Mobile Mapping is an efficient technology to acquire spatial data of the environment.The spatial data is fundamental for applications in crisis management, civil engineering orautonomous driving. The extrinsic calibration of the Mobile Mapping System is a decisive factorthat affects the quality of the spatial data. Many existing extrinsic calibration approaches requirethe use of artificial targets in a time-consuming calibration procedure. Moreover, they are usuallydesigned for a specific combination of sensors and are, thus, not universally applicable. We introducea novel extrinsic self-calibration algorithm, which is fully automatic and completely data-driven.The fundamental assumption of the self-calibration is that the calibration parameters are estimatedthe best when the derived point cloud represents the real physical circumstances the best. The costfunction we use to evaluate this is based on geometric features which rely on the 3D structure tensorderived from the local neighborhood of each point. We compare different cost functions based ongeometric features and a cost function based on the Rényi quadratic entropy to evaluate the suitabilityfor the self-calibration. Furthermore, we perform tests of the self-calibration on synthetic and twodifferent real datasets. The real datasets differ in terms of the environment, the scale and the utilizedsensors. We show that the self-calibration is able to extrinsically calibrate Mobile Mapping Systemswith different combinations of mapping and pose estimation sensors such as a 2D laser scannerto a Motion Capture System and a 3D laser scanner to a stereo camera and ORB-SLAM2. For thefirst dataset, the parameters estimated by our self-calibration lead to a more accurate point cloud thantwo comparative approaches. For the second dataset, which has been acquired via a vehicle-basedmobile mapping, our self-calibration achieves comparable results to a manually refined referencecalibration, while it is universally applicable and fully automated.