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

3D Noisy Discrete Objects: Segmentation and Application to Smoothing

International audienceWe propose in this paper a segmentation process that can deal with noisy discrete objects. A flexible approach considering arithmetic discrete planes with a variable width is used to avoid the over-segmentation that might happen when classical segmentation algorithms based on regular discrete planes are used to decompose the surface of the object. A method to choose a seed and different segmentation strategies according to the shape of the surface are also proposed, as well as an application to smooth the border of convex noisy discrete objects

Segmentation of Noisy Discrete Surfaces

International audienceWe propose in this paper a segmentation process that can deal with noisy discrete objects. A flexible approach considering arithmetic discrete planes with a variable width is used to avoid the over-segmentation that might happen when classical segmentation algorithms based on regular discrete planes are used to decompose the surface of the object. A method to choose a seed and different segmentation strategies according to the shape of the surface are also proposed

Thick Line Segment Detection with Fast Directional Tracking

International audienceThis paper introduces a fully discrete framework for a new straight line detector in gray-level images, where line segments are enriched with a thickness parameter intended to provide a quality criterion on the extracted feature. This study is based on a previous work on interactive line detection in gray-level images. At first, a better estimation of the segment thickness and orientation is achieved through two main improvements: adaptive directional scans and control of assigned thickness. Then, these advances are exploited for a complete unsupervised detection of all the line segments in an image. The new thick line detector is left available in an online demonstration

Automatic forest road extraction from LiDAR data of mountainous areas

International audienceIn this paper, a framework is proposed to extract forest roads from LiDAR (Light Detection and Ranging) data in mountainous areas. For that purpose, an efficient and simple solution based on discrete geometry and mathematical morphology tools is proposed. The framework is composed of two steps: (i) detecting road candidates in DTM (Digital Terrain Model) views using a mathematical morphology filter and a fast blurred segment detector in order to select a set of road seeds; (ii) extracting road sections from the obtained seeds using only the raw LiDAR points to cope with DTM approximations. For the second step, a previous tool for fast extraction of linear structures directly from ground points was adapted to automatically process each seed. It first performs a recognition of the road structure under the seed. In case of success, the structure is tracked and extended as far as possible on each side of the segment before post-processing validation and cleaning. Experiments on real data over a wide mountain area (about 78 km^2) have been conducted to validate the proposed method

Sugar crystal size characterization using digital image processing.

Thesis (PhD)-University of KwaZulu-Natal, Durban, 2007.The measurement of the crystal size distribution is a key prerequisite in optimising the growth of sugar crystals in crystalisation pans or for quality control of the final product. Traditionally, crystal size measurements are carried out by inspection or using mechanical sieves. Apart from being time consuming, these techniques can only provide limited quantitative information. For this reason, a more quantitative automatic system is required. In our project, software routines for the automated measurement of crystal size using classical image analysis techniques were developed. A digital imaging technique involves automatically analyzing a captured image of a representative sample of ~ 100 crystals for the automated measurement of crystal size has been developed. The main problem of crystals size measurements using image processing is the lack of an efficient algorithm to identify and separate overlapping and touching crystals which otherwise compromise the accuracy of size measurement. This problem of overlapping and touching crystals was addressed in two ways. First, 5 algorithms which identify and separate overlapping and touching crystals, using mathematical morphology as a tool, were evaluated. The accuracy of the algorithms depends on the technique used to mark every crystal in the image. Secondly, another algorithm which used convexity measures of the crystals based on area and perimeter, to identify and reject overlapping and touching crystals, have been developed. Finally, the two crystal sizing algorithms, the one applies ultimate erosion followed by a distance transformation and the second uses convexity measures to identify overlapping crystals, were compared with well established mechanical sieving technique. Using samples obtained from a sugar refinery, the parameters of interest, including mean aperture (MA) and coefficient of variance (CV), were calculated and compared with those obtained from the sieving method. The imaging technique is faster, more reliable than sieving and can be used to measure the full crystal size distributions of both massecuite and dry product

Structural and Computational Existence Results for Multidimensional Subshifts

Symbolic dynamics is a branch of mathematics that studies the structure of infinite sequences of symbols, or in the multidimensional case, infinite grids of symbols. Classes of such sequences and grids defined by collections of forbidden patterns are called subshifts, and subshifts of finite type are defined by finitely many forbidden patterns. The simplest examples of multidimensional subshifts are sets of Wang tilings, infinite arrangements of square tiles with colored edges, where adjacent edges must have the same color. Multidimensional symbolic dynamics has strong connections to computability theory, since most of the basic properties of subshifts cannot be recognized by computer programs, but are instead characterized by some higher-level notion of computability. This dissertation focuses on the structure of multidimensional subshifts, and the ways in which it relates to their computational properties. In the first part, we study the subpattern posets and Cantor-Bendixson ranks of countable subshifts of finite type, which can be seen as measures of their structural complexity. We show, by explicitly constructing subshifts with the desired properties, that both notions are essentially restricted only by computability conditions. In the second part of the dissertation, we study different methods of defining (classes of ) multidimensional subshifts, and how they relate to each other and existing methods. We present definitions that use monadic second-order logic, a more restricted kind of logical quantification called quantifier extension, and multi-headed finite state machines. Two of the definitions give rise to hierarchies of subshift classes, which are a priori infinite, but which we show to collapse into finitely many levels. The quantifier extension provides insight to the somewhat mysterious class of multidimensional sofic subshifts, since we prove a characterization for the class of subshifts that can extend a sofic subshift into a nonsofic one.Symbolidynamiikka on matematiikan ala, joka tutkii äärettömän pituisten symbolijonojen ominaisuuksia, tai moniulotteisessa tapauksessa äärettömän laajoja symbolihiloja. Siirtoavaruudet ovat tällaisten jonojen tai hilojen kokoelmia, jotka on määritelty kieltämällä jokin joukko äärellisen kokoisia kuvioita, ja äärellisen tyypin siirtoavaruudet saadaan kieltämällä vain äärellisen monta kuviota. Wangin tiilitykset ovat yksinkertaisin esimerkki moniulotteisista siirtoavaruuksista. Ne ovat värillisistä neliöistä muodostettuja tiilityksiä, joissa kaikkien vierekkäisten sivujen on oltava samanvärisiä. Moniulotteinen symbolidynamiikka on vahvasti yhteydessä laskettavuuden teoriaan, sillä monia siirtoavaruuksien perusominaisuuksia ei ole mahdollista tunnistaa tietokoneohjelmilla, vaan korkeamman tason laskennallisilla malleilla. Väitöskirjassani tutkin moniulotteisten siirtoavaruuksien rakennetta ja sen suhdetta niiden laskennallisiin ominaisuuksiin. Ensimmäisessä osassa keskityn tiettyihin äärellisen tyypin siirtoavaruuksien rakenteellisiin ominaisuuksiin: äärellisten kuvioiden muodostamaan järjestykseen ja Cantor-Bendixsonin astelukuun. Halutunlaisia siirtoavaruuksia rakentamalla osoitan, että molemmat ominaisuudet ovat olennaisesti laskennallisten ehtojen rajoittamia. Väitöskirjan toisessa osassa tutkin erilaisia tapoja määritellä moniulotteisia siirtoavaruuksia, sekä sitä, miten nämä tavat vertautuvat toisiinsa ja tunnettuihin siirtoavaruuksien luokkiin. Käsittelen määritelmiä, jotka perustuvat toisen kertaluvun logiikkaan, kvanttorilaajennukseksi kutsuttuun rajoitettuun loogiseen kvantifiointiin, sekä monipäisiin äärellisiin automaatteihin. Näistä kolmesta määritelmästä kahteen liittyy erilliset siirtoavaruuksien hierarkiat, joiden todistan romahtavan äärellisen korkuisiksi. Kvanttorilaajennuksen tutkimus valottaa myös niin kutsuttujen sofisten siirtoavaruuksien rakennetta, jota ei vielä tunneta hyvin: kyseisessä luvussa selvitän tarkasti, mitkä siirtoavaruudet voivat laajentaa sofisen avaruuden ei-sofiseksi.Siirretty Doriast