@article {796, title = {A Second Order Multi-Stencil Fast Marching Method With a Non-Constant Local Cost Model}, journal = {IEEE Transactions on Image Processing}, volume = {28}, year = {2019}, month = {04/2019}, pages = {1967{\textendash}1979}, abstract = {

The fast marching method is widely employed in several fields of image processing. Some years ago a multi-stencil version (MSFM) was introduced to improve its accuracy by solving the equation for a set of stencils and choosing the best solution at each considered node. The following work proposes a modified numerical scheme for MSFM to take into account the variation of the local cost, which has proven to be second order. The influence of the stencil set choice on the algorithm outcome with respect to stencil orthogonality and axis swapping is also explored, where stencils are taken from neighborhoods of varying radius. The experimental results show that the proposed schemes improve the accuracy of their original counterparts, and that the use of permutation-invariant stencil sets provides robustness against shifted vector coordinates in the stencil set.

}, keywords = {Approximation algorithms, Differential equations, Eikonal equation, Frequency modulation, MSFM, Mathematical model, Silicon, Three-dimensional displays, Unmanned aerial vehicles, Vectors, axis swapping, difference equations, fast marching methods, finite difference methods, finite differences, image processing, iterative methods, least squares approximations, multi-stencil schemes, multistencil version, nonconstant local cost model, permutation-invariant stencil sets, second order multistencil fast marching method, stencil orthogonality, stencil set}, issn = {1057-7149}, doi = {10.1109/TIP.2018.2880507}, url = {https://ieeexplore.ieee.org/document/8531783/}, author = {S. Merino-Caviedes and Lucilio Cordero-Grande and M. T. P{\'e}rez and Pablo Casaseca-de-la-Higuera and M. Mart{\'\i}n-Fern{\'a}ndez and R. Deriche and C. Alberola-L{\'o}pez} } @conference {615, title = {Spatial and Spectral Anisotropy in HARP Images: An Automated Approach}, booktitle = {International Symposium on Biomedical Imaging: From Nano to Macro (ISBI2016)}, year = {2016}, month = {2016}, address = {Prague, Czech Republic}, abstract = {

Strain and related tensors play a major role in cardiac function\ characterization, so correct estimation of the local phase\ in tagged images is crucial for quantitative myocardial motion\ studies. We propose an Harmonic Phase related procedure\ that is adaptive in the spatial and the spectral domains: as for\ the former, we use an angled-steered analysis window prior to\ the Fourier Transform; as for the latter, the bandpass filter is\ also angle-adaptive. Both of them are narrow in the modulation\ direction and wide in the orthogonal direction.

Moreover,\ no parameters are manually set since their values are partially\ based on the information available at the DICOM headers and\ additional information is estimated from data. The procedure
is tested in terms of accuracy (on synthetic data) and reproducibility\ (on real data) of the deformation gradient tensor,\ measured by means of the distribution of the Frobenius norm\ differences between two tensor datasets.

}, keywords = {Anisotropic Gaussian Window, Automatic Band-Pass Filtering, HARmonic Phase, Strain Tensor, Tagged Magnetic Resonance Imaging, Thresholding}, author = {Santiago Sanz-Est{\'e}banez and Lucilio Cordero-Grande and Santiago Aja-Fern{\'a}ndez and Marcos Martin-Fernandez and Carlos Alberola-Lopez} } @conference {520, title = {Single Breath Hold Whole Heart Cine MRI With Iterative Groupwise Cardiac Motion Compensation and Sparse Regularization (kt-WiSE)}, booktitle = {Proceedings of the International Society for Magnetic Resonance in Medicine 23}, year = {2015}, author = {J Royuela-del-Val and Muhammad Usman and Lucilio Cordero-Grande and Federico Simmross-Wattenberg and Marcos Martin-Fern{\'a}ndez and Claudia Prieto and Carlos Alberola-Lopez} } @conference {vegas2008strain, title = {Strain Rate Tensor estimation in cine cardiac MRI based on elastic image registration}, booktitle = {Computer Vision and Pattern Recognition Workshops, 2008. CVPRW{\textquoteright}08. IEEE Computer Society Conference on}, year = {2008}, pages = {1{\textendash}6}, publisher = {IEEE}, organization = {IEEE}, author = {Gonzalo Vegas-S{\'a}nchez-Ferrero and Antonio Trist{\'a}n-Vega and Lucilio Cordero-Grande and Pablo Casaseca-de-la-Higuera and Santiago Aja-Fern{\'a}ndez and Marcos Martin-Fernandez and Carlos Alberola-Lopez} }