Lecture 15 - 19 · Lecture 15 - 19: Spatial Referencing and Geographic Transformation ... • Via...

Lecture 15 - 19: Spatial Referencing and Geographic

Transformation

URP 1281 Surveying and Cartography

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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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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



• 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


● ‘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


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.



Georeferencing

Source: ESRI Help

Georeferencing Concepts Coordinate surfaces in the


• 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


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


●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


●Write down the x, y coordinate of each point



• Georeferencing the image: typing coordinates ●Use the software's georeferencing tools to

select and add control points



●Click the mouse pointer over a known point on the raster layer for which you have the x and y coordinates

click



●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).



●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.



●RMS smaller than one pixel: OK



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


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.



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


• 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


• 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


--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


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



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


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


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


• 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


• 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


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


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



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.



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)



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



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)



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



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



Spatial Adjustment Process

Spatial Referencing

• Cad Data Adjustment



• 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



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

parameters

XCAD Source YCAD Source XREAL Map YREAL Map

240.000000, 750.500000 2505108.552674, 7046646.373472

4134.000000, 2550.000000 2505523.148640, 7046837.967062

Note:

heading

not

included in

file



Positioning CAD Files - Implementation

In ArcGIS 9.1 and earlier

• Must have, a priori, X,Y coordinates for two pairs of corrresponding points in the CAD and the real world

• Points may be entered:

• via the Properties/Transformations tab of the CAD layer itself (not available in ArcGIS 9.2)

• By creating a CAD world file containing corresponding XY coordinate pairs

• Named the same as the CAD file, with extension .wld

• Note: CAD world file differs from JPEG or TIFF world file!

XCAD Source YCAD Source XREAL Map YREAL Map

240.000000, 750.500000 2505108.552674, 7046646.373472

4134.000000, 2550.000000 2505523.148640, 7046837.967062

Note:

heading

not

included in

file



Positioning CAD Files - Implementation

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


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



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.



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



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



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


∆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



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.



Thank You For being with me

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