An Orientation Selective Neural Network 
for Pattern Identification in Particle 
Detectors 
Halina Abramowicz, David Horn, Ury Naftaly, Carmir Sahar-Piklelny 
School of Physics and Astronomy, Tel Aviv University 
Tel Aviv 69978, Israel 
halinapost. tau. ac. il, hornneuron. tau. ac. il 
urypost. tau. ac. il, carmitpost. tau. ac. il 
Abstract 
We present an algorithm for identifying linear patterns on a two- 
dimensional lattice based on the concept of an orientation selective 
cell, a concept borrowed from neurobiology of vision. Construct- 
ing a multi-layered neural network with fixed architecture which 
implements orientation selectivity, we define output elements cor- 
responding to different orientations, which allow us to make a se- 
lection decision. The algorithm takes into account the granularity 
of the lattice as well as the presence of noise and inefficiencies. The 
method is applied to a sample of data collected with the ZEUS 
detector at HERA in order to identify cosmic muons that leave 
a linear pattern of signals in the segmented calorimeter. A two 
dimensional representation of the relevant part of the detector is 
used. The algorithm performs very well. Given its architecture, 
this system becomes a good candidate for fast pattern recognition 
in parallel processing devices. 
I Introduction 
A typical problem in experiments performed at high energy accelerators aimed at 
studying novel effects in the field of Elementary Particle Physics is that of prese- 
lecting interesting interactions at as early a stage as possible, in order to keep the 
data volume manageable. One class of events that have to be eliminated is due to 
cosmic muons that pass all trigger conditions. 
926 H. Abrarnowicz, D. Hbrn, U. Nafialy and C. Sahar-Pikielny 
The most characteristic feature of cosmic muons is that they leave in the detector 
a path of signals aligned along a straight line. The efficiency of pattern recognition 
algorithms depends strongly on the granularity with which such a line is probed, on 
the level of noise and the response efficiency of a given detector. Yet the efficiency 
of a visual scan is fairly independent of those features [1] . This lead us to look for 
a new approach through application of ideas from the field of vision. 
The main tool that we borrow from the neuronal circuitry of the visual cortex is 
the orientation selective simple cell [2]. It is incorporated in the hidden layers of a 
feed forward neural network, possessing a predefined receptive field with excitatory 
and inhibitory connections. Using these elements we have developed [3] a method 
for identifying straight lines of varying slopes and lengths on a grid with limited 
resolution. This method is then applied to the problem of identifying cosmic muons 
in accelerator data, and compared with other tools. 
By using a network with a fixed architecture we deviate from conventional ap- 
proaches of neural networks in particle physics [4]. One advantage of this approach 
is that the number of free parameters is small, and it can, therefore, be determined 
using a small data set. The second advantage is the fact that it opens up the pos- 
sibility of a relatively simple implementation in hardware. This is an important 
feature for particle detectors, since high energy physics experiments are expected 
to produce in the next decade a flux of data that is higher than present analysis 
methods can cope with. 
II Description of the Task 
In a two-dimensional representation, the granularity of the rear part of the ZEUS 
calorimeter [6] can be emulated roughly by a 23 x 23 lattice of 20 x 20 cm 2 squares. 
While such a representation does not use the full information available in the de- 
tector, it is sufficient for our study. In our language each cell of this lattice will 
be denoted as a pixel. A pixel is activated if the corresponding calorimeter cell is 
above a threshold level predetermined by the properties of the detector. 
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Figure 1: Example of patterns corresponding to a cosmic muon (left), a typical 
accelerator event (middle), and an accelerator event that looks like a muon (right), 
as seen in a two dimensional projection. 
A cosmic muon, depending on its angle of incidence, activates along its linear path 
typically from 3 to 25 neighboring pixels anywhere on the 23 x 23 grid. The pattern 
of signals generated by accelerator events consists on average of 3 to 8 clusters, 
of typically 4 adjacent activated pixels, separated by empty pixels. The clusters 
Orientation Selective Neural Network 927 
tend to populate the center of the 23 x 23 lattice. Due to inherent dynamics of 
the interactions under study, the distribution of clusters is not isotropic. Examples 
of events, as seen in the two-dimensional projection in the rear part of the ZEUS 
calorimeter, are shown in figure 1. 
The lattice discretizes the data and distorts it. Adding conventional noise levels, 
the decision of classification of the data into accelerator events and cosmic muon 
events is difficult to obtain through automatic means. Yet, it is the feeling of exper- 
imentalists dealing with these problems, that any expert can distinguish between 
the two cases with high efficiency (identifying a muon as such) and purity (not 
misidentifying an accelerator event). We define our task as developing automatic 
means of doing the same. 
III The Orientation Selective Neural Network 
Our analysis is based on a network of orientation selective neurons (OSNN) that 
will be described in this chapter. We start out with an input layer of pixels on a 
two dimensional grid with discrete labeling i = (x, y) of the neuron (pixel) that can 
get the values $i = i or 0, depending on whether the pixel is activated or not. 
Figure 2: Connectivity patterns for orientation selective cells on the second layer 
of the OSNN. From left to right are examples of orientations of 0, rr/4 and 5rr/8. 
Non-zero weights are defined only within a 5 x 5 grid. The dark pixels have weights 
of +1, and the grey ones have weights of-1. White pixels have zero weights. 
The input is being fed into a second layer that is composed of orientation selective 
neurons V 'a at location i with orientation 0a where c belongs to a discrete set of 
;i,a is the analog of a simple cell in the 
16 labels, i.e. 0a = crr/16. The neuron v 2 
visual cortex. Its receptive field consists of an array of dimension 5 x 5 centered at 
pixel i. Examples of the connectivity, for three different choices of c, are shown in 
Fig. 2. The weights take the values of 1,0 and -1. 
The second layer consists then of 23 x 23 x 16 neurons, each of which may be thought 
of as one of 16 orientation elements at some (x, y) location of the input layer. Next 
we employ a modified Winner Take All (WTA) algorithm, selecting the leading 
orientation c,a(i) for which the largest V/' is obtained at the given location i. 
If we find that several V/' at the same location i are close in value to the maximal 
one, we allow up to five different V 'a neurons to remain active at this stage of the 
processing, provided they all lie within a sector of c,a q- 2, or 0, q- rr/8. All 
other V ' are reset to zero. If, however, at a given location i we obtain several 
928 H. Abramowicz, D. Horn, U. Nafialy and C. Sahar-Pikielny 
large values of V'o` that correspond to non-neighboring orientations, all are being 
discarded. 
The third layer also consists of orientation selective cells. They are constructed 
with a receptive field of size 7 x 7, and receive inputs from neurons with the same 
orientation on the second layer. The weights on this layer are defined in a similar 
fashion to the previous ones, but here negative weights are assigned the value of 
-3, not -1. For linear patterns, the purpose of this layer is to fill in the holes due 
to fluctuations in the pixel activation, i.e. complete the lines of same orientation 
of the second layer. As before, we keep also here up to five highest values at each 
location, following the same WTA procedure as on the second layer. 
The fourth layer of the OSNN consists of only 16 components, Do`, each corre- 
sponding to one of the discrete orientations c. For each orientation we calculate 
the convolution of the first and third layers, D ' = '.i V'o`$i . The elements 
Do` carry the information about the number of the input pixels that contribute to a 
given orientation 0o`. Cosmic muons are characterized by high values of Do` whereas 
accelerator events possess low values, as shown in figure 3 below. 
The computational complexity of this algorithm is O(n) where n is the number of 
pixels, since a constant number of operations is performed on each pixel. There 
are basically four free parameters in the algorithm. These are the sizes of the 
receptive fields on the second and third layer and the corresponding activation 
thresholds. Their values can be tuned for the best performance, however they are 
well constrained by the spatial resolution, the noise level in the system and the 
activation properties of the input pixels. The size of the receptive field determines 
to a large extent the number of orientations allowed to survive in the modified WTA 
algorithm. 
IV OSNN and a Selection Criterion on the Training Set 
The details of the design of the OSNN and the tuning of its parameters were fixed 
while training it on a sample of 250 cosmic muons and a similar amount of acceler- 
ator events. The sample was obtained by preselection with existing algorithms and 
a visual scan as a cross-check. 
For cosmic muon events the highest value of Do`, Dmax, determines the orientation 
of the straight line. In figure 3 we present the correlation between Dmax and the 
number np of activated input pixels for cosmic muon and accelerator events. As 
expected one observes a linear correlation between Drnax and np for the muons 
while almost no correlation is observed for accelerator events. This allows us to set 
a selection criterion defined by the separator in this figure. We quantify the quality 
of our selection by quoting the efficiency of properly identifying a cosmic muon for 
100% purity, corresponding to no accelerator event misidentified as a muon. In 
OSNN-D, which we define according to the separator shown in Fig 3, we obtain 
93.0% efficiency on the training set. 
On the right hand side of Fig 3 we present results of a conventional method for 
detecting lines on a grid, the Hough transform [7, 8, 9]. This is based on the 
analysis of a parameter space describing locations and slopes of straight lines. The 
cells of this space with the largest occupation number, Nmx, are the analogs of 
our Dmax. In the figure we show the correlation of Nrnax with np which allows us 
to draw a separator between cosmic muons and accelerator events, leading to an 
efficiency of 88% for 100% purity. Although this number is not much lower than the 
Orientation Selective Neural Network 929 
2O 
15 
lO 
np 
3o 
Nmax 
25 
2O 
15 
10 
Hough ..   
.ae. ...... 6 0 oO 
...'"  
' 5 10 15      
np 
Figure 3: Left: Correlation between the maximum value of D *, Dmax, and the 
number nj, of input pixels for cosmic muon (dots) and accelerator events (open cir- 
cles). The dashed line defines a separator such that all events above it correspond 
to cosmic muons (100% purity). This selection criterion has 93% efficiency. Right: 
Using the Hough Transform method, we compare the values of the largest accumu- 
lation cell Nmax with nj, and find that the two types of events have different slopes, 
thus allowing also the definition of a separator. In this case, the efficiency is 88%. 
efficiency of OSNN-D, we note that the difference between the two types of event 
distributions is not as significant as in OSNN-D. In the test set, to be discussed in 
the next chapter, we will consider 40,000 accelerator events contaminated by less 
than 100 cosmic muons. Clearly the expected generalization quality of OSNN-D 
will be higher than that of the Hough transform. It should of course be noted that 
the OSNN is a multi-layer network, whereas the Hough transform method that we 
have described is a single-layer operation, i.e. it calculates global characteristics. If 
one wishes to employ some quasi-local Hough transform one is naturally led back 
to a network that has to resemble our OSNN. 
V Training and Testing of OSNN-S 
If instead of applying a simple cut we employ an auxiliary neural network to search 
for the best classification of events using the OSNN outputs, we obtain still better 
results. The auxiliary network has 6 inputs, one hidden layer with 5 nodes and one 
output unit. The input consists of a set of five consecutive D * centered around 
Dmax and the total number of activated input pixels, np. The cosmic muons are 
assigned an output value s = 1 and the accelerator events s = 0. The net is trained 
on our sample with error back-propagation. This results in an improved separation 
of cosmic muon events from the rest. Whereas in OSNN-D we find a continuum 
of cosmic muons throughout the range of Dmax, here we obtain a clear bimodal 
distribution, as seen in Figure 4. For s _> 0.1 no accelerator events are found and 
the muons are selected with an efficiency of 94.7%. This selection procedure will be 
denoted as OSNN-S. 
As a test of our method we apply OSNN-S to a sample of 38,606 data events 
930 H. Abramowicz, D. Horn, U. Nafialy and C. Sahar-Pikielny 
that passed the standard physics cuts [5]. The distribution of the neural network 
output s is presented in Figure 4. It looks very different from the one obtained with 
the training sample. Whereas the former consisted of approximately 500 events 
distributed equally among accelerator events and cosmic muons, this one contains 
mostly accelerator events, with a fraction of a percent of muons. This proportion is 
characteristic of physics samples. The vast majority of accelerator events are found 
in the first bin, but a long tail extends throughout s. The last bin in s is indeed 
dominated by cosmic muons. 
We performed a visual scan of all 181 events with s > 0.1 using the full information 
from the detector. This allowed us to identify the cosmic-muon events represented 
by shaded areas in figure 4. For s _> 0.1 we find 55 cosmic-muon events and 
123 accelerator events, 55 of which resemble muons on the rear segment of the 
calorimeter. The latter, together with the genuine cosmic muons, populate mainly 
the region of large s values. 
We conclude that our method picked out the cosmic muons from the very large 
sample of data, in spite of the fact that it relied just on two-dimensional infor- 
mation from the rear part of the detector. This fact is, however, responsible for 
the contamination of the high s region by accelerator events that resemble cosmic 
muons. Even with all its limitations, our method reduces the problem of rejecting 
cosmic-muon events down to scanning less than one percent of all the events. We 
conclude that we have achieved the goal that we set for ourselves, that of replacing 
a laborious visual scan by a computer algorithm with similar reliability. 
N 
lO 
OSNN-S (Train) 
0.2 0.4 O.S 0. 1 
s 
N 
.1o ,4 
lO: 
lO 2 
lO 
Test 
0.2 0.4 O.S 0.8 
8 
Figure 4: Left: Number of events as a function of the output s of an auxiliary neural 
net. Choosing the separator to be s = 0.1 we obtain an efficiency of 94.7% on our 
training set. This bimodal distribution holds the promise of better generalization 
than the OSNN-D method depicted in Figure 3. Muons are represented by shaded 
areas. Right: Distribution of the auxiliary neural network output s obtained with 
the OSNN-$ selector for the test sample of 38,606 events. The tail of the distribution 
of accelerator events leads to 123 accelerator events with s > 0.1, including 55 that 
resemble straight lines on the input layer. 55 genuine cosmic muons were identified 
in the high s region. 
Orientation Selective Neural Network 931 
VI Summary 
We have presented an algorithm for identifying linear patterns on a two-dimensional 
lattice based on the concept of an orientation selective cell, a concept borrowed 
from neurobiology of vision. Constructing a multi-layered neural network with 
fixed architecture that implements orientation selectivity, we define output elements 
corresponding to different orientations, that allow us to make a selection decision. 
The algorithm takes into account the granularity of the lattice as well as the presence 
of noise and inefficiencies. 
Our feed-forward network has a fixed set of synaptic weights. Hence, although the 
number of neurons is very high, the complexity of the system, as determined by the 
number of free parameters, is low. This allows us to train our system on a small 
data set. We are gratified to see that, nontheless, it generalizes well and performs 
excellently on a test sample that is larger by two orders of magnitude. 
One may regard our method as a refinement of the Hough transform, since each of 
our orientation selective cells acts as a filter of straight lines on a limited grid. The 
major difference from conventional Hough transforms is that we perform semi-local 
calculations, and proceed in several stages, reflected by the different layers of our 
network, before evaluating global parameters. 
The task that we have set to ourselves in the application described here is only one 
example of problems of pattern recognition that are encountered in the analysis of 
particle detectors. Given the large flux of data in these experiments, one is faced 
by two requirements: correct identification and fast performance. Using a structure 
like our OSNN for data classification, one can naturally meet the speed require- 
ment through its realization in hardware, taking advantage of the basic features of 
distributed parallel computation. 
Acknowledgement s 
We are indebted to the ZEUS Collaboration for allowing us to use the sample of 
data for this analysis. This work was partly supported by a grant from the Israel 
Science Foundation. 
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Methods in Phys. Res. A378 (1996) 305. 
[4] B. Denby, Neural Computation, 5 (1993) 505. 
[5] ZEUS Calorimeter Group, A. Andresen et al., Nucl. Inst. Meth. A 309 (1991) 101. 
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