1130:). Easily visible locations that be precisely located are preferred as GCP's, such as a road intersection or the corner of a building. When very high accuracy registration is required, it is common to place or paint high-contrast markers on the ground at survey control monuments before the photography is taken, and use GNSS-measured coordinates for the output. In most software, these are entered by pointing at the location on the image, then pointing at the same location on a vector base map or
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The entered GCPs are rarely perfectly located and are even more rarely perfectly representative of the distortion in the rest of the image, but the algebraic solution, which appears to be a perfect match, masks any error. To avoid this, it is common to create many more than the minimal required set
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to create a new raster grid that is natively tied to the coordinate system. Rectification was traditionally the only option, until the computing power became available for the intense calculations of dynamic coordinate transformations; even now, drawing and analysis performance is better with a
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Very essential information may be contained in data or images that were produced at a different point of time. It may be desired either to combine or compare this data with that currently available. The latter can be used to analyze the changes in the features under study over a period of
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Once the function parameters are determined, the transformation functions can be used to transform every pixel of the image to its real-world location. Two options are usually available for making this transformation permanent. One option is to save the parameters themselves as a form of
57:
or within the image file to specify the transformation, or the process of manually or automatically aligning the image to the real world to create such metadata. The most common result is that the image can be visually and analytically integrated with other geographic data in
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Several types of functions are available in most GIS and remote sensing software for georeferencing. As the simplest type of two-dimensional curve is a straight line, so the simplest form of coordinate transformation is a linear transformation, the most common type being the
77:
techniques to generate a parametric (or piecewise parametric) formula to transform the rest of the image. Once the parameters of the formula are stored, the image may be transformed dynamically at drawing time, or resampled to generate a georeferenced
1237:
regression to derive a set of function parameters that most closely matches the points. This is almost never a perfect match, so the variance between each GCP location and the location predicted by the functions can be measured and summarized as a
164:
The registration of an image to a geographic space is essentially the transformation from an input coordinate system (the inherent coordinates of pixels in the images based on row and column number) to an output coordinate system, a
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824:
1258:). With this metadata, the software can perform the transformation dynamically as it displays the image, so that it appears to align with other data in the desired coordinate system. The alternative method is
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to determine the coefficients and derive the formulas to use for the entire grid. For example, the linear affine transformation above has six unknown coefficients, so six equations with known <
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software provides an interactive environment for visually aligning the image to the destination coordinate system. The most common method for doing this is to create a series of
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1018:(GCP). A ground control point is a location that can be identified on both the image and the ground, so that it has precise coordinates in both the image coordinate system (
987:
The second-order terms (and third-order terms in a third-order polynomial) allow for the variable warping of the image, which is especially useful for removing the inherent
380:
1225:> are needed to derive them, which will require three ground control points. The second-order polynomial requires a minimum of six ground control points, and so on.
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With a minimal set of GCPs, the known coordinates can be entered into the mathematical equations for the desired type of transformation, which can then be solved using
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In addition to global parametric formulas, piecewise formulas can also be used, which transform different parts of the image in different ways. A common example is a
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Different maps may use different projection systems. Georeferencing tools contain methods to combine and overlay these maps with minimum distortion.
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supports various transformation algorithms (including the Thin Plate Spline transformation), and the computation of distortions, through it's
89:
The term georeferencing has also been used to refer to other types of transformation from general expressions of geographic location (
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Higher order polynomial transformations are also commonly used. For example, a Second-order polynomial transformation would be:
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that binds a digital raster image or vector database that represents a geographic space (usually a scanned map or
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a relationship between two variables to four dimensions. The goal is to have a pair of functions of the form:
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A number of mathematical methods are available, but the process typically involves identifying several sample
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that is already in the desired coordinate system. This can then be moved and adjusted to improve accuracy.
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being its column and row number, respectively), a corresponding real-world coordinate can be calculated.
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It is very rare that a user would specify the parameters for the transformation directly. Instead, most
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is preferred by some to refer to the image transformation. Occasionally, this process has been called
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GIS software has had this capability for many years, including the
Georeferencing tool in ArcGIS Pro.
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34:
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Where A-F are constant coefficients set for the entire image. These formulas allow an image to be
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has a
Georeferencer tool, originally developed as an add-on but now integrated into the software.
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Discovering
Location Indicators of Toponyms from News to Improve Gazetteer-Based Geo-Referencing
1409:
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555:(the C and F coefficients specify the desired location of the top left corner of the image),
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130:, usually raster images, useful for mapping as it explains how other data, such as the above
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110:
49:. The term can refer to the mathematical formulas used to perform the transformation, the
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1242:(RMSE). A lower RMSE thus means that the transformation formulas closely match the GCPs.
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95:) to coordinate measurements, but most of these other methods are more commonly called
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International
Encyclopedia of Geography: People, the Earth, Environment and Technology
45:, thus locating the digital data in the real world. It is thus the geographic form of
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Longley, Paul A.; Goodchild, Michael F.; Maguire, David J.; Rhind, David W. (2011).
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977:{\displaystyle y_{out}=Gx_{in}+Hy_{in}+Ix_{in}^{2}+Jy_{in}^{2}+Kx_{in}y_{in}+L}
819:{\displaystyle x_{out}=Ax_{in}+By_{in}+Cx_{in}^{2}+Dy_{in}^{2}+Ex_{in}y_{in}+F}
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105:
63:
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109:, but that term is more commonly applied to a very similar process applied to
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559:(without rotation, the A and E coefficients specify the size of each cell or
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GIS Fundamentals: A First Text on
Geographic Information Systems
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that specifies these six coefficients for image georeferencing.
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online tutorial material from the
University of Southampton, UK
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in both the x and y directions, and the image is to be rotated
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International
Encyclopedia of Human Geography (Second Edition)
73:
with known locations on the image and the ground, then using
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1556:
Leidner, J.L. (2017). "Georeferencing: From Texts to Maps".
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Hackeloeer, A.; Klasing, K.; Krisp, J.M.; Meng, L. (2014).
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16:
Identification of something to locations in physical space
131:
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Geographical referencing resources for social scientists
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1250:, either in the header of the image file itself (e.g.,
1507:"Georeferencing: a review of methods and applications"
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zone. It is thus the extension of the typical task of
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648:{\displaystyle A=E=r\cos(\alpha ),B=D=r\sin(\alpha )}
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1078:= pixel row) and the ground coordinate system (
1679:Introduction to Geographic Information Systems
1681:(7th ed.). McGraw-Hill. pp. 50–57.
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1218:{\displaystyle x_{in},y_{in},x_{out},y_{out}}
1600:Geographic Information Systems & Science
160:Graphical view of the affine transformation.
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541:{\displaystyle y_{out}=Dx_{in}+Ey_{in}+F}
463:{\displaystyle x_{out}=Ax_{in}+By_{in}+C}
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567:. In the last case, if the cell size is
336:Such that for every pixel in the image (
326:{\displaystyle y_{out}=G(x_{in},y_{in})}
251:{\displaystyle x_{out}=F(x_{in},y_{in})}
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1611:
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1463:, Oxford: Elsevier, pp. 111–117,
1289:Image Georeferencing and Rectification
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659:developed by Esri is a commonly used
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1454:
13:
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1469:10.1016/b978-0-08-102295-5.10548-7
169:of the user's choice, such as the
122:Georeferencing is crucial to make
14:
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1767:- paper presented at Geoinfo 2008
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1431:"What does "georeferenced" mean?"
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575:degrees counter-clockwise, then
1787:Geographic data and information
1572:10.1002/9781118786352.wbieg0160
1123:{\displaystyle x_{out},y_{out}}
1549:
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1459:, in Kobayashi, Audrey (ed.),
1457:"Georeferencing and Geocoding"
1455:Yao, Xiaobai A. (2020-01-01),
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134:points, relate to the imagery.
60:geographic information systems
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375:{\displaystyle x_{in},y_{in}}
175:Universal Transverse Mercator
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99:. Because of this ambiguity,
1617:"Overview of georeferencing"
1534:10.1080/19475683.2013.868826
171:geographic coordinate system
7:
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10:
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1677:Chang, Kang-tsung (2014).
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18:
1651:. Ann Arbor, MI: XanEdu.
1298:Image to Map Registration
35:coordinate transformation
1621:ArcGIS Pro Documentation
1437:. U.S. Geological Survey
1405:Transport infrastructure
1395:Spatial reference system
1271:Software implementations
1262:, in which the image is
167:spatial reference system
152:Geometric transformation
43:spatial reference system
19:Not to be confused with
1735:Hill, Linda L. (2006).
1710:QGIS 3.22 documentation
991:in aerial photographs.
1647:Bolstad, Paul (2019).
1602:(3rd ed.). Wiley.
1240:Root-mean-square error
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1706:"16.3 Georeferencer"
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1375:Linear referencing
1370:Image registration
1311:@allmaps/transform
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47:image registration
1688:978-0-07-352290-6
1658:978-1-59399-552-2
1478:978-0-08-102296-2
1380:Reverse geocoding
1267:rectified image.
996:Thin plate spline
128:satellite imagery
39:aerial photograph
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1434:
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1340:Geomessaging
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1233:), and use
146:Mathematics
1492:2022-01-04
1441:2022-01-04
1417:References
1360:Geotagging
1256:world file
1132:orthophoto
989:distortion
657:world file
117:Motivation
111:vector GIS
84:orthophoto
66:software.
1716:8 January
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1355:GeoReader
1345:Geoportal
1335:Geocoding
1325:Altimetry
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1781:Category
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1318:See also
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1248:metadata
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