As is well known in photogrammetry, the 2D projective transformation can be written as a linear relationship in terms of its 8 parameters. Now the question is
Is there is any impact of the linear formulation of the 2D projective transformation on the accuracy of its estimated/computed parameters?
interesting question! I don't know if there's been any research on this, but I can imagine that the linear formulation is more accurate. The nonlinear formulation will require an iterative solution, the accuracy of which will be dependent on the number of iterations and the threshold for stopping the iterations. But the linear formulation has a direct solution, which means the estimates will be accurate up to the machine round-off error.
However, this is my guesswork for exact observations. In reality the observations are noisy and the solutions will behave differently in presence of noise. You should do some experiments and write a paper on this, so we know the correct answer!
Dear Kourosh:
Thank you very much for your interesting feedback. I will investigate this issue in an experiment.
Regards,
Gamal
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