Modelling character motions on infinite-dimensional manifolds
Modelling character motions on infinite-dimensional manifolds
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DOI：
10.1007/s00371-014-1001-y
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发表时间：
2015-09-01
期刊：
影响因子：
3.5
通讯作者：
Eslitzbichler, Markus
中科院分区：
文献类型：
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作者：
Eslitzbichler, Markus
在本文中，我们将制定一个数学框架，使我们能够将角色动画视为无限维希尔伯特流形上的点。在这些流形上构建动画之间的测地线路径允许我们推导距离函数来测量不同运动的相似性。这种方法来源于几何形状分析领域，这种形式已经被用来促进物体识别任务。类似于形状空间的思想，我们构造了由重参数化下的等价动画类组成的运动空间。特别是循环运动可以在这个框架中优雅地表示出来。我们证明了这种方法在计算机动画领域的多种应用中的适用性。首先，我们展示了如何通过应用计算效率高的流形投影方法来去除循环动画中的视觉伪影。我们接下来强调如何使用测地线路径以计算稳定的方式计算各种动画之间的插值。最后，我们展示了如何使用相同的数学框架对大型动作捕捉数据库进行聚类分析，这些数据库可用于或作为动作检索问题的一部分。
In this article, we will formulate a mathematical framework that allows us to treat character animations as points on infinite-dimensional Hilbert manifolds. Constructing geodesic paths between animations on those manifolds allows us to derive a distance function to measure similarities of different motions. This approach is derived from the field of geometric shape analysis, where such formalisms have been used to facilitate object recognition tasks. Analogously to the idea of shape spaces, we construct motion spaces consisting of equivalence classes of animations under reparametrizations. Especially cyclic motions can be represented elegantly in this framework. We demonstrate the suitability of this approach in multiple applications in the field of computer animation. First, we show how visual artefacts in cyclic animations can be removed by applying a computationally efficient manifold projection method. We next highlight how geodesic paths can be used to calculate interpolations between various animations in a computationally stable way. Finally, we show how the same mathematical framework can be used to perform cluster analysis on large motion capture databases, which can be used for or as part of motion retrieval problems.