Earth curvature and other additional corrections


Earth curvature corrections are applied by some Aerotriangulation solutions to minimize distortions resulting from the use of some coordinate systems. These can be, for example, projected coordinates systems in UTM, which are made for 2D projections and use a separate height definition.

However, an Aerotriangulation is executed in 3D space, using tie points and control points on elevated structures and often covering large areas of the Earth’s surface. Therefore, using a standard 3D cartesian coordinate system (perpendicular axes and same scale on all axes) would be the correct solution. In the case of production of 2D results, their projection onto the 2D plane of the target coordinate system should be executed at the time of their creation.

Some solutions still use image space based correction terms to compensate the before mentioned distortions. The definition of these terms is proprietary and in some cases insufficient for high resolution or oblique imagery.

This article describes solutions to retrieve results with SURE, with good accuracy.

Impact on SURE

SURE relies on a Cartesian coordinate system, where the classical pinhole camera model projects points from a Cartesian global coordinate system to a Cartesian camera coordinate system. Additionally, various camera lens distortion models are supported. When using SURE, it should always be ensured that a consistent camera model definition is applied. Please make sure that the input data is derived without Earth curvature compensation and other additional corrections, in order to generate accurate results. Otherwise, shifts of up to multiple decimeters can occur for the results, particularly in undulating terrain.

If the Aerotriangulation solution has been generated with Earth-curvature or other corrections, please refer to the following section, explaining the available options. This allows you to use the orientation data as input to SURE and generate accurate results.

AT Processed with Earth-Curvature Corrections: Solutions






The simpler way. This is a viable option in case AT is already delivered

Reprocess Bundle Adjustment without earth-curvature corrections




For highest accuracy requirements

Reprocess AT using a Cartesian Coordinate System



Solution 1: Reprocess Bundle Adjustment step of AT without Earth-curvature corrections

If an Aerotriangulation result has been generated with such corrections, you can re-perform the Bundle Adjustment step with this corrections disabled. This way, just the Adjustment is repeated but not the tie point extraction.

The remaining distortion effects will be compensated through the adjustment of the Exterior Orientation parameters, leading to accurate results produced by SURE.

This solution satisfies typical accuracy requirements and is useful when Solution 2 is either too complicated or an AT is already given.

Solution 2: Reprocess AT using a Cartesian coordinate system

In order to get an optimal result with full consistency, a cartesian coordinate system should be used through all processes including the following steps:

  1. Choose a Cartesian coordinate system (recommended: local tangential coordinate system approximating the target system if 2.5D products such as a DSM or True Orthophoto are desired. Geocentric coordinates EPSG:4978 for 3D products only (point clouds, meshes etc.), which is supported in all SURE functions that perform a coordinate system transformation and works with 3D Tiles)

  2. Transfer all GPS/INS as well as all gound control point measurements to this coordinate system

  3. Set up the Aerotrianguation specifying the used coordinate system

  4. Execute Aerotriangulation

  5. Pass results of Aerotriangulation to SURE

  6. If local coordinate system is close to desired result (e.g. one approximating the tangential coordinate system), it can be used right away.

Additional remarks and recommendations

  • If the Bundle Adjustment was carried out without such corrections, but the Inpho/Trimble Match-AT project file is created with having the respective check boxes being activated (e.g. when importing from BINGO or other software), please edit the first lines of the Inpho/Trimble Match-AT project file with these options by using a text editor ($REFRACT_CORR_DEFAULT : off | $CURV_CORR_DEFAULT : off). Alternatively, you can also use the “Ignore Earth Curvature” option (prompt in GUI or --ignore-earth-curvature in CLI). If the Adjustment was done with corrections, it has to be repeated firstly without corrections.

  • General note: the Earth curvature correction is depending on the image depth. Consequently, no camera-constant image correction methods such as distortion grids or radial distortion parameters should be used to compensate effects – in particular in undulating terrain and for oblique imagery. 

  • By specifying an EPSG coordinate system (e.g. in the Inpho Match-AT project file), the coordinate system Information WKT will be transferred to Point Clouds, True Ortho and DSM. This is also necessary for SURE functions that require a coordinate system transformation, e.g. SLPK and 3D Tiles export.

  • If an optimal transfer to a projected coordinate system like UTM is desired for the DSM, you have the option to transform the raw point cloud (Point_Cloud_Raw) with tools like lastools before executing a custom DSM step using the 2.5D tool or the command line. Please note, that for the True Orthophoto also the orientations need to be in the same coordinate system to yield a correct result.

  • Using ellipsoidal heights generally simplifies transformation steps to the tangential coordinate system and for compatibility with subsequent software packages.