Given dense image feature correspondences of a non-rigidly moving object
across multiple frames, this paper proposes an algorithm to estimate its 3D
shape for each frame. To solve this problem accurately, the recent
state-of-the-art algorithm reduces this task to set of local linear subspace
reconstruction and clustering problem using Grassmann manifold representation
\cite{kumar2018scalable}. Unfortunately, their method missed on some of the
critical issues associated with the modeling of surface deformations, for e.g.,
the dependence of a local surface deformation on its neighbors. Furthermore,
their representation to group high dimensional data points inevitably introduce
the drawbacks of categorizing samples on the high-dimensional Grassmann
manifold \cite{huang2015projection, harandi2014manifold}. Hence, to deal with
such limitations with \cite{kumar2018scalable}, we propose an algorithm that
jointly exploits the benefit of high-dimensional Grassmann manifold to perform
reconstruction, and its equivalent lower-dimensional representation to infer
suitable clusters. To accomplish this, we project each Grassmannians onto a
lower-dimensional Grassmann manifold which preserves and respects the
deformation of the structure w.r.t its neighbors. These Grassmann points in the
lower-dimension then act as a representative for the selection of
high-dimensional Grassmann samples to perform each local reconstruction. In
practice, our algorithm provides a geometrically efficient way to solve dense
NRSfM by switching between manifolds based on its benefit and usage.
Experimental results show that the proposed algorithm is very effective in
handling noise with reconstruction accuracy as good as or better than the
competing methods.

通过利用高维 Grassmann 流形进行重建以及等效的低维表示进行推理聚类的算法，该研究提出了一种解决密集非刚性运动目标多帧图像 3D 形状估计的算法。