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Georeferencing
Georeferencing
Georeferencing
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Georeferencing or georegistration is a type of coordinate transformation that binds a digital raster image or vector database that represents a geographic space (usually a scanned map or aerial photograph) to a spatial reference system, thus locating the digital data in the real world.[1][2] It is thus the geographic form of image registration or image rectification. The term can refer to the mathematical formulas used to perform the transformation, the metadata stored alongside 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 geographic information systems and remote sensing software.

A number of mathematical methods are available, but the process typically involves identifying a sample of several ground control points (GCPs) with known locations on the image and the ground, then using curve fitting techniques to generate a parametric (or piecewise parametric) formula to transform the rest of the image.[3] Once the parameters of the formula are stored, the image may be transformed dynamically at drawing time, or resampled to generate a georeferenced raster GIS file or orthophoto.

The term "georeferencing" has also been used to refer to other types of transformation from general expressions of geographic location (geocodes) to coordinate measurements,[4] but most of these other methods are more commonly called geocoding. Because of this ambiguity, georegistration is preferred by some to refer to the image transformation.[5]: 141–143  Occasionally, this process has been called rubbersheeting, but that term is more commonly applied to a very similar process applied to vector GIS data.[5]: 240  Compared to georeferencing, orthorectification accounts for the Earth's topography, sensor optical distortions, and sometimes other artifacts [6] and is often preferred as a result.

Motivation

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  • Georeferencing is crucial to make aerial and satellite imagery, usually raster images, useful for mapping as it explains how other data, such as the above GPS points, relate to the imagery.
  • 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 time.
  • Different maps may use different projection systems. Georeferencing tools contain methods to combine and overlay these maps with minimum distortion.

Mathematics

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Main article: Geometric transformation
Graphical view of the affine transformation.

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 spatial reference system of the user's choice, such as the geographic coordinate system or a particular Universal Transverse Mercator zone. It is thus the extension of the typical task of curve fitting a relationship between two variables to four dimensions. The goal is to have a pair of functions of the form:

Such that for every pixel in the image ( being its column and row number, respectively), a corresponding real-world coordinate can be calculated.

Several types of functions are available in most GIS and remote sensing software for georeferencing.[7] 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 affine transformation:[8]: 171 

Where A-F are constant coefficients set for the entire image. These formulas allow an image to be moved (the C and F coefficients specify the desired location of the top left corner of the image), scaled (without rotation, the A and E coefficients specify the size of each cell or spatial resolution), and rotated.[9]: 115  In the last case, if the cell size is r in both the x and y directions, and the image is to be rotated α degrees counter-clockwise, then . The world file developed by Esri is a commonly used sidecar file that specifies these six coefficients for image georeferencing.

Higher order polynomial transformations are also commonly used. For example, a Second-order polynomial transformation would be:

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 distortion in aerial photographs.

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 Thin plate spline transformation.[10]

The GCP method

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It is very rare that a user would specify the parameters for the transformation directly. Instead, most GIS and remote sensing 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 ground control points (GCP).[8]: 170  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 ( = pixel column, = pixel row) and the ground coordinate system (). 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 orthophoto that is already in the desired coordinate system. This can then be moved and adjusted to improve accuracy.

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 linear algebra to determine the coefficients and derive the formulas to use for the entire grid.[9]: 116  For example, the linear affine transformation above has six unknown coefficients, so six equations with known <> are needed to derive them, which will require three ground control points.[8]: 171  The second-order polynomial requires a minimum of six ground control points, and so on.

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 (creating an overdetermined system), and use least squares regression to derive a set of function parameters that most closely matches the points.[9]: 116  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 Root-mean-square error (RMSE). A lower RMSE thus means that the transformation formulas closely match the GCPs.

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 metadata, either in the header of the image file itself (e.g., GeoTIFF), or in a sidecar file stored alongside the image file (e.g., a world file). 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 rectification, in which the image is resampled 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 rectified image.

Software implementations

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See also

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References

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Further reading

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Georeferencing

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Georeferencing is the process of aligning geographic data, such as raster images, scanned maps, or aerial photographs, to a known by assigning real-world spatial coordinates to enable integration, viewing, querying, and with other geospatial datasets in geographic information systems (GIS). This technique relates the internal coordinate system of a digital map or image to a ground-based system of geographic coordinates, such as or Universal Transverse Mercator (UTM), allowing precise referencing on Earth's surface. The importance of georeferencing lies in its ability to transform non-spatial or legacy data into usable geospatial information, facilitating applications in fields like , , historical analysis, and . Without georeferencing, scanned paper maps or unlocated images cannot be overlaid with vector data, , or digital elevation models, limiting such as distance calculations, area measurements, or feature identification. It is particularly vital for preserving and reusing historical maps, where georeferencing enables comparison with modern datasets to study changes over time. The georeferencing process typically involves selecting control points—pairs of corresponding locations between the unreferenced image and a reference map with known coordinates—to define the spatial transformation. Common methods include affine transformations for simple scaling, rotation, and translation; polynomial transformations for handling in more complex images; and advanced techniques like rubber sheeting or orthorectification to correct for terrain relief or lens . Metadata, including the , , and datum (a model of Earth's shape), must be specified to ensure accuracy and compatibility across systems. In practice, georeferencing is performed using GIS software tools, such as the Georeferencing toolbar in or the Georeferencer plugin in , which automate control point selection, transformation application, and output in formats like or GeoPDF that embed spatial information. These tools often include error assessment features, like root mean square (RMS) error, to validate the alignment quality. Post-georeferencing steps may involve clipping extraneous areas or compressing files to optimize storage and performance in GIS workflows.

Fundamentals

Definition and Scope

Georeferencing is the process of assigning real-world geographic coordinates, such as latitude and longitude or projected coordinates, to spatial data including images, maps, or scanned documents, in order to align them with a known coordinate reference system (CRS). This alignment relates the internal coordinate system of the data to a ground-based geographic framework, enabling precise spatial positioning. The scope of georeferencing encompasses a range of spatial data types, primarily raster formats like aerial photographs and , but also extends to vector data and historical maps that lack inherent geographic referencing. It focuses on transforming and registering these datasets to a common CRS for integration in geospatial workflows. Importantly, georeferencing differs from geocoding, which involves converting textual addresses or place names into point coordinates, and from geolocation, which identifies the real-time position of devices or users via technologies like GPS. Central to georeferencing are concepts like spatial alignment, which ensures datasets overlay accurately by adjusting for distortions such as or scaling, and datum transformations, which convert between different reference frameworks to maintain positional consistency. These elements are fundamental to its role in geographic information systems (GIS), where georeferenced data facilitates overlay analysis by allowing multiple layers to be combined and interrogated for patterns or relationships. In fields like and , georeferencing supports the fusion of diverse datasets for enhanced mapping and .

Historical Context

The roots of georeferencing trace back to 19th-century advancements in , where manual techniques for aligning images to geographic coordinates emerged through the use of control points for rectification. German architect Meydenbauer pioneered the application of to architectural and topographic surveys in the 1860s, developing methods to measure and images by identifying fixed ground control points to correct distortions and align them with known positions. In 1867, Meydenbauer, in collaboration with geographer Otto Kersten, coined the term "" for these practices. A key milestone occurred in the 1930s with the maturation of alignment techniques, as the formation of the American Society of Photogrammetry in 1934 spurred standardized methods for stereoscopic viewing and rectification of aerial images using control points, enabling more accurate large-scale mapping. Following , georeferencing advanced through the integration of computing technology in the 1960s, particularly via U.S. Geological Survey (USGS) programs that digitized aerial imagery for production. The USGS began experimenting with computer-assisted during this decade, using early digital tools to automate aspects of the rectification process into georeferenced orthophotos by applying mathematical transformations based on control points, which significantly reduced manual labor and improved topographic mapping efficiency. These efforts laid the groundwork for systematic digital georeferencing, transitioning from analog plotting to computational alignment of images with coordinate systems. The digital era saw georeferencing emerge prominently in the with the rise of (GIS) software, which incorporated raster data alignment as a core function for integrating diverse spatial datasets. Commercial GIS platforms, such as those developed by , introduced user-friendly tools for georeferencing scanned maps and aerial photos to standard projections using control points, enabling widespread application in and . By the 2000s, evolution toward automated methods accelerated with the integration of (GPS) and satellite data, allowing direct georeferencing without extensive ground control through integrated sensor models that fused inertial navigation and orbital parameters for real-time image alignment. A pivotal event was the 1972 launch of the , which provided the first systematic multispectral of Earth's land surfaces, necessitating advanced georeferencing protocols to correct for orbital geometry and enable global-scale analysis in applications like land-use monitoring.

Theoretical Foundations

Coordinate Reference Systems

Coordinate reference systems (CRS) provide the foundational framework for locating positions on the Earth's surface in georeferencing processes. A CRS defines how coordinates relate to real-world locations by specifying a reference framework that accounts for the 's irregular shape. A CRS is a coordinate system that is related to the by a datum. There are three primary types of CRS used in georeferencing: geographic, , and local. Geographic coordinate systems (GCS) represent positions using angular measurements of on an ellipsoidal model of the , such as the World Geodetic System 1984 (WGS84), which employs degrees as units and is widely used in global positioning systems. coordinate systems (PCS) transform these angular coordinates into linear units like meters via map projections, for example, the Universal Transverse Mercator (UTM) system, which divides the into zones to minimize distortion in regional mapping. Local systems, such as state plane coordinates, are tailored to specific areas for high-precision applications, often using custom datums to reduce errors in localized surveys. Key components of a CRS include the datum, , units, and vertical elements. The datum establishes the reference surface, typically a comprising a reference —such as the (GRS80) for the 1983 (NAD83)—that approximates the Earth's shape, along with parameters tying it to the physical Earth. The , conventionally the Greenwich meridian (0° ), defines the origin for longitude measurements, while units specify the measurement scale, such as decimal degrees for GCS or meters for PCS. Vertical datums, like the North American Vertical Datum of 1988 (NAVD88), provide a reference for , often independent of horizontal datums and based on mean or models to handle height measurements. Transformations between CRS are essential to align data from different frameworks, involving datum shifts and projections. Datum shifts correct for differences in reference ellipsoids and orientations, often using a 7-parameter Helmert transformation, which includes translations, rotations, and scale factors; for instance, converting from WGS84 to NAD83 requires such a transformation to account for their slight positional offsets, typically on the order of 1-2 meters in . Projections mathematically flatten the ellipsoidal surface onto a plane, introducing distortions in area, , , or direction depending on the method, such as the Transverse Mercator used in UTM. These transformations ensure compatibility but must be applied carefully to preserve spatial integrity. In georeferencing, a critical prerequisite is ensuring that input data's CRS matches the target CRS to prevent distortions or misalignment. Mismatched systems can lead to errors in positioning, such as scale inaccuracies or positional offsets, so data must be reprojected or transformed beforehand using standardized methods to align with the project's reference framework. This alignment supports subsequent geometric transformations by providing a consistent spatial base.

Geometric Transformations

Geometric transformations form the mathematical backbone of georeferencing, enabling the alignment of spatial data from various sources to a common coordinate reference system by modeling distortions such as translation, rotation, scaling, and shearing. These transformations map coordinates from a source system to a target system using parametric equations derived from ground control points (GCPs), ensuring that features in the input data correspond accurately to their real-world positions. The choice of transformation depends on the nature of the distortions; linear models suffice for uniform changes, while higher-order or non-rigid methods address complex deformations. Affine transformations, also known as first-order or linear transformations, are widely used for their simplicity and ability to handle global distortions while preserving parallelism and straight lines. They involve six parameters: two for scaling (a and e), two for rotation and shear (b and d), and two for (c and f). The 2D affine transformation equations are: x′=ax+by+c,y′=dx+ey+f,\begin{align} x' &= a x + b y + c, \\ y' &= d x + e y + f, \end{align} where (x, y) are source coordinates and (x', y') are transformed coordinates. A special case is the similarity transformation, which maintains shape (conformal) by incorporating isotropic scaling and a , typically with four parameters: scale factor s, rotation angle θ, and translation components tx, ty. The equations incorporate the rotation matrix as: (x′y′)=s(cos⁡θ−sin⁡θsin⁡θcos⁡θ)(xy)+(txty).\begin{pmatrix} x' \\ y' \end{pmatrix} = s \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} t_x \\ t_y \end{pmatrix}. These models require a minimum of three non-collinear GCPs to solve for the parameters. For more complex distortions, transformations extend the affine model to higher orders, capturing non-linear effects like . A of order n in 2D has (n+1)(n+2)/2(n+1)(n+2)/2 parameters per dimension; for example, second-order (quadratic) uses 6 parameters per axis (12 total), and third-order (cubic) uses 10 per axis (20 total), suitable for moderate to severe distortions in scanned maps or . The general form for second-order is: x′=a0+a1x+a2y+a3x2+a4xy+a5y2,x' = a_0 + a_1 x + a_2 y + a_3 x^2 + a_4 x y + a_5 y^2, y′=b0+b1x+b2y+b3x2+b4xy+b5y2.y' = b_0 + b_1 x + b_2 y + b_3 x^2 + b_4 x y + b_5 y^2. Projective transformations, or homographies, address perspective distortions in oblique or scanned maps, using eight parameters () and requiring at least four GCPs. They model central projection effects, where straight lines remain straight but parallelism is not preserved, with the general form involving a 3x3 matrix normalized to one degree of freedom. Thin-plate spline (TPS) transformations provide a non-rigid, elastic alternative for localized distortions, such as those in historical maps due to irregular scanning or aging; TPS minimizes bending energy for smooth between GCPs without a fixed parametric form, making it ideal for rubber-sheeting applications. Parameters for these transformations are typically estimated using least-squares optimization to fit the model to an overdetermined set of GCPs, minimizing residuals between observed and predicted coordinates. The process begins by establishing a from the GCP pairs: for m GCPs and p parameters, this yields 2m equations (one per ). The least-squares solution solves the normal equations ATAβ=ATb\mathbf{A}^T \mathbf{A} \boldsymbol{\beta} = \mathbf{A}^T \mathbf{b}, where A\mathbf{A} is the of GCP coordinates, β\boldsymbol{\beta} the parameter vector, and b\mathbf{b} the target coordinates vector. For affine models, this is linear and solved directly via matrix inversion; higher-order polynomials may require iterative non-linear least-squares (e.g., Gauss-Newton) if the model is non-linearized. The is assessed using the error (RMSE), calculated as RMSE=∑i=1n(exi2+eyi2)n\text{RMSE} = \sqrt{\frac{\sum_{i=1}^{n} (e_{x_i}^2 + e_{y_i}^2)}{n}}
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