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Georeferencing

Georeferencing or georegistration is a type of coordinate transformation that binds a digital raster image or vector database that represents a geographic space to a spatial reference system, thus locating the digital data in the real world. 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.

Motivation
• 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==
Mathematics
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: :x_{out} = F(x_{in}, y_{in}) :y_{out} = G(x_{in}, y_{in}) Such that for every pixel in the image (x_{in}, y_{in} 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. 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: :x_{out} = Ax_{in} + By_{in} + C :y_{out} = Dx_{in} + Ey_{in} + F 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. ==The GCP method==
The GCP method
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). 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==
Software implementations
Esri GIS software has had this capability for many years, including the Georeferencing tool in ArcGIS Pro. • QGIS has a Georeferencer tool, originally developed as an add-on but now integrated into the software. • Image Georeferencing and Rectification in ERDAS Imagine • Image to Map Registration in ENVI • Allmaps supports various transformation algorithms (including the Thin Plate Spline transformation), and the computation of distortions, through its @allmaps/transform package. ==See also==
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