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. 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. 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, 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. Occasionally, this process has been called rubbersheeting, but that term is more commonly applied to a very similar process applied to vector GIS data. Compared to georeferencing, orthorectification accounts for the Earth's topography, sensor optical distortions, and sometimes other artifacts and is often preferred as a result.

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 (${\displaystyle x_{in},y_{in}}$ 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:

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. 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 ${\displaystyle A=E=r\cos(\alpha ),B=D=r\sin(\alpha )}$. 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: