  Mapping with uncertainty representation is required in many research domains,
especially for localization. Although there are many investigations regarding
the uncertainty of the pose estimation of an ego-robot with map information,
the quality of the reference maps is often neglected. To avoid potential
problems caused by the errors of maps and a lack of uncertainty quantification,
an adequate uncertainty measure for the maps is required. In this letter,
uncertain building models with abstract map surfaces using Gaussian Processes
(GPs) are proposed to describe the map uncertainty in a probabilistic way. To
reduce the redundant computation for simple planar objects, extracted facets
from a Gaussian Mixture Model (GMM) are combined with an implicit GP map, also
employing local GP-block techniques. The proposed method is evaluated on LiDAR
point clouds of city buildings collected by a mobile mapping system. Compared
to the performance of other methods such as OctoMap, GP Occupancy Map (GPOM),
Bayesian Generalized Kernel OctoMap (BGKOctoMap), Local automatic relevance
determination Hilbert map (LARD-HM) and Gaussian Implicit Surface map (GPIS),
our method achieves a higher Precision-Recall AUC for the evaluated buildings.
