Projective geometric model for automatic determination of X-ray-emitting source of a standard radiographic system

Currently, many orthopedic operations are planned by analyzing X-rays. The exact position of the focus is needed to calculate the real size of an object that is represented in conical projection, although in practice, this position is difficult to determine using current X-ray commercial systems. In this paper, a new geometric model is proposed in order to determine accurately, practically, and economically the location of the emitting source of commercial imaging systems using a single standard X-ray image.

The method requires a specific reference locator object to be positioned in the visual field of radiographic image. Because this object cannot implement ideal geometric points, but instead works with small spheres, it was necessary to experimentally validate the proposed methodology. The implemented software that was developed to validate the model was used in four series of tests. In these tests, we studied the influence on the final result of: 1. the selection of a specific set of markers in radiography, 2. the focus position variation in relation to radiograph and 3. the possible rotated angle of locator object about Z axis.

The results for 164 tests that were performed with this software showed that the expected error for 99.5% of values ranges with maximum error of [-0.35%, +0.39%], which shows that the model is independent of the design of locator object and its position and orientation in the radiographic field. The software used to validate the proposed model has been found useful to verify its reliability, effectiveness, ease of implementation, and accuracy.

This model is effective to calculate the precise position of the X-ray focus of any standard radiographic system accurately.