IEEE Trans Image Process. 2012 Aug;21(8):3416-28. doi: 10.1109/TIP.2012.2197008. Epub 2012 May 1.
Most of previous shape based human activity models were built with either a linear assumption or an extrinsic interpretation of the nonlinear geometry of the shape space, both of which proved to be problematic on account of the nonlinear intrinsic geometry of the associated shape spaces. In this paper we propose an intrinsic stochastic modeling of human activity on a shape manifold. More importantly, within an elegant and theoretically sound framework, our work effectively bridges the nonlinear modeling of human activity on a nonlinear space, with the classic stochastic modeling in a Euclidean space, and thereby provides a foundation for a more effective and accurate analysis of the nonlinear feature space of activity models. From a video sequence, human activity is extracted as a sequence of shapes. Such a sequence is considered as one realization of a random process on a shape manifold. Different activities are then modeled as manifold valued random processes with different distributions. To address the problem of stochastic modeling on a manifold, we first construct a nonlinear invertible map of a manifold valued process to a Euclidean process. The resulting process is then modeled as a global or piecewise Brownian motion. The mapping from a manifold to a Euclidean space is known as a stochastic development. The advantage of such a technique is that it yields a one-one correspondence, and the resulting Euclidean process intrinsically captures the curvature on the original manifold. The proposed algorithm is validated on two activity databases [15], [5] and compared with the related works on each of these. The substantiating results demonstrate the viability and high accuracy of our modeling technique in characterizing and classifying different activities.
大多数之前基于形状的人类活动模型都是基于线性假设或形状空间的非线性几何的外在解释构建的，这两者都被证明是有问题的，因为相关形状空间的非线性内在几何。在本文中，我们提出了一种基于形状流形的人类活动的内在随机建模。更重要的是，在一个优雅而理论上合理的框架内，我们的工作有效地将人类活动在非线性空间中的非线性建模与欧几里得空间中的经典随机建模联系起来，从而为更有效地分析活动模型的非线性特征空间提供了基础。从视频序列中，人类活动被提取为一系列形状。这样的序列被认为是形状流形上随机过程的一个实现。然后，不同的活动被建模为具有不同分布的流形值随机过程。为了解决流形上的随机建模问题，我们首先构造了一个流形值过程到欧几里得过程的非线性可逆映射。然后，将得到的过程建模为全局或分段布朗运动。从流形到欧几里得空间的映射称为随机发展。这种技术的优点是它产生一一对应，并且得到的欧几里得过程内在地捕获了原始流形上的曲率。所提出的算法在两个活动数据库[15]，[5]上进行了验证，并与这些数据库中的相关工作进行了比较。充分的结果证明了我们的建模技术在刻画和分类不同活动方面的可行性和高精度。
