Computing largest circles separating two sets of segments

A circle $C$ separates two planar sets if it encloses one of the sets and its open interior disk does not meet the other set. A separating circle is a largest one if it cannot be locally increased while still separating the two given sets. An Theta(n log n) optimal algorithm is proposed to find all largest circles separating two given sets of line segments when line segments are allowed to meet only at their endpoints. In the general case, when line segments may intersect $\Omega(n^2)$ times, our algorithm can be adapted to work in O(n alpha(n) log n) time and O(n \alpha(n)) space, where alpha(n) represents the extremely slowly growing inverse of the Ackermann function.Comment: 14 pages, 3 figures, abstract presented at 8th Canadian Conference on Computational Geometry, 199

An elementary algorithm for digital arc segmentation

International audienceThis paper concerns the digital circle recognition problem, especially in the form of the circular separation problem. General fundamentals, based on classical tools, as well as algorithmic details are given (the latter by providing pseudo-code for major steps of the algorithm). After recalling the geometrical meaning of the separating circle problem, we present an incremental algorithm to segment a discrete curve into digital arcs

Star-galaxy separation in the AKARI NEP Deep Field

Context: It is crucial to develop a method for classifying objects detected in deep surveys at infrared wavelengths. We specifically need a method to separate galaxies from stars using only the infrared information to study the properties of galaxies, e.g., to estimate the angular correlation function, without introducing any additional bias. Aims. We aim to separate stars and galaxies in the data from the AKARI North Ecliptic Pole (NEP) Deep survey collected in nine AKARI / IRC bands from 2 to 24 {\mu}m that cover the near- and mid-infrared wavelengths (hereafter NIR and MIR). We plan to estimate the correlation function for NIR and MIR galaxies from a sample selected according to our criteria in future research. Methods: We used support vector machines (SVM) to study the distribution of stars and galaxies in the AKARIs multicolor space. We defined the training samples of these objects by calculating their infrared stellarity parameter (sgc). We created the most efficient classifier and then tested it on the whole sample. We confirmed the developed separation with auxiliary optical data obtained by the Subaru telescope and by creating Euclidean normalized number count plots. Results: We obtain a 90% accuracy in pinpointing galaxies and 98% accuracy for stars in infrared multicolor space with the infrared SVM classifier. The source counts and comparison with the optical data (with a consistency of 65% for selecting stars and 96% for galaxies) confirm that our star/galaxy separation methods are reliable. Conclusions: The infrared classifier derived with the SVM method based on infrared sgc- selected training samples proves to be very efficient and accurate in selecting stars and galaxies in deep surveys at infrared wavelengths carried out without any previous target object selection.Comment: 8 pages, 8 figure

Arc segmentation in linear time

International audienceA linear algorithm based on a discrete geometry approach is proposed for the detection of digital arcs and digital circles using a new representation of them. It is introduced by inspiring from the work of Latecki. By utilizing this representation, we transform the problem of digital arc detection into a problem of digital straight line recognition. We then develop a linear method for arc segmentation of digital curves

The Recognition of Unusual Objects in the Sloan Digital Sky Survey Color System

We present 5 filter photometry of 21 carbon stars, 15 asteroids, 15 cataclysmic variables, 6 metal-poor stars, 5 Cepheids, 1775 field stars, blue horizontal branch (BHB) stars and RR Lyrae stars in the globular clusters M 15 and M 2, two primary standards, and 19 secondary standards. The photometry was carried out using a filter set identical to that which will be used for the Sloan Digital Sky Survey. We find that carbon stars, CVs, R-type, J-type, and V-type asteroids, BHB stars, and RR Lyr stars should be identifiable on the basis of SDSS photometry alone, while Cepheids, metal-poor stars, and many types of asteroids are indistinguishable from the stellar locus of field stars.Comment: 44 pages, 13 postscript figures. Accepted for publication in Publications of the Astronomical Society of the Pacific, vol. 110, November 1998. Uses AAS Latex style file, version 4.