Outline of the linear algorithms

The linear algorithms described above can be outlined as follows:

• Preprocessing of the data: compute the inter-point distances and the cosines of the angular separations using the image points and calibration matrix of the camera.
• Solve for the depths of the reference points: from the 4th degree polynomial equations of form , form the matrix , then use SVD to solve linearly either in two steps for 4 points or in one step for 5 or more points. The square of the depth x is obtained from Equation (6), then the depth is set to .

• Absolute orientation: the recovered depths of the reference points are converted into a camera rotation and translation using the absolute orientation method briefly described in 2.

The experimental results of these linear algorithms have been reported in [5].