Abstract: Gielis curves (GC) can represent a wide range of shapes and patterns ranging from star shapes to symmetric and asymmetric polygons, and even self intersecting curves. Such patterns appear in natural objects or phenomena, such as flowers, crystals, pollen structures, animals, or even wave propagation. Gielis curves and surfaces are an extension of Lamé curves and surfaces (superquadrics) which have benefited in the last two decades of extensive researches to retrieve their parameters from various data types, such as range images, 2D and 3D point clouds, etc. Unfortunately, the most efficient techniques for superquadrics recovery, based on deterministic methods, cannot directly be adapted to Gielis curves. Indeed, the different nature of their parameters forbids the use of a unified gradient descent approach, which requires initial pre-processings, such as the symmetry detection, and a reliable pose and scale estimation. Furthermore, even the most recent algorithms in the literature remain extremely sensitive to initialization and often fall into local minima in the presence of large missing data. We present a simple evolutionary algorithm which overcomes most of these issues and unifies all of the required operations into a single though efficient approach. The key ideas in this paper are the replacement of the potential fields used for the cost function (closed form) by the shortest Euclidean distance (SED, iterative approach), the construction of cost functions which minimize the shortest distance as well as the curve length using R-functions, and slight modifications of the evolutionary operators. We show that the proposed cost function based on SED and R-function offers the best compromise in terms of accuracy, robustness to noise, and missing data.

Abstract: Nowadays, X-ray fluorescence spectrometry (XRF) is a well-established analytical technique for qualitative and quantitative elemental analysis (sometimes from Be to U) of a wide variety of samples. In particular, the truly multi-element character, acceptable speed and economy, ease of automation and the possibility to directly analyse solid samples are the most important features among the many that have made it a very mature analytical tool for routine quality controls in many industries, as well as for analytical support for the research laboratory.e recent technological advances, including the design of low-power micro-focus tubes and the novel X-ray optics and detectors have made it possible to extend XRF to the determination of low-Z elements and to obtain 2D or 3D information on a micrometre-scale. Furthermore, the recent development and commercialisation of benchtop and portable instrumentation, that offer extreme simplicity of operation in a low-cost design, have promoted even more the approach of XRF for many analytical problems.is article highlights this state-of-the art technique with regards to currently available XRF instrumentation on the market as well as recent applications in environmental and industrial fields.