I am posting this question in order to gain a better understand of what the Fréchet mean is for a generalised shape space.
So firstly I gather that the Fréchet mean of a probabilty measure $\mu$ on a general metric space $(M,dist)$ is a generalisation of the mean or the expectation of a probability distribution on a Euclidean space and is defined as any global minimum of the function $$F(x)=\int_Mdist(x,y)^2d\mu(y).$$ This concept can be further generalised by replacing 'dist' in the integrand by a suitable function of the distance.
My question is, what exactly does this formula do? I think it has something to do with minimising the mean between a data set, however I am not sure of this. Also I am not sure how I would use this formula. What exactly is the 'probability measure' in this case? I think it's some kind of statistical distribution, but again I am really not sure.
Any help with this question will be much appreiciated, thank you.