# Occupancy octree metrics (Kullback-Leibler)

As I'm currently working on scan matching for outdoor environments I was wondering about the best metric to compare two occupancy octrees (one resulted from the scan matching and one ground truth reference octree). So far I came up with a few different approaches:

Ignoring the occupancy values:

• Calculate the true positives, false positives and false negatives in order to get the recall and precision rate

• Hausdorff distance (prone to outliers)

• Average Hausdorff distance

Using the occupancy values of the octree nodes:

• Kullback-Leibler divergence (Zero probability might be a problem)

The problem arises if there is a node in the reference octree and corresponding node of the matching octree is not occupied (= zero probability). Is there a way to deal with that problem? Additionaly, as far as I know the KLD is only calculated in one direction. That means falsely occupied nodes in the matching octree are not considered.

What is the best way to compare two occupancy octrees? Any comment or suggestion is really appreciated.