Uncertainty of monoplotted features from historical single oblique images

Historical images are an important resource for documenting the early states of our environment after the last little ice age. To extract a feature (e.g. glacier outline) from a single historical oblique image in a global coordinate system monoplotting is commonly used: Rays originating from the projection center passing through the pixel vertices, which represent the considered feature, in the image are intersected with a reference terrain model. A subsequent spatial analysis not only requires the 3D position of these vertices as result of monoplotting but also their positional accuracy. The derivation of the latter has not been properly addressed so far.

Existing approaches for assessing the monoplotting accuracy are either based on i) reference data or ii) selected ground control points (GCPs). The first approach is generally not suitable for historical images as reference data is mostly not available. Evaluation based on GCPs is only a rough measure for the potentially achievable accuracy as the monoplotting accuracy varies strongly within an image and the number of GCPs is usually limited. 

Hence, we propose a new approach based on variance propagation. Formulating the monoplotting principle using projective geometry both the accuracy of the estimated camera parameters as well as the reference terrain are considered within the estimation of the uncertainty for the 3D position of each vertex. Estimating the uncertainty for each vertex of the monoplotted feature further allows to derive a differentiated analysis of the results. Furthermore, being independent from necessary reference data our approach is well suited for historical images. Hence, with the developed approach it becomes possible to consider the uncertainty of monoplotted features in subsequent spatial analyses which is especially important when comparing these features with modern reference datasets; e.g. in order to judge the significance of possible changes or deformations.