## Coordinate Systems

SURE expects a cartesian coordinate system in order to perform best.

You can work with projected coordinate systems as well - see the article on Earth Curvature on details.

In order to pass a coordinate system for SURE to be stored in the output such as gtif, las, Cesium please use the WKT string interface.

In general, SURE does at this point not apply transformations, but will maintain the system of the orientation. Exceptions exist for output formats that require a specific coordinate system, e.g. Cesium or slpk. To be able to use this functionality, the project must use a coordinate system for which transformations are supported. To make it possible to generate these output formats for other coordinate systems as well, SURE supports for example the height shift option.

## Camera Coordinate System

Assume an object point X (4x1 homogenous coordinates) is mapped to the image coordinates x (3x1 homogenous coordinates) by multiplication of the projection matrix P (3x4):

x = PX

The matrix P is composed of the rotation matrix (3x3), the translation t vector (3x1) and the camera matrix (3x3). The matrix P (3x4) is shaped as follows

P = K[R|t].

Thereby the translation is t = -RC. C (3x1) represents the coordinates of projective center of the camera with respect to the object COS. The z-axis of the camera is oriented in viewing direction. \$ExtOri_RotationMatrix R \$ExtOri_TranslationVector C

## Image Coordinate System

Let X_cam = [R|t]X be the coordinates of an object point in the cam system. X_cam(3x1) can be mapped to homogenous image coordinates using the camera matrix K

x = KX_cam.

K is shaped as follows: Thereby f_x, f_y represent focal lengths in pixels. Parameters c_x, c_y represent the offsets to the principle point in terms of pixel dimensions. The parameter s_x specifies the skew parameter. In the image COS (0,0) corresponds to the center of the upper left pixel. ##### Image coordinate system
 \$IntOri_CameraMatrix K \$IntOri_SensorSize Image width, Image height in pixels \$IntOri_PixelSize Pixel size in mm, if not known specify with 1.0 (not used by the algorithm) \$IntOri_FocalLength Focal length in mm, if not known or f_x, f_y vary specify wit 1.0 (not used by the algorithm)