rejection of potentially wrong corrspondences

[hupo-jun]

Thank you for your work in simpleICP, I have used this method to register 3D point cloud in the given DataSet and the result is good. However, when it is used to register the 2D point cloud, this method can't get the right result. I have extended the 2D point (x, y) to 3D point (x, y, z) with z=0, but it still can't calculate the true planarity, which cause all selected correspondences is rejected in the condition (P_i = (ev2-ev3)/ev1 and P_i < min_planarity).
I want to know what is the definition of planarity when the dimension decrease to 2D, and what is the rejection criteria of planarity.