DEM/DSM usage in BA

[Jakob Kirkegaard]

Hi, 

I have a number of aerial images obtained with very little overlap (solid correspondences can be obtained though) and a GPS/INS position/orientation for each camera observation. I do not have any ground points with known GPS coords.

Previously discussed here https://groups.google.com/d/msg/ceres-solver/su9xLTKCl9A/kcl-xQzEBAAJ

For simplicity, say I have a 3x3 grid of images with ~5% overlap at each border. I find the correspondences for each pair, estimate the initial 3D position for each tie point (using DEM). Then I fix the pose of the center camera, and optimize the poses (6 DOF) for the remaining 8 in ECEF. 

In the current setup I have 3 cost functions.

a) Re-projection error relating a camera position, camera orientation and 3D point to an image observation.

b) Difference between actual and initial GPS position for each camera (in absoulte ECEF)

c) Difference between actual and initial position (e.g. altitude) for each 3D tie point on the ground.

I am struggling a bit with finding the correct combination of cost functions and especially in designing cost c), i.e. the one constraining the ground points. In the current version I just calculate the difference between initial and actual altitude, which is obviously wrong, if the initial estimate is far off (due to initial camera extrinsics being off).

As I have poor overlap I need to constrain the movement of the 3D points, otherwise they are all over the place. I assume this is due to not having more than two pixel observations of each 3D points.

Ideally I would need to constrain the 3D points to be some where on the ground surface (DEM/DSM), although it would be a costly search for each 3D point in each iteration.

Any input is much appreciated.

-- 

Jakob