Pattern Recognition in OPERA Tracking

A.Chukanov, S.Dmitrievsky, Yu.Gornushkin

OPERA collaboration meeting, Mizunami, Japan, 20-22 of January 2009

JINR, Dubna

Outline

• Problem of pattern recognition in standard OPERA tracking

• Method of Hough transform for straight track recognition

• Simple tracing method for curved track reconstruction

• Method of spanning tree tracing for curved track candidate selection

• Status of proposed pattern recognition package.

Standard track

Mushower extrap

Pictures are taken from Dario’s reportof 29/10/2008

Problem of standard OPERA tracking originates in fact from incorrect pattern recognition. Mushower procedure doesn’t eliminate the reason of the problem but just serves as a patch for tracking algorithm. It simply makes a linear extrapolation of found track direction through a shower without taking into account hit positions in the beginning part of an event.

Hence the OPERA pattern recognition needs to be improved.

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

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 easily distinguished by a pike in HT histogram. Moreover, the result of HT recognition coincides with Mushower extrapolation while Hough transform can be performed just at the stage of pattern recognition.

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 (2 empty TT planes, 8 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

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.

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

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

Resolution of Tracking

Prelim

inar

y

Preliminary results of tracking resolution for XZ and YZ projections have been obtained with help of tracks found in CS. is comparable with standard tracking resolution.

cm5.2

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: under test

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

not yet in OPERA release