Kavli Affiliate: Yi Zhou
| First 5 Authors: Bangyan Liao, Zhenjun Zhao, Haoang Li, Yi Zhou, Yingping Zeng
| Summary:
Determining the vanishing points (VPs) in a Manhattan world, as a fundamental
task in many 3D vision applications, consists of jointly inferring the line-VP
association and locating each VP. Existing methods are, however, either
sub-optimal solvers or pursuing global optimality at a significant cost of
computing time. In contrast to prior works, we introduce convex relaxation
techniques to solve this task for the first time. Specifically, we employ a
"soft" association scheme, realized via a truncated multi-selection error, that
allows for joint estimation of VPs’ locations and line-VP associations. This
approach leads to a primal problem that can be reformulated into a
quadratically constrained quadratic programming (QCQP) problem, which is then
relaxed into a convex semidefinite programming (SDP) problem. To solve this SDP
problem efficiently, we present a globally optimal outlier-robust iterative
solver (called GlobustVP), which independently searches for one VP and its
associated lines in each iteration, treating other lines as outliers. After
each independent update of all VPs, the mutual orthogonality between the three
VPs in a Manhattan world is reinforced via local refinement. Extensive
experiments on both synthetic and real-world data demonstrate that GlobustVP
achieves a favorable balance between efficiency, robustness, and global
optimality compared to previous works. The code is publicly available at
https://github.com/WU-CVGL/GlobustVP.
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