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Fast Hough Transform Method

Explore the fast Hough Transform method, its implementation, and enhancements for peak finding in ALICE offline data processing. See improved efficiency, timing, and resolution results with future plans addressed.

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Fast Hough Transform Method

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  1. Fast Hough Transform Method Cvetan Cheshkov ALICE offline week

  2. Contents • Introduction • Fast Hough Transform method • Demo • Results on timing, efficiency and resolution • Concluding remarks and future plans ALICE offline week

  3. HLT (high multiplicity case) Hough Transform Local Peak finder TPC digits Find, deconvolute and associate clusters Track fit • Hough Transform takes 1000-2300s in linear mode (dn/dy3500; PIII 800MHz) ALICE offline week

  4. Hough Transform (HT) • Each TPC digit is transformed into a curve in the Hough parameter space corresponding to all possible tracks to which the digit could be associated: (x,y)(k=1/R,) k – track curvature; - track emission angle • The Hough approach: • Assumes that the tracks are coming from (or close to) the primary vertex • Neglects any energy losses and multiply scattering in the detector volume ALICE offline week

  5. HLT implementation of HT • TPC data input is splitted in sectors, r/o patchesand  slices (50-100) • Hough transform is performed on each of these slices separately (in parallel) • The HT parameter space is binned and stored in histograms • The histograms are summed over the patches • Local peaks are identified by a peak finder and transmitted as track seeds to the cluster finder ALICE offline week

  6. Improving HT • Originally HT was done filling the digits charge  Large amount of fakes in a high occupancy case  Sophisticated peak finder • Studying the HT performance it turned out that the performance can be improved by counting: digits charge #digits #clusters (TPC rows) ALICE offline week

  7. “Counting Rows & Gaps” HT • Naturally the studies lead to the idea to count consecutive TPC rows • Idea: Good track candidate must have not only some amount of digit’s charge, digits or rows along its trajectory, but also must occupy consecutive TPC rows • Now the algorithm counts as #gaps between occupied rows • Weight used to fill HT space: • #rows/#gaps • #rows (#gaps<N) ALICE offline week

  8. Example Corresponding HT space  Slice of 1 TPC sector • Central HIJING dn/dy=3500, 0.2T ALICE offline week

  9. New Peak Finder (PF) • The improvement in the HT quality  simpler PF • The new PF looks for neighbor bins with the same weight • Track parameters are extracted by averaging the peak edge points both in  and 1/R (track curvature) directions  track is guided by the cluster borders ALICE offline week

  10. Comparison Standard HT New HT • New Hough seeds much more clear • It seems that now the cluster fitter is • the limiting factor (it is also the slowest part) ALICE offline week

  11. Fast Hough Transform • Assuming ordered TPC digits (in time bins, pads, padrows)  new algorithm offers big space for speeding up • HT is monotonic along the padrows  do it only for the first and last (in paw index direction) digits which belong to a cluster and fill a the corresponding ribbon in the HT space • Stopping rules using already accumulated #gaps ALICE offline week

  12. Fast Hough Transform • By introducing the new HT and substituting sin and cos by LUTs  a factor of 10 in the speed 2300s  230s • Which are the sources: • LUTs - factor of 2 • HT algorithm – factor of 5 • Additional factor of 2 • Code improvement • #gaps stopping rule • Filter on the data (consistent with HT algorithm) ALICE offline week

  13. Demo! • Demo with central HIJING event (dn/dy=3500) on one of the GDCs (oplapro machines) used in the Computing DC • The event is stored as DATE formatted file and is processed by a stand-alone exe (see Thomas’ talk) • Oplapro – Itanium II; 1.5GHz; 4Mb L3 cache ALICE offline week

  14. Timings • HT space size: • (75 in )x(140 in 1/R)x(100 in ) • Time consumption is: • strictly proportional to the HT space size • roughly proportional to the event multiplicity ALICE offline week

  15. Performance • Try to run Hough stand-alone (without a consecutive cluster fitter and etc) • 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 ghost • Good tracks – primaries from offline comparison ALICE offline week

  16. Performance /Efficiencies/ Parameterized HIJING dn/dy=8000 B=0.2T B=0.4T B=0.5T ALICE offline week

  17. Performance /Efficiencies/ dn/dy=2000 dn/dy=4000 B=0.2T B=0.4T B=0.4T ALICE offline week

  18. Performance /Efficiency/ • Summary: • The efficiency is almost unaffected by the event multiplicity!! • About ½ of the ghosts are coming from the high occupancy ALICE offline week

  19. Performance /Resolution/ Parameterized HIJING dn/dy=4000, 0.4T Pt/Pt(%)=0.7+2.7xPt =6.3x10-3 =7.2mrad ALICE offline week

  20. Performance /Resolution/ • Summary: • The relative Pt resolution rises linearly with Pt consistent with the expectations from HT binning! • It is almost proportional to 1/B • The resolution on eta,psi and Pt (high Pt tracks) increase by <10% when dn/dy goes from 2000 to 8000 (the effect is due mostly to ghosts) • At low Pt one can see clearly the effect of ghosts ALICE offline week

  21. Known problems • The Peak Finder has certain problems with the cut on the peaks size • The main source of inefficiencies • We need cut which depends on the position inside Hough space • Special treatment of tracks crossing 2 sectors • They give significant contribution to the #ghosts • Need in a proper global (between eta slices and sectors) track merger! ALICE offline week

  22. Concluding remarks • The new Hough method shows reasonable performance and is much much faster! • Needs some further optimization and evaluation • The answer about its applicability can be given only by trying some real physics trigger algorithms (hopefully using PDC’04 data) ALICE offline week

  23. Concluding remarks • Impact on physics cases: • Jet finder • The efficiency for Pt above 2-2.5 GeV is high • The ghosts almost disappear at 2.5 GeV • The eta and psi resolutions are pretty good for any cone jet-finder sizes (0.1,0.2,…) • The Pt resolution for high Pt tracks does not explode • Open charm track filter • The efficiency between 0.5 and 1 GeV looks reasonable • The ghosts in principle do not hurt too much because they are close to the good tracks ALICE offline week

  24. Future plans • Next week everything to CVS • Work on Peak Finder and investigation of inefficiencies and ghosts • Preparation of physics trigger algorithms and their evaluation • As soon as Computing DC is restarted try the whole machinery in online mode • Closer integration with AliRoot ALICE offline week

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