Pattern Recognition in OPERA Tracking

A.Chukanov, S.Dmitrievsky, Yu.Gornushkin

OPERA collaboration meeting, Ankara, Turkey, 1-4 of April 2009

JINR, Dubna

Outline

• Problems of pattern recognition in OPERA tracking

• Hough Transform method for straight track recognition

• Simple Tracing method for curved track reconstruction

• Spanning Tree method for curved tracks

• Status of proposed pattern recognition package.

Standard track

Mushower extrap

Pictures from Dario’s report 29/10/2008

• There is a problem in standard OpRelease pattern recognition algorithm. •Mushower doesn’t solve the problem but just serves as a patch for tracking algorithm.

Antoine’s presentation at LNGS end of 2008

A few examples from the latest RECO file

The OpRelease pattern recognition definitely needs to be improved.

The efficiente pattern recognition method widely used in HEP experiments (e.g. MINOS, ALICE, CBM, etc) is Hough transform (HT) algorithm

The algorithm is a part of the BrickFinder and is fully integrated in the OpRelease

For each of given point iteration through different angles gives us corresponding values of . Points are saved in a 2D histogram. If there are some straight tracks (or parts of tracks) in an event there should exist distinct pikes in the histogram. By determining of centers of gravity of that pikes it is possible to reconstruct parameters of track lines by the following formulas:

Hough transform uses representation of a line in normal form:This equation specifies a line passing through point . That line is perpendicular to the line drawn from the origin to point in polar space. It can be shown that in case of points belonging to the same line and are constants.

),( yx),(

sincos yx

),( ii yxj ),( jj

),( 00

Hough Transform for Straight Track Recognition

kk BxAy

0

0

0 sin,)tan(

1

kk BA

)360,0( j

Example of HT Track Recognition: event 234948251

73.770 42.990 and

give track parameters: ,217.0AcmB 07.193

Proposed HT track finding

Found

OpRelease tracking:solid line - Kalman extrapolation,dash line - Mushower extrapolation.

Example of HT Track Recognition: event 234643825

OpRelease tracking:solid line - Kalman extrapolation,dash line - Mushower extrapolation.

7.920 62.1260 and

give track parameters: ,047.0AcmB 89.38

Proposed HT track finding

Found

Example of HT Track Recognition: event 234655944

45.840 01.910 and

give track parameters: ,097.0AcmB 67.112

Proposed HT track finding

Found

OpRelease tracking:solid line - Kalman extrapolation,dash line - Mushower extrapolation.

Example of HT Track Recognition: event 234862308

69.1030 79.1640 and

give track parameters: ,243.0AcmB 02.43

Proposed HT track finding

Found

OpRelease tracking:solid line - Kalman extrapolation,dash line - Mushower extrapolation.

Example of HT Track Recognition: event 234917207

63.970 64.920 and

give track parameters: ,13.0AcmB 28.45

Proposed HT track finding

Found

OpRelease tracking:solid line - Kalman extrapolation,dash line - Mushower extrapolation.

As shown in the given examples the muon track is unambiguously distinguished by a pike in HT histogram in case of so called difficult events. Moreover, the result of Hough transform coincides with Mushower extrapolation already at the pattern recognition level (without a fit).

With ~300 events with a muon found in the CS (from Giovanni) a general performance was estimated

• There are still events with muon track not found in the CS (out of list of Giovanni) (badly reconstructed in std tracking procedure?)

Houph Transform reconstruction of the same event

Houph Transform reconstruction of the same event

But sometimes due to low momentum of the particle it is really difficult

Simple Tracing Method for Curved Track Finding

After the initial straight part of a track is determined by a Hough transform in the beginning of an event it is possible to find the rest tail part of the track with help of proposed tracing method (which in fact is a simplified kind of a Kalman filter):

1) Finding a search direction Linear fit on 7 last found hits of a track; 2) Setting of search angle range Its own angle range for each detector is used taking into account its geometry and uncertainties. 3) Finding hits in the following detector planes inside the search angle range Inefficiency of detectors (3 empty TT planes, 11 empty RPC planes) is taken into account. If there are more than 1 candidates to track hits only the hit accepted that is the nearest to the search direction. 4) Including found hit to the TrackElement and iterating steps 1-3 for next planes or stop procedure in case of no hits found

Backward Tracing with Background When particle’s momentum is small the track can be curved already in its beginning part. The curved tracks are difficult for HT reconstruction and even the simple tracing method can fail within the shower environment. On the picture below such a specific case is shown.

Y, cm

Z, cm

T T planes

Line found by aHough transform

wrong hits

track hits

There are no moresequential hits inthe search area

Event 217982179

Example of Forward Tracing Procedure

Event 23356121

TT1 TT2RPC1 RPC2Y, cm

Z, cm

Simple tracing along the beam direction works easily (as shown on the picture) because there are no background hits far away of the vertex.

To solve such a problem it is useful to iterate on all possible chains of the hits to select among them the best chain. It can be done with help of method of spanning tree tracing. It finds different reliable track trajectories and than consider the longest and most smooth chain of hits to be the best track candidate.

Spanning Tree Tracing Method for Track Selection

Event 217982179

Y, cm

Z, cm

T T planes

As a result the longestand most smooth trackwill be selected

Status of Proposed Pattern Recognition Package

1) Event cleaning (removing of CT and isolated hits): done

2) Method of Hough Transform to find straight part of a track: done

3) Tracing method to find curved tail part of a track: done

4) Method of Spanning Tree Tracing to select the best track candidate within a shower:

done