Don't forget that the centroid can lie outside of the object itself.

Don't forget that the centroid can lie outside of the object itself.

Sorry was my mistake.

I read that the centroid is the same no matter how the points distribution is.

I really want to know if the centroid is the same if a shape is represented by its region function or if a shape is represented by its contour.

I do not use the term 'region function'. Can you define it? Is it an analytical function that determines the object outline?

Yes of course, region function:

f(x,y) = { 1 if (x,y) belongs to D

               0 otherwise  }

where D is the domain of a binary shape.

In that case Remi is correct, within a small error. The image is discrete and so there will be a small difference between using all of the pixels and only those in the outline.

I disagree with James and Remi; you need to take all the pixels/voxels of the object into account in order to compute the centroid.

This polyp for example has a lot of surface at the tentacles, that would shift the centroid too much upward if only contour pixels are used.

It's some (but not all) times the same, here is an example of the centroid for an object and its boundary, you can see that the values of Y are shifted a little bit.

It is very unlikely that those centroids are the same. There is also something wrong with your computation. It should be around here:

you are totally right, here is the correct centroid.