Background The use of a medical simulator should enhance the goals of minimally invasive surgery: patient safety, cosmesis, shortening the length of hospital admissions, and reducing cost. Using an innovative approach to the handling of ultrasound images in virtual reality simulation, this article describes a process that employs a hybrid model of deformable models that can be applied in the te...

Learning fruitful representation from data is one of fundamental problems in machine learning and pattern recognition. Various methods have been developed, including factor analysis, principal component analysis (PCA), independent component analysis (ICA), manifold learning, and so on. Among those, nonnegative matrix factorization (NMF) has recently drawn extensive attention, since promising re...

We study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesX_{i}. We introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by X boxtimesY. We investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...

The rapid increase of multidimensional data (a.k.a. tensor) like videos brings new challenges for low-rank data modeling approaches such as dynamic data size, complex high-order relations, and multiplicity of low-rank structures. Resolving these challenges require a new tensor analysis method that can perform tensor data analysis online, which however is still absent. In this paper, we propose ...

A new and significant source of information on earthquake studies has been provided by space geodesy. The data which are gathered by various techniques of space geodesy, can quantify potential of seismic activity in the region of interest. To achieve this goal, the main advantage of extra-terrestrial geodetic data in comparison with the conventional data from geology and seismology is the abili...

Modern applications such as neuroscience, text mining, and large-scale social networks generate massive amounts of data with multiple aspects and high dimensionality. Tensors (i.e., multi-way arrays) provide a natural representation for such massive data. Consequently, tensor decompositions and factorizations are emerging as novel and promising tools for exploratory analysis of multidimensional...

Major advances in medical imaging raised the need for adapted methods and softwares. The recent emergence of diffusion tensor MRI (DT-MRI) was challenging since data produced by this modality are not simple grey-value images but complex diffusion tensor fields. Tensors are symmetric, positive definite matrices and suffer from a lack of adapted theoretical tools to manipulate them. In this paper...