In this paper, we address the problem of curb detection for a pedestrian robot navigating in urban environments. We devise an unsupervised method that is mostly view-independent, makes no assumptions about the environment, restricts the set of hand-tuned parameters, and builds on sound probabilistic reasoning from the input data to the outcome of the algorithm. In our approach, we construct a piecewise planar model of the environment and determine curbs at plane segment boundaries. Initially, we sense the environment with a nodding laser range-finder and project the 3D measurements into an efficient Digital Elevation Map (DEM). Each cell of the DEM maintains an error model that is propagated throughout the entire algorithm. Plane segments are further estimated with a mixture of linear regression models on the DEM. Here, we propose an original formulation of the standard Expectation-Maximization (EM) algorithm for mixture models. Specifically, in the E-step, responsibilities are computed with a Conditional Random Field that introduces dependencies between the covariates of the mixture model. A graph-based segmentation of the DEM provides an estimate of the number of planes and initial parameters for the EM. We show promising results of the algorithm on simulated and real-world data.
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