This paper addresses the problem of simultaneously recovering 3D shape, pose and the elastic model of a deformable object from only 2D point tracks in a monocular video. This is a severely under-constrained problem that has been typically addressed by enforcing the shape or the point trajectories to lie on low-rank dimensional spaces. We show that formulating the problem in terms of a low-rank force space that induces the deformation and introducing the elastic model as an additional unknown, allows for a better physical interpretation of the resulting priors and a more accurate representation of the actual object's behavior. In order to simultaneously estimate force, pose, and the elastic model of the object we use an expectation maximization strategy, where each of these parameters are successively learned by partial M-steps. Once the elastic model is learned, it can be transfered to similar objects to code its 3D deformation. Moreover, our approach can robustly deal with missing data, and encode both rigid and non-rigid points under the same formalism. We thoroughly validate the approach on Mocap and real sequences, showing more accurate 3D reconstructions than state-of-the-art, and additionally providing an estimate of the full elastic model with no a priori information.

中文翻译：

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非刚性形状和弹性模型估计的基于力的表示


本文解决了仅从单目视频中的 2D 点轨迹同时恢复可变形物体的 3D 形状、姿态和弹性模型的问题。这是一个严重欠约束的问题，通常通过强制形状或点轨迹位于低秩维空间上来解决。我们表明，根据引起变形的低阶力空间来制定问题，并引入弹性模型作为附加未知数，可以更好地对所得先验进行物理解释，并更准确地表示实际物体的行为。为了同时估计物体的力、姿态和弹性模型，我们使用期望最大化策略，其中每个参数都通过部分 M 步连续学习。一旦学习了弹性模型，就可以将其转移到类似的对象以对其 3D 变形进行编码。此外，我们的方法可以稳健地处理丢失的数据，并在相同的形式下对刚性点和非刚性点进行编码。我们在 Mocap 和真实序列上彻底验证了该方法，显示出比最先进技术更准确的 3D 重建，并另外提供了在没有先验信息的情况下对完整弹性模型的估计。