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Representing 3D shape deformations by linear models in high-dimensional spacehas many applications in computer vision and medical imaging, such asshape-based interpolation or segmentation. Commonly, using Principal ComponentsAnalysis a low-dimensional (affine) subspace of the high-dimensional shapespace is determined. However, the resulting factors (the most dominanteigenvectors of the covariance matrix) have global support, i.e. changing thecoefficient of a single factor deforms the entire shape. In this paper, amethod to obtain deformation factors with local support is presented. Thebenefits of such models include better flexibility and interpretability as wellas the possibility of interactively deforming shapes locally. For that, basedon a well-grounded theoretical motivation, we formulate a matrix factorisationproblem employing sparsity and graph-based regularisation terms. We demonstratethat for brain shapes our method outperforms the state of the art in localsupport models with respect to generalisation ability and sparse shapereconstruction, whereas for human body shapes our method gives more realisticdeformations.

Linear Shape Deformation Models with Local Support Using Graph-based Structured Matrix Factorisation