UPDATE TO THE APOLLONIUS HOUGH TRACK FINDER 05.11.2019 I ANNA - - PowerPoint PPT Presentation

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UPDATE TO THE APOLLONIUS HOUGH TRACK FINDER 05.11.2019 I ANNA SCHOLL INTRODUCTION Implement track finding algorithm for barrel part Use hits from MVD, STT, GEM detector Track passes through MVD and GEM hit points Track is

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SLIDE 1

UPDATE TO THE APOLLONIUS HOUGH TRACK FINDER

05.11.2019 I ANNA SCHOLL

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SLIDE 2

INTRODUCTION

5 Nov 2019 Seite 2

x interaction point (IP)

  • Implement track finding algorithm for barrel part
  • Use hits from MVD, STT, GEM detector
  • Track passes through MVD and GEM hit points
  • Track is tangent to STT isochrones
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SLIDE 3

HOW TO INCLUDE ISOCHRONE INFORMATION IN TRACKING ALGORITHMS?

5 Nov 2019 Seite 3

  • Track is tangent to the isochrone

βž”First idea: Hough transformation

  • Separate dimensions
  • 3D helix (R, , z) βž” 2D circle (R, ) + line (z)
  • Apply Hough transform to detect tracks in a set of hits
  • For each hit, generate all possible tracks compatible with

it (Circles in xy plane, passing through IP and are tangent to the isochrone)

  • Collect generated track parameters for all hits (2D Hough

Space)

  • Count: most frequent values = parameters of actual tracks

x (IP)

πœ’ πœ’

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SLIDE 4

HOW TO INCLUDE ISOCHRONE INFORMATION IN TRACKING ALGORITHMS?

5 Nov 2019 Seite 3

  • Track is tangent to the isochrone

βž”First idea: Hough transformation

  • Separate dimensions
  • 3D helix (R, , z) βž” 2D circle (R, ) + line (z)
  • Apply Hough transform to detect tracks in a set of hits
  • Problem: a lot of false combinations for increasing

number of tracks per event

  • Idea: reduce combinatrics by using 2 Isochrones and IP

βž”problem of Apollonius x (IP)

πœ’ πœ’

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SLIDE 5

APOLLONIUS PROBLEM

5 Nov 2019 Seite 4

  • General Apollonius problem for 3 circles:

Find circles that are tangent to three given circles in a plane

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SLIDE 6

APOLLONIUS PROBLEM

5 Nov 2019 Seite 4

For each circle there are 2 possibilities for an Apollonius circle

  • 1. 𝑠

π΅π‘žπ‘π‘šπ‘šπ‘π‘œπ‘—π‘£π‘‘ =

𝑠

π‘‘π‘“π‘œπ‘’π‘“π‘  + 𝑠 𝑗

  • General Apollonius problem for 3 circles:

Find circles that are tangent to three given circles in a plane

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SLIDE 7

APOLLONIUS PROBLEM

5 Nov 2019 Seite 4

For each circle there are 2 possibilities for an Apollonius circle

  • 1. 𝑠

π΅π‘žπ‘π‘šπ‘šπ‘π‘œπ‘—π‘£π‘‘ =

𝑠

π‘‘π‘“π‘œπ‘’π‘“π‘  + 𝑠 𝑗

  • 2. 𝑠

π΅π‘žπ‘π‘šπ‘šπ‘π‘œπ‘—π‘£π‘‘ =

𝑠

π‘‘π‘“π‘œπ‘’π‘“π‘  βˆ’ 𝑠 𝑗

  • General Apollonius problem for 3 circles:

Find circles that are tangent to three given circles in a plane

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SLIDE 8

APOLLONIUS PROBLEM

5 Nov 2019 Seite 4

23 = 8 In total Apollonius circles For each circle there are 2 possibilities for an Apollonius circle

  • 1. 𝑠

π΅π‘žπ‘π‘šπ‘šπ‘π‘œπ‘—π‘£π‘‘ =

𝑠

π‘‘π‘“π‘œπ‘’π‘“π‘  + 𝑠 𝑗

  • 2. 𝑠

π΅π‘žπ‘π‘šπ‘šπ‘π‘œπ‘—π‘£π‘‘ =

𝑠

π‘‘π‘“π‘œπ‘’π‘“π‘  βˆ’ 𝑠 𝑗

  • General Apollonius problem for 3 circles:

Find circles that are tangent to three given circles in a plane

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SLIDE 9

HOUGH TRANSFORMATION BASED ON THE APOLLONIUS PROBLEM

5 Nov 2019 Seite 5

  • Works quiet well if

track candidate is known (IdealTrackFinder)

Implemetation in PandaRoot and testing with simulated data

Example for one Track

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SLIDE 10

HOUGH TRANSFORMATION BASED ON THE APOLLONIUS PROBLEM

5 Nov 2019 Seite 6

Implemetation in PandaRoot and testing with simulated data

  • Works quiet well if

track candidate is known (IdealTrackFinder)

  • For one event

(many tracks): high combinatorics with (still) many false combinations

Example for one Event

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SLIDE 11

PRESELECTION

5 Nov 2019 Seite 7

  • Using Apollonius transform for all tracks in one event is very

time consuming and leads to a lot of false combinations βž”preselection for possible tracklets is needed

  • Idea:
  • preselection by cellular automaton
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SLIDE 12

CELLULAR AUTOMATON

5 Nov 2019 Seite 8

  • Combine directly adjacent hits to

tracklets

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SLIDE 13

CELLULAR AUTOMATON

5 Nov 2019 Seite 8

  • Combine directly adjacent hits to

tracklets

  • Problem: Tracks can be divided in

several tracklets βž”How to merge tracklets βž”Find relevant parameters for merging

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SLIDE 14

MERGING TRACKLETS

5 Nov 2019 Seite 9

  • Both tracks are represented by

circles

  • Calculate intersection area of both

circles and divide it by the area of the larger circle Compare two different parameters for merging:

  • 1. intersection area fraction
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SLIDE 15

MERGING TRACKLETS

5 Nov 2019 Seite 10

πœ’1 πœ’2

  • Define line perpendicular in the

middle between two tracklets

  • propagate both tracks to this line
  • Calculate distance between both

intersection points

  • Calculate angular difference at the

intersection points Compare two different parameters for merging:

  • 1. intersection area fraction
  • 2. middle line
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SLIDE 16

MERGING TRACKLETS

5 Nov 2019 Seite 11

Only STT data

accuracy: 93.5% FP: 3.9% TP: 85.1%

false positive rate true positive rate

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SLIDE 17

TESTING ALGORITHM WITH MERGING

5 Nov 2019 Seite 12

  • Applying merging to the algorithm leads still to a high rate of not found tracks

(42% not found)

  • Reason:
  • after Cellular Automaton and merging tracklets still hits are not added to a

track

  • A track is divided in so many small tracklets that the track could not be

found

  • Searching for tracks in remaining hits
  • leads to high combinatorics and many false combinations
  • Again use a preselection

β†’ dividing remaining hits in Segments and perform hough transformation to hits found with segmentation algorithm

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SLIDE 18

SEGMENTATION ALGORITHM

5 Nov 2019 Seite 13

IP

  • Filling
  • values of all hits

into a histogram: #

πœ’

πœ’

  • Divide in - sectors
  • Hough transformation for all

hits in one sector πœ’

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SLIDE 19

RESULTS

5 Nov 2019 Seite 14

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SLIDE 20

NEXT STEPS

5 Nov 2019 Seite 15

  • Speed up computing time (at the moment ~0.5 s /event) and enable

GPU calculation

  • Try to decrease ghost ratio and increase number of fully found tracks
  • Insert z-direction