发表机构
Florida State University; Missouri University of Science and Technology（佛罗里达州立大学; 密苏里科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用多视图运动恢复结构（SfM）实现三维有向射影形状（OPS）分析，首次在三维中计算OPS指数并进行统计推断，验证了SfM重建的高精度与稳健性。
AI 中文摘要
射影形状分析为针孔相机获取的数字图像中的地标配置提供了一种几何框架。在经典射影形状（PS）模型中，三维配置（k元组）表示为$(\nathrm{RP}^3)^q$中的点，其中$q = k - 5$。Patrangenaru等人[12]针对该框架开发了一种非参数检验，以确定物体是否与设计蓝图匹配，每个配置由单个未标定立体像对重建。这种两视图重建仅在三维射影变换下被识别，该变换可能反转方向，因此在最近考虑有向射影形状（OPS）之前，符号盲的PS摘要曾是唯一可用的方法。多视图运动恢复结构（SfM）技术消除了这一障碍：其光束法平差在保向射影变换下被识别。在本文中，我们重新审视了Patrangenaru等人[12]中一个被广泛引用的三立方体物体，使用Agisoft Metashape Professional 2.3.0构建了$n = 8$个SfM重建，并通过从原始数据复现已发表的立体构建来验证我们的实现。这使我们能够进行据我们所知的首次三维OPS分析，计算其外在总方差指数，并在这一新颖设置中进行统计推断。由于SfM数据的高度集中，OPS指数渐近地为PS指数的一半，这是集中的结构性结果而非物体的属性。在此，对于$q = 14$个非框架地标中的任何一个，我们的蓝图假设均未被拒绝，而SfM重建的集中度约为立体重建的26倍，这是重建精度的显著提升。样本量、照片数量和帧顺序分析支持了这些结论的稳健性。
英文摘要
Projective shape analysis provides a geometric framework for studying landmark configurations in digital images acquired by pinhole cameras. In the classical projective shape (PS) model, three-dimensional configurations ($k$-ads) are represented as points in $(\mathrm{RP}^3)^q$, $q = k - 5$. A nonparametric test is developed in Patrangenaru et al. [12], for this framework, to determine whether an object matches a design blueprint, with each configuration reconstructed from a single uncalibrated stereo pair. Such two-view reconstructions are identified only up to a 3D projective transformation, which may reverse orientation, so that the sign-blind PS summary was the only available, before oriented projective shape (OPS) was recently considered. Multi-view Structure-from-Motion (SfM) technology removes this obstruction: its bundle adjustment is identified up to an orientation-preserving projective transformation. In this paper we revisit a well-cited three-cube object, from Patrangenaru et al. [12], with $n = 8$ SfM reconstructions built in Agisoft Metashape Professional 2.3.0, and validate our implementation by reproducing the published stereo construction from the original data. This allows us to perform what is to the best of our knowledge the first three-dimensional OPS analysis, compute its extrinsic total-variance index and perform statistical inference in this novel setting. Due to the high concentration of SfM data, the OPS index is asymptotically one-half the PS index, a structural consequence of concentration rather than a property of the object. Here our blueprint hypothesis is not rejected for any of the $q = 14$ non-frame landmarks, while the SfM reconstructions are about 26 times more concentrated than the stereo ones, a substantial gain in reconstruction precision. Sample-size, photograph-count, and frame-ordering analyses support the robustness of these conclusions.
Comments19 pages, 9 figures
