A Method for Error Analysis and Orientation Statistics of Best-Fitting Planes from Remote-Sensing Data

PLANES FROM REMOTE-SENSING DATA D.P. Quinn1 and B.L. Ehlmann1,2 Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California, USA (davenquinn@caltech.edu), Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA. The orientations of planar rock layers are fundamental to our understanding of structural geology and stratigraphy. Bedding orientation measurements are conducted in-situ at sub-meter scale, using a compass clinometer. High-resolution elevation models open the possibility of assessing bedding attitudes from aerial and orbital data. Remotely-gathered bedding orientations underpin foundational studies of sedimentary [6, 4] and structural [5] processes on early Mars. With the advent of unmanned aerial vehicles (UAVs) and photogrammetric structure-from-motion terrain models, this technique is increasingly used in Earth science as well [e.g. 7]. The planar orientation of a 3D point cloud is found using linear optimization techniques such as regression and principal-component analysis. These minimization algorithms excel at the delivery of nominal fits but do not provide means of assessing the uniqueness or statistical quality of orientations. Dataset noise, measurement uncertainties, and the geometry of the input point cloud contribute to total errors in planar orientations. In the pathological case shown in Figure 2, an exposure of bedding on a planar hillslope has large errors along one axis of the plane. We propose a method to assess the quality of planar fits and visualize their error distributions, in order to support high-precision structural analysis of bedding. A new statistical method: The statistical method developed in this project is based on principalcomponent analysis (PCA), which has been used for planar fitting in paleomagnetism [3, 2] and robotics [8]. Error is minimized orthogonal to the fitted line, removing the implicit null assumption of horizontality inherent in linear least-squares fitting. Error sensitivity can be rescaled independently on any axis of the input dataset. This allows the incorporation of horizontal errors (e.g. photogrammetric imageregistration error), which are especially important for data collected at high incidence angles, such as UAV imagery from alongside a cliff face.