  Surveying 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. We
introduce 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 local
surface roughness. The measurement of the mean change along the normal
direction is then performed with an explicit calculation of a 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 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. Combined with mm-range
local georeferencing of the point clouds, levels of detection down to 6 mm can
be routinely attained in situ over ranges of 50 m. We provide evidence for the
self-affine behavior of different surfaces. We show how this impacts the
calculation of normal vectors and demonstrate the scaling behavior of the level
of change detection.
