Geometric distortion of historical images for 3D visualisation

Archivists, historians and national mapping agencies, among others, are archiving large datasets of historical photographs. Nevertheless, the capturing devices used to acquire these images possessed a diversity of effects that influenced the quality of the final resulting picture, e.g. geometric distortion, chromatic aberration, depth of field variation, etc. This paper examines singularly the topic of geometric distortion for a co-visualization of historical photos within a 3D model of the photographed scene. A distortion function of an image is ordinarily estimated only on the image domain by adjusting its parameters to observations of point correspondences. This mathematical function may exhibit overfits, oscillations or may not be well defined outside of this domain. The contribution of this work is the description of a distortion model defined on the whole undistorted image plane. We extrapolate the distortion estimated only on the image domain and then transfer this distortion information to the view of the 3D scene. This enables to look at the scene through an estimated camera and zoom out to see the context around the original photograph with a well-defined and behaved distortion. These findings may be a significant addition to the overall purpose of creating innovative ways to examine and visualize old photographs.