An overview of GeoTransformers
Georeferencing describes the process of locating an entity in 'real world' coordinates. Once an entity has been georeferenced, the relationship between the entity and its 'real world' location can be used to map and display information about the entity. This relationship can be described as a chain of transformations that can be modeled mathematically. Each of these transformations can be defined through a set of parameters and will process coordinates from one virtual space to another. Such transformations applied to rasters are implemented by a GeoTransformer. The set of parameters defining the transformation forms the GeoTransformer Definition, which is stored as XML for extensibility considerations.
GeoTransformers can be applied in a chain with a certain order, as well as encapsulated one into another. Specific Raster Processes that perform coordinate transformations are called georeferencing processes. Because in most generic cases a composition of GeoTransformers represents a sensor model, a georeferencing process will be identified by what we've called a Sensor Definition. There are no restrictions on what kind of transformations are defined within a sensor definition (SDef), meaning it doesn't have to describe a physical sensor.
A Raster process is defined by a raster process definition (RPDef) which consists of two parts: Raster Group and Rasters. Both Raster Group & Rasters definitions can have georeferencing processes defined by Sensor Definitions. Their only purpose is to affect the geometry of a raster to match a certain projection in 'real world' coordinates that is defined by its Spatial Reference System (PRJ).
GeoTransformers are used within ArcGIS Image Server processing chains (for details, see ArcGIS Image Server processing chain). They are processing 3D coordinates, and those which do not utilize the 3rd coordinate (Z) must maintain the value. Whenever possible, a GeoTransformer implements the coordinate transformation in both directions, defined as FromGlobal (FG) and ToGlobal (TG).
When imagery is rectified within ArcGIS Image Server, only the FG transformation is applied thus needs to be written as efficient as possible. The TG transformations are primarily used within components such as the Service Editor when have to compute ground coordinates based on image coordinates and where the efficiency of the transform is not critical.
Several GeoTransformers were implemented within a component of ArcGIS Image Server, named GeoTransCore. A brief overview description of each follows:
Affine GeoTransformer 

Performs an affine transformation. An affine transformation is also called an affinity. X = A0 + A1 * x + A2 * y Type: 2D (changes only X,Y) 

StdFrame GeoTransformer 

Implements the sensor model of a standard frame photogrammetric camera. ground (G) <> corrected camera (CC) <> camera (C) <> film (F) <> image (I) Interior Orientation (IO) Radial distortion is a function of the distance to the principal point of best symmetry, presented in the form of an evenpower polynomial (ConradyBrown model): x' = x  ppsX y' = y  ppsY dx = (k1 + k2 * r^2 + k3 * r^4) * x' dy = (k1 + k2 * r^2 + k3 * r^4) * y' X = dx + x Y = dy + y Decentring distortion uses 2 coefficients: x' = x  ppsX y' = y  ppsY dx = C1 * (r^2 + 2 * x'^2) + 2 * C2 * x' * y' dy = C2 * (r^2 + 2 * y'^2) * 2 * C1 * x' * y' X = dx + x Y = dy + y Exterior Orientation (EO) X = polarity * (x * M11 + y * M12 + z * M13) * focalLenth / (x * M31 + y * M32 + z * M33) where M is the rotation matrix. M11 = cos(kappaR)*cos(phiR) M12 = (rotSys)*sin(kappaR)*cos(omegaR) + cos(kappaR)*(rotSys)*sin(phiR)*(rotSys)*sin(omegaR) M13 = (rotSys)*sin(kappaR)*(rotSys)*sin(omegaR) + cos(kappaR)*(rotSys)*sin(phiR)*cos(omegaR)
M21 = (rotSys)*sin(kappaR)*cos(phiR) M22 = cos(kappaR)*cos(omegaR) + (rotSys)*sin(kappaR)*(rotSys)*sin(phiR)*(rotSys)*sin(omegaR) M23 = cos(kappaR)*(rotSys)*sin(omegaR) + (rotSys)*sin(kappaR)*(rotSys)*sin(phiR)*cos(omegaR)
M31 = (rotSys)*sin(phiR) M32 = cos(phiR)*(rotSys)*sin(omegaR) M33 = cos(phiR)*cos(omegaR) where rotSys has value 1 for clockwise rotation and value 1 for counterclockwise rotation system. rFLp2 = 1.0 / (focalLength^2) earthR2km = 2.0 * earthRadius / 1000.0 REFC = (1.0) * ( (12.7  0.95 * (averageZ/1000.0))* ((frameCenter.Z  averageZ) / 1000.0)  (0.49  0.045 * (averageZ / 1000.0))* ((frameCenter.Z  averageZ) / 1000.0)*((sp.Z  averageZ) / 1000.0) ) / 1000000.0 rp2=x^2+y^2 drr = 1.0+REFC+(((frameCenter.ZZ)/1000.0)/(earthR2km)+REFC)*rp2*rFLp2 X = x * drr Y = y * drr Type: 3D (Zaware) 

Rational GeoTransformer 

Implements the rational polynomial functions transformation, defined as a division of cubic polynoms applied to normalized coordinates. C,L,P,H,LP,LH,PH,L2,P2,H2,PLH,L3,LP2,LH2,L2P,P3,PH2,L2H,P2H,H3 where L  longitude, P  latitude, H  height and C denotes the constant term of the polynom. 

WarpGrid GeoTransformer 

Performs a 2D warp based on a grid of points. 

LSR GeoTransformer 

Performs a 3D rotation representing coordinates transformation from Universal Space Rectangular (USR) to Local Space Rectangular (LSR). M11 M12 M13 It can be used in conjunction with a StdFrame GeoTransformer which transforms LSR coordinates into image coordinates. 

Geodetic GeoTransformer 

Converts Cartesian EarthCentered, EarthFixed (ECEF) XYZ coordinates into geodeticmapping coordinates, based on a reference ellipsoid described by a series of parameters that define its shape. Given the semimajor axis (a) and the inverse flattening (denF) of the ellipsoid, the semiminor axis (b) is computed as: b = a * (denF  1) / denF First and second eccentricity at the power 2 are also computed: e1sqr = (a * a  b * b) / (a * a) e2sqr = (a * a  b * b) / (b * b) Denoting the geoid separation with N, the geodetic to ECEF transformation is: Lon = x * PI / 180.0 Lat = y * PI / 180.0 Alt = z + N RCPV = a / sqrt(1.0  e1sqr * sin(Lat) * sin(Lat)) X = (RCPV + Alt) * cos(Lat) * cos(Lon) Y = (RCPV + Alt) * cos(Lat) * sin(Lon) Z = (RCPV * (1.0  e1sqr) + Alt) * sin(Lat) The ECEF to geodetic transformation is: Alt = ip.Z p = sqrt(x * x + y * y) T = atan((Alt * a) / (p * b)) sT = sin(T) cT = cos(T) Lat = atan((Alt + e2sqr * b * sT * sT * sT) / (p  e1sqr * a * cT * cT * cT)) RCPV = a / sqrt(1.0  e1sqr * sin(Lat) * sin(Lat)) if (y != 0.0) { sig = y / fabs(y) } else { sig = 1.0 } if (x == 0.0) { Lon = sig * PI / 2.0 } else { Lon = atan(y / x) if (x < 0.0) { if (y < 0.0) { Lon = Lon  PI } else { Lon = Lon + PI } } } Alt = p / cos(Lat)  RCPV X = Lon * 180.0 / PI Y = Lat * 180.0 / PI Z = Alt  N Type: 3D (Zaware) 

Projective GeoTransformer 

Performs an projective transformation (preserves collinearity). X = (A * x + B * y + C) / (G * x + H * y + 1) It can be constructed from coefficients, or they can be computed from minimum four given control points that represent the matching (X,Y) pairs in both spaces.

Note: All the XADefs mentioned above (with details about each GeoTransformer's parameters) are located at: "[ArcGIS Image Server installation folder]\Developer Kit\GeoTransformers\XADefs"
An additional GeoTransformer wraps the ESRI projection engine in order to provide coordinates transformations from one Spatial Reference System to another. Called SRSTransformer, was implemented as an external module, loaded on demand by the Core component.
As the SRSTransformer, other custom GeoTransformer modules can be loaded by GeoTransCore component. When these existing transformations, even concatenated, cannot describe some other mathematical model required to georeference your custom Raster Types, you can implement a custom GeoTransformer that does. Basically, you will need to create a Dynamic Link Library (DLL) that implements custom GeoTransformers. For details, please see Implementing a custom GeoTransformer. Note that custom GeoTransformer modules are loaded on demand and for security reasons are reported in ArcGIS Image Server logs.