Structure Characterization Using Mathematical Morphology
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Linguistic Interpretation of Mathematical Morphology
Eureka-2013. Fourth International Workshop Proceedings Linguistic Interpretation of Mathematical Morphology Agustina Bouchet1,2, Gustavo Meschino3, Marcel Brun1, Rafael Espin Andrade4, Virginia Ballarin1 1 Universidad Nacional de Mar de Plata, Mar de Plata, Argentina. 2 CONICET, Mar de Plata, Argentina. 3 Universidad Nacional de Mar de Plata, Mar de Plata, Argentina. 4 ISPJAE, Universidad Técnica de La Habana, Cuba. [email protected], [email protected], [email protected], [email protected], [email protected] Abstract strains imposed by t-norms and s-norms, which are by themselves also conjunctions and disjunctions. Mathematical Morphology is a theory based on geometry, By replacing t-norm and s-norm by conjunction and algebra, topology and set theory, with strong application disjunction, respectively, we obtain the dilation and ero- to digital image processing. This theory is characterized sion operators for the Compensatory Fuzzy Mathematical by two basic operators: dilation and erosion. In this work Morphology (CMM), called compensatory dilation and we redefine these operators based on compensatory fuzzy compensatory erosion, respectively. Two different im- logic using a linguistic definition, compatible with previ- plementations of the CMM were presented at this moment ous definitions of Fuzzy Mathematical Morphology. A [12,21]. comparison to previous definitions is presented, assessing In this work new operators based on the definition of robustness against noise. the CMM are presented, but replacing the supreme and infimum by logical operators, which allow for a linguistic Keywords: Fuzzy Logic, Compensatory Fuzzy Logic, interpretation of their meaning. We call the New Com- Mathematical Morphology, Fuzzy Mathematical Mor- pensatory Morphological Operators. -
Lecture 5: Binary Morphology
Lecture 5: Binary Morphology c Bryan S. Morse, Brigham Young University, 1998–2000 Last modified on January 15, 2000 at 3:00 PM Contents 5.1 What is Mathematical Morphology? ................................. 1 5.2 Image Regions as Sets ......................................... 1 5.3 Basic Binary Operations ........................................ 2 5.3.1 Dilation ............................................. 2 5.3.2 Erosion ............................................. 2 5.3.3 Duality of Dilation and Erosion ................................. 3 5.4 Some Examples of Using Dilation and Erosion . .......................... 3 5.5 Proving Properties of Mathematical Morphology .......................... 3 5.6 Hit-and-Miss .............................................. 4 5.7 Opening and Closing .......................................... 4 5.7.1 Opening ............................................. 4 5.7.2 Closing ............................................. 5 5.7.3 Properties of Opening and Closing ............................... 5 5.7.4 Applications of Opening and Closing .............................. 5 Reading SH&B, 11.1–11.3 Castleman, 18.7.1–18.7.4 5.1 What is Mathematical Morphology? “Morphology” can literally be taken to mean “doing things to shapes”. “Mathematical morphology” then, by exten- sion, means using mathematical principals to do things to shapes. 5.2 Image Regions as Sets The basis of mathematical morphology is the description of image regions as sets. For a binary image, we can consider the “on” (1) pixels to all comprise a set of values from the “universe” of pixels in the image. Throughout our discussion of mathematical morphology (or just “morphology”), when we refer to an image A, we mean the set of “on” (1) pixels in that image. The “off” (0) pixels are thus the set compliment of the set of on pixels. By Ac, we mean the compliment of A,or the off (0) pixels. -
Introduction to Mathematical Morphology
COMPUTER VISION, GRAPHICS, AND IMAGE PROCESSING 35, 283-305 (1986) Introduction to Mathematical Morphology JEAN SERRA E. N. S. M. de Paris, Paris, France Received October 6,1983; revised March 20,1986 1. BACKGROUND As we saw in the foreword, there are several ways of approaching the description of phenomena which spread in space, and which exhibit a certain spatial structure. One such approach is to consider them as objects, i.e., as subsets of their space of definition. The method which derives from this point of view is. called mathematical morphology [l, 21. In order to define mathematical morphology, we first require some background definitions. Consider an arbitrary space (or set) E. The “objects” of this :space are the subsets X c E; therefore, the family that we have to handle theoretically is the set 0 (E) of all the subsets X of E. The set p(E) is incomparably less arbitrary than E itself; indeed it is constructured to be a Boolean algebra [3], that is: (i) p(E) is a complete lattice, i.e., is provided with a partial-ordering relation, called inclusion, and denoted by “ c .” Moreover every (finite or not) family of members Xi E p(E) has a least upper bound (their union C/Xi) and a greatest lower bound (their intersection f7 X,) which both belong to p(E); (ii) The lattice p(E) is distributiue, i.e., xu(Ynz)=(XuY)n(xuZ) VX,Y,ZE b(E) and is complemented, i.e., there exist a greatest set (E itself) and a smallest set 0 (the empty set) such that every X E p(E) possesses a complement Xc defined by the relationships: XUXC=E and xn xc= 0. -
CALL for PAPERS IEEE Journal of Selected Topics In
CALL FOR PAPERS IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing Special Issue on “Mathematical Morphology in Remote Sensing and Geoscience” Historically, mathematical morphology was the first consistent non-linear image analysis theory, which from the very start included not only theoretical results but also many practical aspects. Mathematical morphology is capable of handling the most varied image types, in a way that is often subtle yet efficient. It can also be used to process general graphs, surfaces, implicit and explicit volumes, manifolds, time or spectral series, in both deterministic and stochastic contexts. In the last five years, connected signal representations and connected operators have emerged as tools for segmentation and filtering, leading to extremely versatile techniques for solving problems in a variety of domains including information science, geoscience, and image and signal analysis and processing. The application of mathematical morphology in processing and analysis of remotely sensed spatial data acquired at multi-spatial-spectral-temporal scales and by-products such as Digital Elevation Model (DEM) and thematic information in map forms has shown significant success in the last two decades. From data acquisition to the level of making theme-specific predictions, there exists several phases that include feature extraction (information retrieval), information analysis/characterization, information reasoning, spatio-temporal modelling and visualization. Relatively, numerous approaches/frameworks/schemes/ algorithms are available to address information retrieval when compare to those approaches available to address the rest of the topics. With the availability of data across various spatial/spectral/temporal resolutions, besides information extraction, other topics like pattern retrieval, pattern analysis, spatial reasoning, and simulation and modeling of spatiotemporal behaviors of several terrestrial phenomena and processes also need to be given emphasis. -
Imagemap Simplification Using Mathematical Morphology
Jalal Amini Imagemap simplification using mathematical morphology M.R.Saradjian ** J. Amini , * Department of Surveying Engineering, Faculty of Engineering *,** Tehran University, Tehran, IRAN. * Department of Research, National Cartographic Center (N.C.C) Tehran, IRAN. [email protected] KEY WORDS: Morphology, Photogrammetry, Remote sensing, Segmentation, Simplification, Thinning. ABSTRACT For a variety of mapping applications, images are the most important primary data sources. In photogrammetry and remote sensing, particular procedures are used for image and map data integration in order to perform change detection and automatic object extraction. The recognition of an object in an image is a complex task that involves a broad range of techniques. In general, three steps are used in this study. The first step is segmentation to object regions of interest. In this step, regions which may contain unknown objects, have to be detected. The second step focuses on the extraction of suitable features and then extraction of objects. The main purpose of feature extraction is to reduce data by means of measuring certain features that distinguish the input patterns. The final step is classification. It assigns a label to an object based on the information provided by its descriptors. At the end of segmentation stage, the images are too still complex. So it is necessary to simplify image for further processes. In this paper, investigation is made on the mathematical morphology operators for simplification of a gray-scale image or imagemap. Then an structure element, ()L 4 , is applied on binary images to extract the skeletonized image. In this stage, there will remain lots of skeletal legs in the resultant image. -
Third Harmonic Generation Microscopy Zhang, Z
VU Research Portal Third harmonic generation microscopy Zhang, Z. 2017 document version Publisher's PDF, also known as Version of record Link to publication in VU Research Portal citation for published version (APA) Zhang, Z. (2017). Third harmonic generation microscopy: Towards automatic diagnosis of brain tumors. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. E-mail address: [email protected] Download date: 05. Oct. 2021 Third harmonic generation microscopy: towards automatic diagnosis of brain tumors This thesis was reviewed by: prof.dr. J. Hulshof VU University Amsterdam prof.dr. J. Popp Jena University prof.dr. A.G.J.M. van Leeuwen Academic Medical Center prof.dr. M. van Herk The University of Manchester dr. I.H.M. van Stokkum VU University Amsterdam dr. P. de Witt Hamer VU University Medical Center © Copyright Zhiqing Zhang, 2017 ISBN: 978-94-6295-704-6 Printed in the Netherlands by Proefschriftmaken. -
Topics in Mathematical Morphology for Multivariate Images Santiago Velasco-Forero
Topics in mathematical morphology for multivariate images Santiago Velasco-Forero To cite this version: Santiago Velasco-Forero. Topics in mathematical morphology for multivariate images. General Mathematics [math.GM]. Ecole Nationale Supérieure des Mines de Paris, 2012. English. NNT : 2012ENMP0086. pastel-00820581 HAL Id: pastel-00820581 https://pastel.archives-ouvertes.fr/pastel-00820581 Submitted on 6 May 2013 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. !"#$!$%$&'(#&#)!(")(#&($&$()*"+,+-!(# École doctorale nO432 : Sciences des Métiers de l’Ingénieur Doctorat ParisTech THÈSE pour obtenir le grade de docteur délivré par l’École nationale supérieure des mines de Paris Spécialité « Morphologie Mathématique » présentée et soutenue publiquement par Santiago Velasco-Forero le 14 juin 2012 Contributions en morphologie mathématique pour l’analyse d’images multivariées Directeur de thèse : Jesús ANGULO ! Jury M. Dominique JEULIN, Professeur, CMM-MS, Mines ParisTech Président " M. Jos B.T.M. ROERDINK, Professeur, University of Groningen Rapporteur M. Pierre SOILLE, Directeur de recherche, Joint Research Centre of the European Commission Rapporteur # M. Jón Atli BENEDIKTSSON, Professeur, University of Iceland Examinateur M. Fernand MEYER, Directeur de recherche, CMM, Mines ParisTech Examinateur $ M. Jean SERRA, Professeur émérite, ESIEE, Université Paris-Est Examinateur M. -
Computer Vision – A
CS4495 Computer Vision – A. Bobick Morphology CS 4495 Computer Vision Binary images and Morphology Aaron Bobick School of Interactive Computing CS4495 Computer Vision – A. Bobick Morphology Administrivia • PS7 – read about it on Piazza • PS5 – grades are out. • Final – Dec 9 • Study guide will be out by Thursday hopefully sooner. CS4495 Computer Vision – A. Bobick Morphology Binary Image Analysis Operations that produce or process binary images, typically 0’s and 1’s • 0 represents background • 1 represents foreground 00010010001000 00011110001000 00010010001000 Slides: Linda Shapiro CS4495 Computer Vision – A. Bobick Morphology Binary Image Analysis Used in a number of practical applications • Part inspection • Manufacturing • Document processing CS4495 Computer Vision – A. Bobick Morphology What kinds of operations? • Separate objects from background and from one another • Aggregate pixels for each object • Compute features for each object CS4495 Computer Vision – A. Bobick Morphology Example: Red blood cell image • Many blood cells are separate objects • Many touch – bad! • Salt and pepper noise from thresholding • How useable is this data? CS4495 Computer Vision – A. Bobick Morphology Results of analysis • 63 separate objects detected • Single cells have area about 50 • Noise spots • Gobs of cells CS4495 Computer Vision – A. Bobick Morphology Useful Operations • Thresholding a gray-scale image • Determining good thresholds • Connected components analysis • Binary mathematical morphology • All sorts of feature extractors, statistics (area, centroid, circularity, …) CS4495 Computer Vision – A. Bobick Morphology Thresholding • Background is black • Healthy cherry is bright • Bruise is medium dark • Histogram shows two cherry regions (black background has been removed) Pixel counts Pixel 0 Grayscale values 255 CS4495 Computer Vision – A. Bobick Morphology Histogram-Directed Thresholding • How can we use a histogram to separate an image into 2 (or several) different regions? Is there a single clear threshold? 2? 3? CS4495 Computer Vision – A. -
Visualize Yolo
MSc Artificial Intelligence Master Thesis Open the black box: Visualize Yolo by Peter Heemskerk 11988797 August 18, 2020 36 EC credits autumn 2019 till summer 2020 Supervisor: Dr. Jan-Mark Geusebroek Assessor: Prof. Dr. Theo Gevers University of Amsterdam Contents 1 Introduction 2 1.1 Open the neural network black box . .2 1.2 Project Background . .2 1.2.1 Wet Cooling Towers . .2 1.2.2 The risk of Legionellosis . .2 1.2.3 The project . .3 2 Related work 4 2.1 Object Detection . .4 2.2 Circle detection using Hough transform . .4 2.3 Convolutional Neural Networks (ConvNet) . .5 2.4 You Only Look Once (Yolo) . .5 2.4.1 Yolo version 3 - bounding box and class prediction . .6 2.4.2 Yolo version 3 - object recognition at different scales . .7 2.4.3 Yolo version 3 - network architecture . .7 2.4.4 Feature Pyramid Networks . .7 2.5 The Black Box Explanation problem . .9 2.6 Network Visualization . 10 3 Approach 10 3.1 Aerial imagery dataset . 10 3.2 Yolo version 3 . 12 3.2.1 Pytorch Implementation . 12 3.2.2 Tuning approach . 12 3.3 Evaluation . 12 3.3.1 Training, test and validation sets . 12 3.3.2 Evaluation Metrics . 12 3.4 Network Visualization . 13 3.4.1 Introduction . 13 3.4.2 Grad-CAM . 13 3.4.3 Feature maps . 14 4 Experiment 15 4.1 Results . 15 4.1.1 Hough Transform prediction illustration . 15 4.1.2 Yolo Prediction illustration . 16 4.1.3 Yolo Tuning . 17 4.1.4 Yolo Validation . -
Morphological Operations on Matrix-Valued Images
Morphological Operations on Matrix-Valued Images Bernhard Burgeth, Martin Welk, Christian Feddern, and Joachim Weickert Mathematical Image Analysis Group Faculty of Mathematics and Computer Science, Bldg. 27 Saarland University, 66041 Saarbruc¨ ken, Germany burgeth,welk,feddern,weickert @mia.uni-saarland.de f g http://www.mia.uni-saarland.de Abstract. The output of modern imaging techniques such as diffusion tensor MRI or the physical measurement of anisotropic behaviour in materials such as the stress-tensor consists of tensor-valued data. Hence adequate image processing methods for shape analysis, skeletonisation, denoising and segmentation are in demand. The goal of this paper is to extend the morphological operations of dilation, erosion, opening and closing to the matrix-valued setting. We show that naive approaches such as componentwise application of scalar morphological operations are unsatisfactory, since they violate elementary requirements such as invariance under rotation. This lead us to study an analytic and a geo- metric alternative which are rotation invariant. Both methods introduce novel non-component-wise definitions of a supremum and an infimum of a finite set of matrices. The resulting morphological operations incorpo- rate information from all matrix channels simultaneously and preserve positive definiteness of the matrix field. Their properties and their per- formance are illustrated by experiments on diffusion tensor MRI data. Keywords: mathematical morphology, dilation, erosion, matrix-valued imaging, DT-MRI 1 Introduction Modern data and image processing encompasses more and more the analysis and processing of matrix-valued data. For instance, diffusion tensor magnetic reso- nance imaging (DT-MRI), a novel medical image acquisition technique, measures the diffusion properties of water molecules in tissue. -
Design of a Video Processing Algorithm for Detection of a Soccer Ball with Arbitrary Color Pattern
Design of a video processing algorithm for detection of a soccer ball with arbitrary color pattern R. Woering DCT 2009.017 Traineeship report Coach(es): Ir. A.J. den Hamer Supervisor: prof.dr.ir. M. Steinbuch Technische Universiteit Eindhoven Department Mechanical Engineering Dynamics and Control Technology Group Eindhoven, March, 2009 Contents 1 Introduction 2 2 Literature 4 3 Basics of image processing 5 3.1 YUVandRGBcolorspaces ............................ ... 5 3.2 LinearFilters ................................... .... 7 Averagingfiltering .................................. .. 8 Gaussianlow-passfilter .. .. .. .. .. .. .. .. .. .. .. .. .. ... 8 LaplacianofGaussianfilter(LoG) . ..... 8 Unsharpfilter....................................... 9 3.3 Edgedetection ................................... ... 9 Cannymethod ...................................... 10 Sobelmethod....................................... 11 4 Circle Hough Transform (CHT) 12 4.1 Extraballcheck .................................. ... 12 5 Matlab 17 6 OpenCV 22 6.1 OpenCVreal-timetesting . ...... 23 7 Conclusion and Recommendations 25 References 28 1 1 Introduction This research is performed within the RoboCup project at the TU/e. RoboCup is an international joint project to promote A.I. (Artificial Intelligence), robotics and related fields. The idea is to perform research in the field of autonomous robots that play football by adapted FIFA rules. The goal is to play with humanoid robots against the world champion football of 2050 and hopefully win. Every year new challenges are set to force research and development to make it possible to play against humans in 2050. An autonomous mobile robot is a robot that is provided with the ability to take decisions on its own without interference of humans and work in a nondeterministic environment. A very important part of the development of autonomous robots is the real-time video processing, which is used to recognize the object in its surroundings. -
Mathematical Morphology: a Tool for Automated GIS Data Acquisition from Scanned Thematic Maps
Mathematical Morphology: A Tool for Automated GIs Data ~cquisitionfrom Scanned Thematic Maps Marc M. Ansoult and Pierre J. Soille Unit of Agricultural Engineering, Universite Catholique de Louvain, Place Croix du Sud, 3, 8-1348 Louvain-la-Neuve, BeIgium Jean A. Loodts Eurosense Technologies N.V., Ne~erslaan,54, B-1810 Wemmel, Belgium ABSTRACT:Over several years, the demand for digital data has grown as geographical information systems were im- plemented. Because of the cost of database creation, data acquisition should unquestionably be automated as much as possible. Today, scanning devices produce a huge amount of data that still needs complex processing. This paper proposes an original approach using image processing tools coming from Mathematical Morphology theory to acquire GIs data from scanned thematic maps. These tools are used in order to obtain a segmentation prior to radiometric analysis. To illustrate the methodology, a subset of the Belgian soil map is treated. INTRODUCTION tures characterize the Belgian soil map (Tavernier & Marechal, URING THE LAST FIFTEEN YEARS, dramatic growth in the use 1958): Dof geographical information systems (GIs) occurred in many More than 200 classes are offset printed using 12 fundamental disciplines. This technology provides multipurpose land infor- colors. mation systems as a means of dealing with the land records Black border lines delimit thematic colored areas. modernization problem. Natural resources modeling and man- Text labeling lays inside some areas. agement also benefit greatly from this technology by integrating Presence of a background gray colored topographic overlay. Typical features inside some areas like black and colored patterns a tremendous amount of data.