A Statistical Model of Recreational Trails

Abstract

We present a statistical model of recreational trails, and a method to infer trail routes from geophysical data, namely aerial imagery and terrain elevation. We learn a set of textures (textons) that characterize the imagery, and use the textons to segment each image into super-pixels. We also model each texton's probability of generating trail pixels, and the direction of such trails. From terrain elevation, we model the magnitude and direction of terrain gradient on-trail and off-trail. These models lead to a likelihood function for image and elevation. Consistent with Bayesian reasoning, we combine the likelihood with a prior model of trail length and smoothness, yielding a posterior distribution for trails, given an image. We search for good values of this posterior using both a novel stochastic variation of Dijkstra's algorithm, and an MCMC-inspired sampler. Our experiments, on trail images and groundtruth collected in the western continental USA, show substantial improvement over those of the previous best trail-finding methods.