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

TL;DR

This paper introduces a novel matrix factorisation approach that produces local support deformation factors for 3D shapes, enhancing flexibility, interpretability, and local shape manipulation in computer vision and medical imaging.

Contribution

It presents a new graph-based structured matrix factorisation method that yields deformation factors with local support, improving over traditional global PCA factors.

Findings

Outperforms state-of-the-art local support models in brain shape generalisation.

Achieves more realistic deformations for human body shapes.

Enhances interpretability and local control in shape deformation models.

Abstract

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.