Updates to the Circle Hough Trackfinding Algorithm

Transcription

1 Updates to the Circle Hough Trackfinding Algorithm L. BIANCHI PANDA CM58 HIM, Mainz Sep 14, 16

2 Circle Hough Algorithm Circle Hough algorithm principles Generate all possible tracks Accumulate track parameters Most likely parameters = real tracks 2

3 Circle Hough Algorithm Circle Hough algorithm principles Generate all possible tracks Accumulate track parameters Most likely parameters = real tracks CH Features High efficiency Flexibility Applicable to all types of hits in the central detector Robustness/stability Intrinsic parallelism Tuneability: computing vs physics performance Online/offine: same algorithms with different working points Hit association and extraction of track parameters at the same time Information from STT isochrone radius taken into accout 2

4 CH: Principles Hough element: projection of primary track in the transverse plane = Circle passing through IP and hit Circle uniquely described by center: 2D parameter space Use one parameter as sampling parameter Calculate center coordinates from hit contact condition 3

5 CH: Principles Hough element: projection of primary track in the transverse plane = Circle passing through IP and hit Circle uniquely described by center: 2D parameter space Use one parameter as sampling parameter Calculate center coordinates from hit contact condition 1 Direct calculation For each hit, calculate (x, y) from set of R values Accumulate coordinates in (x, y) Accumulator Array 3

6 CH: Principles Hough element: projection of primary track in the transverse plane = Circle passing through IP and hit Circle uniquely described by center: 2D parameter space Use one parameter as sampling parameter Calculate center coordinates from hit contact condition 1 Direct calculation For each hit, calculate (x, y) from set of R values Accumulate coordinates in (x, y) Accumulator Array 2 Equation of circle centers known analytically Locus is hyperbola or straight line Accumulate parameters exploiting locus properties (rasterization, analytical intersection) 3

7 CH: Principles 8 8 4

8 Hit Pair CH Find intersections of Hough loci belonging to different hits = Consider directly pairs of hits Hough element: primary track compatible with two hits = Circle passing through IP, tangent to two hits at the same time Explicit analytical solution: problem of Apollonius Given three circles, find circles tangent to all of them For primary tracks: one of the circles is IP (Apollonius PCC) Combinatorial complexity, but 1 fewer degree of freedom 5

9 Hit Pairs 8 8 6

10 Hit Pairs 8 8 6

11 Hit Pairs 8 8 6

12 Hit Pairs 8 8 6

13 Hit Pairs 8 8 6

14 Hit Pairs 8 8 6

15 Hit Pair CH: Peakfinding Identify most likely track parameters Extract hit information from Hough elems in peak region Calculate track parameters from coordinates of peak region Basic strategy: 2D Accumulator Array (histogram) + peakfinding Track center angle / deg Track radius / cm

16 Hit Pair CH: Peakfinding Features of peakfinding Hough elems aligned in ρ direction Critical density close to the real peak (ρ, ϕ) less coupled for Hit Pair CH Strategies 2D peakfinding: rel. threshold + local maximum Also considered: striped peakfinding in parallel in one direction + combine with reduce/fold algorithm Caveats Discrete binning causes artifacts and unstable behavior Tune parameters One simple solution: 1 Use (binned) peakfinding to find location of peak 2 Select (unbinned) Hough elems in interval centered on peak 8

17 Testing the algorithm PandaRoot data Single tracks generated with BoxGenerator Useful for: Algorithm exploration/optimization Approximate indication for later, more accurate physics performance tests At this point, definitely not useful for: Quoting performance numbers 9

18 Performance Set of 7 tracks 14 Distribution of coverage 12 1 Frequency Coverage 1

19 Performance Set of 7 tracks 16 Distribution of relative p t difference Frequency Relative pt difference 11

20 Parameter Study Width of ρ Interval Features of candidate tracks calculated by combining info from Hough elems in interval around peak position Main parameter: width of interval in ρ direction Tradeoff between: coverage, purity, p t resolution, Track center angle / deg Track radius / cm

21 Parameter Study Width of ρ Interval Features of candidate tracks calculated by combining info from Hough elems in interval around peak position Main parameter: width of interval in ρ direction Tradeoff between: coverage, purity, p t resolution, Track center angle / deg Track radius / cm

22 Parameter Study Width of ρ Interval Coverage Ratio of duplicates Width of radius acceptance interval / cm.1 13

23 Parameter Study Width of ρ Interval.8 6 Relative diff. (pt.reco, pt.mc) / percent Width of radius acceptance interval / cm 5 Stddev of reconstructed radius / cm

24 Parameter Study (ρ, ϕ) Bin Width Performance of peakfinding depends on binning of AA Vary N ρ, N ϕ at the same time Study inpact of performance metrics on 2D grid Track center angle / deg Track radius / cm

25 Parameter Study (ρ, ϕ) Bin Width 35 Rel. diff(p t.reco, p t.mc) Number of ϕ bins / deg Number of ρ bins / cm

26 Parameter Study (ρ, ϕ) Bin Width 35 Difference between peak value for radius in Hough space and MC track radius 3 Number of ϕ bins / deg Number of ρ bins / cm

27 Parameter Study Binning 35 3 Coverage Number of ϕ bins / deg Number of ρ bins / cm

28 Summary & Outlook Work in progress Characterization of algorithm Exploration of parameter space Optimization Identify performance tradeoffs Systematic testing with PandaRoot simulated data Single tracks (BoxGenerator) Full events (background; physics channels;...) In the immediate future Reference implementation of algorithm in C/C++ Identify performance bottlenecks = Parallelization targets Integration with PandaRoot 19

29 Backup Single Hit CH with ρ/ϕ Coord. Central idea: use one set of sampling values (R... R N ) for all hits Use radial coordinates (ρ, ϕ) of centers Physically meaningful: ρ p t Cells of AA in ρ direction coincide with R values Peakfinding greatly simplified Optimal patterns for filling in parallel (memory writes) Improve p t resolution: zooming in recursively Use same points in subregion of AA with finer density in ϕ direction 19