Measurability of radiographic images

Projective distortion has been recognized since the first attempts were made to measure images on x-ray films. However, the nature of this distortion has not been thoroughly investigated by the dental profession. Part of the difficulty in addressing the problem is the necessity of the researcher's having knowledge and training in nonmetric mathematical thinking. To demonstrate the nonmetric nature of projective transformation, seven precision line gauges were made of glass tubes filled with steel balls 1/8 inch in diameter and were attached to a skull at various locations. Cephalometric x-ray films of the prepared skull with gauges in place were taken to simulate lateral and other views. The image lengths of the gauges were directly measured from the x-ray films. The results showed that the image length can be longer, shorter, or the same as the object gauge and cannot be predicted, corrected, or compensated for from the images alone. Linear projective transformation measured in this study ranged from 7.32 percent elongation to 69.63 percent foreshortening. Thus, it is illogical to measure radiographic images without restrictions. The basic limitation of measuring radiographic images on x-ray film is that the parallel relation must be established between the object line (or plane) and the image line (or plane). Technical restrictions should be established as a convention by those who have had the most experience in using radiographic measurements.