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SUMMARY:Journal Club: &quot\;A Bayesian Analysis of Projective Incidence&q
 uot\; - Piotr Zielinski
DTSTART:20060822T100000Z
DTEND:20060822T110000Z
UID:TALK5200@talks.cam.ac.uk
CONTACT:Oliver Stegle
DESCRIPTION:http://www.cs.cmu.edu/~rcollins/Pub/aicv93.html\n\nThe theorem
 s of projective geometry were developed with mathematically\nprecise objec
 ts in mind. In contrast\, a practical vision system must\ndeal with errorf
 ul measurements extracted from real image sensors. A\nmore robust form of 
 projective geometry is needed\, one that allows for\npossible imprecision 
 in its geometric primitives. In this paper\,\nuncertainty in projective el
 ements is represented and manipulated\nusing probability density functions
  in projective space. Projective\nn-space can be visualized using the surf
 ace 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 t
 wo-to-one map\nfrom the unit sphere to projective space enables probabilit
 y density\nfunctions on the sphere to be interpreted as probability densit
 y\nfunctions over the points of projective space. Standard constructions\n
 of projective geometry can then be augmented by statistical inferences\non
  the sphere. In particular\, a Bayesian analysis is presented for\nfusing 
 multiple noisy observations related by known projective\nincidence relatio
 ns.
LOCATION:Room 911\, Rutherford Building\, Cavendish Laboratory\, Departmen
 t of Physics
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