SPATIAL UNCERTAINTY IN LINE-SURFACE INTERSECTIONS WITH APPLICATIONS TO PHOTOGRAMMETRY

Abstract. The fields of photogrammetry and computer vision routinely use line-surface intersections to determine the point where a line intersects with a surface. The object coordinates of the intersection point can be found using standard geometric and numeric algorithms, however expressing the spatial uncertainty at the intersection point may be challenging, especially when the surface morphology is complex. This paper describes an empirical method to characterize the unknown spatial uncertainty at the intersection point by propagating random errors in the stochastic model using repeated random sampling methods. These methods accommodate complex surface morphology and nonlinearities in the functional model, however the penalty is the resulting probability density function associated with the intersection point may be non-Gaussian in nature. A formal hypothesis test is presented to show that straightforward statistical inference tools are available whether the data is Gaussian or not. The hypothesis test determines whether the computed intersection point is consistent with an externally-derived known truth point. A numerical example demonstrates the approach in a photogrammetric setting with a single frame image and a gridded terrain elevation model. The results show that uncertainties produced by the proposed empirical method are intuitive and can be assessed with conventional methods found in textbook hypothesis testing.