One of the approaches in diffusion tensor imaging is to consider a Riemannian metric given by the inverse diffusion tensor. Such a metric is used for geodesic tractography and connectivity analysis in white matter. We propose a metric tensor given by the adjugate rather than the previously proposed inverse diffusion tensor. The adjugate metric can also be employed in the sharpening framework. Tractography experiments on synthetic and real brain diffusion data show improvement for high-curvature tracts and in the vicinity of isotropic diffusion regions relative to most results for inverse (sharpened) diffusion tensors, and especially on real data. In addition, adjugate tensors are shown to be more robust to noise.

}, issn = {1573-7683}, doi = {10.1007/s10851-015-0586-8}, url = {http://dx.doi.org/10.1007/s10851-015-0586-8}, author = {Andrea Fuster and Tom Dela-Haije and Antonio Trist{\'a}n-Vega and Birgit Plantinga and Carl-Fredik Westin and Luc Florack} } @conference {cordero20123d, title = {3D fusion of cine and late-enhanced cardiac magnetic resonance images}, booktitle = {Biomedical Imaging (ISBI), 2012 9th IEEE International Symposium on}, year = {2012}, pages = {286{\textendash}289}, publisher = {IEEE}, organization = {IEEE}, author = {Lucilio Cordero-Grande and S. Merino-Caviedes and Alba, X{\`e}nia and Figueras i Ventura, RM and Frangi, Alejandro F and Carlos Alberola-Lopez} } @conference {arenillas2011diffusion, title = {Diffusion Tensor Imaging (DTI) Monitoring Of Motor Function Recovery After Middle Cerebral Artery Infarction: Searching For A DTI-Marker Of Neurorepair}, booktitle = {STROKE}, volume = {42}, number = {3}, year = {2011}, pages = {E119{\textendash}E119}, publisher = {LIPPINCOTT WILLIAMS \& WILKINS 530 WALNUT ST, PHILADELPHIA, PA 19106-3621 USA}, organization = {LIPPINCOTT WILLIAMS \& WILKINS 530 WALNUT ST, PHILADELPHIA, PA 19106-3621 USA}, author = {Arenillas, Juan F and Daniel Argibay-Qui{\~n}ones and Garcia-Bermejo, Pablo and Calleja, Ana I and Diego Mart{\'\i}n-Mart{\'\i}nez and Jose M Sierra and Juan Jos{\'e} Fuertes-Alija and Marcos Martin-Fernandez} } @proceedings {584, title = {Modelado Estad{\'\i}stico de Se{\~n}ales Fotopletismogr{\'a}ficas para la Construcci{\'o}n de Atlas Poblacionales Orientados a la Evaluaci{\'o}n y Seguimiento del Remodelado Cardiovascular}, volume = {29}, year = {2011}, pages = {607-610}, address = {C{\'a}ceres, Spain}, author = {Diego Mart{\'\i}n-Mart{\'\i}nez and Pablo Casaseca-de-la-Higuera and Mart{\'\i}n Fern{\'a}ndez, Marcos and Carlos Alberola-Lopez} } @article {cardenes2010analysis, title = {Analysis of the pyramidal tract in tumor patients using diffusion tensor imaging}, journal = {NeuroImage}, volume = {50}, number = {1}, year = {2010}, pages = {27{\textendash}39}, publisher = {Elsevier}, author = {Rub{\'e}n C{\'a}rdenes-Almeida and Emma Mu{\~n}oz-Moreno and Sarabia-Herrero, Rosario and Rodr{\'\i}guez-Velasco, Margarita and Juan Jos{\'e} Fuertes-Alija and Marcos Martin-Fernandez} } @inbook {vegas2010probabilistic, title = {Probabilistic-driven oriented speckle reducing anisotropic diffusion with application to cardiac ultrasonic images}, booktitle = {Medical Image Computing and Computer-Assisted Intervention{\textendash}MICCAI 2010}, year = {2010}, pages = {518{\textendash}525}, publisher = {Springer Berlin Heidelberg}, organization = {Springer Berlin Heidelberg}, author = {Gonzalo Vegas-S{\'a}nchez-Ferrero and Santiago Aja-Fern{\'a}ndez and Marcos Martin-Fernandez and Frangi, Alejandro F and Cesar Palencia} } @conference {aja2010soft, title = {Soft thresholding for medical image segmentation}, booktitle = {Engineering in Medicine and Biology Society (EMBC), 2010 Annual International Conference of the IEEE}, year = {2010}, pages = {4752{\textendash}4755}, publisher = {IEEE}, organization = {IEEE}, author = {Santiago Aja-Fern{\'a}ndez and Gonzalo Vegas-S{\'a}nchez-Ferrero and Fernandez, Martin} } @proceedings {cardenes2007usimagtool, title = {Usimagtool: an open source freeware software for ultrasound imaging and elastography}, year = {2007}, pages = {117{\textendash}127}, author = {Rub{\'e}n C{\'a}rdenes-Almeida and Antonio Trist{\'a}n-Vega and Ferrero, GVS and Santiago Aja-Fern{\'a}ndez} } @article {lopez2004cardiovascular, title = {Cardiovascular risk factors in the circadian rhythm of acute myocardial infarction}, journal = {Revista Espa{\~n}ola de Cardiolog{\'\i}a (English Edition)}, volume = {57}, number = {9}, year = {2004}, pages = {850{\textendash}858}, publisher = {Elsevier}, author = {L{\'o}pez Messa, Juan B and Garmendia Leiza, Jos{\'e} R and Aguilar Garc{\'\i}a, Mar{\'\i}a D and Jes{\'u}s Mar{\'\i}a And De Llano and Alberola L{\'o}pez, Carlos and Fern{\'a}ndez, Julio Ardura} } @article {lopez2004factores, title = {Factores de riesgo cardiovascular en el ritmo circadiano del infarto agudo de miocardio}, journal = {Revista Espa{\~n}ola de Cardiolog{\'\i}a (English Edition)}, volume = {57}, number = {9}, year = {2004}, pages = {850{\textendash}858}, publisher = {Elsevier}, author = {L{\'o}pez Messa, Juan B and Garmendia Leiza, Jos{\'e} R and Aguilar Garc{\'\i}a, Mar{\'\i}a D and Jes{\'u}s Mar{\'\i}a And De Llano and Alberola L{\'o}pez, Carlos and Ardura Fern{\'a}ndez, Julio} } @article {409, title = {Cost functions to estimate a posteriori probabilities in multiclass problems}, journal = {IEEE Transactions on Neural Networks}, volume = {10}, year = {1999}, pages = {645-656}, abstract = {The problem of designing cost functions to estimate a posteriori probabilities in multiclass problems is addressed in this paper. We establish necessary and sufficient conditions that these costs must satisfy in one-class one-output networks whose outputs are consistent with probability laws. We focus our attention on a particular subset of the corresponding cost functions; those which verify two usually interesting properties: symmetry and separability (well-known cost functions, such as the quadratic cost or the cross entropy are particular cases in this subset). Finally, we present a universal stochastic gradient learning rule for single-layer networks, in the sense of minimizing a general version of these cost functions for a wide family of nonlinear activation functions.

}, keywords = {Cost functions, Estimation, Functions, Learning algorithms, Multiclass problems, Neural networks, Pattern recognition, Probability, Problem solving, Random processes, Stochastic gradient learning rule}, issn = {10459227}, doi = {10.1109/72.761724}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0032643080\&partnerID=40\&md5=d528195bd6ec84531e59ddd2ececcd46}, author = {Jes{\'u}s Cid-Sueiro and J I Arribas and S Urban-Munoz and A R Figueiras-Vidal} } @conference {412, title = {Estimates of constrained multi-class a posteriori probabilities in time series problems with neural networks}, booktitle = {Proceedings of the International Joint Conference on Neural Networks}, year = {1999}, publisher = {IEEE, United States}, organization = {IEEE, United States}, address = {Washington, DC, USA}, abstract = {In time series problems, where time ordering is a crucial issue, the use of Partial Likelihood Estimation (PLE) represents a specially suitable method for the estimation of parameters in the model. We propose a new general supervised neural network algorithm, Joint Network and Data Density Estimation (JNDDE), that employs PLE to approximate conditional probability density functions for multi-class classification problems. The logistic regression analysis is generalized to multiple class problems with softmax regression neural network used to model the a-posteriori probabilities such that they are approximated by the network outputs. Constraints to the network architecture, as well as to the model of data, are imposed, resulting in both a flexible network architecture and distribution modeling. We consider application of JNDDE to channel equalization and present simulation results.

}, keywords = {Approximation theory, Computer simulation, Constraint theory, Data structures, Joint network-data density estimation (JNDDE), Mathematical models, Multi-class a posteriori probabilities, Neural networks, Partial likelihood estimation (PLE), Probability density function, Regression analysis}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0033325263\&partnerID=40\&md5=8c6134020b0b2a9c5ab05b131c070b88}, author = {J I Arribas and Jes{\'u}s Cid-Sueiro and T Adali and H Ni and B Wang and A R Figueiras-Vidal} } @conference {411, title = {Neural architectures for parametric estimation of a posteriori probabilities by constrained conditional density functions}, booktitle = {Neural Networks for Signal Processing - Proceedings of the IEEE Workshop}, year = {1999}, publisher = {IEEE, Piscataway, NJ, United States}, organization = {IEEE, Piscataway, NJ, United States}, address = {Madison, WI, USA}, abstract = {A new approach to the estimation of {\textquoteright}a posteriori{\textquoteright} class probabilities using neural networks, the Joint Network and Data Density Estimation (JNDDE), is presented in this paper. It is based on the estimation of the conditional data density functions, with some restrictions imposed by the classifier structure; the Bayes{\textquoteright} rule is used to obtain the {\textquoteright}a posteriori{\textquoteright} probabilities from these densities. The proposed method is applied to three different network structures: the logistic perceptron (for the binary case), the softmax perceptron (for multi-class problems) and a generalized softmax perceptron (that can be used to map arbitrarily complex probability functions). Gaussian mixture models are used for the conditional densities. The method has the advantage of establishing a distinction between the network parameters and the model parameters. Complexity on any of them can be fixed as desired. Maximum Likelihood gradient-based rules for the estimation of the parameters can be obtained. It is shown that JNDDE exhibits a more robust convergence characteristics than other methods of a posteriori probability estimation, such as those based on the minimization of a Strict Sense Bayesian (SSB) cost function.

}, keywords = {Asymptotic stability, Constraint theory, Data structures, Gaussian mixture models, Joint network and data density estimation, Mathematical models, Maximum likelihood estimation, Neural networks, Probability}, doi = {https://doi.org/10.1109/NNSP.1999.788145}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0033321049\&partnerID=40\&md5=7967fa377810cc0c3e6a4d9020024b80}, author = {J I Arribas and Jes{\'u}s Cid-Sueiro and T Adali and A R Figueiras-Vidal} } @conference {410, title = {Neural networks to estimate ML multi-class constrained conditional probability density functions}, booktitle = {Proceedings of the International Joint Conference on Neural Networks}, year = {1999}, publisher = {IEEE, United States}, organization = {IEEE, United States}, address = {Washington, DC, USA}, abstract = {In this paper, a new algorithm, the Joint Network and Data Density Estimation (JNDDE), is proposed to estimate the {\textquoteleft}a posteriori{\textquoteright} probabilities of the targets with neural networks in multiple classes problems. It is based on the estimation of conditional density functions for each class with some restrictions or constraints imposed by the classifier structure and the use Bayes rule to force the a posteriori probabilities at the output of the network, known here as a implicit set. The method is applied to train perceptrons by means of Gaussian mixture inputs, as a particular example for the Generalized Softmax Perceptron (GSP) network. The method has the advantage of providing a clear distinction between the network architecture and the model of the data constraints, giving network parameters or weights on one side and data over parameters on the other. MLE stochastic gradient based rules are obtained for JNDDE. This algorithm can be applied to hybrid labeled and unlabeled learning in a natural fashion.

}, keywords = {Generalized softmax perceptron (GSP) network, Joint network and data density estimation (JNDDE), Mathematical models, Maximum likelihood estimation, Neural networks, Probability density function, Random processes}, doi = {https://doi.org/10.1109/IJCNN.1999.831174}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0033326060\&partnerID=40\&md5=bb38c144dac0872f3a467dc12170e6b6}, author = {J I Arribas and Jes{\'u}s Cid-Sueiro and T Adali and A R Figueiras-Vidal} }