Abstract: The disclosed terrain model is a generative, probabilistic approach to modeling terrain that exploits the 3D spatial structure inherent in outdoor domains and an array of noisy but abundant sensor data to simultaneously estimate ground height, vegetation height and classify obstacles and other areas of interest, even in dense non-penetrable vegetation. Joint inference of ground height, class height and class identity over the whole model results in more accurate estimation of each quantity. Vertical spatial constraints are imposed on voxels within a column via a hidden semi-Markov model. Horizontal spatial constraints are enforced on neighboring columns of voxels via two interacting Markov random fields and a latent variable. Because of the rules governing abstracts, this abstract should not be used to construe the claims.