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Surveying techniques such as Terrestrial Laser Scanner have recently beenused to measure surface changes via 3D point cloud (PC) comparison. Two typesof approaches have been pursued: 3D tracking of homologous parts of the surfaceto compute a displacement field, and distance calculation between two pointclouds when homologous parts cannot be defined. This study deals with thesecond approach, typical of natural surfaces altered by erosion, sedimentationor vegetation between surveys. Current comparison methods are based on aclosest point distance or require at least one of the PC to be meshed withsevere limitations when surfaces present roughness elements at all scales. Weintroduce a new algorithm performing a direct comparison of point clouds in 3D.Surface normals are first estimated in 3D at a scale consistent with the localsurface roughness. The measurement of the mean change along the normaldirection is then performed with an explicit calculation of a confidenceinterval. Comparison with existing methods demonstrates the higher accuracy ofour approach, as well as an easier workflow due to the absence of surfacemeshing or DEM generation. Application of the method in a rapidly erodingmeandering bedrock river (Rangitikei river canyon) illustrates its ability tohandle 3D differences in complex situations (flat and vertical surfaces on thesame scene), to reduce uncertainty related to point cloud roughness by localaveraging and to generate 3D maps of uncertainty levels. Combined with mm-rangelocal georeferencing of the point clouds, levels of detection down to 6 mm canbe routinely attained in situ over ranges of 50 m. We provide evidence for theself-affine behavior of different surfaces. We show how this impacts thecalculation of normal vectors and demonstrate the scaling behavior of the levelof change detection.

Accurate 3D comparison of complex topography with terrestrial laser scanner: application to the Rangitikei canyon (N-Z)