Status of Hough Transform Method

1. Status of Hough TransformMethod Cvetan Cheshkov CERN Cvetan Cheshkov

2. Contents • Introduction • New Hough space variables definition • Results: • Efficiency, fakes • Investigation of inefficiency and fake track sources • Resolution and its dependence upon event multiplicity • Time consumption • Conclusions & Plans Cvetan Cheshkov

3. Introduction • The HLT Hough Transform method presented on last off-line week: • was already fast (~40s for event multiplicity of dN/dy~8000) • but suffered from relatively large amount of fakes which limited the performance of the consecutive cluster fitter (or in case of stand-alone mode – most likely physics performance) • On the other hand, Hough Transform still seems a very promising in overcoming the common problems at high multiplicity events. • Is it possible to improve the time and tracking performances of the Hough method? • Another interesting question is: could a stand-alone Hough Transform tracker survive in high multiplicity environment? Cvetan Cheshkov

4. Hough Space (I) • Two main problems with the current definition of the HT space variables k(=1/R) and  • The variables are strongly correlated  “Butterfly”-like shape of the peaks • complex peak finder • relatively high fake peak rate • Non-linear functions in the filling of HT space • Need in LUTs inside HT filling loop • “Time consuming” FP operations inside HT filling loop • Can we find better solution? Cvetan Cheshkov

5. Hough Space (II) • The choice of the new HT variables was inspired by: • Search for natural variables connected to the physical setup of the TPC (an example is the seeding in the offline reconstruction) • Search for variables which lead to linear HT • Why not use the Conformal Map transformation variables! Cvetan Cheshkov

6. (x1,y1) (x2,y2) Hough Space (III) • Lets define two curves inside a TPC sector by x/R2 = constant = 1(2) • Each primary track is represented • by two points on these curves • One can parameterize the track using 1=y1/R12 and 2=y2/R22 • For each space-point along the track trajectory: (y/R2-1)/(x/R2-1)=(2-1)/(2-1) y X Cvetan Cheshkov

7. Hough Space (IV) • One can use the variables 1 and 2 to define the Hough space • In this way each space-point inside a TPC sector will be represented in the Hough space by a straight line: 1 = A + B x 2 with A=y/R2(1-2)/(x/R2-2) and B=(x/R2- 1)/(x/R2- 2) • Linear filling of the Hough space! • The parameters A and B could be calculated in advance and used via LUTs Cvetan Cheshkov

8. Hough Space (V) • Which position of the defining curves 1,2? • Requirement I: we need as uncorrelated as possible Hough peaks • Requirement II: we have to preserve the monotonic behavior of the HT (used for fast filling of Hough space) • Lets consider a primary track which crosses all 159 rows inside one sector: • (x/R2-1) should change sign in the middle of the sector  half of the SPs with B>0 and half with B<0 • (x/R2-2)>0  A always increases with y/R2 • Conclusion: 1 - in the middle (close to padrow 80) and 2 - at the outer edge (close to padrow 159) Cvetan Cheshkov

9. Example – old Hough Space variables Central HIJING dN/dy=3500, 0.2T Cvetan Cheshkov

10. Example – new Hough Space variables Parameterized HIJING dN/dy=8000, 0.4T • Uncorrelated Hough peaks • Gain of 30-40% in the time consumption Cvetan Cheshkov

11. Testing conditions (I) • Limits on Hough space variables correspond to a track with minimum Pt[GeV/c] = Bfield[T] which crosses the middle of the TPC sector • Hough space binning is fixed to 76(1)x140(2)x100(eta) The size is roughly equal to the pad size in the corresponding TPC rows • Hough Transform runs stand-alone (without a consecutive cluster fitter) Cvetan Cheshkov

12. Testing conditions (II) • The method requires new definitions in order to determine the performance: • No clusters associated  assign only 1 MC label to each track • High occupancy (and therefore overlapping clusters) in general does not affect the track parameters, but cause appearance of “ghosts”  fakes tracks  ghost tracks • If more than 1 track with the same MC label, take randomly one as good and second as fake (or ghost) • Good tracks – primaries from offline comparison macro Cvetan Cheshkov

13. Efficiency and Fakes (I) 0.4T dN/dy=8000 dN/dy=4000 dN/dy=2000 Cvetan Cheshkov

14. Efficiency and Fakes (II) 0.5T HIJINGparam dN/dy=8000 Full HIJING dN/dy~8000 Cvetan Cheshkov

15. Efficiency and Fakes (III) dN/dy=8000 0.2T 0.4T 0.5T Cvetan Cheshkov

16. Sources of Inefficiency (I) • Merging of the tracks (1-2% for dN/dy=8000, 0.4T) when: • their peaks overlap in the hough space • their peaks are close to each other and one is removed during the track merging (both in hough space and  bins) • Low pt tracks at high  (close to 1). The  bins efficiently get narrower (+mult.scat. in ITS?) • Tracks close to the TPC sector borders (affects mainly tracks with Pt>1-1.5GeV/c) Cvetan Cheshkov

17. Sources of Inefficiency (II) Cvetan Cheshkov

18. Sources of Inefficiency (III) • The only way to recover these low Pt ineff is to redefine  bins. For example, use angle  instead of  • On the other hand, the multiplicity should be more or less constant as a function of  and therefore the amount of fakes as well • Compromise between efficiency <-> fakes • In any case, the ineff at Pt<0.6 is not so important for the HLT • The work is in progress... Cvetan Cheshkov

19. Sources of Inefficiency (IV) Cvetan Cheshkov

20. Ghost tracks • The final merging is still under investigation (hopefully will use PDC’04 data) • Therefore we still have tracks from different TPC sectors and  slices to be merged • The “real” fakes would be at the level of <1% for central event, of course with a small decrease in the efficiency In 2 or more  slices In 2 TPC sectors Overall Cvetan Cheshkov

21. Relative Pt resolution for tracks with Pt>2GeV/c in % Cvetan Cheshkov

22. Relative Pt resolution for tracks with Ptmin<Pt<2GeV/c in % Cvetan Cheshkov

23. Eta resolution in 10-3 Only tracks with Pt>0.5GeV/c Cvetan Cheshkov

24.  Resolution in mrads Only tracks with Pt>0.5GeV/c Cvetan Cheshkov

25. Resolution for parameterized HIJING (dN/dy=8000,0.4T) event Cvetan Cheshkov

26. Benchmarks • HT was tested mainly on Itanium II (1.5 GHz, 6Mb L3 cache) machines – these are our present GDCs • Compiled with Intel ecc with aggressive optimization • Time consumption is: • strictly proportional to the HT space size • roughly proportional to the event multiplicity Cvetan Cheshkov

27. Conclusions • The new definition of Hough space variables improved both time and tracking performances of Hough Transform method • Main sources of ineff and fakes well understood • The performance results prove that the HT could work even as a stand-alone tracker • The high occupancy does not affect significantly the performance of the algorithm Cvetan Cheshkov

28. Plans • The new HT as well as the standard HLT tracker will be run during the event reconstruction in the second step of the Physics DC’04 • Try both of them on real physics trigger algorithms, compare the results… • Still some minor problems with the efficiency, fakes, track merging to be solved • Start to add another detectors to HLT: ITS,Muon,TRD,... Cvetan Cheshkov