Representing 3D shape deformations by linear models in high-dimensional space
has many applications in computer vision and medical imaging, such as
shape-based interpolation or segmentation. Commonly, using Principal Components
Analysis a low-dimensional (affine) subspace of the high-dimensional shape
space is determined. However, the resulting factors (the most dominant
eigenvectors of the covariance matrix) have global support, i.e. changing the
coefficient of a single factor deforms the entire shape. In this paper, a
method to obtain deformation factors with local support is presented. The
benefits of such models include better flexibility and interpretability as well
as the possibility of interactively deforming shapes locally. For that, based
on a well-grounded theoretical motivation, we formulate a matrix factorisation
problem employing sparsity and graph-based regularisation terms. We demonstrate
that for brain shapes our method outperforms the state of the art in local
support models with respect to generalisation ability and sparse shape
reconstruction, whereas for human body shapes our method gives more realistic
deformations.

本文提出了一种基于稀疏性和基于图形的正则化项的矩阵分解问题的方法，用于获得具有局部支持的变形因子，该方法在医学图像处理中具有较好的适用性和实用性。