Minimization improvement

[sflotron]

[Added] Numerical Differentiation of order 5 for gradient computation
[Added] Use now backtracking and Conjugated gradient for minimization
[Added] gitignore file
[Modified] Use 6 points instead of 8 for relative pose estimations
[Modified] Use cayley2_rot instead of cayley2_rot_reduced in ge::composeWithJacobian
[Modified] Error function for relative pose is now max(1-f1.b1,1-f2.d2) (previous was 1-f1.b1+1-f2.d2)

Comparison results (with same error function for both code and averaging over 1000 trials). Trends

• increasing the number of iteration with the proposed minimization procedure leads to a better precision
• decreasing the tolerance yields to better accuracy with the minimization procedure I proposed, but it takes more times to evaluate the model.
• doing at most 50 iterations for minimization and using a stopping value of 1.0e-5 for the increment of descent method yields almost the same precision between yours and my minimization.
• in your version, decreasing the stopping tolerance for descent does not seem to improve the accuracy of the estimated model
• in your version, increasing the number of iteration of the minimization seems to slightly improve the quality of the estimated model. Nevertheless, the precision is still of the same order of magnitude.
  • with more iterations and a smaller threshold for the stopping criterion, the precision on rotation could me improved with my minimization. Actually, accuracy is improved by a factor 4 on the rotation and a factor 2 on translation.
  • there is still a lot of tests to do to ensure the above conclusions.

Do not hesitate to contact me by e-mail if you have any further questions.