Lecture 15 - 19: Spatial Referencing and Geographic Transformation URP 1281 Surveying and Cartography 1 January 25, 2016 Course Teacher: Md. Esraz-Ul-Zannat Assistant Professor Department of Urban and Regional Planning Khulna University of Engineering & Technology
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Lecture 15 - 19: Spatial Referencing and Geographic
Transformation
URP 1281 Surveying and Cartography
1
January 25, 2016
Course Teacher: Md. Esraz-Ul-Zannat Assistant Professor
Department of Urban and Regional Planning Khulna University of Engineering & Technology
2
These slides are aggregations for better understanding
of Cartography. I acknowledge the contribution of all
the authors and photographers, power point slides
from where I tried to accumulate the info and used for
better presentation.
ACKNOWLEDGEMENT
Spatial Referencing
• Georeferencing
• Spatial Adjustment and
• Cad Data Adjustment
Correctly positioning data to its true world location.
Coordinate surfaces in the
Spherical coordinate system
Spatial Referencing
• Georeferencing
Coordinate surfaces in the
Spherical coordinate system
• Georeferencing of an Image (Raster data)
• Via Georeferencing toolbar
• Typically used for:
• satellite images
• aerial photographs
• scanned CAD drawings
• Spatial Adjustment (Transformation) of Vector data
• Via Spatial Adjustment toolbar
• Positioning a vector CAD file
• Via Georeferencing Toolbar in ArcGIS 10, or via Properties/Transformation in ArcGIS 10
• Is planimetrically accurate to start with (or should be)
• Only requires translation of origin and scale change
Spatial Referencing Types Coordinate surfaces in the
Spherical coordinate system
● ‘To georeference the act of assigning locations to atoms of information
●Is essential in GIS, since all information must be linked to the Earth’s surface
●The method of georeferencing must be:
• Unique, linking information to exactly one location
• Shared, so different users understand the meaning of a georeference
• Persistent through time, so today’s georeferences are still meaningful tomorrow
Georeferencing Coordinate surfaces in the
Spherical coordinate system
Georeferencing is about using map coordinates to assign a spatial location to map features. All the elements in a map layer have a specific geographic location and extent that enables them to be located on or near the earth's surface. The ability to accurately locate geographic features is critical in both mapping and GIS. The number of the non-correlated control points required for this method must be 3 for a first order, 6 for a second order, and 10 for a third order. The first-order polynomial transformation is commonly used to georeference an image.
Use a first-order or affine transformation to shift, scale, and rotate a raster dataset. With a minimum of three links, the mathematical equation used with a first-order transformation can exactly map each raster point to the target location.
Coordinate surfaces in the
Spherical coordinate system
Georeferencing
Source: ESRI Help
Georeferencing Concepts Coordinate surfaces in the
Spherical coordinate system
Source: ESRI Help
Georeferencing Concepts Coordinate surfaces in the
Spherical coordinate system
• Used for positioning rasters and vector CAD data in ArcGIS
• Yes, this is an “odd couple”
• CAD is a vector data set type!
• Implemented via the Georeferencing toolbar
• Use for scanned maps, scanned CAD drawings, photographs, satellite images, etc. in standard image formats such as .jpg, .gif, .tif
• Raster data sets in GRID, ERDAS IMAGINE, etc format
• CAD vector data sets in .dxf (AutoCAD) ,dwg (AutoCAD) and .dgn (Microstation) format
Use to help “Fit image to display”
Create control point links
(displacement links)
Open Links table
Use to
start all
over
again
Georeferencing Using ArcGIS Coordinate surfaces in the
Spherical coordinate system
Find control points in
Image
Get coordinates for each
point
Use Georeferencing
toolbar for adjusting the
image
Georeferencing Google Earth Images Coordinate surfaces in the
Spherical coordinate system
●Establish control points from the base map
●At least four points with known coordinates should be marked on the map
Georeferencing: What to Do? Coordinate surfaces in the
Spherical coordinate system
●Write down the x, y coordinate of each point
Georeferencing: What to Do? Coordinate surfaces in the
Spherical coordinate system
• Georeferencing the image: typing coordinates ●Use the software's georeferencing tools to
select and add control points
Georeferencing: What to Do? Coordinate surfaces in the
Spherical coordinate system
●Click the mouse pointer over a known point on the raster layer for which you have the x and y coordinates
click
Georeferencing: What to Do? Coordinate surfaces in the
Spherical coordinate system
●After you add at least four points, you can evaluate the transformation.
●In most GIS software, you can examine the “residual” error for each point and the “RMS” (Root Mean Square) error.
●In the ideal situation, the RMS error should not be greater than one pixel (Allowable: 1.5 times the pixel size).
Georeferencing: What to Do? Coordinate surfaces in the
Spherical coordinate system
●Table shows residual errors of control points resulting in an RMS error greater than one pixel
●If RMS is greater than one pixel, delete the control points with the greatest residual errors and create new points.
Georeferencing: What to Do? Coordinate surfaces in the
Spherical coordinate system
●RMS smaller than one pixel: OK
Georeferencing: What to Do? Coordinate surfaces in the
Spherical coordinate system
1. Zero order polynomial • A zero-order polynomial is used to shift your data. • This is commonly used when your data is already georeferenced,
but a small shift will better line up your data. • Only one link is required to perform a zero-order polynomial
shift. 2. 1st order polynomial (affine)
• requires a minimum of 3 displacement links, but should have more even though 3 gives RMSE=0!
• is a homogeneous transformation: only shifts origin, scales and rotates
• straight lines will be preserved 3. 2nd order polynomial
• requires 6 points (displacement links) minimum • is a differential transformation so it “warps” the raster • straightlines on raster may no longer be straight
4. 3rd order polynomial • requires 10 points minimum
Polynomials are global transformations which strive to achieve a best fit globally or overall. Only 1st order with exactly 3 points will exactly match control points.
Types of Transformation for Georeferencing Coordinate surfaces in the
Spherical coordinate system
Types of Transformation for Georeferencing Coordinate surfaces in the
Spherical coordinate system
5. Spline transformation • Often referred to as a “rubbersheeting” transformation
• optimizes for local accuracy but not global accuracy.
• control points exactly match to target control points
• useful when the control points are very important and must be
registered precisely.
• requires a minimum of three control points 6. Adjust transformation • optimizes for both global Least Squares Fit and local accuracy.
• Uses an algorithm that combines a polynomial transformation and
TIN interpolation techniques.
• requires a minimum of three control points. 7. Projective Transformation • A transformation that can warp lines so they remain straight.
• In doing so, lines that were once parallel may no longer remain
parallel.
• The projective transformation is especially useful for oblique
imagery, scanned maps, and for some imagery products.
Types of Transformation for Georeferencing Coordinate surfaces in the
Spherical coordinate system
All transformation types are selected by going to: Georeferencing/Transformation
• Example equation for second degree polynomial for the X coordinate transformation:
X’ = b1+b2X+b3Y+b4X2+b5Y
2+b6XY
• Since there are six unknowns, a minimum of 6 displacement points is required
• Higher order polynomials provide more flexibility for warping the surface to fit the control points, however
• More displacement points are required
• They can significantly deform the non-control point coordinates and produce significant distortions—be careful!
• RMSE (root mean square error) can be used to assess “goodness of fit” to control points but this does not measure the non-control point distortion
• ESRI calls this LSF-least squares fit.
• RMSE is only comparable within a given polynomial level • It automatically goes down as higher order polynomials are used
where ei is the distance between the source
control point i after transformation and the
target control point i
e12 + e2
2 + e32 +...+ en
2
n-1 rmse =
Comments on Polynomials and Goodness of Fit Coordinate surfaces in the
Spherical coordinate system
• Update Georeferencing
• Adds world file only, which contains transformation parameters
for rasters
• Image file unchanged
• Rectify
• Rewrites image file
• Use if need to do spatial analysis on file, in which case choose
GRID as output type
• Can save output as JP2, JPG, GIF, GRID, ERDAS IMAGINE,
TIFF or BMP
• New square output cells created, so issue arises how the raster
values are assigned from input to output cells since the source will
have been “warped”
• Nearest neighbor takes the value from the cell closest to the
transformed cell. It’s the fastest. Should always be used for
categorical data since it preserves original values (a 3 will
never become 3.25).
Saving Georeferencing Results Coordinate surfaces in the
Spherical coordinate system
• Bilinear interpolation takes average of values for four nearest
cells in the untransformed data weighted by distance to the
transformed cell location. Use only for continuous data such as
elevation, slope.
• Bilinear smooths data like a low pass filter.
• Cubic convolution takes average of values for 16 nearest cells
in the untransformed data weighted by distance to the
transformed cell location. Again, use only for continuous data.
Commonly used for photographs and similar data.
• Cubic tends to sharpen data like a high pass filter.
Saving Georeferencing Results Coordinate surfaces in the
Spherical coordinate system
--not the same as for CAD
--contains affine equation parameters
World file for Parameters
raster data
1.60000002384186 - A
0.00000000000000 - D
0.00000000000000 - B
-1.60000002384186 - E
2496000.75 - C
7049998.50 - F
(for UTD image: 24967042.jgw)
x1 = Ax + By + C
y1 = Dx + Ey + F
Equation for
Affine
transformation
The y-scale (E) is negative because the origin of an image is located in the upper left corner,
whereas the origin of the map coordinate system is located in the lower left corner. Row
values in the image increase from the origin downward, while y-coordinate values in the map
increase from the origin upward. (See ArcHelp)
World File for Raster data Coordinate surfaces in the
Spherical coordinate system
The higher the transformation order, the more complex the distortion that can be corrected. However, transformations higher than third order are rarely needed. Higher-order transformations require more links and, thus, will involve progressively more processing time.
The spline transformation is a true rubber sheeting method and optimizes for local accuracy but not global accuracy. It is based on a spline function—a piecewise polynomial that maintains continuity and smoothness between adjacent polynomials
The adjust transformation optimizes for both global least squares fitting (LSF) and local accuracy. The adjust transformation performs a polynomial transformation using two sets of control points and adjusts the control points locally to better match the target control points using a TIN interpolation technique. Adjust requires a minimum of three control points.
Summary: Georeferencing
Spatial Referencing
• Spatial Adjustment and
Coordinate surfaces in the
Spherical coordinate system
Applicable for Vector data.
Geometric distortions commonly occur in source maps. They may be introduced by imperfect registration in map compilation, lack of geodetic control in source data, or a variety of other causes. Rubbersheeting is used to make small geometric adjustments in the data—usually to align features with more accurate information.
Spatial Adjustment Coordinate surfaces in the
Spherical coordinate system
Spatial Adjustment Toolbar provides three spatial adjustment capabilities:
• Repositioning of a source vector layer to correspond with a correctly positioning target layer (which may be vector or raster)
• Via Homogeneous transformations (overlay)
• Can select among Affine, Similarity, or Projective transforms
• Via Differential Transformation (overlay)
• Rubber sheeting using a TIN-like (set of triangles) structure
• Edge Matching (side-by-side)
• Use Edge Snapping of features at map edges to align two adjacent data sets (map sheets)
• Attribute Transfer (non-spatial attributes)
• Transfer of non-spatial attributes from a feature in one layer to a feature in another layer
• Intended for Conflation applications
Displacement
links Links
Table
Adjustment area
Spatial Adjustment Capabilities Coordinate surfaces in the
Spherical coordinate system
Essentially involves five steps
1. Open the layer’s folder or gdb for editing on Editor toolbar
2. Select the layer to be transformed on Spatial Transformation toolbar
3. Create Displacement Links which link source coordinates to destination coordinates
-- several ways to do this (see following slides)
4. Select a Transformation Method -- several choices (see following slides for detail)
5. Perform the actual transformation and save results Warnings:
--be sure that the coordinate system of the data frame has been defined before you start
--always insert a new data frame or open a new map document for each layer you wish to transform
--start a new map document if you wish to use the transformed layer in a layout
Implementing a Spatial Transformation Coordinate surfaces in the
Spherical coordinate system
• displacement links define the source and destination coordinates for the adjustment.
• Links are represented as arrows with the arrowhead pointing towards the destination location.
• They are stored in the displacement links table (click to open)
• Displacement links can be created:
• Interactively one at a time using the displacement link tool
• Must click source (file to be moved) first, then destination
• Can adjust an existing link with the modify link tool
• Can “lock” a location so it does not move using identity link tool
• Can limit adjustment to a specific area
• By reading in a link file (tab delimited text format) containing two sets of X,Y coordinates (four columns) for source and destination (may also contain an initial column with Ids, for a total of five columns)
Creating Displacement Links for Vector Coordinate surfaces in the
Spherical coordinate system
• Created in Excel or other editing program
• Saved from the displacement links table in a previous adjustment session
• By reading in a control file (tab delimited text format) containing one set of X,Y coordinates (two columns) of control points for destinations
• Derived from GPS for example
Go to Help/Spatial Adjustment for Editing in ArcMap for details
Creating Displacement Links for Vector Coordinate surfaces in the
Spherical coordinate system
The affine transformation function is: x’ = Ax + By + C
y’ = Dx + Ey + F •where x and y are coordinates of the input layer and x’
and y’ are the transformed coordinates.
•The C and F parameters control shift in origin
(translation)
•A, B, D, E control scale and rotation
• their values are determined by comparing the location
of source and destination control points.
•Scales, skews, rotates, and translates
•6 unknowns( A,B,C,D,E,F) so a minimum
of three “displacement links” required •Usually estimated via statistical techniques
which minimize RMSE
• this requires four links minimum but more
usually used to “average the error”
•Little benefit from more than 18-30 links
•The most common choice
Transformation Types: Affine Coordinate surfaces in the
Spherical coordinate system
The similarity transform function is:
x’ = Ax + By + C
y’ = -Bx + Ay + F
where:
– A = s · cos t B = s · sin t C = translation in x direction F = translation in y direction and:
– s = scale change (same in x and y directions) t = rotation angle, measured counter-clockwise from the x-axis
• Scales, rotates, and translates the data
• Does not independently scale the axes, nor introduce any skew.
• It maintains the aspect ratio of the features transformed (e.g. squares remain squares)
• Four unknowns (A,B,C,F) thus requires a minimum of two displacement links
Coordinate surfaces in the
Spherical coordinate system
Transformation Types: Similarity/Conformal
• based upon a more complex formula
x’ = (Ax + By + C) / (Gx + Hy + 1) y’ = (Dx + Ey + F) / (Gx + Hy + 1)
• used to transform data captured directly from aerial photography.
• requires a minimum of four displacement links.
• For information see:
Moffitt, F.H. and E.M. Mikhail. Photogrammetry. Third Edition. Harper & Row, Inc., 1980.
Slama, C.C., C. Theurer, and S.W. Henriksen (eds.). Manual of Photogrammetry. 4th Edition. Chapter XIV, pp. 729-731. ASPRS, 1980.
Coordinate surfaces in the
Spherical coordinate system
Transformation Types: Projective
• “Uneven” Geometric distortions commonly occur in source data.
• imperfect registration in map compilation,
• lack of geodetic control in source data,
• Rubber sheeting corrects flaws through the geometric adjustment of coordinates through a differential transformation
• The source layer is adjusted to the more accurate target layer.
• surface is literally stretched, moving features using a piecewise transformation that preserves straight lines.
• Two types of processing: Natural Neighbor and Linear
Source layer
(inaccurate)
Target layer
(accurate)
Coordinate surfaces in the
Spherical coordinate system
Transformation Types: Rubber sheeting
• Two temporary TIN-like structures are created for source (from) and target (to) layers using Thiessen Polygons/Delauney triangles constructed from the control points (displacement links)
• Each corner of triangle has X,Y,Z coordinates
• The z value in the source (from) layer codes the amount of adjustment (rather than “elevation as in standard TIN)
• Since adjustment is known at each corner of triangle it can then be interpolated for all other points
• Two interpolation methods used
• Linear, quick and accurate if you have lots of displacement points over the area being adjusted, but doesn’t take into account “the neighborhood”
• Natural neighbor (similar to IDW--inverse distance weighting), slower but more accurate if you don’t have many displacement links
Coordinate surfaces in the
Spherical coordinate system
How Rubber Sheeting Works for Spatial Transformations
• aligns features along the edge of one layer to features of an adjoining layer.
• The layer with the less accurate features is adjusted, while the adjoining layer is used as the control.
Source
(less accurate) Target
(more accurate)
Coordinate surfaces in the
Spherical coordinate system
Edge Matching
• Attribute transfer is typically used to copy attributes from a less accurate layer to a more accurate one.
• Conflation: “the creation of a new master coverage from quality spatial data in one source and quality attribute data in another,”
• For example, it can be used to transfer the names of hydrological features from a previously digitized and highly generalized 1:500,000 scale map to a more detailed and positionally accurate 1:24,000 scale
• To transfer street names from a TIGER-derived file to a line layer digitized from positionally accurate digital orthos
• you can specify which attributes to transfer between layers, then interactively choose the source and target features.
• Typically, Rubbersheeting is used first to align the layers spatially then Attribute Transfer is used to transfer the attributes
• In practice, I’ve often found it easier to do it in the reverse order!
• if layers too close, difficult to establish the link necessary for the attribute transfer.
• Attribute transfer tool is not as useful as might appear because it’s feature by feature
• only really helps if have multiple attributes to transfer
• An alternative is to do a Rubbersheeting first, the use a Spatial Join to accomplish a “batch transfer” for multiple features simultaneously
Coordinate surfaces in the
Spherical coordinate system
Attribute Transfer and Conflation
• Create Links • Set Adjust source • Set Adjustment
Method • Preview • Adjust
Set Adjustment Source
Create Link
Elements
Preview
Adjustment
Adjust data
Set Adjustment
Method
Coordinate surfaces in the
Spherical coordinate system
Spatial Adjustment Process
Spatial Referencing
• Cad Data Adjustment
Coordinate surfaces in the
Spherical coordinate system
• A CAD layer is planimetrically accurate at start (or should
be!)
• Planimetric: map accurate in two dimensions
• Only requires translation of origin, and homogeneous scale
change (same change on both X and Y axes)
• Equivalent to a similarity transformation which is conformal
and preserves all local angles
• Based on identifying only two common points
• Thus, transformation is solved mathematically rather than
statistically
• Thus assumes there is no error in the data
Coordinate surfaces in the
Spherical coordinate system
Positioning CAD Files - Concept
In ArcGIS 9.2 and later
• Use Georeferencing toolbar to obtain two control point pairs (displacement links) only • Methodology same as for georeferencing raster file
• Any of the CAD feature class layers may be used--the transformation is applied to all
• A CAD world file is created when you click Update Georeferencing
• Named the same as the CAD file, with extension .wld
• Note: CAD world file differs from JPEG or TIFF world file! • Contains X,Y control point pair coordinates, not transformation
A geographic transformation always converts geographic (latitude–longitude) coordinates. Some methods convert the geographic coordinates to geocentric (X,Y,Z) coordinates, transform the X,Y,Z coordinates, and convert the new values back to geographic coordinates. These include the Geocentric Translation, Molodensky, and
Coordinate Frame methods.
Geographic Transformation Methods Coordinate surfaces in the
Spherical coordinate system
Transformation
The process by which move data from one coordinate system to
another coordinate system and vice versa is called transformation.
Transformation Methods:
Three-parameter method : The simplest datum transformation method is a
geocentric, or three-parameter, transformation. It requires ∆X,∆Y,∆Z distance
parameters.
Seven-parameter method : The seven parameters are three linear shifts (∆X,∆Y,∆Z),
three angular rotations around each axis (rx,ry,rz), and scale factor(s).
Molodensky method: The Molodensky method requires three shifts (∆X,∆Y,∆Z) and the differences
between the semimajor axes (∆a) and the flattenings (∆f) of the two spheroids. The Projection Engine
automatically calculates the spheroid differences according to the datums involved
Abridged Molodensky method: The Abridged Molodensky method is a simplified version of the
Molodensky method. Used some simplified equations
Coordinate surfaces in the
Spherical coordinate system
The simplest datum transformation method is a geocentric, or three-parameter,
transformation. The geocentric transformation models the differences between two
datums in the XYZ or 3D Cartesian coordinate system. One datum is defined with its
center at 0,0,0. The center of the other datum is defined at some distance (dx,dy,dz
or ΔX,ΔY,ΔZ) in meters away.
Geocentric Transformation- Three Para…
Usually the transformation parameters are defined as
going "from" a local datum "to" World Geodetic
System (WGS) 1984 or another geocentric datum.
The three parameters are linear shifts and are
always in meters.
Coordinate surfaces in the
Spherical coordinate system
A more complex and accurate datum transformation is possible by adding four more
parameters to a geocentric transformation. The seven parameters are three linear
shifts (dx,dy,dz), three angular rotations around each axis (rx,ry,rz), and a scale
factor.
Geocentric Transformation- Seven Para…
The rotation values are given in decimal seconds,
while the scale factor is in parts per million (ppm). The
rotation values are defined in two different ways: as
positive either clockwise or counterclockwise as you
look toward the origin of the XYZ systems.
Seven parameters are dx, dy, dz, rx, ry, rz, and s
Coordinate surfaces in the
Spherical coordinate system
The Molodensky method converts directly between two geographic coordinate
systems without actually converting to an XYZ system. The Molodensky method
requires three shifts (dx,dy,dz) and the differences between the semimajor axes (Δa)
and the flattenings (Δf) of the two spheroids. The Projection Engine automatically
calculates the spheroid differences according to the datums involved.
Geocentric Molodensky method…
Parameters are…..
h = ellipsoid height (meters)
Φ = latitude
λ = longitude
a = semimajor axis of the spheroid (meters)
b = semiminor axis of the spheroid (meters)
f = flattening of the spheroid
e = eccentricity of the spheroid
Coordinate surfaces in the
Spherical coordinate system
NADCON and HARN methods
The United States uses a grid-based method to convert between geographic
coordinate systems. Grid-based methods allow you to model the differences
between the systems and are potentially the most accurate. The area of interest is
divided into cells. The National Geodetic Survey (NGS) publishes grids to convert
between North American Datum (NAD) 1927 and other older geographic coordinate
systems and NAD 1983. These transformations are grouped into the NADCON
method.
Grid-based transformation Coordinate surfaces in the
Spherical coordinate system
∆X = 283.729
∆Y = 735.942
∆Z = 261.143
WGS84 to Everest Bangladesh 1937
∆X = -283.729
∆Y = -735.942
∆Z = -261.143
Everest Bangladesh 1937 to WGS84
∆X = 283.729
∆Y = 735.942
∆Z = 261.143
Transformation Parameters Everest 1830 and WGS 84
Coordinate surfaces in the
Spherical coordinate system
Converting GIS Vector Data to KML
• KML are Google Earth's file format for storing placemarks, network link information, and much more
• KML stands for Keyhole Markup Language (Keyhole was the name of the application before Google bought it and added their own features and larger databases)
• KMZ stands for KML-Zipped. It is the default format for KML because it is a compressed version of the file. One of the more powerful features of KMZ is that it allows any images you use - say custom icons, or images in your descriptions - to be zipped up within the KMZ file.