Status of Hough Transform Method

Alice offline week 29 June 2004Alice offline week 29 June 2004 Cvetan CheshkovCvetan Cheshkov 11

Status of Hough TransformStatus of Hough TransformMethodMethod

Cvetan CheshkovCvetan Cheshkov

CERNCERN


ContentsContents IntroductionIntroduction

New Hough space variables definitionNew Hough space variables definition

Results:Results: Efficiency, fakesEfficiency, fakes Investigation of inefficiency and fake track sourcesInvestigation of inefficiency and fake track sources Resolution and its dependence upon event multiplicityResolution and its dependence upon event multiplicity Time consumptionTime consumption

Conclusions & PlansConclusions & Plans


IntroductionIntroduction

The HLT Hough Transform method presented on last off-line week:The HLT Hough Transform method presented on last off-line week: was already was already fastfast (~ (~40s40s for event multiplicity of for event multiplicity of dN/dy~8000dN/dy~8000) ) but suffered from relatively but suffered from relatively large amount of fakeslarge amount of fakes which which limitedlimited the the

performance of the consecutive cluster fitter (or in case of stand-alone performance of the consecutive cluster fitter (or in case of stand-alone mode – most likely physics performance)mode – most likely physics performance)

On the other hand, Hough Transform still seems a very promising in On the other hand, Hough Transform still seems a very promising in overcoming the common problems at high multiplicity events.overcoming the common problems at high multiplicity events.

Is it possible to improve the time and tracking performances of the Is it possible to improve the time and tracking performances of the Hough method?Hough method?

Another interesting question is: could a Another interesting question is: could a stand-alone Hough stand-alone Hough Transform trackerTransform tracker survive in high multiplicity environment? survive in high multiplicity environment?


Hough Space (I)Hough Space (I)

Two main problems with the current definition of Two main problems with the current definition of the HT space variables the HT space variables k(=1/R)k(=1/R) and and The variables are The variables are strongly correlatedstrongly correlated “Butterfly”-like “Butterfly”-like

shape of the peaksshape of the peaks• complex peak findercomplex peak finder• relatively high fake peak raterelatively high fake peak rate

Non-linearNon-linear functions in the filling of HT space functions in the filling of HT space• Need in LUTs Need in LUTs inside HT filling loopinside HT filling loop• ““Time consuming” FP operationsTime consuming” FP operations inside HT filling loop inside HT filling loop

Can we find better solution?Can we find better solution?


Hough Space (II)Hough Space (II)

The choice of the new HT variables was The choice of the new HT variables was inspired by:inspired by: Search for natural Search for natural variables connected to the variables connected to the

physical setup of the TPCphysical setup of the TPC (an example is the (an example is the seeding in the offline reconstruction)seeding in the offline reconstruction)

Search for variables which lead to Search for variables which lead to linear HTlinear HT Why not use the Conformal Map Why not use the Conformal Map

transformation variables!transformation variables!


Hough Space (III)Hough Space (III) Lets define two curves inside a TPC sector byLets define two curves inside a TPC sector by

x/Rx/R2 2 = constant = = constant = 1(1(2)2)

(x1,y1)

(x2,y2)

• Each primary track is representedby two points on these curves

One can parameterize the trackusing

1=y1/R12 and 2=y2/R22

For each space-point along thetrack trajectory:

(y/R2-1)/(x/R2-1)=(2-1)/(2-1)X

y


Hough Space (IV) Hough Space (IV) One can use the variables One can use the variables 1 and 1 and 2 to define 2 to define

the Hough spacethe Hough space In this way each space-point inside a TPC sector In this way each space-point inside a TPC sector

will be represented in the Hough space by a will be represented in the Hough space by a straight linestraight line:: 1 = A + B x 1 = A + B x 22with A=y/Rwith A=y/R22((1-1-2)/(x/R2)/(x/R22--2) and2) and

B=(x/RB=(x/R22- - 1)/(x/R1)/(x/R22- - 2) 2) Linear filling of the Hough space!Linear filling of the Hough space! The parameters A and B could be calculated in The parameters A and B could be calculated in

advance and used via LUTsadvance and used via LUTs


Hough Space (V)Hough Space (V) Which position of the defining curves Which position of the defining curves 1,1,2?2? Requirement I:Requirement I: we need as we need as uncorrelateduncorrelated as possible as possible

Hough peaksHough peaks Requirement II:Requirement II: we have to preserve the we have to preserve the monotonicmonotonic

behavior of the HT (used for fast filling of Hough space)behavior of the HT (used for fast filling of Hough space) Lets consider a primary track which crosses all 159 rows Lets consider a primary track which crosses all 159 rows

inside one sector:inside one sector: (x/R(x/R22--1) should change sign in the middle of the sector 1) should change sign in the middle of the sector half of half of

the SPs with B>0 and half with B<0the SPs with B>0 and half with B<0 (x/R(x/R22--2)>0 2)>0 A always increases with y/R A always increases with y/R22

Conclusion:Conclusion:1 - in the middle (close to padrow 80) and1 - in the middle (close to padrow 80) and2 - at the outer edge (close to padrow 159)2 - at the outer edge (close to padrow 159)


Example – old Hough Space variablesExample – old Hough Space variables

Central HIJING dN/dy=3500, 0.2TCentral HIJING dN/dy=3500, 0.2T


Example – new Hough Space variablesExample – new Hough Space variablesParameterized HIJING dN/dy=8000, 0.4T

• Uncorrelated Hough peaks• Gain of 30-40% in the time consumption


Testing conditions (I)Testing conditions (I) Limits on Hough space variables correspond to Limits on Hough space variables correspond to

a a track with minimum Pttrack with minimum Pt[GeV/c] = B[GeV/c] = Bfieldfield[T] which [T] which crosses the middlecrosses the middle of the TPC sector of the TPC sector

Hough space binning is fixed to Hough space binning is fixed to 76(76(1)x140(1)x140(2)x100(eta)2)x100(eta)The size is roughly equal to the pad size in the The size is roughly equal to the pad size in the corresponding TPC rowscorresponding TPC rows

Hough Transform runs stand-alone (without a Hough Transform runs stand-alone (without a consecutive cluster fitter)consecutive cluster fitter)


Testing conditions (II)Testing conditions (II) The method requires The method requires new definitionsnew definitions in order to in order to

determine the performance:determine the performance: No clusters associatedNo clusters associated

assign assign only 1only 1 MC label to each track MC label to each track High occupancy (and therefore overlapping clusters) High occupancy (and therefore overlapping clusters)

in general in general does not affectdoes not affect the track parameters, but the track parameters, but cause cause appearance of “ghosts”appearance of “ghosts” fakes tracks fakes tracks ghost tracks ghost tracks

If more than 1 track with the same MC label, take If more than 1 track with the same MC label, take randomlyrandomly one as good and second as fake (or ghost) one as good and second as fake (or ghost)

Good tracks – primaries from offline comparison Good tracks – primaries from offline comparison macromacro


Efficiency and Fakes (I)Efficiency and Fakes (I)

0.4T dN/dy=8000dN/dy=4000dN/dy=2000


Efficiency and Fakes (II)Efficiency and Fakes (II)

0.5THIJINGparam dN/dy=8000Full HIJING dN/dy~8000


Efficiency and Fakes (III)Efficiency and Fakes (III)

dN/dy=80000.2T0.4T0.5T


Sources of Inefficiency (I)Sources of Inefficiency (I)

MergingMerging of the tracks ( of the tracks (1-2%1-2% for dN/dy=8000, for dN/dy=8000, 0.4T) when:0.4T) when: their peaks their peaks overlapoverlap in the hough space in the hough space their peaks are their peaks are close to each otherclose to each other and one is and one is

removed during the track merging (removed during the track merging (both in hough both in hough space and space and bins bins))

Low pt tracks at high Low pt tracks at high (close to 1). The (close to 1). The bins bins efficiently get narrower (+mult.scat. in ITS?)efficiently get narrower (+mult.scat. in ITS?)

Tracks Tracks close to the TPC sector bordersclose to the TPC sector borders (affects (affects mainly tracks with Pt>1-1.5GeV/c)mainly tracks with Pt>1-1.5GeV/c)


Sources of Inefficiency (II)Sources of Inefficiency (II)


Sources of Inefficiency (III)Sources of Inefficiency (III)

The only way to recover these low Pt ineff is to The only way to recover these low Pt ineff is to redefine redefine bins bins. For example, use angle . For example, use angle instead of instead of

On the other hand, the multiplicity should be On the other hand, the multiplicity should be more or less more or less constant as a function of constant as a function of and and therefore the amount of fakes as welltherefore the amount of fakes as well

Compromise between efficiency <-> fakesCompromise between efficiency <-> fakes In any case, the ineff at Pt<0.6 is not so In any case, the ineff at Pt<0.6 is not so

important for the HLTimportant for the HLT The work is in progress... The work is in progress...


Sources of Inefficiency (IV)Sources of Inefficiency (IV)


Ghost tracksGhost tracks

The final merging is still The final merging is still under investigation under investigation (hopefully will use (hopefully will use PDC’04 dataPDC’04 data))

Therefore we still have Therefore we still have tracks from different TPC tracks from different TPC sectors and sectors and slices to be slices to be mergedmerged

The The “real” fakes“real” fakes would be would be at the at the level of <1%level of <1% for for central event, of course central event, of course with a small decrease in with a small decrease in the efficiencythe efficiency

In 2 or more slicesIn 2 TPC sectorsOverall


Relative Pt resolution for tracks Relative Pt resolution for tracks with Pt>2GeV/c in %with Pt>2GeV/c in %

dN/dy=8000dN/dy=8000 dN/dy=4000dN/dy=4000 dN/dy=2000dN/dy=2000

0.5T0.5T 6.4 6.4 0.5 0.5 -- --

0.4T0.4T 8.2 8.2 0.5 0.5 7.5 7.5 0.7 0.7 8.7 8.7 1.3 1.3

0.2T0.2T 16.9 16.9 1.4 1.4 -- --


Relative Pt resolution for tracks with Relative Pt resolution for tracks with PtPtminmin<Pt<2GeV/c in %<Pt<2GeV/c in %


0.5T0.5T (0.9(0.90.2)+(2.30.2)+(2.30.3)P0.3)Ptt

0.4T0.4T (1.3(1.30.3)+(2.40.3)+(2.40.3)P0.3)Ptt

(0.9(0.90.5)+(2.70.5)+(2.70.5)Pt0.5)Pt (0.4(0.40.5)+(3.4+0.6)Pt0.5)+(3.4+0.6)Pt

0.2T0.2T (2.2(2.20.5)+(4.50.5)+(4.50.5)P0.5)Ptt


Eta resolution in 10Eta resolution in 10-3-3


0.5T0.5T 6.0 6.0 0.1 0.1 -- --

0.4T0.4T 5.6 5.6 0.1 0.1 5.5 5.5 0.1 0.1 5.2 5.2 0.2 0.2

0.2T0.2T 5.6 5.6 0.1 0.1 -- --

Only tracks with Pt>0.5GeV/c


Resolution in mradsResolution in mrads


0.5T0.5T 6.6 6.6 0.1 0.1 -- --

0.4T0.4T 6.3 6.3 0.1 0.1 6.1 6.1 0.1 0.1 6.0 6.0 0.2 0.2

0.2T0.2T 6.3 6.3 0.1 0.1 -- --

Only tracks with Pt>0.5GeV/c


Resolution for parameterized Resolution for parameterized HIJING (dN/dy=8000,0.4T) eventHIJING (dN/dy=8000,0.4T) event


BenchmarksBenchmarks HT was tested mainly on Itanium II (1.5 GHz, 6Mb L3 HT was tested mainly on Itanium II (1.5 GHz, 6Mb L3

cache) machines – these are our present GDCscache) machines – these are our present GDCs Compiled with Intel ecc with aggressive optimizationCompiled with Intel ecc with aggressive optimization

dN/dydN/dy 80008000 40004000 20002000

Hough TransHough Trans29.4s29.4s

(136ms/patch)(136ms/patch)

17.3s17.3s


9.3s9.3s


Calc WeightCalc Weight 1.2s1.2s 1.2s1.2s 1.1s1.1s

Peak FinderPeak Finder 1.8s1.8s 1.3s1.3s 0.9s0.9s

Time consumption is:• strictly proportional to the HT space size• roughly proportional to the event multiplicity


ConclusionsConclusions The new definition of Hough space variables The new definition of Hough space variables

improved both time and tracking performances improved both time and tracking performances of Hough Transform methodof Hough Transform method

Main sources of ineff and fakes well understoodMain sources of ineff and fakes well understood

The performance results prove that the HT could The performance results prove that the HT could work even as a stand-alone trackerwork even as a stand-alone tracker

The high occupancy does not affect significantly The high occupancy does not affect significantly the performance of the algorithmthe performance of the algorithm


PlansPlans

The new HT as well as the standard HLT tracker will be The new HT as well as the standard HLT tracker will be run during the event reconstruction in the second step of run during the event reconstruction in the second step of the Physics DC’04the Physics DC’04

Try both of them on real physics trigger algorithms, Try both of them on real physics trigger algorithms, compare the results…compare the results…

Still some minor problems with the efficiency, fakes, Still some minor problems with the efficiency, fakes, track merging to be solvedtrack merging to be solved

Start to add another detectors to HLT: ITS,Muon,TRD,...Start to add another detectors to HLT: ITS,Muon,TRD,...

Status of Hough Transform Method

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