Related papers: Level sets estimation and Vorob'ev expectation of …

An unbiased estimator for the ellipticity of an object in a noisy image is given in terms of the image moments. Three assumptions are made: i) the pixel noise is normally distributed, although with arbitrary covariance matrix, ii) the image…

The surface area of a set which is only observed as a binary pixel image is often estimated by a weighted sum of pixel configurations counts. In this paper we examine these estimators in a design based setting -- we assume that the observed…

In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has…

According to the concept of typicality, an ensemble average can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space. This random-vector approximation,…

Given a random sample of points from some unknown density, we propose a data-driven method for estimating density level sets under the r-convexity assumption. This shape condition generalizes the convexity property. However, the main…

Multiclass classification problems such as image annotation can involve a large number of classes. In this context, confusion between classes can occur, and single label classification may be misleading. We provide in the present paper a…

Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…

In the framework of shape constrained estimation, we review methods and works done in convex set estimation. These methods mostly build on stochastic and convex geometry, empirical process theory, functional analysis, linear programming,…

This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role…

Anomaly detection aims to identify data instances that deviate significantly from majority of data, which has been widely used in fraud detection, network security, and industrial quality control. Existing methods struggle with datasets…

In this paper, we present an abstract framework to obtain convergence rates for the approximation of random evolution equations corresponding to a random family of forms determined by finite-dimensional noise. The full discretization error…

The existing object classification techniques based on descriptive features rely on object alignment to compute the similarity of objects for classification. This paper replaces the necessity of object alignment through sorting of feature.…

A refined a priori error analysis of the lowest order (linear) Virtual Element Method (VEM) is developed for approximating a model two dimensional Poisson problem. A set of new geometric assumptions is proposed on shape regularity of…

This paper presents a new Bayesian estimation technique for hidden Potts-Markov random fields with unknown regularisation parameters, with application to fast unsupervised K-class image segmentation. The technique is derived by first…

We consider the estimation of high-dimensional network structures from partially observed Markov random field data using a penalized pseudo-likelihood approach. We fit a misspecified model obtained by ignoring the missing data problem. We…

Estimation of the level set of a function (i.e., regions where the function exceeds some value) is an important problem with applications in digital elevation mapping, medical imaging, astronomy, etc. In many applications, the function of…

We address the problem of estimating the edge of a bounded set in R^d given a random set of points drawn from the interior. Our method is based on a transformation of estimators dedicated to uniform point processes and obtained by smoothing…

Identifying anomalies and contamination in datasets is important in a wide variety of settings. In this paper, we describe a new technique for estimating contamination in large, discrete valued datasets. Our approach considers the normal…

We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In…

This article deals with error estimates for the finite element approximation of variational normal derivatives and, as a consequence, error estimates for the finite element approximation of Dirichlet boundary control problems with energy…