Gis Concepts 3/5
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Gis Concepts 3/5



Introduction to basic concepts on Geographical Information Systems

Introduction to basic concepts on Geographical Information Systems
Autor: Msc. Alexander Mogollón Diaz



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Gis Concepts 3/5 Gis Concepts 3/5 Presentation Transcript

  • Concepts and Functions of Geographic Information Systems (3/5) MSc GIS - Alexander Mogollon Diaz Department of Agronomy 2009
  • Concepts and Functions of GIS .PPT Topic #1 Topic #2 Topic #3 1 A GIS is an information system GIS is a technology 2 Spatial Data modelling Sources of data for geodatasets Metadata 3 Geospatial referencing Coordinate transformations 4 Database management 5 Spatial Analysis
  • Transformations for building a spatial model / gDB
    • Of the geometric data (coordinates, cell definition)
    • Of the attribute data
      • change of units
      • combination of attributes: e.g. time = distance/speed
      • ...
  • Transformation of coordinates and Geospatial refence systems
    • Spatial reference system is required to define geometric location and shape; uses ‘coordinates’
    • Geospatial reference system (‘ coordinate reference system – CRS ’) is required for modelling entities and terrain occurring on/below/above the surface of the Earth
    • A/D-conversion, remote sensing, ... provide data about location and shape in a technical spatial reference system
      • Transformation of coordinates towards a geospatial reference system is imperative
    • Two classes of geospatial reference systems
        • Geographic
        • Projected
        • Very many variants exist of both
    • Transformations required for vertical integration
  • Planet Earth
  • The Earth’s shape is irregular Positioning needs simplification
    • Planet earth = a 3D-body, spherical but (abstraction from relief)
    • When abstraction is made from relief, the Earth can be described by:
      • The geoid (equipotential surface of gravity force - mean sea level) or by
      • A sphere slightly flattened at the poles (spheroid/ellipsoid)
  • Geoid versus Ellipsoid
    • Geoid
      • 3D-physical datamodel of the Earth’s surface, based on measurements of the gravity force
    • Local and Global Ellipsoids
      • Mathematical 3D-models of the Earth’s surface
      • Global ellipsoids are defined to represent the full Earth with acceptable accuracy
      • Local ellipsoids are defined to represent a part of the Earth’s surface only, with high accuracy
  • Geoid versus Ellipsoid
  • Geospatial locations are expressed relative to an ellipsoid (1)
    • Geographic coordinates:
      • Expressed as angles with respect to 2 of 3 axes through the gravity point of the ellipsoid
      • LONGITUDE: 0° (Greenwich) to 180° East and 0° to 180° West measured in the horizontal plane
      • LATITUDE: 0° (Equator) to 90 North and 0° to 90° South) measured in the vertical plane
      • Degrees-Minutes-Seconds or Decimal Degrees: 20° 15’ 15” = 20,2525
  • Geospatial locations are expressed relative to an ellipsoid (2) LON LAT 45° N; 120°E
  • Geospatial locations are expressed relative to an ellipsoid (3)
    • Several ellipsoids are in use !
      • Major radius or major semi-axis a
      • Minor radius or minor semi-axis b
      • Flattening f of the ellipsoid: a-b/a = 1/f
  • Frequently used ellipsoids S
  • Geospatial locations are expressed relative to an ellipsoid (4)
    • Geodetic datum = further specification of the ellipsoid
      • Initial location
      • Initial azimuth to define the north direction
      • Distance between geoid and ellipsoid at the initial location
      • Basis for conversion between LON-LAT and geocentric coordinates (x,y,z)
      • A given point has different LON-LAT when expressed against different ellipsoids !
      • A given point has different geocentric coordinates x,y,z when expressed against different datums, even if the ellipsoid is identical
  • From geographic coordinates to projected coordinates
    • Common GIS-systems model the geographic reality in planimetric 2D
      • traditional map view
      • Carthesian X-Y coordinates, meters
    • LON-LAT (angles, 3D) need to be transformed into X-Y (2D)
    • Such a transformation = a projection
    • Projected coordinates = map coordinates
  • From geographic coordinates to projected coordinates
    • gDB may store
      • Geographic coordinates or
      • Projected coordinates
    • Distances, lengths and areas cannot be expressed in geographic coordinates = Essential for most queries and spatial analyses
    • If geographic coordinates are stored, most often run time or “on the fly” transformation into projected coordinates is done by the GIS-software when querying, analysing the gDB
  • Arc distances
  • Computation of arc-distances
  • From geographic coordinates to projected coordinates
    • From LON-LAT to X-Y = mathematical, analytical operation
    • 1. Shape of earth needs to be parameterised by means of a geodetic datum
      • global or local approximation of the geoid
  • From geographic coordinates to projected coordinates
    • From LON-LAT to X-Y = mathematical, analytical operation
    • 2. One of very many projection functions needs to be choosen
      • Cylinder, plane or cone as projection surface
      • Tangent or secant at selected locations
      • Normal, transversal, arbitrary
      • False easting, false northing
  • Plane – cone - cylinder Tangent - secant Normal – transversal - oblique
  • Choice of the projection function
    • From 3D to 2D => deformation cannot be avoided
      • shape
      • direction
      • area
      • distance
    • Local datum and projection function are choosen in order to minimise deformation for the study area
      • position and shape of study area
      • conditioned by objective of cartography (density mapping requires ‘true’ areas) and type of analysis
  • Projection creates geometric distortion
  • Conformal projections Shape and/or direction is preserved Distances and areas are distorted
  • Mercator-projection = conformal
  • Transverse Mercator-projection = conformal
  • Universal Transverse Mercator projection
    • Secant cylinder at 80° North and South
    • 60 strips of 6° East-West
    • Central meridian: X = 500.000 m
    • Equator: Y = 0 m for N.Hemisphere
    • Equator: Y = 10.000.000 m for S.Hemisphere
    • Applied to various ellipsoids
  • Standard projected coordinate system for the Philippines
    • Ellipsoid: Clark’s spheroid of 1866
      • Semi-major axis = 6.378.206,4 m
      • Semi-minor axis = 6.356.583,8 m
    • Projection: Philippines Transverse Mercator
      • UTM
        • Zone 50 (114 – 120 °East)
        • Zone 51 (120 – 126 °East)
        • Further subdivided in 6 subzones with central meridian
          • 117 °East
          • 119 °East
          • 121 °East
          • 123 °East
          • 125 °East
        • False northing = 0; False easting = 500.000 meters
  • Lambert conformal conical projection
  • Standard projected coordinate system for Belgium
    • Belgian Datum = local orientation of Hayford’s ellipsoid of 1909, recommended as International ellipsoid in 1924
    • Projection function : Lambert 72/50
    • Conformal conical projection with 2 secant parallels
      • 49°50’0.0204” and 51°10’0.0204”
      • Longitude of central meridian: 4°22’2.952”
      • Latitude of origin: 90°
      • Fase easting: 150.000,013 meter
      • False northing: 5.400.088,4398 meter
    • Vertical reference system = TAW (average low tide level in Oostende (North Sea Channel )
  • Other coordinate systems: examples
  • A gDB
    • Can have one coordinate reference system only (effective or virtual)
    • The coordinates in all geodatasets must be expressed according to that system
      • Vertical integration
      • Horizontal integration
    • Most commonly, the choosen coordinate system is
      • Geographic coordinates (LON-LAT) or
      • National coordinate system (from the National Mapping Agency, used for printing topographic / military maps)
  • Vertical integration
  • Horizontal integration
  • Transformation of coordinates for vertical/horizontal integration
    • Analytical conversion between geographic coordinates expressed according to different geodetic datums = datum conversion
    • Analytical conversion of geographic coordinates (e.g. from GPS) in projected coordinates and vice versa = (inverse) projection
    • Analytical conversion between different types of projected coordinates (e.g. between Philippine and Belgian system)
    • Numerical coordinate transformation (e.g. geo-referencing, using control points)
  • Numeric coordinate transformation
    • Numeric coordinate shifts, based on control points, for vertical and horizontal integration of geodatasets in a gDB
      • systematic shifts (e.g. conversion of digitiser/scan coordinates in projected coordinates)
      • non-systematic shifts: rubber sheeting, edge matching
  • Geo-referencing
    • When coordinates are expressed according to an analytical reference system, the term ‘georeferenced data’ is used.
    • A/D conversion using tablet digitising or scanning provide digitiser and scan coordinates. Also raw satellite images are not georeferenced.
    • Transformation of « technical » coordinates into geographical or projected coordinates = georeferencing .
  • Numeric transformation of coordinates after A/D-conversion via digitization
    • Digitisation provides (Xi,Yi) of point objects, nodes, vertices
    • Xi,Yi are digitizer-coordinates, expressed according to a technical, flat reference system
    • Xi,Yi must be transformed into a projected reference system
    X Y (0,0)
    • Xo = f (Xi,Yi); Yo = f (Xi,Yi)
    (X i ,Y i )
  • Numeric transformation of digitizer- to gDB-coordinates
    • AFFINE polynomial transformation function f = popular
      • Xo = A + BXi + CYi
      • Yo = D + EXi + FYi
      • 2 * 3 unknowns: A, B, C and D, E, F
      • 2 * 3 equations required to compute the unknonws
      • Equations are derived from 3 control points (3X and 3Y) (GCP)
      • GCP = ground control point = point location that can be unambiguously detected and located on both the dataset which must be transformed and on the reference geodataset or reality
      • System of equations has one single EXACT solution for A ... F
      • Transformation error is apparently 0
    • If more than 3 GCP are available, more equations than unknowns
      • System of equations has more than one solution for A ... F
      • Best solution for A ... F can be found by the Least-Squares method
      • Transformation error can be computed (RMSe - ROOT MEAN SQUARE ERROR)
    • If RMSe is sufficiently low
      • Parameterised AFFINE equations can be applied to all input-points (point objects, nodes, vertices). Result = transformed output-geodataset
  • AFFINE transformation of digitizer- to gDB-coordinates
  • AFFINE-transformation & RMSe: X
  • AFFINE-transformation & RMSe: Y
  • AFFINE-transformation & RMSe: X & Y
  • Judgement of the RMSe
    • To be based on the spatial detail (scale for A/D-converted analog documents) of the source document
      • 1 mm distortion and/or digitizing error on a 1:50.000 analog map = 50 meter RMSe
    • To be based on the intended use of the output-geodataset
      • Requirements for vertical and horizontal integration
    • Translation:
      • X o = A + X i
      • Y o = D + Y i
    • Change of scale:
      • X o = BX i
      • Y o = EY i
    • Rotation:
      • X o = BX i + CY i
      • Y o = EX i +FY i
    • AFFINE = All combined
      • X o = A + BX i + CY i
      • Y o = D + EX i + FY i
    AFFINE = polynomial transformation of the 1st order
    • X o = a 0 +(a 1 X i +a 2 Y i )+(a 3 X i 2 +a 4 .X i Y i +a 5 Y i 2 )+…
    • Y o = b 0 +(b 1 X i +b 2 Y i )+(b 3 X i 2 +b 4 .X i Y i +b 5 Y i 2 )+…
    • Order of the polynomial p determines the minimum number of required GCP to find the polynomial coefficients: N = (p+1)*(p+2)/2
    Polynomial transformations of higher orders (rubber sheeting, warping)
  • Numeric transformation of coordinates after A/D-conversion via Scanning
  • Numeric transformation of scan- to gDB-coordinates
    • A scanned document is not georeferenced
    • Scan-coordinates are relative to the reference system of the scan-device
    • Transformation of the scan-coordinates is necessary, using GCP
      • Regular cell-raster is distorted
      • A new ‘empty’ cell-raster is created according to the output-reference system
      • Based on the established transformation function, cell values are resampled from the input raster to compute the values for the cells in the output raster
        • Neirest neighbour
        • Other algorithms
    • Also valid for remotely sensed images !
  • Forward GCP-based transformation distorts the raster 1 2 3 Xo = f (Xi,Yi); Yo = f (Xi,Yi): NOT valid
  • Backward/Inverse polynomial transformation of scan- to gDB-coordinates
      • Creation of a new ‘empty’ rasterstructure in the output-coordinate system
      • Calibration of the inverse polynomial transformation
        • Xi = f(Xo,Yo)
        • Yi = f(Xo,Yo
      • Use of the calibrated transformation function to ‘fill’ the empty cells of the output raster with (a combination of) the value(s) of the corresponding cell(s) in the input raster
  • Resampling
    • GCP are used to calibrate an inverse polynomial transformation function, e.g. AFFINE
        • X i = G + HX o + IY o
        • Y i = K + LX o + MY o
    • By means of this function, for the mid point of every output-cell (Xo,Yo) the corresponding point (Xi,Yi) in the input raster is computed
    • Xi,Yi is the ‘nearest neighbour’
      • With ‘nearest neighbour resampling’, the cell value of the cell in which Xi,Yi is located is attributed to the output cell with midpoint Xo,Yo
      • Also bi-linear and curbic re-sampling are possible
  • Resampling is necessary after transformation of scan- into gDB-coordinates R = input raster; R’ = output raster Antrop & De Maeyer, 2005 Xi,Yi = Xo,Yo (change of resolution only) Xi,Yi <>Xo,Yo (nearest neighbour) Xi,Yi <> Xo,Yo (bilinear interpolation) Xi,Yi <> Xo,Yo (cubic convolution)
  • Numeric coordinate transformation
    • Similar systematic numeric transformation is applicable to coordinates coming from other data sources
      • Remotely sensed images
      • Theodolites, tachymeters with digital reading
      • Global Positioning Systems (GPS)
  • (Non-)systematic numeric coordinate-transformations
    • Previous numeric polynomial coordinate transformations are based on GCP
    • One set of coefficients A, B, C, … is computed and applied to all input-points to obtain the output-coordinates
    • Such transformations are systematic
  • Non-systematic transformations for further improvement of the positional quality of the georeferenced geodatasets
    • First step in georeferencing is most often a systematic transformation of coordinates
      • Polynomial function of low order
    • The result is often not of sufficient quality or not sufficiently fit for use (vertical/horizontal integration in the gDB)
    • In a next step, non-systematic transformation can be performed to make the geodataset geometrically more conformal to the reference geodataset
  • Non-systematic coordinate transformations
    • Edge-matching
    • Rubber-sheeting
  • Rubber-sheeting 1 2 3 GCP1: X i1 ,Y i1 -> X o1 ,Y o1 GCP2: X i2 ,Y i2 -> X o2 ,Y o2 GCP3: X i3 ,Y i3 -> X o3 ,Y o3 GCPA...GCPF: X i = X o ; Y i = Y o A B D E F G C
  • Rubber-sheeting
    • Point-by-point correction of the location and shape of objects or of resampling of cell attributes
    • Based on 2 linear “piece wise” TIN-interpolations (7.PPT), 1 for X and 1 for Y
    • Z-value to interpolate = X o resp. Y o
    • Result = not-constant translation/rotation/change of scale
    • Shifts decrease with increasing distance
    • Both forward (for vectorial geodatasets) and backward (for raster datasets)
  • Edge-matching
    • Special case of rubber sheeting
    • Applied for horizontal integration of adjacent (A/D converted) map sheets or images (mosaicking)
    • Definition of links between coinciding points on two map sheets
    • Differential displacement of points based on (mostly inverse distance; TIN) interpolation
  • Edge-matching
  • Summary of important items
    • Geospatial reference systems
      • Based on a geodetic datum (LON-LAT) and (possibly) a projection function to convert LON-LAT (angles - 3D) into planimetric coordinates (X,Y – 2D)
      • Projection leads to distortion of one or more of shape, direction, area, distance
      • If the national standards are not used, a rational, functional choice of datum and projection function is required
      • The datum for elevation is most often the geoid (approximated by mean sea level)
    • Transformation of coordinates
      • Between parameterised geographic and/or projected coordinate systems is an analytical operation which does not need external ground truth
      • Between technical coordinates and projected coordinates is a numeric operation based on ground truth (GCP)
        • There are systematic and non-systematic numeric transformation functions
        • Systematic transformation is most often based on a polynomial function
        • Non-systematic transformation (rubber sheeting and edge-matching) is based on TIN-interpolation
      • The latter is also valid for projected coordinates which need correction
  • Questions or remarks ? Thank you …