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We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we…
Texture segmentation constitutes a standard image processing task, crucial to many applications. The present contribution focuses on the particular subset of scale-free textures and its originality resides in the combination of three key…
In this paper we address the uncertainty issues involved in the low-level vision task of image segmentation. Researchers in computer vision have worked extensively on this problem, in which the goal is to partition (or segment) an image…
We study the problem of distinguishing between two symmetric probability distributions over $n$ bits by observing $k$ bits of a sample, subject to the constraint that all $k-1$-wise marginal distributions of the two distributions are…
The estimation of regression parameters in spatially referenced data plays a crucial role across various scientific domains. A common approach involves employing an additive regression model to capture the relationship between observations…
Any subset of the plane can be approximated by a set of square pixels. This transition from a shape to its pixelation is rather brutal since it destroys geometric and topological information about the shape. Using a technique inspired by…
We present a study of the dependencies of shear bias on simulation (input) and measured (output) parameters, noise, point-spread function anisotropy, pixel size, and the model bias coming from two different and independent galaxy shape…
Rapid growth in the field of quantitative digital image analysis is paving the way for researchers to make precise measurements about objects in an image. To compute quantities from the image such as the density of compressed materials or…
This note concerns the area growth and bottom spectrum of complete stable minimal surfaces in a three-dimensional manifold with scalar curvature bounded from below. When the ambient manifold is the Euclidean space, by an elementary…
How to distribute a set of points uniformly on a spherical surface is a very old problem that still lacks a definite answer. In this work, we introduce a physical measure of uniformity based on the distribution of distances between points,…
Small area estimators that ignore the sampling design lack design consistency when the sampling mechanism is complex and may be severely biased under informative designs. Existing procedures that account for the survey weights under…
This paper presents a technique for finding the surface normal of an object from a set of images obtained under different lighting positions. The method presented is based on the principles of Photometric Stereo (PS) combined with Optimum…
In this paper, we consider adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function on a uniform grid. Both the problem of estimating the support function at a point and that of estimating…
The issue of a "mean shape" of a random set $X$ often arises, in particular in image analysis and pattern detection. There is no canonical definition but one possible approach is the so-called Vorob'ev expectation $\E_V(X)$, which is…
In this paper, we explore the two-point zeroth-order gradient estimator and identify the distribution of random perturbations that minimizes the estimator's asymptotic variance as the perturbation stepsize tends to zero. We formulate it as…
Image based diagnostics are interpreted in the context of spatial resolution. The same is true for tomographic image reconstruction. Current empirically driven approaches to quantify spatial resolution rely on a deterministic formulation…
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…
In this paper, we model the salient object detection problem under a probabilistic framework encoding the boundary connectivity saliency cue and smoothness constraints in an optimization problem. We show that this problem has a closed form…
Even though the computation of local properties, such as densities or radial distribution functions, remains one of the most standard goals of molecular simulation, it still largely relies on straighforward histogram-based strategies. Here…
Smoothing splines have been used pervasively in nonparametric regressions. However, the computational burden of smoothing splines is significant when the sample size $n$ is large. When the number of predictors $d\geq2$, the computational…