Uncertainty Analysis of 3D Line Reconstruction in a New Minimal Spatial Line Representation

Abstract

Line segments are common in urban scenes and contain rich structural information. However, different from point-based reconstruction, reconstructed 3D lines may have large displacement from the ground truth in spite of a very small sum of reprojection error. In this work, we present a method to analyze the uncertainty of line reconstruction and provide a quantitative evaluation of accuracy. A new minimal four-vector line representation based on Plücker line is introduced, which is tailed for uncertainty analysis of line reconstruction. Each component of the compact representation has a certain physical meaning about the 3D line’s orientation or position. The reliability of the reconstructed lines can be measured by the confidence interval of each component in the proposed representation. Based on the uncertainty analysis of two-view line triangulation, the uncertainty of multi-view line reconstruction is also derived. Combining the proposed uncertainty analysis with reprojection error, a more reliable 3D line map can be obtained. Experiments on simulation data, synthetic and real-world image sequences validate the feasibility of the proposed method.

Keywords

• line reconstruction
• line representation
• uncertainty analysis
• plücker coordinates