Piecewise-Planar 3D Reconstruction with Edge and Corner Regularization

• Published in: Computer graphics forum Vol. 33; no. 5; pp. 55 - 64
• Main Authors: Boulch, Alexandre, de La Gorce, Martin, Marlet, Renaud
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.08.2014; Wiley
• Subjects: 3-D graphics; Analysis; Anisotropy; Categories and Subject Descriptors (according to ACM CCS); Computational Geometry; Computer Science; Computer Vision and Pattern Recognition; Corners; I.2.10 [Artificial Intelligence]: Vision and Scene Understanding-3D/stereo scene analysis; I.4.8 [Image Processing and Computer Vision]: Scene Analysis-Range data; I.5.4 [Pattern Recognition]: Applications-Computer vision; Linear programming; Magnetorheological fluids; Mathematical models; Optimization; Polygons; Reconstruction; Regularization; Regularization methods; Studies; Three dimensional; Topological manifolds
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12431

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.