$\DeclareMathOperator{\arccosh}{arccosh} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator{\Exp}{Exp} \newcommand{\geo}[2]{\gamma_{\overset{\frown}{#1,#2}}} \newcommand{\geoS}{\gamma} \newcommand{\geoD}[2]{\gamma_} \newcommand{\geoL}[2]{\gamma(#2; #1)} \newcommand{\gradM}{\nabla_{\M}} \newcommand{\gradMComp}[1]{\nabla_{\M,#1}} \newcommand{\Grid}{\mathcal G} \DeclareMathOperator{\Log}{Log} \newcommand{\M}{\mathcal M} \newcommand{\N}{\mathcal N} \newcommand{\mat}[1]{\mathbf{#1}} \DeclareMathOperator{\prox}{prox} \newcommand{\PT}[3]{\mathrm{PT}_{#1\to#2}#3} \newcommand{\R}{\mathbb R} \newcommand{\SPD}[1]{\mathcal{P}(#1)} \DeclareMathOperator{\Tr}{Tr} \newcommand{\tT}{\mathrm{T}} \newcommand{\vect}[1]{\mathbf{#1}}$

# The mid point on a geodesic

The function returns a mid point of the two input points. Since the logarithm is deterministic and returns a unique value, this function is also deterministic, though the mid point might not be unique.

### Matlab Documentation

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% m = midPoint(x,z)
%   Compute the (geodesic) mid point of x and z.
%
% INPUT
%    x,z : two point(sets) of manifold points
%
% OUTPUT
%      m : resulting mid point( sets)
%
% ---
% Manifold-valued Image Restoration Toolbox 1.0
% R. Bergmann ~ 2014-10-19 | 2015-01-29