Direct Linear Transformation Method for Three-Dimensional Cinematography

Abstract

This study evaluated the “direct linear transformation” method developed by Abdel-Aziz and Karara (1971) for use with high-speed cine techniques. Two high-speed cameras were used to film a series of points with known spatial coordinates. From knowledge of these “control” points, the parameters representing interior and exterior orientations were determined. The spatial coordinates of unknown points were then calculated. Position data were very accurate. The mean deviations of computed coordinates from the actual coordinates were .4 cm in the vertical direction (Z), .4 cm in the horizontal direction (X), and .5 cm in the horizontal direction (Y). Displacement-time data in the X, Y, and Z directions for the dynamic test were as expected. The calculated vertical accelerations of a ball during free flight were within 1% to 4% of the value of g (−9.8 m/sec²). It was concluded that the photogrammetric method is applicable to cinematographic techniques. Additionally, the flexibility of this technique appeared to be superior to any of the existing three-dimensional cinematographic methods.