Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing oriented texture fields
CVGIP: Graphical Models and Image Processing
Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow
IEEE Transactions on Pattern Analysis and Machine Intelligence
Coherence-Enhancing Diffusion Filtering
International Journal of Computer Vision
Orthonormal Vector Sets Regularization with PDE's and Applications
International Journal of Computer Vision
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Statistical Computing on Manifolds: From Riemannian Geometry to Computational Anatomy
Emerging Trends in Visual Computing
Oriented Morphometry of Folds on Surfaces
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Anisotropic diffusion of tensor fields for fold shape analysis on surfaces
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
| Hi-index | 0.00 |
In this paper, we present a novel framework to carry out computations on tensors, i.e. symmetric positive definite matrices. We endow the space of tensors with an affine-invariant Riemannian metric, which leads to strong theoretical properties: The space of positive definite symmetric matrices is replaced by a regular and geodesically complete manifold without boundaries. Thus, tensors with non-positive eigenvalues are at an infinite distance of any positive definite matrix. Moreover, the tools of differential geometry apply and we generalize to tensors numerous algorithms that were reserved to vector spaces. The application of this framework to the processing of diffusion tensor images shows very promising results. We apply this framework to the processing of structure tensor images and show that it could help to extract low-level features thanks to the affine-invariance of our metric. However, the same affine-invariance causes the whole framework to be noise sensitive and we believe that the choice of a more adapted metric could significantly improve the robustness of the result.