3
votes
0answers
38 views

Optimization of Möbius transformation

Say I have a family of points $(w_i, z_i)$ for $i=1,2,...,n$, and I wish to find $a,b,c,d$ such that $\sum_i \left|\frac{a z_i -b}{c z_i - d} - w_i \right|^2 $ is minimized. I realize there are things ...
3
votes
2answers
403 views

Jacobian of Reprojection Error

I am writing a program to find the transformation between two sets of 3D points extracted from a moving stereo camera. I am using an 'out of the box' Levenberg-Marquardt implementation to find this ...
3
votes
1answer
101 views

Fraction of SO(3) within an angle

SO(3) describes a space of rotations. These rotations can be described in axis-angle representation. I would like to know what fraction of SO(3) has an angle less than 30 degrees.
2
votes
1answer
419 views

Derivative of function including matrix logarithm

Is the following equation a first order approximation or incorrect for general matrix Lie groups? And what are the higher order terms? $$\frac{\partial}{\partial\mathbf x} (\log(\mathtt ...