A Scanning Method for Industrial Data Matrix Codes marked on Spherical Surfaces
|
|
- Gladys Shelton
- 6 years ago
- Views:
Transcription
1 A Scanning Method for Industrial Data Matrix Codes marked on Spherical Surfaces ION-COSMIN DITA, MARIUS OTESTEANU Politehnica University of Timisoara Faculty of Electronics and Telecommunications Bd. Vasile Parvan 2, Timisoara ROMANIA cosmin.dita@etc.upt.ro, marius.otesteanu@etc.upt.ro FRANZ QUINT, NAGARAJU ANNAMDEVULA University of Applied Sciences, Karlsruhe Faculty of Electrical Engineering and Information Technology Moltkestrasse 30, Karlsruhe GERMANY franz.quint@hs-karlsruhe.de, raajz43@gmail.com Abstract: In this paper we provide a method to localize the modules of the industrial Data Matrix Code (DMC) marked on curved surfaces. An imaginary grid of points is constructed which has the same orientation as the surface. The imaginary grid is projected on to the image and according to this grid the modules of the code are scanned. If the surface considered is not a perfect sphere then the results are not accurate. To overcome this using an error correction based on the assumed centers and the computed centers a better approximation is obtained. Using this method we can localize the modules irrespective of the camera view or orientation of the DMC. Key Words: DMC Scanning Method, Industrial Data Matrix Codes, Data Matrix Code Reader Introduction Data Matrix Code (DMC) is a matrix (two dimensional) bar code which may have a square or rectangular shape made up of individual dots or squares called []. DMCs are composed of two separate parts, the finder pattern which is used to locate the symbol, and the data region. The finder pattern defines the shape (square or rectangle) and the number of rows and columns of the DMC. The finder pattern itself has two separate parts: the L finder pattern and the Clock track or timing pattern. In Fig., we can see that there are two edges with continuous modules and the other two with modules marked alternately. The L shaped edges that have the continuous modules is the L finder pattern. It is primarily used to determine the size, orientation and distortion of the code. Initially, DMC s have been developed to be printed with dark color on bright and plane surfaces (usually printed on paper). However, more and more DMC s are used in industrial environment to identify parts in a manufacturing process. Then, they are not only printed, but also milled, etched or laser marked directly on different kind of surfaces like metal, plastic etc. The surface on which they are marked are no longer plane, so their appearance in the image will no longer be that of a rectangular grid. This, combined with small contrast due to the various materials they are marked on, and with the typical disturbances in industrial environment like scratches, rust, oil drops etc. makes localization and decoding a challenging task. In this paper we present a method for localizing the modules of a DMC on curved surfaces. 2 Overview of the localization method Figure : Finder pattern and encoded data The other two edges of the finder pattern with alternating light and dark elements are known as timing pattern. This defines the basic structure of the code and can also help to determine its size and the distortion []. The number of rows and columns varies between 8x8 up to 44x44. The DMC is capable of encoding up to 2KB data. Fig. 2 gives an overview of the localization process of the Data Matrix Code dotted on curved surfaces. After image acquisition, the process starts with the coarse localization of the Data Matrix Code. This step is used to determine a Region of Interest (ROI) inside which the Data Matrix Code lies [2]. For this it considers the real world size of Data Matrix Code, the surface radius and as well as the focal length of the camera s lens to be approximately known. The ISBN:
2 image is thresholded using an adaptive threshold level [3] []. To reliable detect the Data Matrix Code it is convenient to have a solid shape rather than separated modules. For that, using morphological operations, the image is closed in order to fill the empty spaces between modules [5]. The maximum and the minimum coordinates gives us the four corners of each object. After the image is thresholded, in the image are objects. Heaving now established a coarse localization of the DMC, the process continues with scanning the DMC to find the positions of the individual modules. First we search for the positions of the modules along the edges of the DMC. Out of the modules on the edges, we choose control points. These will be used to calculate the transformation matrix between the module positions in a 3D-coordinate system locally attached to the code ( imaginary grid ) and the module positions in the image. Due to the fact, that the curved surfaces will not necessarily be spherical or cylindrical as the model assumes, we will need to correct, i.e. relocate the module positions during the scanning process. We will subsequently explain this in more detail. Video Camera Image acquisition Data Matrix Localization Data Matrix Corners Detection Labeling Coarse DMC Localization Scanning process for DMC marked s Input parameters ~ The radius of curvature ~ The length of the DMC Scanning along the edges Identifying modules and computing Centers Control Points and Surface Classification Matrix Construction Relocating the module position DMC Matrix Figure 2: The flow process of the Data Matrix Codes for spherical surfaces Figure 3: Scanning for modules along the edges 3 Scanning along the edges All edges are scanned to find the locations of the modules along the timing and the finder pattern of the DMC. In Fig. 3 a labeled image of DMC is shown with its corners named. Corners A and B are used to find the orientation of the first edge with the x-axis (eq. ). ( ) yb y A θ = atan, () x B x A The point that stands at distance d at an angle θ with point A is computed (eq.2,3). d being a first estimate of the distances between modules. x = x + d cos(θ ), (2) y = y + d sin(θ ), (3) In the case of the spherical surface the distance between the modules will not be constant in the image. But the distance between adjacent modules will be almost the same. So for that reason every time the distance value has to be updated with the value computed from the latest points that is known. Every time a new point is computed, it is taken as a current point. First, the distance and angle values are computed using the current point and the point B, being updated. Starting with point A as a current point we repeatedly estimate the module position of the next point cf. eq. 2 and 3. A frame is constructed around that approximate position, searching for the desired object inside of it, computing the centers of this object. The currentpoint is updated with this value and the process continues. For the angle computation, A and B are used at beginning. After then the angle is computed using A and the current point, the values being updated after each iteration. For the distance computation the last two points from the previous edge are used at beginning. Then the corner A and the current point are used to update the value after every iteration. ISBN:
3 4 Selection of control points Selection of the control points is important because the transformation process dependents on the matrices that are computed from these values. The control points are picked from the modules along the edges of the DMC. We have chosen to select fifteen control points from different parts of the code. Five fixed points are used as control points, which represent the corners of the DMC. The modules that are adjacent to the corner points are also considered as the control points. The rest of the points are chosen to be distributed evenly across the finder pattern. Having this control points and other information about the code like real world size and radius curvature, we can construct the estimated grid for the DMC modules. This estimated grid is a connection between the real world modules position and the position of them in the image. 5 Cylindrical and Spherical Surfaces We use cylindrical and spherical models for our surfaces. To differentiate between the cylindrical and spherical surface we use the orientation of the edges of the DMC. If the surface is a cylindrical then irrespective of the camera view every time two of the DMC edges will be linear and if the camera view is orthogonal to the axis of cylinder then all the four sides will be linear. When it comes to the spherical surfaces all the edges are curved. Furthermore opposite sides are curved in opposite directions. Consider a straight line L with slope m and a y-intercept c, Fig. 4. The points P (x, y ) and P 2 (x 2, y 2 ) are two points in the xy-plane. If the point P lies on the line, then L(P ) will be zero i.e., y = m x + c, where as if P and P 2 lie on either side of the straight line then the value will be of opposite sign. Using this it can be determined if the sides are curved or linear. Y-axis ve egion ve region X- axis y=4x+5 Random points Figure 4: Demonstrating the classification of surfaces Table : The possible values for the edges of the DMC on a cylinder or on a sphere Surface lin lin2 lin3 lin4 lin Planar +4 Cylindrical Spherical Every time opposite sides are oriented in opposite directions hence giving the sum as zero We observe that this way there are two regions defined in the image. The region above the line is the negative region and the region below the line is the positive region. The line L shall be the line joining the two corners of the DMC code and the other points represent the centers of the modules along the edge. By substituting these points in the line equation, we can find whether they lie on the line or in the negative region or in the positive region. If a point lies approximately on the line, it is given a value of unity. If the number of points lie on either side of the edge then a value of 2 or +2 is given depending on the sign of the residuals. Assume that the residuals of the second edge are positive and so it has a value +2 and it is the same with the fourth edge. So it also have the same value +2. Whereas the first and third edges are linear so they take a value of. The sum of the values given to all the edges are used to classify the surfaces. For a spherical surface it may have all the edges curved and the opposite edges are curved in a direction opposite to each other. That indicates the overall sum will be zero for a spherical surface. Matrix Construction Due to the imprinting of the modules on non-planar surfaces, the modules in the image will not appear on a rectilinear and equidistant grid. The relation between the local real world coordinates and the image coordinates is given by the projection equation: ku kv k = H H 2 H 3 H 4 H 5 H H 7 H 8 H 9 H 0 H H 2 x y z (4) ISBN:
4 where, (x, y, z) are the coordinates of the objects in the real world and the (u, v) represents the projected points in the image. Since the real world dimension of the DMC is approximatively known and also the radius of the curvature is known, the real world coordinates of the corner points of the DMC can be calculated. Having the real world coordinates of the control points and also their coordinates in the image, one can solve eq. 5 for the unknown projection parameters H. x y z u x x y z v x x 2 y 2 z u 2 x x 2 y 2 z 2 v 2 x x n y n z n u n x n x n y n z n v n x n u y u z u H v y v z v H 2 u 2 y 2 u 2 z 2 u 2 H 3 v 2 y v 2 z v 2 H 4 = [0]... u n y n u n z n u n v n y n v n z n v n. H H 2 (5) 8 Conclusion To localize the modules in DMC, scanning inside the image of DMC is necessary. The programmer does not know where to start the scanning process. In that case this implementation will provide the scanner with some approximate locations where the modules are located. It can scan around that location to find the exact position of the module. This algorithm works in many different situations like the DMC is rotated in its plane, the view of the camera is not orthogonal with the surface of the object and the DMC is not a square. One only needs an approximately value for the size of the DMC whereas the current value is estimated during the localization process. (a) Data Matrix Code (b) Predicted grid (c) Detected modules Figure 5: Ex. Industrial Data Matrix Code marked where, (x i, y i, z i ) are the real world coordinates of the control points and the (u i, v i ) represents the coordinates of the control points in the image. This is solved using the singular value decomposition method to obtain the values of H-matrix [4]. Having these parameters one can predict the location of any real world coordinates in the image. (a) Data Matrix Code (b) Predicted grid (c) Detected modules Figure : Ex.2 Industrial Data Matrix Code marked 7 Relocating the module position Projecting the grid on to the image, all the modules can be located approximately. There is some error because of the inaccurate points of correspondence that are used. Due to this reason, using a frame, one searches in rows and columns for each dot creating a matrix of coordinates of the dotted and un-dotted modules. The size of the frame is equal with the distance between the modules. The center of the frame follows the predicted grid(transformation matrix) of Data Matrix Code. If in the frame exists a module then the matrix element is an one. If the frame is empty then the matrix element is a zero [2]. (a) Data Matrix Code DMC detected: Angle=29, Distance= (b) Detected modules Figure 7: Ex.3 Industrial Data Matrix Code marked ISBN:
5 In Fig. 5-7, are presented two examples of situation with Data Matrix Code marked s. The proposed method takes the extreme points of the Data Matrix pattern computing the predicted grid where the Data Matrix modules should be distributed. The information is extracted based on this predicted grid, only the modules which intersect with the grid being analyzed. This method works well for all images where the extremes modules of the code can be seen, doesn t depend by the orientation angle or the size of the pattern or the type of the materiel where the pattern is marked. Using this, not the image is geometrical transformed, only a grid is created based on the image. The goal is that the image is not processed and no information from the image is loosed, also the processing system doesn t need to much power for Data Matrix scanning. Acknowledgements: This work was partially supported by the strategic grant POSDRU /.5/S/3, (2008) of the Ministry of Labour, Family and Social Protection, Romania, co-financed by the European Social Fund Investing in People. References: [] INTERNATIONAL STANDARD: Information technology International symbology specification Data matrix ( ) [2] Ion-Cosmin Dita, Marius Otesteanu, Frant Quint: Data Matrix Code - A Reliable Optical Identification of Microelectronic Components. 20 IEEE 7th International Symposium for Design and Technology in Electronic Packaging (SIITME) (20) [3] N. Otsu: A Threshold Selection Method from Gray-Level Histograms. IEEE Transactions on Systems, Man and Cybernetics, DOI /TSMC (Systems, Man and Cybernetics, IEEE Transactions on) 9(), 2 (979) [4] Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing, (3rd ed.) edn. New York: Cambridge University Press (2007) [5] V Gui, D Lacrama, D Pescaru: Prelucrarea imaginilor, vol. ISBN Editura Politehnica Timisoara (999) [] Ye Zhang, Hongsong Qu, Yanjie Wang: Adaptive Image Segmentation Based on Fast Thresholding and Image Merging. Artificial Reality and Telexistence Workshops, 200. ICAT 0. th International Conference on pp (200) ISBN:
Using Mean Shift Algorithm in the Recognition of Industrial Data Matrix Codes
Using Mean Shift Algorithm in the Recognition of Industrial Data Matrix Codes ION-COSMIN DITA, VASILE GUI, MARIUS OTESTEANU Politehnica University of Timisoara Faculty of Electronics and Telecommunications
More informationA Study of Medical Image Analysis System
Indian Journal of Science and Technology, Vol 8(25), DOI: 10.17485/ijst/2015/v8i25/80492, October 2015 ISSN (Print) : 0974-6846 ISSN (Online) : 0974-5645 A Study of Medical Image Analysis System Kim Tae-Eun
More informationChapter 3 Image Registration. Chapter 3 Image Registration
Chapter 3 Image Registration Distributed Algorithms for Introduction (1) Definition: Image Registration Input: 2 images of the same scene but taken from different perspectives Goal: Identify transformation
More informationDD2429 Computational Photography :00-19:00
. Examination: DD2429 Computational Photography 202-0-8 4:00-9:00 Each problem gives max 5 points. In order to pass you need about 0-5 points. You are allowed to use the lecture notes and standard list
More information521493S Computer Graphics Exercise 2 Solution (Chapters 4-5)
5493S Computer Graphics Exercise Solution (Chapters 4-5). Given two nonparallel, three-dimensional vectors u and v, how can we form an orthogonal coordinate system in which u is one of the basis vectors?
More informationCHAPTER - 10 STRAIGHT LINES Slope or gradient of a line is defined as m = tan, ( 90 ), where is angle which the line makes with positive direction of x-axis measured in anticlockwise direction, 0 < 180
More information[10] Industrial DataMatrix barcodes recognition with a random tilt and rotating the camera
[10] Industrial DataMatrix barcodes recognition with a random tilt and rotating the camera Image processing, pattern recognition 865 Kruchinin A.Yu. Orenburg State University IntBuSoft Ltd Abstract The
More informationFlexible Calibration of a Portable Structured Light System through Surface Plane
Vol. 34, No. 11 ACTA AUTOMATICA SINICA November, 2008 Flexible Calibration of a Portable Structured Light System through Surface Plane GAO Wei 1 WANG Liang 1 HU Zhan-Yi 1 Abstract For a portable structured
More informationThe Three Dimensional Coordinate System
The Three-Dimensional Coordinate System The Three Dimensional Coordinate System You can construct a three-dimensional coordinate system by passing a z-axis perpendicular to both the x- and y-axes at the
More informationGeneral Physics II. Mirrors & Lenses
General Physics II Mirrors & Lenses Nothing New! For the next several lectures we will be studying geometrical optics. You already know the fundamentals of what is going on!!! Reflection: θ 1 = θ r incident
More informationCOMP 558 lecture 19 Nov. 17, 2010
COMP 558 lecture 9 Nov. 7, 2 Camera calibration To estimate the geometry of 3D scenes, it helps to know the camera parameters, both external and internal. The problem of finding all these parameters is
More informationLinear algebra deals with matrixes: two-dimensional arrays of values. Here s a matrix: [ x + 5y + 7z 9x + 3y + 11z
Basic Linear Algebra Linear algebra deals with matrixes: two-dimensional arrays of values. Here s a matrix: [ 1 5 ] 7 9 3 11 Often matrices are used to describe in a simpler way a series of linear equations.
More informationE0005E - Industrial Image Analysis
E0005E - Industrial Image Analysis The Hough Transform Matthew Thurley slides by Johan Carlson 1 This Lecture The Hough transform Detection of lines Detection of other shapes (the generalized Hough transform)
More informationReflection and Image Formation by Mirrors
Purpose Theory a. To study the reflection of light Reflection and Image Formation by Mirrors b. To study the formation and characteristics of images formed by different types of mirrors. When light (wave)
More informationCamera model and multiple view geometry
Chapter Camera model and multiple view geometry Before discussing how D information can be obtained from images it is important to know how images are formed First the camera model is introduced and then
More informationGraphics and Interaction Transformation geometry and homogeneous coordinates
433-324 Graphics and Interaction Transformation geometry and homogeneous coordinates Department of Computer Science and Software Engineering The Lecture outline Introduction Vectors and matrices Translation
More informationCOMP30019 Graphics and Interaction Transformation geometry and homogeneous coordinates
COMP30019 Graphics and Interaction Transformation geometry and homogeneous coordinates Department of Computer Science and Software Engineering The Lecture outline Introduction Vectors and matrices Translation
More informationDifferential Geometry: Circle Patterns (Part 1) [Discrete Conformal Mappinngs via Circle Patterns. Kharevych, Springborn and Schröder]
Differential Geometry: Circle Patterns (Part 1) [Discrete Conformal Mappinngs via Circle Patterns. Kharevych, Springborn and Schröder] Preliminaries Recall: Given a smooth function f:r R, the function
More informationUNIT 2 2D TRANSFORMATIONS
UNIT 2 2D TRANSFORMATIONS Introduction With the procedures for displaying output primitives and their attributes, we can create variety of pictures and graphs. In many applications, there is also a need
More informationA Survey of Light Source Detection Methods
A Survey of Light Source Detection Methods Nathan Funk University of Alberta Mini-Project for CMPUT 603 November 30, 2003 Abstract This paper provides an overview of the most prominent techniques for light
More informationLecture 3 Sections 2.2, 4.4. Mon, Aug 31, 2009
Model s Lecture 3 Sections 2.2, 4.4 World s Eye s Clip s s s Window s Hampden-Sydney College Mon, Aug 31, 2009 Outline Model s World s Eye s Clip s s s Window s 1 2 3 Model s World s Eye s Clip s s s Window
More informationform are graphed in Cartesian coordinates, and are graphed in Cartesian coordinates.
Plot 3D Introduction Plot 3D graphs objects in three dimensions. It has five basic modes: 1. Cartesian mode, where surfaces defined by equations of the form are graphed in Cartesian coordinates, 2. cylindrical
More informationHOUGH TRANSFORM CS 6350 C V
HOUGH TRANSFORM CS 6350 C V HOUGH TRANSFORM The problem: Given a set of points in 2-D, find if a sub-set of these points, fall on a LINE. Hough Transform One powerful global method for detecting edges
More informationShort on camera geometry and camera calibration
Short on camera geometry and camera calibration Maria Magnusson, maria.magnusson@liu.se Computer Vision Laboratory, Department of Electrical Engineering, Linköping University, Sweden Report No: LiTH-ISY-R-3070
More informationAP Physics: Curved Mirrors and Lenses
The Ray Model of Light Light often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric
More informationModel Based Perspective Inversion
Model Based Perspective Inversion A. D. Worrall, K. D. Baker & G. D. Sullivan Intelligent Systems Group, Department of Computer Science, University of Reading, RG6 2AX, UK. Anthony.Worrall@reading.ac.uk
More informationStereo Image Rectification for Simple Panoramic Image Generation
Stereo Image Rectification for Simple Panoramic Image Generation Yun-Suk Kang and Yo-Sung Ho Gwangju Institute of Science and Technology (GIST) 261 Cheomdan-gwagiro, Buk-gu, Gwangju 500-712 Korea Email:{yunsuk,
More informationIntegers & Absolute Value Properties of Addition Add Integers Subtract Integers. Add & Subtract Like Fractions Add & Subtract Unlike Fractions
Unit 1: Rational Numbers & Exponents M07.A-N & M08.A-N, M08.B-E Essential Questions Standards Content Skills Vocabulary What happens when you add, subtract, multiply and divide integers? What happens when
More informationChapter 7 Coordinate Geometry
Chapter 7 Coordinate Geometry 1 Mark Questions 1. Where do these following points lie (0, 3), (0, 8), (0, 6), (0, 4) A. Given points (0, 3), (0, 8), (0, 6), (0, 4) The x coordinates of each point is zero.
More informationAberrations in Holography
Aberrations in Holography D Padiyar, J Padiyar 1070 Commerce St suite A, San Marcos, CA 92078 dinesh@triple-take.com joy@triple-take.com Abstract. The Seidel aberrations are described as they apply to
More informationInteractive Math Glossary Terms and Definitions
Terms and Definitions Absolute Value the magnitude of a number, or the distance from 0 on a real number line Addend any number or quantity being added addend + addend = sum Additive Property of Area the
More information3 Identify shapes as two-dimensional (lying in a plane, flat ) or three-dimensional ( solid ).
Geometry Kindergarten Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). 1 Describe objects in the environment using names of shapes,
More information5/27/12. Objectives. Plane Curves and Parametric Equations. Sketch the graph of a curve given by a set of parametric equations.
Objectives Sketch the graph of a curve given by a set of parametric equations. Eliminate the parameter in a set of parametric equations. Find a set of parametric equations to represent a curve. Understand
More informationA DH-parameter based condition for 3R orthogonal manipulators to have 4 distinct inverse kinematic solutions
Wenger P., Chablat D. et Baili M., A DH-parameter based condition for R orthogonal manipulators to have 4 distinct inverse kinematic solutions, Journal of Mechanical Design, Volume 17, pp. 150-155, Janvier
More informationMotion Planning Using Approximate Cell Decomposition Method
Motion Planning Using Approximate Cell Decomposition Method Doina Dragulescu, Mirela Toth-Tascau and Lavinia Dragomir Mechanical Department, Faculty of Mechanical Engineering, Bd. Mihai Viteazul No.1,
More informationVisual Recognition: Image Formation
Visual Recognition: Image Formation Raquel Urtasun TTI Chicago Jan 5, 2012 Raquel Urtasun (TTI-C) Visual Recognition Jan 5, 2012 1 / 61 Today s lecture... Fundamentals of image formation You should know
More informationGeometry Vocabulary. acute angle-an angle measuring less than 90 degrees
Geometry Vocabulary acute angle-an angle measuring less than 90 degrees angle-the turn or bend between two intersecting lines, line segments, rays, or planes angle bisector-an angle bisector is a ray that
More informationLESSON 14 LEARNING OBJECTIVES. After completing this lesson, you will be able to:
LEARNING OBJECTIVES After completing this lesson, you will be able to: 1. Construct 6 Solid model Primitives: Box, Sphere, Cylinder, Cone, Wedge and Torus LESSON 14 CONSTRUCTING SOLID PRIMITIVES AutoCAD
More informationThis document contains the draft version of the following paper:
This document contains the draft version of the following paper: M. Karnik, S.K. Gupta, and E.B. Magrab. Geometric algorithms for containment analysis of rotational parts. Computer Aided Design, 37(2):213-230,
More informationUNIT 5: GEOMETRIC AND ALGEBRAIC CONNECTIONS. Apply Geometric Concepts in Modeling Situations
UNIT 5: GEOMETRIC AND ALGEBRAIC CONNECTIONS This unit investigates coordinate geometry. Students look at equations for circles and use given information to derive equations for representations of these
More information8.B. The result of Regiomontanus on tetrahedra
8.B. The result of Regiomontanus on tetrahedra We have already mentioned that Plato s theory that the five regular polyhedra represent the fundamental elements of nature, and in supplement (3.D) to the
More informationChapter - 2: Geometry and Line Generations
Chapter - 2: Geometry and Line Generations In Computer graphics, various application ranges in different areas like entertainment to scientific image processing. In defining this all application mathematics
More informationSimulation of a mobile robot with a LRF in a 2D environment and map building
Simulation of a mobile robot with a LRF in a 2D environment and map building Teslić L. 1, Klančar G. 2, and Škrjanc I. 3 1 Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana,
More information3D-OBJECT DETECTION METHOD BASED ON THE STEREO IMAGE TRANSFORMATION TO THE COMMON OBSERVATION POINT
3D-OBJECT DETECTION METHOD BASED ON THE STEREO IMAGE TRANSFORMATION TO THE COMMON OBSERVATION POINT V. M. Lisitsyn *, S. V. Tikhonova ** State Research Institute of Aviation Systems, Moscow, Russia * lvm@gosniias.msk.ru
More informationCamera Calibration. Schedule. Jesus J Caban. Note: You have until next Monday to let me know. ! Today:! Camera calibration
Camera Calibration Jesus J Caban Schedule! Today:! Camera calibration! Wednesday:! Lecture: Motion & Optical Flow! Monday:! Lecture: Medical Imaging! Final presentations:! Nov 29 th : W. Griffin! Dec 1
More informationRectification and Distortion Correction
Rectification and Distortion Correction Hagen Spies March 12, 2003 Computer Vision Laboratory Department of Electrical Engineering Linköping University, Sweden Contents Distortion Correction Rectification
More informationVOLUME OF A REGION CALCULATOR EBOOK
19 March, 2018 VOLUME OF A REGION CALCULATOR EBOOK Document Filetype: PDF 390.92 KB 0 VOLUME OF A REGION CALCULATOR EBOOK How do you calculate volume. A solid of revolution is a solid formed by revolving
More informationLecture 17: Recursive Ray Tracing. Where is the way where light dwelleth? Job 38:19
Lecture 17: Recursive Ray Tracing Where is the way where light dwelleth? Job 38:19 1. Raster Graphics Typical graphics terminals today are raster displays. A raster display renders a picture scan line
More informationSPECIAL TECHNIQUES-II
SPECIAL TECHNIQUES-II Lecture 19: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay Method of Images for a spherical conductor Example :A dipole near aconducting sphere The
More informationMath 11 Fall 2016 Section 1 Monday, October 17, 2016
Math 11 Fall 16 Section 1 Monday, October 17, 16 First, some important points from the last class: f(x, y, z) dv, the integral (with respect to volume) of f over the three-dimensional region, is a triple
More informationPARAMETRIC EQUATIONS AND POLAR COORDINATES
10 PARAMETRIC EQUATIONS AND POLAR COORDINATES PARAMETRIC EQUATIONS & POLAR COORDINATES A coordinate system represents a point in the plane by an ordered pair of numbers called coordinates. PARAMETRIC EQUATIONS
More informationArtifacts and Textured Region Detection
Artifacts and Textured Region Detection 1 Vishal Bangard ECE 738 - Spring 2003 I. INTRODUCTION A lot of transformations, when applied to images, lead to the development of various artifacts in them. In
More informationDETECTION AND ROBUST ESTIMATION OF CYLINDER FEATURES IN POINT CLOUDS INTRODUCTION
DETECTION AND ROBUST ESTIMATION OF CYLINDER FEATURES IN POINT CLOUDS Yun-Ting Su James Bethel Geomatics Engineering School of Civil Engineering Purdue University 550 Stadium Mall Drive, West Lafayette,
More informationGlossary of dictionary terms in the AP geometry units
Glossary of dictionary terms in the AP geometry units affine linear equation: an equation in which both sides are sums of terms that are either a number times y or a number times x or just a number [SlL2-D5]
More informationPolar Coordinates. 2, π and ( )
Polar Coordinates Up to this point we ve dealt exclusively with the Cartesian (or Rectangular, or x-y) coordinate system. However, as we will see, this is not always the easiest coordinate system to work
More informationReflection and Refraction
Reflection and Refraction Theory: Whenever a wave traveling in some medium encounters an interface or boundary with another medium either (or both) of the processes of (1) reflection and (2) refraction
More informationSelective Space Structures Manual
Selective Space Structures Manual February 2017 CONTENTS 1 Contents 1 Overview and Concept 4 1.1 General Concept........................... 4 1.2 Modules................................ 6 2 The 3S Generator
More informationMultivariable Calculus
Multivariable Calculus Chapter 10 Topics in Analytic Geometry (Optional) 1. Inclination of a line p. 5. Circles p. 4 9. Determining Conic Type p. 13. Angle between lines p. 6. Parabolas p. 5 10. Rotation
More informationSPACE - A Manifold Exploration Program
1. Overview SPACE - A Manifold Exploration Program 1. Overview This appendix describes the manifold exploration program SPACE that is a companion to this book. Just like the GM program, the SPACE program
More information2D and 3D Transformations AUI Course Denbigh Starkey
2D and 3D Transformations AUI Course Denbigh Starkey. Introduction 2 2. 2D transformations using Cartesian coordinates 3 2. Translation 3 2.2 Rotation 4 2.3 Scaling 6 3. Introduction to homogeneous coordinates
More informationLab 10 - GEOMETRICAL OPTICS
L10-1 Name Date Partners OBJECTIVES OVERVIEW Lab 10 - GEOMETRICAL OPTICS To examine Snell s Law. To observe total internal reflection. To understand and use the lens equations. To find the focal length
More informationCurves and Surfaces. Chapter 7. Curves. ACIS supports these general types of curves:
Chapter 7. Curves and Surfaces This chapter discusses the types of curves and surfaces supported in ACIS and the classes used to implement them. Curves ACIS supports these general types of curves: Analytic
More informationUnwrapping of Urban Surface Models
Unwrapping of Urban Surface Models Generation of virtual city models using laser altimetry and 2D GIS Abstract In this paper we present an approach for the geometric reconstruction of urban areas. It is
More informationIntro. To Graphing Linear Equations
Intro. To Graphing Linear Equations The Coordinate Plane A. The coordinate plane has 4 quadrants. B. Each point in the coordinate plain has an x-coordinate (the abscissa) and a y-coordinate (the ordinate).
More informationPITSCO Math Individualized Prescriptive Lessons (IPLs)
Orientation Integers 10-10 Orientation I 20-10 Speaking Math Define common math vocabulary. Explore the four basic operations and their solutions. Form equations and expressions. 20-20 Place Value Define
More information1 Affine and Projective Coordinate Notation
CS348a: Computer Graphics Handout #9 Geometric Modeling Original Handout #9 Stanford University Tuesday, 3 November 992 Original Lecture #2: 6 October 992 Topics: Coordinates and Transformations Scribe:
More informationOptics II. Reflection and Mirrors
Optics II Reflection and Mirrors Geometric Optics Using a Ray Approximation Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media The
More information3B SCIENTIFIC PHYSICS
3B SCIENTIFIC PHYSICS Instruction sheet 06/18 ALF Laser Optics Demonstration Set Laser Optics Supplement Set Page 1 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 12 12 12 13 13 13 14 14
More informationCorrecting Radial Distortion of Cameras With Wide Angle Lens Using Point Correspondences
Correcting Radial istortion of Cameras With Wide Angle Lens Using Point Correspondences Leonardo Romero and Cuauhtemoc Gomez Universidad Michoacana de San Nicolas de Hidalgo Morelia, Mich., 58000, Mexico
More informationChapter 5. Projections and Rendering
Chapter 5 Projections and Rendering Topics: Perspective Projections The rendering pipeline In order to view manipulate and view a graphics object we must find ways of storing it a computer-compatible way.
More informationCollision Detection of Cylindrical Rigid Bodies for Motion Planning
Proceedings of the 2006 IEEE International Conference on Robotics and Automation Orlando, Florida - May 2006 Collision Detection of Cylindrical Rigid Bodies for Motion Planning John Ketchel Department
More informationWe have already studied equations of the line. There are several forms:
Chapter 13-Coordinate Geometry extended. 13.1 Graphing equations We have already studied equations of the line. There are several forms: slope-intercept y = mx + b point-slope y - y1=m(x - x1) standard
More informationnotes13.1inclass May 01, 2015
Chapter 13-Coordinate Geometry extended. 13.1 Graphing equations We have already studied equations of the line. There are several forms: slope-intercept y = mx + b point-slope y - y1=m(x - x1) standard
More informationPart Images Formed by Flat Mirrors. This Chapter. Phys. 281B Geometric Optics. Chapter 2 : Image Formation. Chapter 2: Image Formation
Phys. 281B Geometric Optics This Chapter 3 Physics Department Yarmouk University 21163 Irbid Jordan 1- Images Formed by Flat Mirrors 2- Images Formed by Spherical Mirrors 3- Images Formed by Refraction
More information2D Object Definition (1/3)
2D Object Definition (1/3) Lines and Polylines Lines drawn between ordered points to create more complex forms called polylines Same first and last point make closed polyline or polygon Can intersect itself
More informationCourse Number: Course Title: Geometry
Course Number: 1206310 Course Title: Geometry RELATED GLOSSARY TERM DEFINITIONS (89) Altitude The perpendicular distance from the top of a geometric figure to its opposite side. Angle Two rays or two line
More informationdq dt I = Irradiance or Light Intensity is Flux Φ per area A (W/m 2 ) Φ =
Radiometry (From Intro to Optics, Pedrotti -4) Radiometry is measurement of Emag radiation (light) Consider a small spherical source Total energy radiating from the body over some time is Q total Radiant
More informationROBUST LINE-BASED CALIBRATION OF LENS DISTORTION FROM A SINGLE VIEW
ROBUST LINE-BASED CALIBRATION OF LENS DISTORTION FROM A SINGLE VIEW Thorsten Thormählen, Hellward Broszio, Ingolf Wassermann thormae@tnt.uni-hannover.de University of Hannover, Information Technology Laboratory,
More information16.6. Parametric Surfaces. Parametric Surfaces. Parametric Surfaces. Vector Calculus. Parametric Surfaces and Their Areas
16 Vector Calculus 16.6 and Their Areas Copyright Cengage Learning. All rights reserved. Copyright Cengage Learning. All rights reserved. and Their Areas Here we use vector functions to describe more general
More informationMathematics (www.tiwariacademy.com)
() Miscellaneous Exercise on Chapter 10 Question 1: Find the values of k for which the line is (a) Parallel to the x-axis, (b) Parallel to the y-axis, (c) Passing through the origin. Answer 1: The given
More informationMathematics High School Geometry
Mathematics High School Geometry An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts interpreting a schematic drawing, estimating the amount of
More informationgraphing_9.1.notebook March 15, 2019
1 2 3 Writing the equation of a line in slope intercept form. In order to write an equation in y = mx + b form you will need the slope "m" and the y intercept "b". We will subsitute the values for m and
More information(Section 6.2: Volumes of Solids of Revolution: Disk / Washer Methods)
(Section 6.: Volumes of Solids of Revolution: Disk / Washer Methods) 6.. PART E: DISK METHOD vs. WASHER METHOD When using the Disk or Washer Method, we need to use toothpicks that are perpendicular to
More informationLecture 9: Hough Transform and Thresholding base Segmentation
#1 Lecture 9: Hough Transform and Thresholding base Segmentation Saad Bedros sbedros@umn.edu Hough Transform Robust method to find a shape in an image Shape can be described in parametric form A voting
More informationcomputational field which is always rectangular by construction.
I. INTRODUCTION The numerical solution of partial differential equations requires some discretization of the field into a collection of points or elemental volumes (cells). The differential equations are
More informationGlossary Common Core Curriculum Maps Math/Grade 6 Grade 8
Glossary Common Core Curriculum Maps Math/Grade 6 Grade 8 Grade 6 Grade 8 absolute value Distance of a number (x) from zero on a number line. Because absolute value represents distance, the absolute value
More informationComputer Vision. Coordinates. Prof. Flávio Cardeal DECOM / CEFET- MG.
Computer Vision Coordinates Prof. Flávio Cardeal DECOM / CEFET- MG cardeal@decom.cefetmg.br Abstract This lecture discusses world coordinates and homogeneous coordinates, as well as provides an overview
More informationRepresenting 2D Transformations as Matrices
Representing 2D Transformations as Matrices John E. Howland Department of Computer Science Trinity University One Trinity Place San Antonio, Texas 78212-7200 Voice: (210) 999-7364 Fax: (210) 999-7477 E-mail:
More informationMoore Catholic High School Math Department
Moore Catholic High School Math Department Geometry Vocabulary The following is a list of terms and properties which are necessary for success in a Geometry class. You will be tested on these terms during
More informationSegmentation of point clouds
Segmentation of point clouds George Vosselman INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION Extraction of information from point clouds 1 Segmentation algorithms Extraction
More informationEE640 FINAL PROJECT HEADS OR TAILS
EE640 FINAL PROJECT HEADS OR TAILS By Laurence Hassebrook Initiated: April 2015, updated April 27 Contents 1. SUMMARY... 1 2. EXPECTATIONS... 2 3. INPUT DATA BASE... 2 4. PREPROCESSING... 4 4.1 Surface
More information2.3 Thin Lens. Equating the right-hand sides of these equations, we obtain the Newtonian imaging equation:
2.3 Thin Lens 6 2.2.6 Newtonian Imaging Equation In the Gaussian imaging equation (2-4), the object and image distances S and S, respectively, are measured from the vertex V of the refracting surface.
More informationMathematics High School Geometry An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts
Mathematics High School Geometry An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts interpreting a schematic drawing, estimating the amount of
More informationResearch in Computational Differential Geomet
Research in Computational Differential Geometry November 5, 2014 Approximations Often we have a series of approximations which we think are getting close to looking like some shape. Approximations Often
More informationVectors and the Geometry of Space
Vectors and the Geometry of Space In Figure 11.43, consider the line L through the point P(x 1, y 1, z 1 ) and parallel to the vector. The vector v is a direction vector for the line L, and a, b, and c
More informationChapter 23. Geometrical Optics: Mirrors and Lenses and other Instruments
Chapter 23 Geometrical Optics: Mirrors and Lenses and other Instruments HITT1 A small underwater pool light is 1 m below the surface of a swimming pool. What is the radius of the circle of light on the
More informationStudy Guide and Review
State whether each sentence is or false. If false, replace the underlined term to make a sentence. 1. Euclidean geometry deals with a system of points, great circles (lines), and spheres (planes). false,
More informationMeasurements using three-dimensional product imaging
ARCHIVES of FOUNDRY ENGINEERING Published quarterly as the organ of the Foundry Commission of the Polish Academy of Sciences ISSN (1897-3310) Volume 10 Special Issue 3/2010 41 46 7/3 Measurements using
More informationPartial Calibration and Mirror Shape Recovery for Non-Central Catadioptric Systems
Partial Calibration and Mirror Shape Recovery for Non-Central Catadioptric Systems Abstract In this paper we present a method for mirror shape recovery and partial calibration for non-central catadioptric
More informationMODULE - 7. Subject: Computer Science. Module: Other 2D Transformations. Module No: CS/CGV/7
MODULE - 7 e-pg Pathshala Subject: Computer Science Paper: Computer Graphics and Visualization Module: Other 2D Transformations Module No: CS/CGV/7 Quadrant e-text Objectives: To get introduced to the
More information