In order to perform a 3-D reconstruction using the created projection data set we need to define the world-coordinate system of our object space and the basic relationship between a point in world coordinates and a projection image.
World Coordinate System
The origin of our 3-D world-coordinate system is set to the C-arm iso-center, i.e. the center of rotation. The space unit is set to millimeter.
Projection Matrices
The geometry of the image acquisition needs to be defined. The data sets are based on a real-world C-arm calibration. The problem with real-world systems is, that the C-arm is wobbling and does not move exactly on a circular trajectory. Therefore for each projection image a projection matrix in homogenous coordinates is calibrated. The projection matrix of the i-th projection image, in the following denoted defines the perspective projection of a voxel in world coordinates and a pixel of the i-th projection image. It is given by:
The projection matrix encodes a lot of system variables, e.g. the pixel size, rotation, etc.
Here the 3x4 projection matrices which encode the perspective projection of a voxel in the world-coordinate system onto the i-th projection image can be downloaded: