Object position and image magnification in dental panoramic radiography: a theoretical analysis

Abstract

Objectives: The purpose of our study was to investigate how image magnification and distortion in dental panoramic radiography are influenced by object size and position for a small round object such as a ball bearing used for calibration.

Methods: Two ball bearings (2.5 mm and 6 mm in diameter) were placed at approximately the same position between the teeth of a plastic skull and radiographed 21 times. The skull was replaced each time. Their images were measured by software using edge detection and ellipse-fitting algorithms. Using a standard definition of magnification, equations were derived to enable an object's magnification to be determined from its position and vice versa knowing the diameter and machine parameters.

Results: The average magnification of the 2.5 mm ball bearing was 1.292 (0.0445) horizontally and 1.257 (0.0067) vertically with a mean ratio of 1.028 (0.0322); standard deviations are in parentheses. The figures for the 6 mm ball bearing were 1.286 (0.0068), 1.255 (0.0018) and 1.025 (0.0061), respectively. Derived positions of each ball bearing from magnification were more consistent horizontally than vertically. There was less variation in either direction for the 6 mm ball bearing than the 2.5 mm one.

Conclusions: Automatic measurement of image size resulted in less variation in vertical magnification values than horizontal. There are only certain positions in the focal trough that achieve zero distortion. Object location can be determined from its diameter, measured magnification and machine parameters. The 6 mm diameter ball bearing is preferable to the 2.5 mm one for more reliable magnification measurement and position determination.

Figure 1

Projection geometry of a ball bearing in a panoramic radiograph. The plane containing the solid lines and circle (for image width) is perpendicular to that containing the dotted ones (for image height). The positions of the sharp layer (not depicted) should be somewhere close to a

Figure 2

Contours of horizontal and vertical magnification for a ball bearing of radius r = 3 mm. Solid lines, horizontal magnification; dashed lines, vertical magnification

Figure 3

Horizontal and vertical magnification plotted against the radius of a ball bearing for three different horizontal ball positions (395 mm, 400 mm and 405 mm)

Figure 4

Positions of the ball bearings (BB) (mm) derived from their measured vertical and horizontal magnifications. Circle, 6 mm diameter ball bearing; dot, 2.5 mm diameter ball bearing

Figure 5

Simulation results of calculated positions for ball bearings (BBs) hypothetically placed at the same position, whose image measurements were subject to random error