A new method for three-dimensional object space reconstruction from optically or opto-electronically recorded images and extensive experience with its practical implementation is reported. The new method improves the reconstruction accuracy by an order of magnitude when compared with conventional techniques. It is based on a fundamental modification of the Direct Linear Transformation (DLT) technique of Marzan and Karara. In the latter technique, certain orthogonality conditions are violated due to the presence of a redundant DLT parameter. The elimination of this parameter by means of a non-linear constraint, the additional elimination of certain implicit variables from one side of the non-linear DLT formulation, and the simultaneous redefinition of the corresponding objective function to be minimized permits the development of new algorithms whose practical application results in a dramatic improvement in reconstruction accuracy. The highest accuracy obtained was 0.035 %, or one part in 2860 (0.733 mm rms mean error). Such super-high precision in essential if, for instance, high-quality first and second time derivatives are to be computed from time sequences of reconstructed spatial points.
Herbert Hatze, Herbert Hatze,
"A New Method For Super-High-Precision 3-D Object Space Reconstruction From Recorded Images", Proc. SPIE 1135, Image Processing III, (11 October 1989); doi: 10.1117/12.961650; https://doi.org/10.1117/12.961650