Automatic Delineation of Drainage Basins from Contour Elevation Data Using Skeleton Construction Techniques
|
|
- Mark Hicks
- 5 years ago
- Views:
Transcription
1 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 1/16 Automatic Delineation of Drainage Basins from Contour Elevation Data Using Skeleton Construction Techniques Giovanni Moretti and Stefano Orlandini University of Modena & eggio Emilia, Italy University Founded in 1175
2 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 2/16 Motivation b m drainage basin The drainage basin determines the area which contributes water and sediments to a given channel cross section and is therefore considered to be the fundamental unit of study of geomorphological and fluvial processes (eopold et al., 1964). a m 414 draining line segment connecting two assigned points 5 1 m divide segment perpendicular to the only upper DB1 4 DB2 39 DB When curved slope line segments are drawn manually in order to delineate a drainage basin (Maxwell, 187), human discernment is used to identify the paths that are most likely followed by imaginary drops of water falling from the upper s and drained by the lower s. On the other hand, when slope lines are drawn using a computer program, no inference on the morphology of the terrain lying within adjacent s is normally made. A curved slope line segment between two adjacent s is approximated by a (single) straight line segment, which is generally unable to satisfy perpendicularity to both s.
3 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 3/16 Fundamental Geometric Constructs (a) P 3 V 1 V 2 P 4 (b) V 1 Delaunay triangulation P 1 P2 Voronoi diagram P 1 P 2 P1 crust V 1 V 2 P 2 circle drawn to perform the incircle test skeleton V2 circle drawn to perform the incircle test A Delaunay triangulation of a set of points in the plane (P 1, P 2,...) is a triangulation with the property that no point in the set of points falls inside the circumcircle of any triangle in the triangulation. A Voronoi diagram of a set of points in the plane (P 1, P 2,...) is a subdivision of the plane into polygonal regions, where each region is that set of points closer to some input point than to any other input point. A Delaunay edge (P 1 P 2 ) belongs to the crust when a circle exists through its two endpoints (circle in dashed line) that does not contain either of its associated Voronoi vertices (V 1 and V 2 ). If this condition is not met, then the corresponding Voronoi edge (V 1 V 2 ) belongs to the skeleton. Crust and skeleton elements can be determined by performing a simple incircle test (Gold, 1999). A circle passing through the endpoints of the Delaunay edges (P 1 and P 2 ) and the closest Voronoi vertex (V 1 ) is drawn (circles in solid line) and a check is made to assess whether the second Voronoi vertex is inside the circle.
4 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 4/16 Simple Theoretical Cases (a) curve/closed (d) curve/upper Two perspectives: (b) set of (sample) points Delaunay triangulation (e) set of (sample) points curve/lower Delaunay triangulation Amenta et al. (1998) defined and proposed to use the crust as a means for reconstructing a curve from a given set of sample points. P 1 P V P 3 2 Voronoi diagram crust skeleton (branch) skeleton (branch) (f) Voronoi diagram crust skeleton (stem) crust skeleton (branch) Gold (1999) proposed to use the skeleton of the s as a means for reconstructing the most plausible morphology of the terrain lying within adjacent s or within a closed contour line.
5 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 5/16 ida Surveys Survey carried out by Helica (Italy) in the Ca ita area (Italian Apennines): Optech ATM (airborne lidar terrain mapping) system mounted on a helicopter. The flight altitude: about 8 m agl (above ground level). Average data density: about 2.9 points per square meter. Horizontal absolute accuracy:.4 m. Vertical absolute accuracy:.15 m. esolution of the gridded elevation data provided:.5 m. Survey carried out by Terrapoint (USA) in the Col odella area (Italian Alps): ATM system of Terrapoint s proprietary design mounted on a fixed-wing aircraft. The flight altitude: about 1 m agl. Average data density: about.5 points per square meter. Horizontal absolute accuracy: 1 m. Vertical absolute accuracy:.3 m. esolution of the gridded elevation data provided: 1 m. Gridded elevation data were resampled to 5-m and contour elevation data with contour intervals of 1, 5, 1, 2, and 5 m were generated.
6 2384 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 6/16 Skeleton Extraction and Drainage Basin Delineation Sampling issues are not a critical point. The program Triangle developed by Shewchuk (1996) is used to compute the Delaunay triangulation and the Voronoi diagram. a skeleton stem from adjacent contour lines representing different elevations P (n) K draining line segment connecting two assigned points m P (n) K P P (a) (a) P P 415 skeleton branches forming a tree structure from a markedly non-straight skeleton stem skeleton branch divide point drainage basin m 2417 skeleton stem skeleton branch saddle branch divide point drainage basin (n) S P (n) P K P B M type 1 saddle (n) S P 2 (n) P K P P b 2415 c S (n) (n) P P K B 5 1 m type 2 saddle 2383 P skeleton stem skeleton branch saddle branch divide point drainage basin P 2 P B K (n) P S (n) = P 1 d P skeleton stem skeleton branch divide point discarded point drainage basin skeleton stem skeleton branch characteristic branch connecting line 355 e skeleton stem skeleton branch characteristic branch connecting line 355 D 1 B 1 B 2 f P 1 2 m 1 K =K first-order skeleton branch connetcting two points of the closed 2 4 m B 6 P 1 B 5 B 4 P 2 B 3 P 3 B 2 B m B 3 D 2 B 4
7 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 7/16 Procedure DIVIDE(P,P ) equire: Contour lines, skeleton, points (P,P ) Ensure: Drainage divide through the two points (P,P Search K while K and K K do Search P (n) and P (n) if ID of the containing P (n) end if P P if a type 1 saddle is identified then Search S (n) and S (n) else if a type 2 saddle is identified then Search S (n) and S (n) end if call DIVIDE(P (n),s(n) P (n) P (n) P(n) Search K end while return S (n) and K ) ) ID of the containing P (n) then
8 Proposed Method (PM) contour 442line skeleton stem skeleton branch ± b drainage basin a m DB1 divide segments 414 perpendicular to both the upper and lower s draining line segment connecting two411 assigned points Drainage divides obtained from the proposed method conform with the general principles that would be applied by an expert hydrologist in solving the same problems manually. esults obtained using 1-m contour data are totally satisfactory and provide some improvements with respect to the results obtained by applying the current state-of-the-art method m m DB2 DB Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 8/16
9 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 9/16 Current Methods (CM) b drainage basin Current methods applied to 1-m contour elevation data (Dawes and Short, 1994; Maunder, 1999; Menduni et al., 22) m a DB divide segment perpendicular to the only upper draining line segment connecting two assigned points 5 1 m m DB2 DB
10 41 41 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 1/16 Increasing the Contour Interval a m 43 DB1 divide from 1-m contour data divide from 1-m contour data DB DB3 34 b m 4 43 DB1 divide from 1-m contour data divide from 1-m contour data DB DB3 34 The improvements offered by the new method are even more significant for the contour elevation data with contour intervals of 5, 1, 2, and 5 m. c m 4 DB1 divide from 2-m contour data divide from 1-m contour data 42 DB2 38 DB3 34 d m 4 DB1 divide from 2-m contour data divide from 1-m contour data 42 DB2 38 DB3 34 One can note that the gain in accuracy is not only due to the skeleton stems as a sort of contour data enrichment, but also to the methodological advance allowed by a profitable use of the entire skeleton structure (stems and branches).
11 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 11/16 Flow Net Construction a automatically identified ridge flow line connecting line flow line automatically identified group of depressions b automatically identified saddle automatically identified peak 1 2 m J C P 1 P 2 E 1 S 2 4 m E 2 P 3 S 2 1 D 1 D 2 E 3 E 4 automatically identified group of peaks S 4 S 3 34 The methodology described in Moore et al. (1988), Moore and Grayson (1991), and Gallant (2) is extended in order to process groups of peaks and/or depressions lying between adjacent s. The ordering of skeleton elements allows skeleton stems and skeleton branches to be recognized and intersected at right angles or followed, respectively, by flow lines and drainage divides.
12 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 12/16 Procedure FOWINES(E 1, E 2 ) equire: Contour lines, connecting lines, points (E 1, E 2 ) Ensure: Insertions or terminations of flow lines between E 1 and E 2 CID = ID of the containing E 1 while E 2 is not found do Travel all elements of the CID Accumulate the distance along the CID if a connecting line is found then Perform insertions or terminations on the CID Travel the connecting line until the connected is found C = point of intersection between the connecting line and the connected contour line call FOWINES(C, E 2 ) end if end while Perform insertions or terminations on the CID return
13 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 13/16 Type 1 and Type 2 Errors in Drainage Areas A 1 DBD1 P A 2 11 P A 3 DBD2 drainage basin determination DBD1 obtained from given contour elevation data and method drainage basin determination DBD2 obtained by varying either the elevation contour data or the method draining line segment connecting two assigned points (P,P ) E 1 = A 1 A 3 A 1 + A 2 E 2 = A 1 + A 3 A 1 + A 2 E 1 E 2 E 2 E 1 One can note that error E 1 is just an indicator of the absolute difference between the drainage areas of DBD1 and DBD2, independently on the location of these two basin determinations, whereas error E 2 also accounts for the nonoverlapping between the two basin determinations.
14 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 14/16 Numerical Analysis Errors relative to the solution obtained from the PM and 1-m contour data. relative error (-) relative error (-) a d DB1 DB b DB2 DB5 E 1, CM E 2, CM E 1, PM E 2, PM e c f DB3 DB contour interval (m) contour interval (m) contour interval (m) elative errors generally increase as the contour interval increases. Using the PM and contour intervals of 5 5 m, relative errors are normally less 2% and rarely greater than 5%.
15 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 15/16 Computational Efficiency The computational burden imposed by the proposed method can be evaluated by considering separately the two contributions to total central processing unit (CPU) time required for (1) skeleton extraction from s and (2) drainage basin delineation or flow net construction. The CPU time required to extract the skeleton from s rapidly decreases as contour interval increases. Using an Intel Core 2 Duo 67 processor, the CPU time required to extract the skeleton from s representing the areas shown in this presentation decreases form 2.43 h to 5. min as the contour interval increases from 1 to 1 m. The CPU time required to delineate a simple drainage basin is in the order of a few seconds for both proposed and current state-of-the-art methods. However, if 1-m contour data are used and specific checks are made in order to attempt to resolve complex topographic structures using the current state-of-the-art method, the CPU time may go beyond 1 h (and accurate results are not always achieved). In this context, the computational burden imposed by skeleton extraction from s appears quite bearable. In scientific studies, CPU times in the order of a few hours appear acceptable in exchange for (accurate) solutions from fine resolution elevation data. In technical applications, CPU times in the order of a few minutes appear acceptable in exchange for accurate solutions from coarse resolution elevation data.
16 Summer School in New York, USA, Polytechnic University, July 21 25, 28 p. 16/16 Conclusions The proposed method allows fully-automated delineations of drainage basins and constructions of flow nets from contour elevation data, even when critical topographic structures such as ridges, saddles, and peaks are present. For any given set of s, the proposed method provides more accurate solutions than previously proposed methods, the gain in accuracy normally increasing as the contour interval increases. Skeleton construction techniques allow the morphological information implicitly present in contour elevation data to be explicitly revealed and correctly processed by a computer program, and are a useful means for improving the accuracy with which physiographic features of drainage basins are determined. The description of the true topography of a real terrain is an ideal process that can be reached only by using infinitely accurate instruments and techniques along with infinitesimal elevation model resolutions. The methods developed in this study are intended to allow the maximum exploitation of elevation data having a given accuracy and resolution.
Automatic delineation of drainage basins from contour elevation data using skeleton construction techniques
WATER RESOURCES RESEARCH, VOL. 44, W543, doi:1.129/27wr639, 28 Automatic delineation of drainage basins from contour elevation data using skeleton construction techniques Giovanni Moretti 1 and Stefano
More informationDetermination of surface flow paths from gridded elevation data
Click Here for Full Article WATER RESOURCES RESEARCH, VOL. 45,, doi:10.1029/2008wr007099, 2009 Determination of surface flow paths from gridded elevation data Stefano Orlandini 1 and Giovanni Moretti 1
More informationCOMPARISON OF TWO METHODS FOR DERIVING SKELETON LINES OF TERRAIN
COMPARISON OF TWO METHODS FOR DERIVING SKELETON LINES OF TERRAIN T. Gökgöz, F. Gülgen Yildiz Technical University, Dept. of Geodesy and Photogrammetry Engineering, 34349 Besiktas Istanbul, Turkey (gokgoz,
More informationTERRAIN MODELLING BASED ON CONTOURS AND SLOPES
TERRAIN MODELLING BASED ON CONTOURS AND SLOPES Christopher Gold and Maciej Dakowicz Department of Land Surveying and Geo-Informatics Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Tel:
More informationApplied Cartography and Introduction to GIS GEOG 2017 EL. Lecture-7 Chapters 13 and 14
Applied Cartography and Introduction to GIS GEOG 2017 EL Lecture-7 Chapters 13 and 14 Data for Terrain Mapping and Analysis DEM (digital elevation model) and TIN (triangulated irregular network) are two
More informationContents of Lecture. Surface (Terrain) Data Models. Terrain Surface Representation. Sampling in Surface Model DEM
Lecture 13: Advanced Data Models: Terrain mapping and Analysis Contents of Lecture Surface Data Models DEM GRID Model TIN Model Visibility Analysis Geography 373 Spring, 2006 Changjoo Kim 11/29/2006 1
More informationComputational Geometry
Lecture 12: Lecture 12: Motivation: Terrains by interpolation To build a model of the terrain surface, we can start with a number of sample points where we know the height. Lecture 12: Motivation: Terrains
More informationSurface Creation & Analysis with 3D Analyst
Esri International User Conference July 23 27 San Diego Convention Center Surface Creation & Analysis with 3D Analyst Khalid Duri Surface Basics Defining the surface Representation of any continuous measurement
More informationDescribe Plane Shapes
Lesson 12.1 Describe Plane Shapes You can use math words to describe plane shapes. point an exact position or location line endpoints line segment ray a straight path that goes in two directions without
More informationCS133 Computational Geometry
CS133 Computational Geometry Voronoi Diagram Delaunay Triangulation 5/17/2018 1 Nearest Neighbor Problem Given a set of points P and a query point q, find the closest point p P to q p, r P, dist p, q dist(r,
More informationGeographic Surfaces. David Tenenbaum EEOS 383 UMass Boston
Geographic Surfaces Up to this point, we have talked about spatial data models that operate in two dimensions How about the rd dimension? Surface the continuous variation in space of a third dimension
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 informationCMSC 425: Lecture 9 Geometric Data Structures for Games: Geometric Graphs Thursday, Feb 21, 2013
CMSC 425: Lecture 9 Geometric Data Structures for Games: Geometric Graphs Thursday, Feb 21, 2013 Reading: Today s materials is presented in part in Computational Geometry: Algorithms and Applications (3rd
More informationA Constrained Delaunay Triangle Mesh Method for Three-Dimensional Unstructured Boundary Point Cloud
International Journal of Computer Systems (ISSN: 2394-1065), Volume 03 Issue 02, February, 2016 Available at http://www.ijcsonline.com/ A Constrained Delaunay Triangle Mesh Method for Three-Dimensional
More informationThe Crust and Skeleton Applications in GIS
The Crust and Skeleton Applications in GIS Christopher Gold and Maciek Dakowicz School of Computing, University of Glamorgan Pontypridd CF37 1DL Wales UK christophergold@voronoi.com Abstract This paper
More informationEngineering Geology. Engineering Geology is backbone of civil engineering. Topographic Maps. Eng. Iqbal Marie
Engineering Geology Engineering Geology is backbone of civil engineering Topographic Maps Eng. Iqbal Marie Maps: are a two dimensional representation, of an area or region. There are many types of maps,
More informationAUTOMATIC EXTRACTION OF TERRAIN SKELETON LINES FROM DIGITAL ELEVATION MODELS
AUTOMATIC EXTRACTION OF TERRAIN SKELETON LINES FROM DIGITAL ELEVATION MODELS F. Gülgen, T. Gökgöz Yildiz Technical University, Department of Geodetic and Photogrammetric Engineering, 34349 Besiktas Istanbul,
More informationLifting Transform, Voronoi, Delaunay, Convex Hulls
Lifting Transform, Voronoi, Delaunay, Convex Hulls Subhash Suri Department of Computer Science University of California Santa Barbara, CA 93106 1 Lifting Transform (A combination of Pless notes and my
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 informationTerrestrial GPS setup Fundamentals of Airborne LiDAR Systems, Collection and Calibration. JAMIE YOUNG Senior Manager LiDAR Solutions
Terrestrial GPS setup Fundamentals of Airborne LiDAR Systems, Collection and Calibration JAMIE YOUNG Senior Manager LiDAR Solutions Topics Terrestrial GPS reference Planning and Collection Considerations
More informationTerrain Reconstruction from Contour Maps
Terrain Reconstruction from Contour Maps Abigail Martínez Rivas and Luis Gerardo de la Fraga Computer Science Section Department of Electrical Engineering. CINVESTAV Av. Instituto Politécnico Nacional
More informationAccuracy of Terrain Elevation Modelling
Accuracy of Terrain Elevation Modelling 0790 0790 07900 07880 0780 0770 0770 07700 1710 17180 1700 170 170 170 1780 1700 170 Accuracy of Terrain Elevation Modelling By A.G. Barnett and H.L. MacMurray Barnett
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 informationMath 366 Lecture Notes Section 11.4 Geometry in Three Dimensions
Math 366 Lecture Notes Section 11.4 Geometry in Three Dimensions Simple Closed Surfaces A simple closed surface has exactly one interior, no holes, and is hollow. A sphere is the set of all points at a
More informationCopyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Chapter 13. TERRAIN MAPPING AND ANALYSIS 13.1 Data for Terrain Mapping and Analysis 13.1.1 DEM 13.1.2 TIN Box 13.1 Terrain Data Format 13.2 Terrain Mapping 13.2.1 Contouring 13.2.2 Vertical Profiling 13.2.3
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 informationWatershed Modeling Advanced DEM Delineation
v. 10.1 WMS 10.1 Tutorial Watershed Modeling Advanced DEM Delineation Techniques Model manmade and natural drainage features Objectives Learn to manipulate the default watershed boundaries by assigning
More informationElementary Planar Geometry
Elementary Planar Geometry What is a geometric solid? It is the part of space occupied by a physical object. A geometric solid is separated from the surrounding space by a surface. A part of the surface
More informationLiDAR data overview. Dr. Keiko Saito Global Facility for Disaster Reduction and Recovery (GFDRR)
LiDAR data overview Dr. Keiko Saito Global Facility for Disaster Reduction and Recovery (GFDRR) LiDAR (Light Detecting And Ranging) 3D height profile Laser emitted from sensor onboard aircraft to measure
More informationOn the Selection of an Interpolation Method for Creating a Terrain Model (TM) from LIDAR Data
On the Selection of an Interpolation Method for Creating a Terrain Model (TM) from LIDAR Data Tarig A. Ali Department of Technology and Geomatics East Tennessee State University P. O. Box 70552, Johnson
More informationLecture 16: Voronoi Diagrams and Fortune s Algorithm
contains q changes as a result of the ith insertion. Let P i denote this probability (where the probability is taken over random insertion orders, irrespective of the choice of q). Since q could fall through
More informationFortune s Algorithm. Notes from the book by de Berg, Van Krevald, Overmars, and Schwarzkpf
Notes from the book by de Berg, Van Krevald, Overmars, and Schwarzkpf Based on sweeping the plane with a horizontal line and computing the Voronoi diagram as the line sweeps Straight forward approach won
More informationSurface Analysis with 3D Analyst
2013 Esri International User Conference July 8 12, 2013 San Diego, California Technical Workshop Surface Analysis with 3D Analyst Khalid H. Duri Esri UC2013. Technical Workshop. Why use 3D GIS? Because
More informationPRIMAL/DUAL SPATIAL RELATIONSHIPS AND APPLICATIONS
Primal/Dual Spatial Relationships and Applications PRIMAL/DUAL SPATIAL RELATIONSHIPS AND APPLICATIONS Christopher Gold Department of Land Surveying and Geo-Informatics Hong Kong Polytechnic University
More information2. POINT CLOUD DATA PROCESSING
Point Cloud Generation from suas-mounted iphone Imagery: Performance Analysis A. D. Ladai, J. Miller Towill, Inc., 2300 Clayton Road, Suite 1200, Concord, CA 94520-2176, USA - (andras.ladai, jeffrey.miller)@towill.com
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 informationMathematics Curriculum
6 G R A D E Mathematics Curriculum GRADE 6 5 Table of Contents 1... 1 Topic A: Area of Triangles, Quadrilaterals, and Polygons (6.G.A.1)... 11 Lesson 1: The Area of Parallelograms Through Rectangle Facts...
More informationHEURISTIC FILTERING AND 3D FEATURE EXTRACTION FROM LIDAR DATA
HEURISTIC FILTERING AND 3D FEATURE EXTRACTION FROM LIDAR DATA Abdullatif Alharthy, James Bethel School of Civil Engineering, Purdue University, 1284 Civil Engineering Building, West Lafayette, IN 47907
More informationNATIONWIDE POINT CLOUDS AND 3D GEO- INFORMATION: CREATION AND MAINTENANCE GEORGE VOSSELMAN
NATIONWIDE POINT CLOUDS AND 3D GEO- INFORMATION: CREATION AND MAINTENANCE GEORGE VOSSELMAN OVERVIEW National point clouds Airborne laser scanning in the Netherlands Quality control Developments in lidar
More informationa triangle with all acute angles acute triangle angles that share a common side and vertex adjacent angles alternate exterior angles
acute triangle a triangle with all acute angles adjacent angles angles that share a common side and vertex alternate exterior angles two non-adjacent exterior angles on opposite sides of the transversal;
More informationSurface Contents Author Index
Surface Contents Author Index Christopher Gold, Maciek Dakowicz & Rebecca Tse VISUALIZATION AND DECISION SUPPORT FOR WATERSHED MANAGEMENT Christopher Gold, Maciek Dakowicz and Rebecca Tse Hong Kong Polytechnic
More informationAspect-Ratio Voronoi Diagram with Applications
Aspect-Ratio Voronoi Diagram with Applications Tetsuo Asano School of Information Science, JAIST (Japan Advanced Institute of Science and Technology), Japan 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan
More informationENY-C2005 Geoinformation in Environmental Modeling Lecture 4b: Laser scanning
1 ENY-C2005 Geoinformation in Environmental Modeling Lecture 4b: Laser scanning Petri Rönnholm Aalto University 2 Learning objectives To recognize applications of laser scanning To understand principles
More informationMunicipal Projects in Cambridge Using a LiDAR Dataset. NEURISA Day 2012 Sturbridge, MA
Municipal Projects in Cambridge Using a LiDAR Dataset NEURISA Day 2012 Sturbridge, MA October 15, 2012 Jeff Amero, GIS Manager, City of Cambridge Presentation Overview Background on the LiDAR dataset Solar
More informationCS 532: 3D Computer Vision 14 th Set of Notes
1 CS 532: 3D Computer Vision 14 th Set of Notes Instructor: Philippos Mordohai Webpage: www.cs.stevens.edu/~mordohai E-mail: Philippos.Mordohai@stevens.edu Office: Lieb 215 Lecture Outline Triangulating
More informationGeometric and Algebraic Connections
Geometric and Algebraic Connections Geometric and Algebraic Connections Triangles, circles, rectangles, squares... We see shapes every day, but do we know much about them?? What characteristics do they
More informationVoronoi diagrams and applications
Voronoi diagrams and applications Prof. Ramin Zabih http://cs100r.cs.cornell.edu Administrivia Last quiz: Thursday 11/15 Prelim 3: Thursday 11/29 (last lecture) A6 is due Friday 11/30 (LDOC) Final projects
More informationComputational Geometry
Computational Geometry 600.658 Convexity A set S is convex if for any two points p, q S the line segment pq S. S p S q Not convex Convex? Convexity A set S is convex if it is the intersection of (possibly
More information1. LiDAR System Description and Specifications
High Point Density LiDAR Survey of Mayapan, MX PI: Timothy S. Hare, Ph.D. Timothy S. Hare, Ph.D. Associate Professor of Anthropology Institute for Regional Analysis and Public Policy Morehead State University
More information(Refer Slide Time: 00:02:00)
Computer Graphics Prof. Sukhendu Das Dept. of Computer Science and Engineering Indian Institute of Technology, Madras Lecture - 18 Polyfill - Scan Conversion of a Polygon Today we will discuss the concepts
More informationTerrain modelling; Delaunay/Voronoi diagrams; Contour lines; skeleton; generalization.
Corresponding Author: Christopher Gold Department of Land Surveying and Geo-Informatics Hong Kong Polytechnic University Hung Hom, Kowloon, Hong Kong Key words: Terrain modelling; Delaunay/Voronoi diagrams;
More informationGeometry Vocabulary Math Fundamentals Reference Sheet Page 1
Math Fundamentals Reference Sheet Page 1 Acute Angle An angle whose measure is between 0 and 90 Acute Triangle A that has all acute Adjacent Alternate Interior Angle Two coplanar with a common vertex and
More informationMöbius Transformations in Scientific Computing. David Eppstein
Möbius Transformations in Scientific Computing David Eppstein Univ. of California, Irvine School of Information and Computer Science (including joint work with Marshall Bern from WADS 01 and SODA 03) Outline
More informationLearn how to delineate a watershed using the hydrologic modeling wizard
v. 10.1 WMS 10.1 Tutorial Learn how to delineate a watershed using the hydrologic modeling wizard Objectives Import a digital elevation model, compute flow directions, and delineate a watershed and sub-basins
More information3D BUILDING MODEL GENERATION FROM AIRBORNE LASERSCANNER DATA BY STRAIGHT LINE DETECTION IN SPECIFIC ORTHOGONAL PROJECTIONS
3D BUILDING MODEL GENERATION FROM AIRBORNE LASERSCANNER DATA BY STRAIGHT LINE DETECTION IN SPECIFIC ORTHOGONAL PROJECTIONS Ellen Schwalbe Institute of Photogrammetry and Remote Sensing Dresden University
More informationGeometry Summative Review 2008
Geometry Summative Review 2008 Page 1 Name: ID: Class: Teacher: Date: Period: This printed test is for review purposes only. 1. ( 1.67% ) Which equation describes a circle centered at (-2,3) and with radius
More informationUAS based laser scanning for forest inventory and precision farming
UAS based laser scanning for forest inventory and precision farming M. Pfennigbauer, U. Riegl, P. Rieger, P. Amon RIEGL Laser Measurement Systems GmbH, 3580 Horn, Austria Email: mpfennigbauer@riegl.com,
More information6 Mathematics Curriculum
New York State Common Core 6 Mathematics Curriculum GRADE GRADE 6 MODULE 5 Table of Contents 1 Area, Surface Area, and Volume Problems... 3 Topic A: Area of Triangles, Quadrilaterals, and Polygons (6.G.A.1)...
More informationContour Simplification with Defined Spatial Accuracy
Contour Simplification with Defined Spatial Accuracy Bulent Cetinkaya, Serdar Aslan, Yavuz Selim Sengun, O. Nuri Cobankaya, Dursun Er Ilgin General Command of Mapping, 06100 Cebeci, Ankara, Turkey bulent.cetinkaya@hgk.mil.tr
More informationUnit 10 Study Guide: Plane Figures
Unit 10 Study Guide: Plane Figures *Be sure to watch all videos within each lesson* You can find geometric shapes in art. Whether determining the amount of leading or the amount of glass needed for a piece
More informationDelaunay Triangulations
Delaunay Triangulations (slides mostly by Glenn Eguchi) Motivation: Terrains Set of data points A R 2 Height ƒ(p) defined at each point p in A How can we most naturally approximate height of points not
More informationKate Collins Middle School Pre-Algebra Grade 6
Kate Collins Middle School Pre-Algebra Grade 6 1 1 - Real Number System How are the real numbers related? *some numbers can appear in more than one subset *the attributes of one subset can be contained
More informationAlaska Mathematics Standards Vocabulary Word List Grade 7
1 estimate proportion proportional relationship rate ratio rational coefficient rational number scale Ratios and Proportional Relationships To find a number close to an exact amount; an estimate tells
More informationAn Introduction to Lidar & Forestry May 2013
An Introduction to Lidar & Forestry May 2013 Introduction to Lidar & Forestry Lidar technology Derivatives from point clouds Applied to forestry Publish & Share Futures Lidar Light Detection And Ranging
More informationA Method to Create a Single Photon LiDAR based Hydro-flattened DEM
A Method to Create a Single Photon LiDAR based Hydro-flattened DEM Sagar Deshpande 1 and Alper Yilmaz 2 1 Surveying Engineering, Ferris State University 2 Department of Civil, Environmental, and Geodetic
More informationVoronoi Diagrams in the Plane. Chapter 5 of O Rourke text Chapter 7 and 9 of course text
Voronoi Diagrams in the Plane Chapter 5 of O Rourke text Chapter 7 and 9 of course text Voronoi Diagrams As important as convex hulls Captures the neighborhood (proximity) information of geometric objects
More informationAn angle that has a measure less than a right angle.
Unit 1 Study Strategies: Two-Dimensional Figures Lesson Vocab Word Definition Example Formed by two rays or line segments that have the same 1 Angle endpoint. The shared endpoint is called the vertex.
More informationTERRAIN RECONSTRUCTION FROM GROUND BASED LASER DATA
TERRAIN RECONSTRUCTION FROM GROUND BASED LASER DATA Bruce King1, Elzbieta Matuk1, Krzysztof Matuk1, Christopher M. Gold 1 Address: The Department of Land Surveying & Geo Informatics The Hong Kong Polytechnic
More informationLearn how to delineate a watershed using the hydrologic modeling wizard
v. 11.0 WMS 11.0 Tutorial Learn how to delineate a watershed using the hydrologic modeling wizard Objectives Import a digital elevation model, compute flow directions, and delineate a watershed and sub-basins
More informationEstimate A number that is close to an exact answer. An approximate answer.
Estimate A number that is close to an exact answer. An approximate answer. Inverse Operations Operations used to undo each other + - X Product The result of multiplying two factors together. 3 x 4=12 Factor
More informationVolume Illumination and Segmentation
Volume Illumination and Segmentation Computer Animation and Visualisation Lecture 13 Institute for Perception, Action & Behaviour School of Informatics Overview Volume illumination Segmentation Volume
More informationSENSOR FUSION: GENERATING 3D BY COMBINING AIRBORNE AND TRIPOD- MOUNTED LIDAR DATA
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXIV-5/W10 SENSOR FUSION: GENERATING 3D BY COMBINING AIRBORNE AND TRIPOD- MOUNTED LIDAR DATA A. Iavarone
More informationWatershed Modeling With DEMs: The Rest of the Story
Watershed Modeling With DEMs: The Rest of the Story Lesson 7 7-1 DEM Delineation: The Rest of the Story DEM Fill for some cases when merging DEMs Delineate Basins Wizard Smoothing boundaries Representing
More informationWhat is a Topographic Map?
Topographic Maps Topography From Greek topos, place and grapho, write the study of surface shape and features of the Earth and other planetary bodies. Depiction in maps. Person whom makes maps is called
More informationSensor Fusion: Generating 3D by Combining Airborne and Tripod mounted LIDAR Data
Sensor Fusion: Generating 3D by Combining Airborne and Tripod mounted LIDAR Data Albert IAVARONE and Daina VAGNERS, Canada Key Words: LIDAR, Laser scanning, Remote sensing, Active sensors, 3D modeling,
More informationGIS LAB 8. Raster Data Applications Watershed Delineation
GIS LAB 8 Raster Data Applications Watershed Delineation This lab will require you to further your familiarity with raster data structures and the Spatial Analyst. The data for this lab are drawn from
More informationEuclid s Muse Directions
Euclid s Muse Directions First: Draw and label three columns on your chart paper as shown below. Name Picture Definition Tape your cards to the chart paper (3 per page) in the appropriate columns. Name
More informationStatistical surfaces and interpolation. This is lecture ten
Statistical surfaces and interpolation This is lecture ten Data models for representation of surfaces So far have considered field and object data models (represented by raster and vector data structures).
More informationNotes in Computational Geometry Voronoi Diagrams
Notes in Computational Geometry Voronoi Diagrams Prof. Sandeep Sen and Prof. Amit Kumar Indian Institute of Technology, Delhi Voronoi Diagrams In this lecture, we study Voronoi Diagrams, also known as
More informationReconnaissance and Surveillance Leader s Course Map Reading self study worksheet (Tenino, Washington Map)
Reconnaissance and Surveillance Leader s Course Map Reading self study worksheet (Tenino, Washington Map) General Knowledge 1. Name the five Basic Colors on a map and what they represent? 1. 2. 3. 4. 5.
More informationField-Scale Watershed Analysis
Conservation Applications of LiDAR Field-Scale Watershed Analysis A Supplemental Exercise for the Hydrologic Applications Module Andy Jenks, University of Minnesota Department of Forest Resources 2013
More informationDigital Image Processing Fundamentals
Ioannis Pitas Digital Image Processing Fundamentals Chapter 7 Shape Description Answers to the Chapter Questions Thessaloniki 1998 Chapter 7: Shape description 7.1 Introduction 1. Why is invariance to
More informationSurface Analysis. Data for Surface Analysis. What are Surfaces 4/22/2010
Surface Analysis Cornell University Data for Surface Analysis Vector Triangulated Irregular Networks (TIN) a surface layer where space is partitioned into a set of non-overlapping triangles Attribute and
More informationLesson Title 2: Problem TK Solving with Trigonometric Ratios
Part UNIT RIGHT solving TRIANGLE equations TRIGONOMETRY and inequalities Lesson Title : Problem TK Solving with Trigonometric Ratios Georgia Performance Standards MMG: Students will define and apply sine,
More informationRoadway Design using GeoTools
Roadway Design using GeoTools Introduction GeoTools is a general-purpose productivity tool for users of all types of geographic data. In the Civil Tools section, there are many tools for Civil engineering
More informationLATEST TRENDS on APPLIED MATHEMATICS, SIMULATION, MODELLING
3D surface reconstruction of objects by using stereoscopic viewing Baki Koyuncu, Kurtuluş Küllü bkoyuncu@ankara.edu.tr kkullu@eng.ankara.edu.tr Computer Engineering Department, Ankara University, Ankara,
More informationTriangulation Based Volume Calculation Andrew Y.T Kudowor and George Taylor Department of Geomatics University of Newcastle
Triangulation Based Volume Calculation Andrew Y.T Kudowor and George Taylor Department of Geomatics University of Newcastle ABSTRACT Delaunay triangulation is a commonly used method for generating surface
More informationWorksheet 2.1: Introduction to Multivariate Functions (Functions of Two or More Independent Variables)
Boise State Math 275 (Ultman) Worksheet 2.1: Introduction to Multivariate Functions (Functions of Two or More Independent Variables) From the Toolbox (what you need from previous classes) Know the meaning
More information11 cm. A rectangular container is 12 cm long, 11 cm wide and 10 cm high. The container is filled with water to a depth of 8 cm.
Diagram NOT accurately drawn 10 cm 11 cm 12 cm 3.5 cm A rectangular container is 12 cm long, 11 cm wide and 10 cm high. The container is filled with water to a depth of 8 cm. A metal sphere of radius 3.5
More informationU.S. Geological Survey (USGS) - National Geospatial Program (NGP) and the American Society for Photogrammetry and Remote Sensing (ASPRS)
U.S. Geological Survey (USGS) - National Geospatial Program (NGP) and the American Society for Photogrammetry and Remote Sensing (ASPRS) Summary of Research and Development Efforts Necessary for Assuring
More informationComputational Geometry. Algorithm Design (10) Computational Geometry. Convex Hull. Areas in Computational Geometry
Computational Geometry Algorithm Design (10) Computational Geometry Graduate School of Engineering Takashi Chikayama Algorithms formulated as geometry problems Broad application areas Computer Graphics,
More informationThe Computational Geometry Algorithms Library. Andreas Fabri GeometryFactory
The Computational Geometry Algorithms Library Andreas Fabri GeometryFactory Mission Statement Make the large body of geometric algorithms developed in the field of computational geometry available for
More informationCreating and Delineating a Watershed from DXF Terrain Data
Creating and Delineating a Watershed from DXF Terrain Data 1. Start up WMS. 2. Switch to the Map Module. 3. Select DXF Import. Select the DXF file to import. 4. Notice that the DXF file imports fine into
More information2D rendering takes a photo of the 2D scene with a virtual camera that selects an axis aligned rectangle from the scene. The photograph is placed into
2D rendering takes a photo of the 2D scene with a virtual camera that selects an axis aligned rectangle from the scene. The photograph is placed into the viewport of the current application window. A pixel
More informationChapter 7. Conclusions
132 Spatial Data Representations Chapter 7. Conclusions This dissertation has addressed three current problems with spatial data representations. First is the need for data representations that support
More informationGrading and Volumes CHAPTER INTRODUCTION OBJECTIVES
CHAPTER 10 Grading and Volumes INTRODUCTION AutoCAD Civil 3D uses surface breaklines, cogo points, contours, feature lines, and grading objects to create a surface design. There are numerous ways to grade
More informationAutoCAD Civil 3D 2010 Education Curriculum Instructor Guide Unit 4: Environmental Design
AutoCAD Civil 3D 2010 Education Curriculum Instructor Guide Unit 4: Environmental Design Lesson 2 Watershed Analysis Overview In this lesson, you learn about how AutoCAD Civil 3D software is used to analyze
More informationProject Report Nooksack South Fork Lummi Indian Nation. Report Presented to:
June 5, 2005 Project Report Nooksack South Fork Lummi Indian Nation Contract #2291-H Report Presented to: Lummi Indian Nation Natural Resources Department 2616 Kwina Road Bellingham, WA 98226 Point of
More informationOn the isomorphism between the medial axis and a dual of the Delaunay graph
Downloaded from orbit.dtu.dk on: Dec 17, 217 On the isomorphism between the medial axis and a dual of the Delaunay graph Sharma, Ojaswa; Anton, François; Mioc, Darka Published in: Sixth International Symposium
More informationMobile LiDAR for Ground Applications. Spar 2006, March Paul Mrstik, Terrapoint Canada Inc. Craig Glennie, Terrapoint USA LLC
Mobile LiDAR for Ground Applications Spar 2006, March 27 2006 Paul Mrstik, Terrapoint Canada Inc. Craig Glennie, Terrapoint USA LLC Agenda Introduction to Terrapoint What is mobile LiDAR? Advantages of
More information