Using recursive spectral registrations to determine brokenness as measure of structural map errors

There are many common error sources that influence mapping, e.g., salt and pepper noise as well as other effects occurring quite uniformly distributed over the map. On the other hand, there are also errors, which occur very rarely but with severe effects. These errors influence not only the local accuracy but the overall spatial layout of the map. Concrete examples include bump noise in the robot´s pose or residual errors in Simultaneous Localization and Mapping (SLAM). Brokenness is presented here to capture one form of structural errors in grid maps. Concretely, brokenness measures the degree with which a map can be partitioned into regions that are locally consistent with ground truth but “off” relative to each other. The concept of brokenness is presented in a formal way and it is shown how it can be computed in an efficient way using recursive spectral registrations. Experimental results show that the metric can indeed be used to automatically determine one structural quality aspect of a map in a quantitative way.