Drones have been widely utilized in various fields, but the number of drones
being used illegally and for hazardous purposes has increased recently. To
prevent those illegal drones, in this work, we propose a novel framework for
reconstructing 3D trajectories of drones using a single camera. By leveraging
calibrated cameras, we exploit the relationship between 2D and 3D spaces. We
automatically track the drones in 2D images using the drone tracker and
estimate their 2D rotations. By combining the estimated 2D drone positions with
their actual length information and camera parameters, we geometrically infer
the 3D trajectories of the drones. To address the lack of public drone
datasets, we also create synthetic 2D and 3D drone datasets. The experimental
results show that the proposed methods accurately reconstruct drone
trajectories in 3D space, and demonstrate the potential of our framework for
single camera-based surveillance systems.

通过利用单个摄像头，我们提出了一种用于重构无人机的三维轨迹的新框架，并通过结合估计的二维无人机位置、实际长度信息和摄像头参数，几何推断了无人机的三维轨迹，进一步证明了我们的框架在基于单个摄像头的监控系统中的潜力。

使用单个摄像头重建无人机的三维轨迹

3D Trajectory Reconstruction of Drones using a Single Camera

Three-dimensional trajectories, or the 3D position and rotation of objects
over time, have been shown to encode key aspects of verb semantics (e.g., the
meanings of roll vs. slide). However, most multimodal models in NLP use 2D
images as representations of the world. Given the importance of 3D space in
formal models of verb semantics, we expect that these 2D images would result in
impoverished representations that fail to capture nuanced differences in
meaning. This paper tests this hypothesis directly in controlled experiments.
We train self-supervised image and trajectory encoders, and then evaluate them
on the extent to which each learns to differentiate verb concepts. Contrary to
our initial expectations, we find that 2D visual modalities perform similarly
well to 3D trajectories. While further work should be conducted on this
question, our initial findings challenge the conventional wisdom that richer
environment representations necessarily translate into better representation
learning for language.

本文测试了 2D 图像和 3D 轨迹编码器在学习动词概念时的效果，发现 2D 图像在语言表示学习方面和 3D 轨迹表现相似，挑战了通常认为更丰富的环境表示一定能够更好地进行语言表示学习的传统智慧。

比较轨迹和视觉模态的动词表示方法

Comparing Trajectory and Vision Modalities for Verb Representation

Conventional structure-from-motion (SFM) research is primarily concerned with
the 3D reconstruction of a single, rigidly moving object seen by a static
camera, or a static and rigid scene observed by a moving camera --in both cases
there are only one relative rigid motion involved. Recent progress have
extended SFM to the areas of {multi-body SFM} (where there are {multiple rigid}
relative motions in the scene), as well as {non-rigid SFM} (where there is a
single non-rigid, deformable object or scene). Along this line of thinking,
there is apparently a missing gap of "multi-body non-rigid SFM", in which the
task would be to jointly reconstruct and segment multiple 3D structures of the
multiple, non-rigid objects or deformable scenes from images. Such a multi-body
non-rigid scenario is common in reality (e.g. two persons shaking hands,
multi-person social event), and how to solve it represents a natural
{next-step} in SFM research. By leveraging recent results of subspace
clustering, this paper proposes, for the first time, an effective framework for
multi-body NRSFM, which simultaneously reconstructs and segments each 3D
trajectory into their respective low-dimensional subspace. Under our
formulation, 3D trajectories for each non-rigid structure can be well
approximated with a sparse affine combination of other 3D trajectories from the
same structure (self-expressiveness). We solve the resultant optimization with
the alternating direction method of multipliers (ADMM). We demonstrate the
efficacy of the proposed framework through extensive experiments on both
synthetic and real data sequences. Our method clearly outperforms other
alternative methods, such as first clustering the 2D feature tracks to groups
and then doing non-rigid reconstruction in each group or first conducting 3D
reconstruction by using single subspace assumption and then clustering the 3D
trajectories into groups.

利用子空间聚类的方法，本文首次提出了一个针对多体非刚性 SFM 的有效框架，能够同时将每个 3D 轨迹重建和分段到其各自的低维子空间中，并通过对合成和真实数据序列进行广泛实验验证其功效，明显优于其他替代方法。