2015/10/28 by Florian Bernard, Bernard, Florian, Peter Gemmar +8
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Medical Image Segmentation Techniques #Morphological variations and asymmetry #Optimization and Control (math.OC) #cs.CV #math.OC #stat.ML
paper · pdf · doi:10.48550/arxiv.1510.08291
Please cite CVPR 2016 version
openalex publication_date 2015/10/28 · arxiv created 2016/05/11 · arxiv updated 2016/05/12 · openalex created_date 2021/05/24 · openalex updated_date 2026/07/28
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.