Neutrino Event Reconstruction
in a Liquid Argon TPC
Gary Barker
University of Warwick
GLA2010, KEK, March 29-31 2010
Bubble Chambers
Liquid argon TPC’s reconstruct events with bubble-chamber
quality
But, automatic
reconstruction in
software is still not
established
Why?
1. Historical
 Not really needed: event
rates low, semi-automatic
reconstruction guided by
operators
 Computing power was
relatively limited
 Collider experiments took
over: ultra-fast trigger
rates, detectors with
flexible geometries,
electronic readout, huge
gains in computing power
 Development of reconstruction algorithms
2. It’s not so easy!
 Tracks and showers develop
side-by-side in the same
volume
 topologically complicated
 No well defined start point
for what initiated the event
 Very high density of
information: mm-scale energy
deposits, delta-rays,
vertices, kinks etc
 Multiple scattering occurring
continuously throughout
volume
ICARUS, arxiv:0812:2373
c.f. Accelerator experiments
 Well defined interaction point
 Relatively sparse space/pulseheight data points radiating from
this point
 Tracks and showers develop in
separate, optimised, sub-detectors
 Multiple scattering happening
mostly at well-defined boundaries
between sub-detectors
 Track search within a welldefined model (circle or helix) to
decide on associated hits
Past developments: Hough transform
 Part of effort to automate bubble chamber reconstruction
(Hough: Proc. Conf. High Energy Acc. Instr., CERN 1959)
y = mx + c
 cos ϑ   r 
y = −
x + 

 sin ϑ   sin ϑ 
r = y sin ϑ + x cos ϑ
A
 A sinusoid in (r,θ)
points (x,y)
intersecting at the parameters of
straight line structures
 Found wide application as feature extraction technique for image
analysis
Past Developments: ICARUS
 Tools developed over
the years by the ICARUS
project: hit definition,
clustering, 2D and 3D
track fitting
 Low multiplicity neutrino
events reconstructed
from a 50L module
exposed to the CERN
WANF beam
 Some degree of visual
scanning/selection
involved before applying
algorithms
ICARUS Collab., Phys. Rev. D74, 112001 (2006)
What do we need to do?
J. Spitz
 Classify
energy deposit
information into shower-like and
track-like objects
 Identify
tracks (µ,π,p) and
showers (e, γ) from topology,
kinemetics and dE/dx in LAr
separation at >90%
An Analysis Strategy
Clustering
 Aim to limit
contamination of cluster
with hits laid down by
other particles
 Develop a hierarchy of
clusters/super-clusters
Density-Based Clustering
 Clusters: a density of points considerably higher than
outside the cluster
 DBSCAN* algorithm: the `density-neighbourhood’
(ε) around each point in the cluster must contain at
least Nmin other points
Kinga Partyka (Yale/ArgoNEUT)
 Implemented in ArgoNeuT data
 Issues with `over-clustering’
being addressed
Colours → Cluster found
by DBSCAN
* Sander et al., Data Mining and knowledge Discovery 2, pp169-194 (1998)
OPTICS
 Ordering Points To Identify the
Clustering Structure*
 DBSCAN-style clustering (ε, Nmin)
but where hits are stored in a
`reachability’ ordering i.e. the εthreshold required to cluster any hit
with any other
 Getting the ε-scale correct helps in
associating disjoint clusters in EMag showers
 Could extend to cluster in more than
spatial coordinates e.g. dE/dx
D. Roythorne, Warwick
ε-scale small
ε-scale larger
* M. Ankerst et al., ACM SIGMOD Int. Conf. on Management of Data pp49-60 (1999)
Track Finding: Hough Transform
Joshua Spitz ArgoNeuT/Yale
 Reasonable job of
reconstructing multiple tracks
in ArgoNeuT events
 Returns only gradient and
intercept of line – definition of
start/end-points of tracks
continuing:
Track Finding: KDTREE
 KDTREE provides convenient data
structure from which to launch a
nearest-neighbour hit search
 Fit straight-line segments through
groups of nearest hits in 3D
 Currently testing on toy Monte
Carlo – observe change in direction
cosine of line segments to tag
kink/vertex with high efficiency
Andrew Bennieston, Warwick
Key Point Detection
Vertex IP 
corner in charge
density
Delta-electron 
corner in charge
density
 Prior knowledge of vertex points, kinks, track end-points etc is
useful in aiding reconstruction algorithms e.g. blank-off hits around a
vertex point from a cluster search
Corner Finding
(
)
 ∆x 
 Harris-Stephens/Plessey Function*: H ( x , y ) = ∆x ∆y A


`cornerness’ measure where
 ∆y 
size/direction governed by the
 ( ∂ / ∂x ) 2
(∂ / ∂x )(∂ / ∂y ) 
Eigenvalues/Eigenvectors of

A = 
2

(
)
(
∂
/
∂
y
)(
∂
/
∂
x
)
∂
/
∂
y


structure tensor, A
HSP Transform
Picks out:
Vertex AND Track Ends!
* C. Harris, M. Stephens, proc. 4th Alvey Vision Conf. pp147-151 (1988)
Corner Finding
 GENIE generated
νµ CCQE events in 3T LAr TPC:
Ben Morgan, Warwick
Vertex picked out
Delta Electron ID!
Proton Stop
 Now implemented in 3D (D. Roythorne, Warwick)– evaluation in progress
Conclusions
 Some preliminary work has started in Europe
and US to reconstruct interactions in LAr
(some collaboration/coordination links made)
 Early conclusions indicate Key Point Detection
(vertices, kinks etc) inconjunction with a
clustering algorithm could work well
 Only scratched surface – also under
consideration are:
- `trained algorithms’ e.g. neural Networks
- Techniques from disciplines of Computer Vision,
Machine Vision and Image Processing
Backup
Corner Finding
Evaluation based on toy MC
V0’s:
 Detection Efficiency
 Expect: Nfound-Ntrue = 0
 >90% efficient.
 Small false positive rate.
 Localization
 Expect: |rfound-rtrue|~0
 >90% efficient at finding
corner within 3 pixels/hits
of truth vertex/end.
 Vertex ID
 Cornerness elliptical.
 >75% efficient at picking
out vertex.
Ben Morgan, Warwick