches on five quantitative metrics.
Elliptically-Contoured Tensor-variate Distributions with Application to Improved Image Learningstat.ME
Improved image learning using elliptically contoured tensor-variate distributions.
problem Inadequate statistical analysis for tensor-valued data, especially with heavier or lighter tails.
method Developed a family of elliptically contoured tensor-variate distributions and derived their properties and procedures for estimation.
result Tensor-variate classification rules and tensor-on-tensor regression better predict and characterize data than TVN-based methods.
We prove the quasimodularity of generating functions for counting torus covers, with and without Siegel-Veech weight. Our proof is based on analyzing decompositions of flat surfaces into horizontal cylinders. The quasimodularity arise as contour integral of quasi-elliptic functions. It provides an alternative proof of …
In this paper we present a new method for motion tracking of tumors in liver ultrasound image sequences. Our algorithm has two main steps. In the first step, we apply mean shift algorithm with multiple features to estimate the center of the target in each frame. Target in the first frame is defined using an ellipse. Ed…
A new algorithm flattens multi-modal distributions for better deep learning.
problem Bayesian learning in big data with multi-modal distributions.
method Contour Stochastic Gradient Langevin Dynamics (CSGLD) algorithm.
result The CSGLD algorithm avoids local traps in deep neural networks.
New method uses contours of segmented images for X-ray classification.
problem Classifying X-ray images of segmented radiography.
method Develops a new approach for image analysis of multivariate planar curves, addressing alignment issues.
result Demonstrates the robustness and appeal of the proposed method through detection of cardiomegaly and numerical experiments.
The contour maps of the error of historical resp. parametric estimates for large random portfolios optimized under the risk measure Expected Shortfall (ES) are constructed. Similar maps for the sensitivity of the portfolio weights to small changes in the returns as well as the VaR of the ES-optimized portfolio are also…
This paper explains the method used in the segmentation challenge (Task 1) in the International Skin Imaging Collaboration's (ISIC) Skin Lesion Analysis Towards Melanoma Detection challenge held in 2018. We have trained a U-Net network to perform the segmentation. The key elements for the training were first to adjust …
Study on Gaussian random fields' singularities on manifolds.
problem Understanding singularities of Gaussian random fields on manifolds.
method Computed expected values of singularities under various conditions.
result Explicit formulae for singularities under different constraints.
We demonstrate how the complex integral formula for the Airy functions arises from Penrose's twistor contour integral formula. We then use the Lax formulation of the isomonodromy problem with one irregular singularity of order four to show that the Airy equation arises from the anti-self-duality equations for conformal…
SympFormer accelerates attention blocks using inertial dynamics on density spaces.
problem Improving the efficiency of self-attention blocks in Transformers.
method Introduced accelerated attention blocks derived from inertial Nesterov dynamics on density spaces.
result Accelerated attention blocks converge faster than classical blocks while preserving oracle calls.
We present an approach for polarimetric Synthetic Aperture Radar (SAR) image region boundary detection based on the use of B-Spline active contours and a new model for polarimetric SAR data: the GHP distribution. In order to detect the boundary of a region, initial B-Spline curves are specified, either automatically or…
Study improves tongue contour recognition in ultrasound images using transfer learning.
problem Difficulty in recognizing tongue gestures due to low-contrast and noisy ultrasound images.
method Transfer learning with U-net and fine-tuning on different ultrasound datasets.
result Fine-tuned U-net models perform well on images from different ultrasound devices.
It is proposed a new code for contours of plane images. This code was applied for optical character recognition of printed and handwritten characters. One can apply it to recognition of any visual images.
For a connected locally path-connected topological space and a continuous function on it such that its Reeb graph is a finite topological graph, we show that the cycle rank of , i.e., the first Betti number , in computational geometry called \emph{number of loops}, is bounded from above by …
We consider a complex Plateau problem for strongly pseudoconvex contours in non Kähler manifolds. A positive solution in the case of manifolds carrying a pluriclosed Hermitian metric forms is given. For the general case we propose a conjecture.
Combines geometric and topological info for complex object boundaries.
problem Boundary estimation for images with complex topologies.
method Topological clustering for initialization of Bayesian active contour model.
result Smart initialization reduces user dependence and improves accuracy.
Wavelet features improve image clustering and segmentation accuracy.
problem Noise and lack of spatial context in pixel intensity-based methods.
method Modified K-means, Fuzzy c-means, and ACWE algorithms incorporating Wavelet features.
result Wavelet-based algorithms converge to different segmentation results based on frequency information.
New method improves combinatorial optimization by overcoming inefficient sampling.
problem Wandering in contours: sampling similar solutions for long periods.
method Reheated Gradient-based Discrete Sampling with a novel mechanism.
result Superior performance across various combinatorial optimization problems.
Projection of crosscapmath.DG
We determine the precise bifurcation diagrams of the apparent contours of generic crosscaps, which contain the information of bifurcations with respect to the images of the singular sets of crosscaps: crosscap points and double point curves. Especially, three different kinds of equivalences play key roles.
New formulas for surface curvature when tangent vector points in asymptotic directions.
problem Formula limitations when tangent vector points in asymptotic directions.
method Analogous formulas for surfaces with cusp singular points.
result Invariants of cusp singular points of contour lines.
Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known as experimental design, that is, how to select the input settings where the compu…
A new method calculates fractional moments using the moment-generating function.
problem Computing fractional moments from probability densities.
method Integral framework based on moment-generating function.
result Exact integral expressions for various types of moments.
New methods for -transform inversion and Wiener-Hopf factorization.
problem Efficient numerical inversion of -transforms and factorization of functions.
method Sinh-deformations of contours, variable changes, and simplified trapezoid rule.
result High precision and speed in evaluating moments and constructing filters.
We study the geometry of the cuspidal edge in derived from its contact with planes and lines (referred to as flat geometry). The contact of with planes is measured by the singularities of the height functions on . We classify submersions on a model of by diffeomorphisms and recover the cont…