How do we reconstruct 3D information?

The unknown arbitray geometry the radiographs were acquired in is computed from image analysis using the projections of the reference spheres as only input information. Based on this information, the radiographs can be arranged in a coordinate system and from backprojection 3D information can be obtained.

Note the position of the three reference spheres colored for illustration purposes. They indicate the position of the object they are attached to.

Traditional three-dimensional (3D) radiographic techniques such as computed tomography (CT) use sophisticated hardware to produce 3D images. Essentially, 3D structure of an object is recovered from a large number of measurments (radiographs) taken from all around the object. For this purpose, the data processing unit rquires the complete information on the underlying imaging geometry, i.e. the spatial position of x-ray-source, object and image receptor for each and every single radiograph. By means of filtered backprojection the 3D structure of the object is reconstructed.

We introduce a new method RSM3D, where normal x-ray equipment is used for exposure of several radiographs of a given object. The radiographs may be exposed completely arbitrarily, i.e. the spatial orientation of x-ray source, object and image-receptor may be chosen arbitrarily. By means of a specific reference-based algorithm (RSM), we register the radiographs into a single coordinate system. Basing on this fundamental information, we subsequently reconstruct 3D structure from normal, two-dimensional radiographs.

What exactly are the technical requirements for the RSM-reconstructions?