Understanding the computation of the Karcher median

[glegarda]

Hello,

I am trying to understand how the Karcher median is calculated in the alignment of a collection of functions. I went over the implementation of the srsf_align() function, but I'm not sure I understand where the steps taken here are coming from:

# Minimization Step
# compute the mean of the matched function
stp = 0.3
vbar = vtil.sum(axis=1) * (1 / dtil.sum())
qtemp = q[:, :, r + 1]
ftemp = f[:, :, r + 1]
mq[:, r + 1] = mq[:, r] + stp * vbar

Could you share some references that would help me get a better understanding of this bit?

Thanks!

[jdtuck]

Please look at the Srivastava and Klassen's book from 2016 entitled Functional and Shape Data Analysis.