Reconstructing noisy LIDAR scans with spline smoothing

In this example a smooth surface has been automatically fitted to LIDAR scans of a well-known fountain in Santa Barbara using spline smoothing - a technique for fitting an RBF which approximates at the data points rather than exactly interpolating.

  • The statue is approximately 2m x 5m and was scanned using a CYRAX 2400 scanner.
  • The data set consists of 350,000 points imaged from several viewpoints in front of the statue
  • Three spheres apparent in the image were used to align the scans 
  • Data courtesy of Allen Instruments & Supplies, 1474 Theresa St, Carpinteria, CA93013, USA

350,000 point cloud taken from several scanner positions in front of the statue.

Note the large occluded regions where no data has been recorded.

The automatically fitted RBF surface.

The data fidelity constraint has been chosen to reflect the estimated level of noise in the data, and hence reconstruct a smooth surface despite the noisy data.

The thin-plate spline basic function has preserved the topology of features such as the arms and the gap between the arms and the rest of the statue, despite having no data in these regions. Even the reference spheres have been correctly reconstructed despite only a partial hemisphere being imaged by the scanner.


   
  Despite having data only from the front view of the statue, the smoothness constraint inherent in the thin-plate basis has correctly preserved the gap between the arm and the rest of the statue.    Detail of corresponding smooth fit. The gap between the arm and the statue is still preserved. 


Spline smoothing

Exact fit. Medium amount of smoothing applied.
The RBF approximates at data points.		 Increased smoothing.