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首页> 外文期刊>Pattern Analysis and Machine Intelligence, IEEE Transactions on >Trajectory Space: A Dual Representation for Nonrigid Structure from Motion
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Trajectory Space: A Dual Representation for Nonrigid Structure from Motion

机译：轨迹空间：运动非刚性结构的双重表示

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摘要

Existing approaches to nonrigid structure from motion assume that the instantaneous 3D shape of a deforming object is a linear combination of basis shapes. These bases are object dependent and therefore have to be estimated anew for each video sequence. In contrast, we propose a dual approach to describe the evolving 3D structure in trajectory space by a linear combination of basis trajectories. We describe the dual relationship between the two approaches, showing that they both have equal power for representing 3D structure. We further show that the temporal smoothness in 3D trajectories alone can be used for recovering nonrigid structure from a moving camera. The principal advantage of expressing deforming 3D structure in trajectory space is that we can define an object independent basis. This results in a significant reduction in unknowns and corresponding stability in estimation. We propose the use of the Discrete Cosine Transform (DCT) as the object independent basis and empirically demonstrate that it approaches Principal Component Analysis (PCA) for natural motions. We report the performance of the proposed method, quantitatively using motion capture data, and qualitatively on several video sequences exhibiting nonrigid motions, including piecewise rigid motion, partially nonrigid motion (such as a facial expressions), and highly nonrigid motion (such as a person walking or dancing).
机译：从运动到非刚性结构的现有方法假定变形对象的瞬时3D形状是基本形状的线性组合。这些基础取决于对象，因此必须为每个视频序列重新估算。相比之下，我们提出了一种通过基本轨迹的线性组合来描述轨迹空间中不断发展的3D结构的对偶方法。我们描述了这两种方法之间的对偶关系，表明它们都具有相等的表示3D结构的能力。我们进一步证明，仅3D轨迹的时间平滑度可用于从移动的相机中恢复非刚性结构。在轨迹空间中表达变形3D结构的主要优点是我们可以定义对象无关的基础。这导致未知数的显着减少以及估计的相应稳定性。我们建议使用离散余弦变换（DCT）作为独立于对象的基础，并凭经验证明它可以对自然运动进行主成分分析（PCA）。我们定量地使用运动捕捉数据并在显示非刚性运动的几个视频序列上定性地报告所提出方法的性能，这些视频序列包括分段刚性运动，部分非刚性运动（例如面部表情）和高度非刚性运动（例如人）走路或跳舞）。

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