Nonlinear optimization

Finally, using the linear estimates of $ R$ , $ T$ and $ f$ as a starting point one can solve for all the parameters, including the radial lens distortion parameter $ k$ which was initialized to 0, by minimizing the image distance

$\displaystyle \sum_{i=1}^N (x_i - x^p_i)^2 + \sum_{i=1}^N (y_i - y^p_i)^2

where $ (x_i,y_i)$ are the observed image points and $ (x^p_i,y^p_i)$ are the positions predicted by the Tsai model. The nonlinear optimization (over all the parameters) can be carried out by an iterative numerical technique like the Levenberg-Marquardt method.

Subhashis Banerjee 2008-01-20