We propose a method for the automatic extraction of fluvial networks in lidar data with the aim to obtain a connected network represented by the fluvial channels' skeleton. For that purpose we develop a two-step approach. First, we fit rectangles to the data using a stochastic optimization based on a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler and simulated annealing. High gradients on the rectangles' border and non-overlapping areas of the objects are introduced as model in the optimization process. In a second step, we determine the principal axes of the rectangles and their intersection points. Based on this a network graph is constructed in which nodes represent junction points or end points, respectively, and edges in-between straight line segments. We evaluate our method on lidar data with a tidal channel network and show some preliminary results.