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SUMMARY:A fast and robust algorithm to count topologically persistent hole
 s in noisy clouds. - Dr Vitaliy Kurlin
DTSTART:20140617T140000Z
DTEND:20140617T150000Z
UID:TALK53055@talks.cam.ac.uk
CONTACT:37004
DESCRIPTION:Preprocessing a 2D image often produces a noisy cloud of inter
 est points. We study the problem of counting holes in unstructured clouds 
 in the plane. The holes in a given cloud are quantified by the topological
  persistence of their boundary contours when the cloud is analysed at all 
 possible scales. We design the algorithm to count holes that are most pers
 istent in the filtration of offsets (neighbourhoods) around given points. 
 The input is a cloud of n points in the plane without any user-defined par
 ameters. The algorithm has O(n log n) time and O(n) space. The output is t
 he array\n(number of holes\, relative persistence in the filtration). We p
 rove theoretical guarantees when the algorithm finds the correct number of
  holes (connected components in the complement) of an unknown shape approx
 imated by a cloud.
LOCATION:Cambridge University Engineering Department\, LT1
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