基于点线关联的3D重建的理论与数值分析
Theoretical and Numerical Analysis of 3D Reconstruction Using Point and Line Incidences
AI总结：
该研究针对3D点线关联三角测量问题，推导了适用于任意图像数量的复临界点数量公式以衡量其固有难度，并通过同伦延拓法实验验证利用关联关系可提升点重建的速度与三视图下的精度。
摘要：
我们研究了与点关联的直线的联合像，即由固定相机观测变化的3D点线关联所得到的图像元组集合。我们证明了三角测量问题的复临界点数量公式，该问题旨在从含噪图像中计算3D点线关联。该公式适用于任意数量的图像，可衡量此三角测量的固有难度。此外，我们使用同伦延拓法开展了数值实验，比较了此类关联的不同三角测量方法。在我们的实验设置中，利用关联关系既能加快点重建速度，在三视图下也能提升精度。
英文摘要：
We study the joint image of lines incident to points, meaning the set of image tuples obtained from fixed cameras observing a varying 3D point-line incidence. We prove a formula for the number of complex critical points of the triangulation problem that aims to compute a 3D point-line incidence from noisy images. Our formula works for an arbitrary number of images and measures the intrinsic difficulty of this triangulation. Additionally, we conduct numerical experiments using homotopy continuation methods, comparing different approaches of triangulation of such incidences. In our setup, exploiting the incidence relations gives both a faster point reconstruction and in three views more accurate.
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