Thank you for your answer. I see, I found that out yesterday after accidentally stumbling over a post in this forum.
In my opinion this should be clarified in the documentation. From what is written there one has to come to the conclusion that the texture is responsible for the collision detection, when actually it is a mesh. I now mapped the texture to the plane and did cut the red areas from the mesh, using that as the collision indicator and that worked.
Maybe it would be better for workflow and understanding if the mesh is assigned to the collision parameter instead of the texture? Or are there technical reasons for using the texture instead?
I will download the First Person demo and have a look at it. Thanks again.