A Computational Model of the Short-Cut Rule for 2D Shape Decomposition

We propose a new 2D shape decomposition method based on the short-cut rule. The short-cut rule originates from cognition research, and states that the human visual system prefers to partition an object into parts using the shortest possible cuts. We propose and implement a computational model for the short-cut rule and apply it to the problem of shape decomposition. The model we proposed generates a set of cut hypotheses passing through the points on the silhouette which represent the negative minima of curvature. We then show that most part-cut hypotheses can be eliminated by analysis of local properties of each. Finally, the remaining hypotheses are evaluated in ascending length order, which guarantees that of any pair of conflicting cuts only the shortest will be accepted. We demonstrate that, compared with state-of-the-art shape decomposition methods, the proposed approach achieves decomposition results which better correspond to human intuition as revealed in psychological experiments.Comment: 11 page

Patch-type Segmentation of Voxel Shapes using Simplified Surface Skeletons

We present a new method for decomposing a 3D voxel shape into disjoint segments using the shape’s simplified surface-skeleton. The surface skeleton of a shape consists of 2D manifolds inside its volume. Each skeleton point has a maximally inscribed ball that touches the boundary in at least two contact points. A key observation is that the boundaries of the simplified fore- and background skeletons map one-to-one to increasingly fuzzy, soft convex, respectively concave, edges of the shape. Using this property, we build a method for segmentation of 3D shapes which has several desirable properties. Our method segments both noisy shapes and shapes with soft edges which vanish over low-curvature regions. Multiscale segmentations can be obtained by varying the simplification level of the skeleton. We present a voxel-based implementation of our approach and illustrate it on several realistic examples.

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

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.Comment: Please cite CVPR 2016 versio