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The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…

Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must…

This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…

Sampling is a pivotal element in the design of metasurfaces, enabling a broad spectrum of applications. Despite its flexibility, sampling can result in reduced efficiency and unintended diffractions, which are more pronounced at high…

It is common in Physiological Optics to fit the corneal and the lens surfaces to conic-based surfaces (usually ellipse-based surfaces), obtaining their characteristic radius of curvature and asphericity. Here we show that the variation in…

Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data lies in a Euclidean space. However, some kinds of data are…

A method to determine the gamma correction curves for displays is presented. An empirical model is first constructed from exhaustive measurements of a few representative units. The model parameters for the remaining units are then fitted…

We consider the problem of estimating filamentary structure from planar point process data. We make some connections with computational geometry and we develop nonparametric methods for estimating the filaments. We show that, under weak…

The paper overviews and investigates several nonparametric methods of estimating covariograms. It provides a unified approach and notation to compare the main approaches used in applied research. The primary focus is on methods that utilise…

While the formulation of most data assimilation schemes assumes an unbiased observation model error, in real applications, model error with nontrivial biases is unavoidable. A practical example is the error in the radiative transfer model…

A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…

This contribution proposes a recursive set-membership method for the ellipsoidal state characterization for discrete-time linear time-varying models with additive unknown disturbances vectors, bounded by possibly degenerate zonotopes and…

The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly…

An ellipsometer is a vital precision tool used for measuring optical parameters with wide applications in many fields, including accurate measurements in film thickness, optical constants, structural profiles, etc. However, the precise…

We study oblique incident light absorption in opaque media with rough surfaces. An analytical approach with modified boundary conditions taking into account the surface roughness in metallic or dielectric films has been discussed. Our…

Error enhancement properties of data processing algorithms in elementary particle physics measurements are discussed. It is argued that a systematic use of continuous weights instead of hard cuts may reduce errors of the results at the cost…

Absorption imaging is a commonly adopted method to acquire, with high temporal resolution, spatial information on a partially transparent object. It relies on the interference between a probe beam and the coherent response of the object. In…

The analysis of the fully three-dimensional and time-varying polarization characteristics of a modulated trivariate, or three-component, oscillation is addressed. The use of the analytic operator enables the instantaneous three-dimensional…

Functional data often exhibit both amplitude and phase variation around a common base shape, with phase variation represented by a so called warping function. The process removing phase variation by curve alignment and inference of the…

Remote sensing measurements have been an important data source of ocean surface roughness. Scatterometers operating at moderate and high incidence angles provide information on the Bragg resonance spectral components of the ocean surface…