Track Finding with Hough Transform

1
Track Finding with Hough Transform

• Joachim Gläß
• Computer Engineering, University of Mannheim
• Contents
• Quantitative Results and Dependencies
• number of tracks - hits (beam energy)
• track quality - peak definition (number of
  hits/track)
• detector geometry (more/less layers)
• Summary

January 24, 2005 CBM Tracking
Workshop
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Hough Transformof Parabola
ltgt
rotated by q (Px/Pz)
Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
3
Hough TransformProcessing Parameters

• Resolution of Hough Transform
• 127 x 383 x 191
• Pz gt 1 GeV/c
• Px/Pz, Py/Pz lt 0.5
• Input Data
• MC data, OCT04 framework
• urqmd.auau.xxgev.yyyyy.0000.mc.root
• xx 15, 25, 35
• yyyyy centr, mbias
• 100 events

Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
4
Hough TransformProcessing Parameters

• detector geometry (more/less layers)
• 5 detector layers (standard geometry)
• 4 and 6 detector layers
• z-positions 20 cm, (30 cm), 40 cm, 60 cm, 80 cm,
  100 cm
• number of tracks - hits
• beam energies 15 GeV, 25 GeV, 35 GeV, central,
  min bias
• track quality - peak definition
• Accepted tracks
• hits in the first 4 or 5 layers (standard
  geometry)
• hits in the first 3, 4 or 5 layers (standard
  geometry)
• hits in the first 4, 5 or 6 layers

Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
5
Hough TransformSimulation Results

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92
• ghost 36
• clone 14
• hits/ev. 5000

Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
6
Hough TransformSimulation Results

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92 92
• ghost 36 24
• clone 14 14
• hits/ev. 5000 4000

Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
7
Hough TransformSimulation Results

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92 92 91
• ghost 36 24 9
• clone 14 14 13
• hits/ev. 5000 4000 3500

Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
8
Hough TransformSimulation Results

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92 92 91 93
• ghost 36 24 9 16
• clone 14 14 13 14
• hits/ev. 5000 4000 3500

Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
9
Hough TransformSimulation Results
25 GeV, 5 layers, gt 4 hits

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92 92 91 93
• ghost 36 24 9 16
• clone 14 14 13 14
• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 3 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 93 95 94 95
• ghost 51 40 26 31
• clone 10 29 10 11

eff. 92
25 GeV, 5 layers, gt 3 hits
eff. 95
Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
10
Hough TransformSimulation Results
25 GeV, 5 layers, gt 4 hits

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92 92 91 93
• ghost 36 24 9 16
• clone 14 14 13 14
• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 3 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 93 95 94 95
• ghost 51 40 26 31
• clone 10 29 10 11

ghost 24
25 GeV, 5 layers, gt 3 hits
ghost 40
Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
11
Hough TransformSimulation Results
25 GeV, 5 layers, gt 4 hits

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92 92 91 93
• ghost 36 24 9 16
• clone 14 14 13 14
• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 3 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 93 95 94 95
• ghost 51 40 26 31
• clone 10 29 10 11

clone 14
25 GeV, 5 layers, gt 3 hits
clone 29
Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
12
Hough TransformSimulation Results
25 GeV, 5 layers, gt 4 hits

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92 92 91 93
• ghost 36 24 9 16
• clone 14 14 13 14
• 4 detector layers (standard geometry)
• z-positions 40 cm, 60 cm, 80 cm, 100
  cm
• gt 3 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 94 95 95 96
• ghost 69 60 40 47
• clone 15 20 29 16

eff. 92
25 GeV, 4 layers, gt 3 hits
eff. 95
Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
13
Hough TransformSimulation Results
25 GeV, 5 layers, gt 4 hits

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92 92 91 93
• ghost 36 24 9 16
• clone 14 14 13 14
• 4 detector layers (standard geometry)
• z-positions 40 cm, 60 cm, 80 cm, 100
  cm
• gt 3 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 94 95 95 96
• ghost 69 60 40 47
• clone 15 20 29 16

ghost 24
25 GeV, 4 layers, gt 3 hits
ghost 60
Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
14
Hough TransformSimulation Results
25 GeV, 5 layers, gt 4 hits

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92 92 91 93
• ghost 36 24 9 16
• clone 14 14 13 14
• 4 detector layers (standard geometry)
• z-positions 40 cm, 60 cm, 80 cm, 100
  cm
• gt 3 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 94 95 95 96
• ghost 69 60 40 47
• clone 15 20 29 16

clone 14
25 GeV, 4 layers, gt 3 hits
clone 20
Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
15
Hough TransformSimulation Results
25 GeV, 5 layers, gt 4 hits

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92 92 91 93
• ghost 36 24 9 16
• clone 14 14 13 14
• 6 detector layers (standard geometry)
• z-positions 20cm,30cm,40cm,60cm,80cm,100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 95 94 94 95
• ghost 17 11 4 6
• clone 19 17 13 13

eff. 92
25 GeV, 6 layers, gt 4 hits
eff. 95
Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
16
Hough TransformSimulation Results
25 GeV, 5 layers, gt 4 hits

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92 92 91 93
• ghost 36 24 9 16
• clone 14 14 13 14
• 6 detector layers (standard geometry)
• z-positions 20cm,30cm,40cm,60cm,80cm,100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 95 94 94 95
• ghost 17 11 4 6
• clone 19 17 13 13

ghost 24
25 GeV, 6 layers, gt 4 hits
ghost 11
Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
17
Hough TransformSimulation Results
25 GeV, 5 layers, gt 4 hits

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 92 92 91 93
• ghost 36 24 9 16
• clone 14 14 13 14
• 6 detector layers (standard geometry)
• z-positions 20cm,30cm,40cm,60cm,80cm,100 cm
• gt 4 hits
• AGeV c 35 c 25 c 15 m 35
• eff. 95 94 94 95
• ghost 17 11 4 6
• clone 19 17 13 13

clone 14
25 GeV, 6 layers, gt 4 hits
clone 17
Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
18
Track Finding with Hough TransformSummary

• Quantitative Results and Dependencies
• number of tracks - hits (beam energy)
• efficiency no dependency
• ghosts
• smaller beam energies
• gt less tracks
• gt less hits
• gt less ghosts

Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
19
Track Finding with Hough TransformSummary

• Quantitative Results and Dependencies
• detector geometry (more/less layers)
• efficiency small dependency (92 -95 )
• main differences at low momentum
• low momentum tracks do not pass through all
  detector planes
• ghosts
• more detector planes -gt less ghosts

Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
20
Track Finding with Hough TransformSummary

• Quantitative Results and Dependencies
• centr. 25 AGeV
• 5 layers, gt 4 hits, 20, 40, 60, 80 eff. 92 ,
  ghosts 24
• 5 layers, gt 3 hits, 20, 40, 60 eff. 95 ,
  ghosts 40
• 4 layers, gt 3 hits, 40, 60, 80 eff. 95
  , ghosts 60
• 6 layers, gt 4 hits, 20, 30, 40, 60 eff. 94 ,
  ghosts 11
• 5 layers minimum for tracking
• open questions
• other groups see same effects?
• add detector at 30 cm?
• skip detector at 80 cm?

Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering
21

• Comments to STS strip detector design
• from view of tracking
• as few as possible fakes
• fakes length2 gt short strips
• fakes sin f gt small stereoangle
• resolution in x more important than in y
• gt strips parallel to y-axis
• use detector modules in all 4 quadrants

y
x
Joachim Gläß, Univ. Mannheim, Institute of
Computer Engineering