[Insight-users] root mean square error

[Kevin H. Hobbs]

On Sat, 2009-08-29 at 15:37 +0200, Boettcher, Dr. Peter wrote:
> Dear all
> 
>  
> 
> As a measure of fit of two 3D surfaces I calculate the absolute
> distance from each point of surface1 to the closes point on surface2
> like we would using a ICP algorithm. Finally I calculate the mean of
> those distances. 
> 
>  
> 
>      1. The term Euclidian distance which appears in the literature is
>         not clear to me. What is the difference to distance between
>         two points in 3D space or is it just a question of
>         terminology?

Euclidean distance is just the distance between the 3D points as
calculated by the square root of the sum of the squared differences of
point positions in each dimemsion.

There are however many other types of distance.

>      1. The metric I calculate doesn’t seem to be different to what is
>         called root mean square error – or am I wrong? In case I am
>         wrong what would you call the metric I described? What would
>         be the difference performing registration with this metric and
>         RMSE unsing non corresponding point sets?

Practically, there would be no difference. RMSE just isn't a very good
name for what you are doing. If I were trying to think of a good name
for what you are doing to use for example as a function name, then I'd
call it the mean of shortest distances.

Are you using a point locator or a kd tree to find the nearest point?
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