ABSTRACT
In this chapter, the authors illustrate this procedure by applying it to maximum likelihood estimation of rotation and computation of the “fundamental matrix,” which plays a central role in 3D reconstruction by computer vision. They also apply it to a 3D reconstruction scheme called “bundle adjustment.” The “Lie algebra” is a linear space generated by infinitesimal rotations around coordinate axes. To explain this, they show the relationship between small rotations and angular velocities. In usual numerical iterations, the variables are successively updated until they no longer change. However, the number of unknowns for bundle adjustment is thousands or even tens of thousands, so an impractically long computation time would be necessary if all variables were required to converge over significant digits.
