vtkCellPicker picks invisible cells when backface culling is on

I have a mesh of a cave captured from inside, so the front faces of the triangles are inside the cave.

To be able to see the cave well, I hide the back faces of the mesh, so that we can see the inside of the cave even when the camera is outside. This works well.

However, when I want to pick a point in the cave while the camera is outside, the vtkCellPicker always hits the hidden back face of the first wall, instead of picking what is shown under the mouse, i.e. the visible opposite wall.

Is there any way to avoid picking those triangles that are culled ?
What should I change to achieve this ?

Thank you !