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CATEGORIES:Machine Learning Journal Club
SUMMARY:Journal Club: "\;A Bayesian Analysis of Projec
tive Incidence"\; - Piotr Zielinski
DTSTART;TZID=Europe/London:20060822T110000
DTEND;TZID=Europe/London:20060822T120000
UID:TALK5200AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/5200
DESCRIPTION:http://www.cs.cmu.edu/~rcollins/Pub/aicv93.html\n\
nThe theorems of projective geometry were develope
d with mathematically\nprecise objects in mind. In
contrast\, a practical vision system must\ndeal w
ith errorful measurements extracted from real imag
e sensors. A\nmore robust form of projective geome
try is needed\, one that allows for\npossible impr
ecision in its geometric primitives. In this paper
\,\nuncertainty in projective elements is represen
ted and manipulated\nusing probability density fun
ctions in projective space. Projective\nn-space ca
n be visualized using the surface of a unit sphere
in\n(n+1)-dimensional Euclidean space. Each point
in projective space is\nrepresented by antipodal
points on the sphere. This two-to-one map\nfrom th
e unit sphere to projective space enables probabil
ity density\nfunctions on the sphere to be interpr
eted as probability density\nfunctions over the po
ints of projective space. Standard constructions\n
of projective geometry can then be augmented by st
atistical inferences\non the sphere. In particular
\, a Bayesian analysis is presented for\nfusing mu
ltiple noisy observations related by known project
ive\nincidence relations.
LOCATION:Room 911\, Rutherford Building\, Cavendish Laborat
ory\, Department of Physics
CONTACT:Oliver Stegle
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