This paper presents a method for the 3D reconstruction of a piecewise‐planar surface from range images, typically laser scans with millions of points. The reconstructed surface is a watertight polygonal mesh that conforms to observations at a given scale in the visible planar parts of the scene, and that is plausible in hidden parts. We formulate surface reconstruction as a discrete optimization problem based on detected and hypothesized planes. One of our major contributions, besides a treatment of data anisotropy and novel surface hypotheses, is a regularization of the reconstructed surface w.r.t. the length of edges and the number of corners. Compared to classical area‐based regularization, it better captures surface complexity and is therefore better suited for man‐made environments, such as buildings. To handle the underlying higher‐order potentials, that are problematic for MRF optimizers, we formulate minimization as a sparse mixed‐integer linear programming problem and obtain an approximate solution using a simple relaxation. Experiments show that it is fast and reaches near‐optimal solutions.