International audienceSurveying techniques such as terrestrial laser scanner have recently been used to measure surface changes via 3D point cloud (PC) comparison. Two types of approaches have been pursued: 3D tracking of homologous parts of the surface to compute a displacement field, and distance calculation between two point clouds when homologous parts cannot be defined. This study deals with the second approach, typical of natural surfaces altered by erosion, sedimentation or vegetation between surveys. Current comparison methods are based on a closest point distance or require at least one of the PC to be meshed with severe limitations when surfaces present roughness elements at all scales. To solve these issues, we introduce a new algorithm performing a direct comparison of point clouds in 3D. The method has two steps: (1) surface normal estimation and orientation in 3D at a scale consistent with the local surface roughness; (2) measurement of the mean surface change along the normal direction with explicit calculation of a local confidence interval. Comparison with existing methods demonstrates the higher accuracy of our approach, as well as an easier workflow due to the absence of surface meshing or Digital Elevation Model (DEM) generation. Application of the method in a rapidly eroding, meandering bedrock river (Rangitikei River canyon) illustrates its ability to handle 3D differences in complex situations (flat and vertical surfaces on the same scene), to reduce uncertainty related to point cloud roughness by local averaging and to generate 3D maps of uncertainty levels. We also demonstrate that for high precision survey scanners, the total error budget on change detection is dominated by the point clouds registration error and the surface roughness. Combined with mm-range local georeferencing of the point clouds, levels of detection down to 6 mm (defined at 95% confidence) can be routinely attained in situ over ranges of 50 m. We provide evidence for the self-affine behaviour of different surfaces. We show how this impacts the calculation of normal vectors and demonstrate the scaling behaviour of the level of change detection. The algorithm has been implemented in a freely available open source software package. It operates in complex 3D cases and can also be used as a simpler and more robust alternative to DEM differencing for the 2D cases. 2013 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS

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Abstract. Symbolic model checking provides partially effective verification procedures that can handle systems with an infinite state space. So-called "acceleration techniques" enhance the convergence of fixpoint computations by computing the transitive closure of some transitions. In this paper we develop a new framework for symbolic model checking with accelerations. We also propose and analyze new symbolic algorithms using accelerations to compute reachability sets.