Reconstruction & Modelling Challenges
for
Large Volume Liquid Argon Detectors
Andrew J. Bennieston
University of Warwick
IPRD 2010, Siena, Italy
7–10 June 2010
Time Projection Chambers
I
Interested in reconstruction for liquid Argon TPCs
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Detectors on the scale of 100 kiloton required for
next-generation ν experiments
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TPCs use ionisation charge to track particles through gas
or liquid volume
Readout
Ionisation Charge
E
Charged
Particle
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2D readout plane (xy ) and z coordinate from drift time
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High-density, fine-grained 3D spatial data
Liquid Argon TPCs
(ICARUS, arxiv:0812:2373)
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LAr TPCs track events with
bubble-chamber quality
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High resolution,
homogeneous volume:
tracks and showers
develop side-by-side
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Automated reconstruction
software not established
Reconstruction Challenges
Collider Experiments
LAr TPCs
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Well-defined primary
vertex
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No well-defined start point
for ν interactions
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Sparse hit data radiating
from this point
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High density of hit
information throughout
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Multiple scattering mostly
at well-defined boundaries
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Multiple scattering
throughout volume
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Tracks and showers
develop separately; track
hits easy to find
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Tracks and showers
develop together; tracks
difficult to find amongst
other hits
Need to classify hit information (energy deposited) as tracks or
showers to do PID and kinematics
Track Reconstruction
Event at 30°
y
Procedure:
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160
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Start with simple geometric
tracks; charge deposited
into cubic voxels (volume
elements)
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Compare reconstruction
algorithms with the same
data
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120
100
80
60
40
20
0
-350
-300
-250
-200
-150
-100
-50
0
x
y
Voxel Data: Event at 30° (Zoom to vertex region)
144
Algorithms:
142
140
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Hough Transform
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KDTree Search
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Corner Detection
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Clustering
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-140
x
Hough Transform
y = mx + c
r = x cos θ + y sin θ
µ
¶
cos θ
r
y= −
x+
sin θ
sin θ
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Maps points in (x, y ) to
sinusoids in (r , θ )
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Intersect at (r , θ )
parameters of straight lines
in the image
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Originally used for bubble
chamber images; now
widely used in image
processing
y
r
θ
x
Hough Transform
Red Allocated hits
Black Unallocated hits
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Highest peak in HT gives
line in a projection
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Hits allocated to line if they
fall within some radius of it
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Iterative HT; allocated
points not included in
subsequent steps
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Projections used for HT;
3D data retained for final
fits
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Segments combined from
projections based on 3D
fits
KDTree
(3, 8)
(8, 9)
(2, 5)
(6, 3)
Data structure:
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Binary search
tree built in
O(N log N) time
Nearestneighbour search
in O(log N) time
Algorithm:
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Pick seed point
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Find nearest (unallocated)
neighbour
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Build up collection of points
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Fit line; histogram direction cosines
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Move onto next line when histogram
develops second peak
KDTree: Angle Reconstruction
Clustering
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Clustering hits based on
density (DBSCANa and
OPTICSb )
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Clustering could be used
to find tracks
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Left: Hits coloured by
clusters found by DBSCAN
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Problems with
over/underclustering
(Kinga Partyka, ArgoNeuT)
a
Sander et al., Data Mining and Knowledge
Discovery 2, pp169–194 (1998)
b
M. Ankerst et al., ACM SIGMOD Int. Conf. on
Management of Data, pp49–60 (1999)
Interest-Point Detection
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Hough Transform provides lines through image but no end
points
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KDTree algorithm relies on moving through corners to see
gradient changes
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KDTree algorithm requires a seed point; any will do, but
some are better than others
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Clustering algorithms pick out related points, but some
clusters ‘wrap around’ corners
Interest-point detection finds corners and endpoints to help
tracking algorithms
Corner Finding
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Harris-Stephens/Plessey1 ‘cornerness’ measure
Image I(x, y ) has structure tensor S(x, y ):
 2

Ix Ix Iy

S(x, y ) = 
2
Ix Iy Iy
1 C. Harris, M. Stephens, Proc. 4th Alvey Vision Conf. pp147–151 (1988)
Corner Finding
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GENIE νµ CCQE event (B. Morgan, Warwick)
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Vertex, proton track endpoint and delta electron identified
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3D implementation (D. Roythorne, Warwick)
Conclusions
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High levels of detail in LAr TPC events
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Promising results with spatial data & image processing
techniques
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Ability to tag feature points with high efficiency is required
for progress
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Showers are complex features which appear side-by-side
with tracks
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Feature detection can be used as input to a variety of track
& shower fitting algorithms
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Many more image processing & feature extraction
techniques to explore
Work is progressing in the UK, Europe and the U.S. —
collaborative links are developing