Track Finding with Hough Transform

1
Track Finding with Hough Transform

• Christian Steinle
• Computer Engineering, University of Mannheim
• Contents
• Hough Transform of Parabola
• Result Dependencies According to
• Beam Energy
• Detector Geometry
• Summary

2
Hough Transform of Parabola
ltgt
rotated by q (Px/Pz)
five hits
five curves
3
Hough Transform Processing Parameters

• Resolution of hough transform space
• 127 x 383 x 191
• Pz gt 1 GeV/c
• Px/Pz, Py/Pz lt 0.5
• Input data
• MC data, OCT04 framework
• Simulation variables
• Beam energy
• Detector geometry
• Track definition

4
Result Dependencies According to Beam Energy

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• Track has 4 or more hits
• AGeV 35 25 15
• eff. 92 92 91
• ghost 36 24 9
• clone 14 14 13
• hits/ev. 5000 4000 3500
• efficiency
• no dependency
• ghost
• smaller beam energies
• gt less hits
• gt less ghosts
• clone
• smaller beam energies
• gt less clones (negligible)

OPTIMIZE
5
Hough TransformThe Task of Peak Finding
- Theoretical Task
five curves
- Concrete Task
6
Hough TransformOptimization of Peak Finding
- Real Task
If neighbourhood is bigger
then delete
- Optimized Task
If neighbourhood is bigger or equal
then delete
7
Result Dependencies According toBeam Energy

• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• Track has 4 or more hits
• AGeV 35 25 15
• eff. 89 91 91
• ghost 37 25 10
• clone 1 1 1
• hits/ev. 5000 4000 3500
• efficiency
• about 1 less
• ghost
• about 1 less
• clone
• less clones
• (total about 1 )

OPTIMIZE
8
Result Dependencies According to Detector
Geometry
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 35 25 15
• eff. 89 91 91
• ghost 37 25 10
• clone 1 1 1
• 5 detector layers (standard geometry)
• z-positions 20 cm, 40 cm, 60 cm, 80 cm, 100 cm
• gt 3 hits
• AGeV 35 25 15
• eff. 90 92 94
• ghost 57 45 31
• clone 1 1 1

ghost 25
25 GeV, 5 layers, gt 3 hits
ghost 45
9
Result Dependencies According to Detector
Geometry
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 35 25 15
• eff. 89 91 91
• ghost 37 25 10
• clone 1 1 1
• 4 detector layers (sub 20cm)
• z-positions 40 cm, 60 cm, 80 cm, 100
  cm
• gt 3 hits
• AGeV 35 25 15
• eff. 87 90 93
• ghost 75 68 50
• clone 1 1 2

ghost 25
25 GeV, 4 layers, gt 3 hits
ghost 68
10
Result Dependencies According to Detector
Geometry
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 35 25 15
• eff. 89 91 91
• ghost 37 25 10
• clone 1 1 1
• 6 detector layers (add 30cm)
• z-positions 20cm, 30cm, 40cm, 60cm, 80cm, 100 cm
• gt 4 hits
• AGeV 35 25 15
• eff. 93 93 93
• ghost 19 12 4
• clone 7 6 5

eff. 91
25 GeV, 6 layers, gt 4 hits
Increase near 1GeV/c
eff. 93
11
Result Dependencies According to Detector
Geometry
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 35 25 15
• eff. 89 91 91
• ghost 37 25 10
• clone 1 1 1
• 6 detector layers (add 30cm)
• z-positions 20cm, 30cm, 40cm, 60cm, 80cm, 100 cm
• gt 4 hits
• AGeV 35 25 15
• eff. 93 93 93
• ghost 19 12 4
• clone 7 6 5

ghost 25
25 GeV, 6 layers, gt 4 hits
ghost 12
12
Result Dependencies According to Detector
Geometry
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 35 25 15
• eff. 89 91 91
• ghost 37 25 10
• clone 1 1 1
• 6 detector layers (add 30cm)
• z-positions 20cm, 30cm, 40cm, 60cm, 80cm, 100 cm
• gt 4 hits
• AGeV 35 25 15
• eff. 93 93 93
• ghost 19 12 4
• clone 7 6 5

clone 1
25 GeV, 6 layers, gt 4 hits
clone 6
13
Result Dependencies According to Detector
Geometry
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 35 25 15
• eff. 89 91 91
• ghost 37 25 10
• clone 1 1 1
• 6 detector layers (add 30cm)
• z-positions 20cm, 30cm, 40cm, 60cm, 80cm, 100 cm
• gt 5 hits
• AGeV 35 25 15
• eff. 85 83 82
• ghost 13 7 1
• clone 5 3 2

eff. 91
25 GeV, 6 layers, gt 5 hits
Decrease near 1GeV/c
eff. 83
14
Result Dependencies According to Detector
Geometry
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 35 25 15
• eff. 89 91 91
• ghost 37 25 10
• clone 1 1 1
• 6 detector layers (add 30cm)
• z-positions 20cm, 30cm, 40cm, 60cm, 80cm, 100 cm
• gt 5 hits
• AGeV 35 25 15
• eff. 85 83 82
• ghost 13 7 1
• clone 5 3 2

ghost 25
25 GeV, 6 layers, gt 5 hits
ghost 7
15
Result Dependencies According to Detector
Geometry
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 35 25 15
• eff. 89 91 91
• ghost 37 25 10
• clone 1 1 1
• 5 detector layers (add 30cm, sub 80cm)
• z-positions 20cm, 30cm, 40cm, 60cm, 100 cm
• gt 4 hits
• AGeV 35 25 15
• eff. 92 93 93
• ghost 23 14 5
• clone 6 6 5

eff. 91
25 GeV, 5 layers, gt 4 hits
Increase near 1GeV/c
eff. 93
16
Track Finding With Hough TransformSummary
25 AGeV
layer hits detector planes detector planes detector planes detector planes detector planes detector planes eff. ghost clone
5 gt4 20 40 60 80 100 91 25 1
5 gt 3 20 40 60 80 100 92 45 1
4 gt 3 40 60 80 100 90 68 1
6 gt 4 20 30 40 60 80 100 93 12 6
6 gt 5 20 30 40 60 80 100 83 7 3
5 gt 4 20 30 40 60 100 93 14 6

• efficiency
• small dependency
• main differences at low momentum
• low momentum tracks do not pass through all
  detector planes
• ghost
• ghosts are dependent of the detector geometry
• more layers gt less ghosts
• clone
• dependent of the peak finding algorithm

17
Track Finding With Hough TransformSummary

• Minimal requirements
• 5 layers for tracking
• efficiency is nearly equal
• less layers -gt heavily increasing ghost rate
• clones are no problem
• Open questions
• Add detector plane at 30 cm ?
• efficiency is nearly equal
• less ghosts (halved ghost rate)
• Skip detector plane at 80 cm ?
• efficiency is nearly equal
• less ghosts (halved ghost rate)
• Next Steps
• Processing strip detectors
• Including hit producer