A post-processing step error correction algorithm for overlapping LiDAR strips from agricultural landscapes

In the processing of light detection and ranging (LiDAR) data, a step error is an abrupt change in estimates of elevation between adjacent strips and must be reduced before building a digital surface model (DSM) of elevation. Existing methodologies in the literature for removing this artifact require an analyst to (1) utilize the sensor and aircraft information of the LiDAR mission, (2) isolate homologous flat surfaces within regions of overlap of adjoining LiDAR strips to estimate the mean offset, or (3) a combination of the two. In this application involving an agricultural landscape, a different methodology was required because the necessary information from the laser scanner or internal navigation system (INS) of the aircraft was unavailable and it was not possible to successfully identify homologous flat surfaces. Therefore, a post-processing, quadratic optimization model was formulated to reduce step artifacts. Using statistics obtained from the geographic overlap of the strips with a benchmark strip, it was possible to determine from the elevation values of the LiDAR point clouds two quantities: the strip variance and the total variance. Using these values and related statistics, the optimization model estimated correction constants, called decision variables, that minimized the among-group variance of the adjoining strips. When the values of these decision variables are added to the point cloud elevations of their respective LiDAR strips, the systematic step errors among adjoining strips are minimized with respect to the elevations provided by the point cloud of the benchmark strip. Decision variable values ranged between −0.087 and 0.078 m. The adjusted LiDAR strip point clouds were used to build a corrected DSM of a 638.2-ha agricultural landscape at a spatial resolution of 0.5 m. The elevation range of the DSM is approximately 44–81 m HAE (height above the ellipsoid), where the higher elevations are the tops of trees. Effectiveness of the optimization model approach to reduce the step errors was evaluated by comparing the DSM before and after adjustment. Several hillshade, gray scale image subsets, and profile plot comparisons between the before and after adjustment of the point clouds of the LiDAR strips illustrate the algorithm's performance in reducing step error effects.