In computer and robotic vision point clouds from depth sensors have to be processed to form higher-level concepts such as lines, planes, and objects. Bayesian methods formulate precisely prior knowledge with respect to the noise and likelihood of points given a line, plane, or object. Nonparametric methods also formulate a prior with respect to the number of those lines, planes, or objects. Recently, a nonparametric Bayesian method has been proposed to perform optimal inference simultaneously over line fitting and the number of lines. In this paper we propose a nonparametric Bayesian method for segment fitting. Segments are lines of finite length. This requires 1.) a prior for line segment lengths: the symmetric Pareto distribution, 2.) a sampling method that handles nonconjugacy: an auxiliary variable MCMC method. Results are measured according to clustering performance indicators, such as the Rand Index, the Adjusted Rand Index, and the Hubert metric. Surprisingly, the performance of segment recognition is worse than that of line recognition. The paper therefore concludes with recommendations towards improving Bayesian segment recognition in future work.