Accuracy of Scaling and DLT Reconstruction Techniques for Planar Motion Analyses

Abstract

Numerous planar analyses of sports activities have utilized scaling techniques to convert image coordinates into real-space locations. While in certain circumstances, such as competition, the camera must be elevated above the activity and its tilt accounted for, the influence of tilt on reconstruction accuracy using scaling is currently unreported. A modification of the direct linear transformation (2D-DLT) which considers only the vertical plane provides an alternative approach for planar reconstruction. This study compared the reconstruction accuracy between scaling and 2D-DLT over a range of tilt angles throughout a 6-m horizontal field of view. Four calibration and 30 reconstruction markers of known locations in a vertical plane were videotaped from nine positions to provide tilt angles varying between –2° and +6°. Both techniques were used to estimate real-space locations for the reconstruction markers, and accuracy was calculated by comparing known and reconstructed locations. The smallest reconstruction errors were obtained using 2D-DLT and were unaffected by camera tilt. The scaling technique produced significantly larger (p < 0.01) errors than 2D-DLT, with the exception of 0° and +1° of tilt, and there was a detrimental effect on accuracy as the magnitude of tilt increased. The largest variations in reconstruction errors were associated with scaling, with markers at the extremes of the image showing the largest errors. The 2D-DLT approach provided accurate reconstruction data for planar analyses across the field of view and throughout the range of tilt angles, and should be preferred over scaling techniques.