We introduce a family of Finsler metrics, called the
 Home
 Search Results
 Page 1 of 1
Search for: All records

Total Resources2
 Resource Type

01000010000
 More
 Availability

20
 Author / Contributor
 Filter by Author / Creator


Bauer, Martin (2)

Le Brigant, Alice (2)

Charon, Nicolas (1)

Klassen, Eric (1)

Lu, Yuxiu (1)

Maor, Cy (1)

#Tyler Phillips, Kenneth E. (0)

#Willis, Ciara (0)

& AbreuRamos, E. D. (0)

& Abramson, C. I. (0)

& AbreuRamos, E. D. (0)

& Adams, S.G. (0)

& Ahmed, K. (0)

& Ahmed, Khadija. (0)

& Aina, D.K. Jr. (0)

& AkcilOkan, O. (0)

& Akuom, D. (0)

& Aleven, V. (0)

& AndrewsLarson, C. (0)

& Archibald, J. (0)

 Filter by Editor


Chen, K (1)

Schönlieb, CB (1)

Tai, XC (1)

Younces, L (1)

& Spizer, S. M. (0)

& . Spizer, S. (0)

& Ahn, J. (0)

& Bateiha, S. (0)

& Bosch, N. (0)

& Brennan K. (0)

& Brennan, K. (0)

& Chen, B. (0)

& Chen, Bodong (0)

& Drown, S. (0)

& Ferretti, F. (0)

& Higgins, A. (0)

& J. Peters (0)

& Kali, Y. (0)

& RuizArias, P.M. (0)

& S. Spitzer (0)


Have feedback or suggestions for a way to improve these results?
!
Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to nonfederal websites. Their policies may differ from this site.

Abstract Fisher–Rao metrics$$L^p$$ ${L}^{p}$ , for$$F_p$$ ${F}_{p}$ , which generalizes the classical Fisher–Rao metric$$p\in (1,\infty )$$ $p\in (1,\infty )$ , both on the space of densities$$F_2$$ ${F}_{2}$ and probability densities$${\text {Dens}}_+(M)$$ ${\text{Dens}}_{+}\left(M\right)$ . We then study their relations to the Amari–C̆encov$${\text {Prob}}(M)$$ $\text{Prob}\left(M\right)$ connections$$\alpha $$ $\alpha $ from information geometry: on$$\nabla ^{(\alpha )}$$ ${\nabla}^{\left(\alpha \right)}$ , the geodesic equations of$${\text {Dens}}_+(M)$$ ${\text{Dens}}_{+}\left(M\right)$ and$$F_p$$ ${F}_{p}$ coincide, for$$\nabla ^{(\alpha )}$$ ${\nabla}^{\left(\alpha \right)}$ . Both are pullbacks of canonical constructions on$$p = 2/(1\alpha )$$ $p=2/(1\alpha )$ , in which geodesics are simply straight lines. In particular, this gives a new variational interpretation of$$L^p(M)$$ ${L}^{p}\left(M\right)$ geodesics as being energy minimizing curves. On$$\alpha $$ $\alpha $ , the$${\text {Prob}}(M)$$ $\text{Prob}\left(M\right)$ and$$F_p$$ ${F}_{p}$ geodesics can still be thought as pullbacks of natural operations on the unit sphere in$$\nabla ^{(\alpha )}$$ ${\nabla}^{\left(\alpha \right)}$ , but in this case they no longer coincide unless$$L^p(M)$$ ${L}^{p}\left(M\right)$ . Using this transformation, we solve the geodesic equation of the$$p=2$$ $p=2$ connection by showing that the geodesic are pullbacks of projections of straight lines onto the unit sphere, and they always cease to exists after finite time when they leave the positive part of the sphere. This unveils the geometric structure of solutions to the generalized Proudman–Johnson equations, and generalizes them to higher dimensions. In addition, we calculate the associate tensors of$$\alpha $$ $\alpha $ , and study their relation to$$F_p$$ ${F}_{p}$ .$$\nabla ^{(\alpha )}$$ ${\nabla}^{\left(\alpha \right)}$ 
Bauer, Martin ; Charon, Nicolas ; Klassen, Eric ; Le Brigant, Alice ( , Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, Springer, Cham.)Chen, K ; Schönlieb, CB ; Tai, XC ; Younces, L (Ed.)