title: Object position and image magnification in dental panoramic radiography: a theoretical analysis.
abstract: OBJECTIVE
  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.
authors.affiliation: School of Dentistry, University of Manchester, Manchester, UK. Hugh.Devlin@manchester.ac.uk
authors.forename: H
authors.initials: H
authors.lastname: Devlin
authors.forename: J
authors.initials: J
authors.lastname: Yuan
mesh_terms: D000465:Algorithms; D006801:Humans; D010469:Perceptual Distortion; D011858:Radiographic Magnification; D011862:Radiography, Panoramic; D012886:Skull / Q000000981:diagnostic imaging