A Hybrid Conditional Random Field for Estimating
the Underlying Ground Surface from Airborne LiDAR Data

IEEE Transactions on Geoscience and Remote Sensing

Wei-Lwun Lu     Kevin P. Murphy     James J. Little     Alla Sheffer     Hongbo Fu

Left: The original DSM of a rural site with vegetation on a slope, and some small buildings. Middle: The classification of 3D points to ground/non-ground (red/green). Right: The extracted DTM of the bare-earth surface. The small white patch near the top right corresponds to missing data.

Recent advances in airborne light detection and ranging (LiDAR) technology allow rapid and inexpensive generation of digital surface models (DSMs), 3D point clouds of buildings, vegetations, cars, and natural terrain features over large regions. However, in many applications, such as flood modeling and landslide prediction, digital terrain models (DTMs), the topography of the bare-earth surface, are needed. This article introduces a novel machine learning approach to automatically extract DTMs from their corresponding DSMs. We first classify each point as being either ground or non-ground, using supervised learning techniques applied to a variety of features. For the points which are classified as ground, we use the LiDAR measurements as an estimate of the surface height, but for the non-ground points, we have to interpolate between nearby values, which we do using a Gaussian random field. Since our model contains both discrete and continuous latent variables, and is a discriminative (rather than generative) probabilistic model, we call it a hybrid Conditional Random Field. We show that a MAP estimate of the surface height can be efficiently estimated by using a variant of the Expectation Maximization (EM) algorithm. Experiments demonstrate that the accuracy of this learning-based approach outperforms the previous best systems, based on manually tuned heuristics.

@ARTICLE{Lu:2009,
     author = {Wei Lwun Lu and Kenji Okuma and James J. Little},
     title = {A Hybrid Conditional Random Field for Estimating the Underlying Ground Surface from Airborne
                LiDAR Data},
     journal = {IEEE Transactions on Geoscience and Remote Sensing},
     year = {2009},
     volume = {To Appear}
}