556
R. Frühwirth et al.
There are many different algorithms for track finding. A selection of them is
described in Sects. 13.1.2.1 and 13.1.2.2. For an extended treatment of the subject,
containing many examples, see the excellent exposition in [1]. The track fit takes a
track candidate and estimates the track parameters (location, direction, momentum
or curvature, see Sect. 13.1.3.2) from the detector hits (Sect. 13.1.3.4), taking into
account the equation of motion (Sect. 13.1.3.2) in the magnetic field (Sect. 13.1.3.1)
and the effects of the detector material on the trajectory (Sect. 13.1.3.3). In the test
stage (Sect. 13.1.3.5) outliers are identified, i.e., hits which apparently do not belong
to the track. If outliers are expected, the estimation procedure should be robust
so that the estimated track is not significantly biased by the outliers. Some robust
methods are discussed in Sect. 13.1.3.5. Section 13.1.4 treats track-based alignment,
and Sect. 13.1.5 contains many useful formulas for determining the approximate
momentum resolution of a tracking detector without extensive simulations.
13.1.2 Pattern Recognition
Pattern recognition or track finding methods can be divided into global and local
methods. In a global method, all detector hits are treated on an equal footing, and all
track candidates are found in parallel; in a local method, there is a privileged subset
of hits which is used to find initial track candidates, which are then completed to
full track candidates.
13.1.2.1 Global Methods
Typical global methods of track finding find the tracks in parallel, for instance by
identifying peaks in a one- or two-dimensional histogram, or by observing the final
state of a recurrent neural network.
Conformal Mapping
A popular method for finding circular particle tracks is the conformal mapping
method [2]. It uses the fact that the mapping
u =
x
x 2 + y 2 , v =
y
x 2 + y 2 ,
transforms circles going through the origin of an x–y coordinate system into straight
lines of the form
v =
1
2b
− u
a
b
,
R. Frühwirth et al.
There are many different algorithms for track finding. A selection of them is
described in Sects. 13.1.2.1 and 13.1.2.2. For an extended treatment of the subject,
containing many examples, see the excellent exposition in [1]. The track fit takes a
track candidate and estimates the track parameters (location, direction, momentum
or curvature, see Sect. 13.1.3.2) from the detector hits (Sect. 13.1.3.4), taking into
account the equation of motion (Sect. 13.1.3.2) in the magnetic field (Sect. 13.1.3.1)
and the effects of the detector material on the trajectory (Sect. 13.1.3.3). In the test
stage (Sect. 13.1.3.5) outliers are identified, i.e., hits which apparently do not belong
to the track. If outliers are expected, the estimation procedure should be robust
so that the estimated track is not significantly biased by the outliers. Some robust
methods are discussed in Sect. 13.1.3.5. Section 13.1.4 treats track-based alignment,
and Sect. 13.1.5 contains many useful formulas for determining the approximate
momentum resolution of a tracking detector without extensive simulations.
13.1.2 Pattern Recognition
Pattern recognition or track finding methods can be divided into global and local
methods. In a global method, all detector hits are treated on an equal footing, and all
track candidates are found in parallel; in a local method, there is a privileged subset
of hits which is used to find initial track candidates, which are then completed to
full track candidates.
13.1.2.1 Global Methods
Typical global methods of track finding find the tracks in parallel, for instance by
identifying peaks in a one- or two-dimensional histogram, or by observing the final
state of a recurrent neural network.
Conformal Mapping
A popular method for finding circular particle tracks is the conformal mapping
method [2]. It uses the fact that the mapping
u =
x
x 2 + y 2 , v =
y
x 2 + y 2 ,
transforms circles going through the origin of an x–y coordinate system into straight
lines of the form
v =
1
2b
− u
a
b
,