Bundle Adjustment with Known Positions

I studied Bundle Adjustment in the particular context of satellite vision, during a 3-months internship in 2017 (2 days per week from January to April, and full time in June) at CMLA (now Centre Borelli) of ÉNS Paris-Saclay.

Bundle Adjustment and satellite vision

Assume that you have a pair of images of the same scene, taken by the same satellite a few seconds apart. If you are able to identify matches between two points of these two images (which has been the case for many years, the SIFT algorithm being very efficient for this), you will be able, by triangulation techniques, to deduce the 3D relief of the scene, from the moment you know precisely the positions of the satellite and its orientation when the pictures are taken.

There are many applications for 3D mapping of pieces of the Earth’s surface: automation of the production of relief maps, rapid estimation of damage during natural disasters, military applications, etc.

However, this is a priori not possible. Indeed, devices measuring the positions and angles of the satellite camera give measurements up to some uncertainty. In the case of satellite images, the main problem is the error made on the angles, because a tiny measurement error leads to large deviations, due to the long distance between the camera and the scene (several hundred kilometers)!

Being able to find the exact shooting parameters is therefore essential if you want to do a 3D mapping of the scenes. In the literature this problem is called Bundle Adjustment. It is very poorly posed and almost impossible in a general context (we can manage to find plausible parameters, which allow an overall correct mapping, but we cannot find the real shooting parameters).

In the satellite framework, however, it is possible to assume known camera positions (precision being very important). With this simplification, the objective of the internship was to see if it is possible to find the real angular parameters of the shot. Being able to do this would not only make it possible to map pieces of the Earth’s surface in 3D, but also to atttach these maps together, and therefore to obtain a 3D map of the entire surface (which is impossible without the actual angular values)!