Riemannian Laplace Distribution on the Space of Symmetric Positive Definite Matrices
AbstractThe Riemannian geometry of the space Pm, of m × m symmetric positive definite matrices, has provided effective tools to the fields of medical imaging, computer vision and radar signal processing. Still, an open challenge remains, which consists of extending these tools to correctly handle the presence of outliers (or abnormal data), arising from excessive noise or faulty measurements. The present paper tackles this challenge by introducing new probability distributions, called Riemannian Laplace distributions on the space Pm. First, it shows that these distributions provide a statistical foundation for the concept of the Riemannian median, which offers improved robustness in dealing with outliers (in comparison to the more popular concept of the Riemannian center of mass). Second, it describes an original expectation-maximization algorithm, for estimating mixtures of Riemannian Laplace distributions. This algorithm is applied to the problem of texture classification, in computer vision, which is considered in the presence of outliers. It is shown to give significantly better performance with respect to other recently-proposed approaches. View Full-Text
Scifeed alert for new publicationsNever miss any articles matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now
Hajri, H.; Ilea, I.; Said, S.; Bombrun, L.; Berthoumieu, Y. Riemannian Laplace Distribution on the Space of Symmetric Positive Definite Matrices. Entropy 2016, 18, 98.
Hajri H, Ilea I, Said S, Bombrun L, Berthoumieu Y. Riemannian Laplace Distribution on the Space of Symmetric Positive Definite Matrices. Entropy. 2016; 18(3):98.Chicago/Turabian Style
Hajri, Hatem; Ilea, Ioana; Said, Salem; Bombrun, Lionel; Berthoumieu, Yannick. 2016. "Riemannian Laplace Distribution on the Space of Symmetric Positive Definite Matrices." Entropy 18, no. 3: 98.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.