Three-dimensional x-ray stereometry from paired coplanar images: A progress report

Geometry of coplanar stereoscopic radiographic pairs for analysis of the lateral cervical radiograph: a study using mathematical models

“…The z-axis represents the central ray and extends away from the midway point at "S" (base of triangle in film plane) toward the radiograph source. "H," the focal film distance or altitude, is defined as the distance along the central ray between the focal spot and the film plane [28][29][30][31] (Fig 3). To calculate the coordinate of a point, designated as any point "P," 4 geometric formulas are derived through the use of the law of similar triangles (triangles are similar if their corresponding angles are congruent [equal] and/or the ratio of their corresponding sides is proportional).…”

“…To calculate the coordinate of a point, designated as any point "P," 4 geometric formulas are derived through the use of the law of similar triangles (triangles are similar if their corresponding angles are congruent [equal] and/or the ratio of their corresponding sides is proportional). 30,31 In addition, the ratio of the base to altitude between similar triangles is also equal. Calculation of coordinate values requires that equation 1 (below) be solved first System parameters.…”

“…Because a 2-generator stationary radiograph system is not used in this study and the spatial relationship between the radiograph tube positions and the film surface is not known before the images are generated, it is necessary to do a calibration at the time the radiographic images are exposed. 30,31 Equation 4, which is also derived from the "Law of Similar Triangles," is solved by taking the data obtained from measurements from radiographic images created by the 4 calibration rods. That data are used to calculate the focal spot to film distance "H" (Fig 4).…”

“…26,27 Small differences between the images are what produce a final 3D image that may be viewed by using various binocular stereoscopic visual techniques. 7,8 However, according to Baumrind et al, [28][29][30][31] information taken from coplanar radiographs may be measured directly from the radiographs provided the following conditions are met: (1) the distances between the 2 radiograph source positions are known (L1 to L2 "base"), (2) the distance from the radiograph source to the film plane is known ("H" altitude), and (3) the 2 views contain the same point of interest ("P") ( Fig 2). The mathematics of making 3D measurements from paired coplanar radiographic images is not mysterious and only requires basic mathematical ability.…”

A three-dimensional photographic method for documentation and measurement of dental conditions

“…By utilizing this technique 3-D photographs may serve documentation purposes. Measurements with high precision and accuracy may be performed using stererophotograrmnetry [1,[3][4][5]. This is also true of different 3-D techniques such as holography [12] and reflex metrography [13].…”