TY - JOUR

T1 - Determination of three-dimensional positions of known sparse objects from a single projection

AU - Hoffmann, Kenneth R.

AU - Esthappan, Jacqueline

PY - 1997/4

Y1 - 1997/4

N2 - A new technique is developed for accurate determination of the three- dimensional position and orientation of known sparse objects, e.g., a configuration of points, from a single-perspective projection. In this technique, a computer model of the known object is translated and rotated so as to align it optimally in a least-squares sense with the projection lines connecting the image points with the focal spot by using a modification of the projection-Procrustes technique. The translational and rotational adjustments are repeated iteratively until the angular change between iterations is less than 0.25°. Simulations indicate that, for rms input image errors of 0.03 cm, the three-dimensional positions and orientations can be determined to within approximately 0.2 cm and 0.3°for a wide range of initially guessed positions and orientations, and positions can be determined with an accuracy of approximately 0.3 cm for objects having as few as four points. In phantom experiments, three-dimensional positions and orientations of a cube phantom were reproducibly determined to within 0.23 cm and 0.13°. The entire calculation requires only 10 s on a VAX 3500 to converge to the solution. The accuracy, precision, and speed of the technique indicate that it will be a useful tool for determination of three- dimensional positions and orientations of known sparse objects.

AB - A new technique is developed for accurate determination of the three- dimensional position and orientation of known sparse objects, e.g., a configuration of points, from a single-perspective projection. In this technique, a computer model of the known object is translated and rotated so as to align it optimally in a least-squares sense with the projection lines connecting the image points with the focal spot by using a modification of the projection-Procrustes technique. The translational and rotational adjustments are repeated iteratively until the angular change between iterations is less than 0.25°. Simulations indicate that, for rms input image errors of 0.03 cm, the three-dimensional positions and orientations can be determined to within approximately 0.2 cm and 0.3°for a wide range of initially guessed positions and orientations, and positions can be determined with an accuracy of approximately 0.3 cm for objects having as few as four points. In phantom experiments, three-dimensional positions and orientations of a cube phantom were reproducibly determined to within 0.23 cm and 0.13°. The entire calculation requires only 10 s on a VAX 3500 to converge to the solution. The accuracy, precision, and speed of the technique indicate that it will be a useful tool for determination of three- dimensional positions and orientations of known sparse objects.

UR - http://www.scopus.com/inward/record.url?scp=0030998759&partnerID=8YFLogxK

U2 - 10.1118/1.597938

DO - 10.1118/1.597938

M3 - Article

C2 - 9127308

AN - SCOPUS:0030998759

SN - 0094-2405

VL - 24

SP - 555

EP - 564

JO - Medical physics

JF - Medical physics

IS - 4

ER -