“Bingham distribution”的意思、由来-开放百科全书

In statistics, the Bingham distribution, named after Christopher Bingham, is an antipodally symmetric probability distribution on the n-sphere.^[1] It is a generalization of the Watson distribution and a special case of the Kent and Fisher-Bingham distributions.

The Bingham distribution is widely used in paleomagnetic data analysis,^[2] and has been reported as being of use in the field of computer vision.^[3]^[4]^[5]

where x is an axis (i.e., a unit vector), M is an orthogonal orientation matrix, Z is a diagonal concentration matrix, and

is a confluent hypergeometric function of matrix argument. The matrices M and Z are the result of diagonalizing the positive-definite covariance matrix of the Gaussian distribution that underlies the Bingham distribution.

See also

References

1. ^Bingham, Ch. (1974) "An antipodally symmetric distribution on the sphere". Annals of Statistics, 2(6):1201–1225.
2. ^Onstott, T.C. (1980) "Application of the Bingham distribution function in paleomagnetic studies". Journal of Geophysical Research, 85:1500–1510.
3. ^S. Teller and M. Antone (2000). Automatic recovery of camera positions in Urban Scenes
4. ^{{cite book|publisher=Springer|date=2008|doi=10.1007/978-3-540-88690-7_58|title = Computer Vision – ECCV 2008|volume=5304|pages=780–791|series = Lecture Notes in Computer Science|last1 = Haines|first1 = Tom S. F.|last2=Wilson|first2=Richard C.|isbn=978-3-540-88689-1|url=http://opus.bath.ac.uk/56745/1/2008_eccv.pdf}}
5. ^{{cite web|title=Better robot vision: A neglected statistical tool could help robots better understand the objects in the world around them.|url=http://web.mit.edu/newsoffice/2013/better-robot-vision-1007.html|publisher=MIT News|date=October 7, 2013|accessdate=October 7, 2013}}