LiDAR and Coordinate Systems: Journey to the Center of the Earth
LiDAR is changing how we model our world in 3D, bringing with it new data transformation challenges and huge data volumes. It also highlights some old and new challenges with coordinate systems. These largely boil down to getting your data into a form where it can be overlaid with other data and where useful properties are maintained (e.g. water flowing downhill).
How are coordinate systems used with LiDAR?
LiDAR data may be captured in a local coordinate system (for smaller projects), in geographic coordinates (latitude, longitude, ellipsoid height), or geocentric coordinates (also called Earth Centered Earth Fixed). Geocentric coordinates are Cartesian coordinates whose x, y, and z ordinates capture the distance from the earth’s center of mass along the interesting axes (based on the International Reference Pole and Meridian; roughly the north pole and Greenwich). This system is very appealing for LiDAR as the x, y, and z ordinates all use the same units (e.g., meters) and can be used seamlessly anywhere in the world.
What are the transformation challenges related to LiDAR and coordinate systems?
The first requirement is transforming your data into a coordinate system suitable for combining with other data. For example, geographic or geocentric data may need to be converted into a projected coordinate system such as a US state plane. Similarly, data in a local coordinate system may need to be georeferenced and converted into a geographic or projected system.
- [Aside: One of the interesting implementation challenges we discovered when we looked at this is how bounding cubes are transformed between geocentric and geographic coordinate systems. Bounding cubes are a key part of LiDAR data as they enable software to optimize how the data is accessed and displayed. When data is reprojected from one coordinate system to another, the bounding cube needs to be transformed as well, and sometimes it makes sense to transform the cube before the data. We found that geocentric to geographic transformations can strain this strategy: Because the geocentric x / y / z axes are unrelated to the latitude / longitude / height axes, you can end up with overly large bounds.]
Second, you may also need to convert the heights into a useful form. Typically, geographic and projected coordinate systems use ellipsoid heights. Ellipsoid heights measure the perpendicular distance to an ellipsoid (flattened sphere) which approximates the earth’s shape, and are easy to measure using GPS anywhere in the world. They aren’t sea-level heights, though, and so they are counter-intuitive near the coast and don’t capture the direction water flows (down) over large areas. As discussed in detail in an earlier post, you can use geoid-based techniques to convert between ellipsoid and orthometric heights to restore these properties.
How is coordinate system metadata stored with LiDAR data?
The most common LiDAR format, LAS, stores coordinate systems using GeoTIFF keys. However, there are a few details yet to work out around geocentric and vertical coordinate systems. Ongoing standardization on this front will be good for interoperability.
The ASTM E57 3D file format, which aims to store 3D and LiDAR data more generally than the LAS format, is under development and its authors are thinking about these issues as well. An early suggestion was to store coordinate systems and datums as names, which I fear would be challenging from an interoperability perspective, but a more recent summary states that OGC specifications will be used instead. I haven’t looked at the specification to see the details (e.g. “Is it OGC Well Known Text?”, “Can I use EPSG references?”, etc) but I will certainly follow the outcome with interest.
Transforming your data (LiDAR, raster, vector, …) into the right coordinate system allows you to combine it with other data and take advantage of important properties like heights. If you’re interested in learning more about the transformation of LiDAR data, join us for a free webinar on April 28 to see how FME can help. What data transformation challenges are you facing today?