Two-view 2D->3D matching with calorimetry in pandora Dom - - PowerPoint PPT Presentation

Two-view 2D->3D matching with calorimetry in pandora

Dom Brailsford, Etienne Chardonnet FD sim/reco meeting 27/04/20

2D->3D matching

• 2D->3D matching takes 2D clusters (e.g. from each wire view)

and matching them across views to make 3D objects


• Pandora’s main 2D->3D matching algorithm requires a cluster in

three distinct views to function

• Combining positions from clusters in two of the views infers a

position in the third view. A pseudo chi2 is calculated for inferred vs actual positions on the cluster


• This is problematic for any detector technology which only has

two views (e.g. the CRP-based dual-phase LArTPCs)

2

Two-view 2D->3D matching

• We are exploring how calorimetry could

enhance two-view 2D->3D matching


• Exploratory algorithm details:
• 1. Make every pairwise comparison of 2D

clusters in the two views

• 2. Find the region that the two clusters
• verlap each other in time
• 3. For that overlap region, produce fractional

profiles of charge for each cluster

• 4. Downsample* the two charge profiles so

that they are coarse and equally binned

• 5. Calculate the charge profiles’ correlation

coefficient and corresponding p-value (p- value calculation on next slide)

• All plots are taken from custom samples made

in ProtoDUNE dual-phase, but all details are directly relevant for the DUNE far detector, both single-phase and dual-phase

3

U view 2D cluster 2D cluster V view Time Time *Resampling method suggested by Andy** **Suggested to Andy by Tom Junk

Correlation coefficient’s p- value

• For uncorrelated bivariate normal distribution pairs, the correlation coefficient

follows a Student t-distribution with n-2 degrees of freedom

• The t-value is


• P-value is calculated by integrating the t-distribution above the calculated t

value (a one tailed test)

• H0: r==0
• H1: r>0
• The t-distribution supposedly approximately holds for non-gaussian variables,

provided the sample sizes are large enough. I’ll revisit this in a few slides

4

Resampled fractional charge profiles (di-muon sample)

10 20 30 40 50

x (cm)

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Fractional value (no units)

U cluster V cluster

5 10 15 20 25 30 35 40 45 50

x (cm)

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Fractional value (no units)

U cluster V cluster

10 20 30 40 50 60 70 80

x (cm)

0.005 0.01 0.015 0.02 0.025 0.03

Fractional value (no units)

U cluster V cluster

5 10 15 20 25 30 35 40 45 50

x (cm)

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Fractional value (no units)

U cluster V cluster

r: 0.142 p-value: 0.062 r: 0.804 p-value: 7e-17 r: 0.821 p-value: 1e-24 r: 0.161 p-value: 0.119

5

Further 2D->3D matching exploration

• We can do a little bit more and try to correlate local regions of

the profiles


• Once the resampled fractional charge profiles have been

constructed

• Slide a fixed-length window of N bins across the equally-

binned charge profiles

• Repeatedly calculate correlation coefficient and p-value as

the window slides across the profiles

• For each p-value calculation, calculate a ‘matching score’
• Score == 1-p

6

10 20 30 40 50

X (in cm)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

10 20 30 40 50

X (in cm)

0.5 0.6 0.7 0.8 0.9 1 10 20 30 40 50 60 70 80 90

X (in cm)

0.5 0.6 0.7 0.8 0.9 1 10 20 30 40 50

X (in cm)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sliding window scores (same di-muon event)

Matching score Matching score Matching score Matching score

7

10 20 30 40 50

x (cm)

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

Fractional value (no units)

U cluster V cluster

10 20 30 40 50

x (cm)

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Fractional value (no units)

U cluster V cluster

10 20 30 40 50

x (cm)

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Fractional value (no units)

U cluster V cluster

10 20 30 40 50 60 70

x (cm)

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Fractional value (no units)

U cluster V cluster

Resampled fractional charge profiles (1mu1p sample)

r: 0.778 p-value: 6e-16 r: 0.449 p-value: 0.010 r: 0.781 p-value: 0.001 r: 0.995 p-value: -6.9e-10

8

10 20 30 40 50 60

X (in cm)

0.5 0.6 0.7 0.8 0.9 1 10 20 30 40 50 60

X (in cm)

0.2 0.4 0.6 0.8 1 10 20 30 40 50

X (in cm)

0.2 0.4 0.6 0.8 1 10 20 30 40 50 60 70

X (in cm)

0.5 0.6 0.7 0.8 0.9 1

Sliding window scores (1mu1p event)

Matching score Matching score Matching score Matching score

9

Toy study

• Revisiting the student t-distribution

assumption


• Produce 10000 fake fractional charge

profiles

• Fill 3 histograms with landau throws,

smeared with a gaussian

• Two hists. are filled with the same

landau values but smeared separately

• Third hist filled with separate landau

values

• Each bin is filled N times with distinct

throws to mimic the downsampling

• Calculate correlation coefficient and p-

value

• Landau (315, 13)
• Gaus (1,0.1)
• N hist bins == 30
• N samples per bin == 5

1 2 3 4 5 6 7 8 9 10 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 1 2 3 4 5 6 7 8 9 10 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

10

Correlated fake profile Uncorrelated fake profile

Toy study

• Top plot shows correlation

coefficient for the 10,000 universes

• Black: correlated

distributions

• Red: uncorrelated

distributions

• Bottom plot shows

corresponding p-values

• The red distribution

should be flat, but it is not

0.2 0.4 0.6 0.8 1

p-value

1 10

2

10

3

10

4

10

• No. universes

1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1

Correlation coefficient

1000 2000 3000 4000 5000

• No. universes

11

P-value vs r (t-distribution)

1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1

r

0.2 0.4 0.6 0.8 1

p

20 40 60 80 100 120 140 160 180 200 220 240

12

0.2 0.4 0.6 0.8 1

p-value

1 10

2

10

3

10

4

10

• No. universes

Toy study

1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1

Correlation coefficient

1000 2000 3000 4000 5000

• No. universes
• Instead, calculate the p-value

using permutation tests

• Randomly shuffle the bins

for one distribution in a comparison and recalculate r

• P-value == fraction of

times you measure an r that is more extreme than your original r measurement

• Top plot shows correlation

coefficient (same as previous slide)

• Bottom plot shows

corresponding p-value

13

p-value vs r (permutation test)

1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1

r

0.2 0.4 0.6 0.8 1

p

10 20 30 40 50 60

14

Future and summary

• Pandora’s main 2D->3D matching algorithm requires three views to
• perate
• Not usable by detectors with two views, such as the CRP-based

dual-phase LArTPCs

• We are exploring the use of calorimetry in a new 2D->3D matching

algorithm, suitable for two-view LArTPCs

• The new matching algorithm tries to correlate the energy

depositions between the two views to match clusters

• So far, the calorimetry-based checks seem to do a good job of

separating matching clusters vs non-matching clusters

• While the t-test based p-value shows strong separation power, it is not

a robust p-value, statistically speaking. Swapping to a permutation- test based p-value would rectify the robustness

15

Backup

16

New two view matching alg

• Overall aim is to 3D match 2D clusters by correlating the charge depositions in the

clusters common transverse (time) overlap region


• Recipe (part 1) *
• Collect candidate matching cluster hits that lie in the overlap region
• Create cumulative distribution for each cluster’s overlap
• Smooth the cumulative distribution using linear/quadratic/cubic interpolation. We

are currently using linear interpolation due to quadratic/cubic instability in some regions of the distributions

• Resample the two smoothed cumulative distributions such that they have

coarser, equal binning. The current scheme downsamples to 1/5th the number

• f hits in the sparser cumulative distribution
• Differentiate the two resampled cumulative distributions to produce two equally

binned fractional charge profiles

• Calculate the correlation coefficient and corresponding p-value between the two

distributions

*resampling suggested by Andy** **suggested to Andy by Tom Junk

17

1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1

Correlation coefficient

500 1000 1500 2000 2500

• No. universes

1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1

Correlation coefficient

1000 2000 3000 4000 5000

• No. universes

1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1

Correlation coefficient

1000 2000 3000 4000 5000

• No. universes

1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1

Correlation coefficient

1000 2000 3000 4000 5000 6000 7000 8000

• No. universes

How binning alters r (toy study)

• N. profile bins: 30
• N. samples ber bin: 1
• N. profile bins: 30
• N. samples ber bin: 5
• N. profile bins: 150
• N. samples ber bin: 1
• N. profile bins: 150
• N. samples ber bin: 5

18

Before

19

Now

20

Now

21

Example event

• Di-muon vertex-like particle gun
• Both particles have the same x-

direction sign

• Both particles aim roughly

downstream in the geometry

• The event on the right will be

used as the example throughout the rest of the slides

22

The first idea

• For each cluster comparison doublet e.g. U1V1, U2V1 U1V2, U2V2
• Find transverse overlap region between two clusters
• Construct fractional cumulative charge distributions for the two

clusters, keeping within the bounds of the overlap region

• Calculate test statistic and probability e.g. KS test
• Store the transverse overlap and matching probability in the

TwoViewTransverseOverlapResult which is stored in the overlap comparison matrix

• Tools then assess each element in the overlap matrix

23

Cumulative distributions from the same event

10 20 30 40 50

x (cm)

0.2 0.4 0.6 0.8 1

Fractional value (no units)

U cluster V cluster

5 10 15 20 25 30 35 40 45 50

x (cm)

0.2 0.4 0.6 0.8 1

Fractional value (no units)

U cluster V cluster

10 20 30 40 50 60 70 80

x (cm)

0.2 0.4 0.6 0.8 1

Fractional value (no units)

U cluster V cluster

5 10 15 20 25 30 35 40 45 50

x (cm)

0.2 0.4 0.6 0.8 1

Fractional value (no units)

U cluster V cluster

KS prob.: 0.525927 Kuiper prob.: 0.196262 Correlation: 0.998779 KS prob.: 1 Kuiper prob.: 1 Correlation: 0.999841 KS prob.: 0.994437 Kuiper prob.: 1 Correlation: 0.999928 KS prob.: 0.994469 Kuiper prob.: 0.996247 Correlation: 0.998721

24

Observations and suggestions

• By eye, it’s pretty clear which clusters should go together
• The KS test looks to be too weak to discern the fine differences

between two charge cumulative distributions

• Kuiper test seems more powerful but still not quite enough to

sufficiently separate

• There is some very, very, very modest separation in the correlation

coefficient, but the monotonically increasing nature of the cumulative distribution is dominating the metric

• Options:
• Segment the cumulative distributions and assess each segment
• Slide a window across the two clusters and assess the cumulative

distribution in each window. The window would slide such that each hit would be at the centre of a window

• Assess fractional charge profiles rather than cumulative distribution

25

Segmenting the distribution (sorry, no segmented plots to show yet)

10 20 30 40 50

x (cm)

0.2 0.4 0.6 0.8 1

Fractional value (no units)

U cluster V cluster

5 10 15 20 25 30 35 40 45 50

x (cm)

0.2 0.4 0.6 0.8 1

Fractional value (no units)

U cluster V cluster

10 20 30 40 50 60 70 80

x (cm)

0.2 0.4 0.6 0.8 1

Fractional value (no units)

U cluster V cluster

5 10 15 20 25 30 35 40 45 50

x (cm)

0.2 0.4 0.6 0.8 1

Fractional value (no units)

U cluster V cluster

Segment KS prob. 1 0.009 2 0.59 3 0.82 4 1 5 0.23 Segment KS prob. 1 0.84 2 1 3 0.97 4 1 5 1 Segment KS prob. 1 0.43 2 1 3 0.98 4 1 5 1 Segment KS prob. 1 0.88 2 0.85 3 0.93 4 1 5 0.99 26

Fractional charge profiles

5 10 15 20 25 30 35 40 45 50

x (cm)

0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045

Fractional value (no units)

U cluster V cluster

10 20 30 40 50 60 70 80

x (cm)

0.001 0.002 0.003 0.004 0.005 0.006

Fractional value (no units)

U cluster V cluster

10 20 30 40 50

x (cm)

0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045

Fractional value (no units)

U cluster V cluster

5 10 15 20 25 30 35 40 45 50

x (cm)

0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.011

Fractional value (no units)

U cluster V cluster

Correlation: -0.000817181 Correlation: +0.0189502 Correlation: +0.00655381 Correlation: -0.0644948

27

Summary

• A draft of the two view overlap result class infrastructure has

now been written

• It is not supposed to be a final blueprint, but enough to

start studying matching metrics

• We’re now looking into calorimetry-based matching metrics

for the two view matching


• Findings so far
• Calorimetry looks to be a powerful hook in the dual phase
• The pain is going to be how best to discern the subtle-yet-
• bvious differences between charge distributions
• We still have some avenues to explore

28