Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
The Beltrami Flow over Implicit Manifolds
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Measuring Graph Similarity Using Spectral Geometry
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
Regularization on discrete spaces
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Image smoothing and segmentation by graph regularization
ISVC'05 Proceedings of the First international conference on Advances in Visual Computing
A general framework for low level vision
IEEE Transactions on Image Processing
The digital TV filter and nonlinear denoising
IEEE Transactions on Image Processing
| Hi-index | 0.00 |
This paper describes a new approach for regularising triangulated graphs. We commence by embedding the graph onto a manifold using the heat-kernel embedding. Under the embedding, each first-order cycle of the graph becomes a triangle. Our aim is to use curvature information associated with the edges of the graph to effect regularisation. Using the difference in Euclidean and geodesic distances between nodes under the embedding, we compute sectional curvatures associated with the edges of the graph. Using the Gauss Bonnet Theorem we compute the Gaussian curvature associated with each node from the sectional curvatures and through the angular excess of the geodesic triangles. Using the curvature information we perform regularisation with the advantage of not requiring the solution of a partial differential equation. We experiment with the resulting regularization process, and explore its effect on both graph matching and graph clustering.