# FF-LOGO: Cross-Modality Point Cloud Registration with Feature Filtering and
Local to Global Optimization

Nan Ma1, Mohan Wang1, Yiheng Han† and Yong-Jin Liu2 1Nan Ma, Mohan Wang and
Yiheng Han are with the Faculty of Information Technology, Beijing University
of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, China
(e-mail: {wangmohan, manan123, hanyiheng}@emails.bjut.edu.cn).2Yong-Jin Liu is
with BNRist, MOE-Key Laboratory of Pervasive Computing, Department of Computer
Science and Technology, Tsinghua University, Beijing, China.
<EMAIL_ADDRESS>
###### Abstract

Cross-modality point cloud registration is confronted with significant
challenges due to inherent differences in modalities between different
sensors. We propose a cross-modality point cloud registration framework FF-
LOGO: a cross-modality point cloud registration method with feature filtering
and local-global optimization. The cross-modality feature correlation
filtering module extracts geometric transformation-invariant features from
cross-modality point clouds and achieves point selection by feature matching.
We also introduce a cross-modality optimization process, including a local
adaptive key region aggregation module and a global modality consistency
fusion optimization module. Experimental results demonstrate that our two-
stage optimization significantly improves the registration accuracy of the
feature association and selection module. Our method achieves a substantial
increase in recall rate compared to the current state-of-the-art methods on
the 3DCSR dataset, improving from 40.59% to 75.74%. Our code will be available
at https://github.com/wangmohan17/FFLOGO.

##  I INTRODUCTION

Point cloud registration, the task of finding rigid transformations to align
two input point clouds, is a pivotal technique in robotics and computer vision
[1]. It finds vital applications in domains such as autonomous driving [2],
augmented or virtual reality systems[3], Simultaneous Localization and Mapping
(SLAM)[4], and robotics[5]. Most prior studies have focused on point cloud
data of the same modality obtained from identical sensor types, with little
attention paid to other modalities. In reality, with the advancement of 3D
data acquisition technologies, the cost of obtaining point clouds has been
reduced, and the methods of acquisition have diversified, including Kinect
depth cameras, LiDAR, or Multi-View Stereo (MVS).

Each existing sensor has its specific advantages and limitations when
capturing 3D scenes. For instance, LiDAR, which gauges the distance to
obstacles using laser pulses to generate point clouds. Benefits from the high
energy of laser pulses, LiDAR generates high-precision point clouds over
extended ranges. However, the density of these point clouds is often sparse.
Depth cameras estimate depth using infrared or stereo vision techniques, which
can produce dense point clouds, but usually within a limited range and with
moderate precision. RGB cameras can generate dense point clouds with texture
information using 3D reconstruction techniques, but their accuracy typically
lags behind that of depth cameras and LiDAR sensors. cross-modality point
cloud fusion or registration combines the strengths of multiple sensors,
overcoming the limitations of a single sensor, ensuring point cloud
acquisition is accurate, efficient, and detailed, resulting in higher-quality
visualizations, comparisons, or localizations. For example, in the robotics
domain, users can align low-cost, easily accessible sensor data with high-
quality data from robotic service providers using cross-modality point cloud
registration, facilitating low-cost robot environment reconstruction and
localization service deployment [6]. In the architectural design domain,
cross-modality comparisons between onsite point cloud scanning data and 3D CAD
design models provide faster and more precise evaluations for building quality
[7].

Homogeneous point cloud registration methods face numerous challenges when
dealing with cross-modality data. Firstly, due to the diverse mechanisms
through which different sensors generate point clouds, the point density
(resolution) distribution varies across modalities. Secondly, in cross-
modality situations, sensor accuracies differ, and outliers can arise from
both perceived objects and sensor noise. Additionally, point clouds captured
from different kinds of sensors seldom guarantee entirely identical poses and
fields of view, making the problem of partial overlap more pronounced in
cross-modality point clouds than in homogeneous ones. Existing methods,
especially traditional optimization-based ones, can achieve precise results in
scenarios with low noise and outliers and are computationally efficient.
However, in cross-modality registration, the presence of numerous inaccurate
point-to-point correspondences makes finding the optimal solution challenging.
Deep learning-based methods, which leverage deep neural networks to extract
point cloud features and either base the transformation estimation on these
feature correspondences or regress directly from the features to the
transformation matrix, offer some robustness. Still, noise and density
variations in cross-modality registration can impact feature extraction,
resulting in transformation estimation that is often less than satisfactory.

To address these challenges, in this paper, we combine the robustness of deep
learning-based cross-modality point cloud feature extraction with the fine-
tuning precision advantages of traditional optimization algorithms. We
introduce a cross-modality point cloud registration framework FF-LOGO based on
feature filtering and local-global optimization. Our method extracts geometric
features from cross-modality point clouds with transformation invariance and
filters the high feature-coupled uniform point sets and initial pose
estimation through a cross-modality feature association filtering module.
Subsequent local adaptability key area aggregation modules and global
modality-consistent fusion optimization modules perform local-global joint
optimization. We observed that the local-global joint optimization process can
significantly enhance the pose estimation accuracy of the cross-modality
feature association filtering module.

Our main contribution is threefold:

  * •

We have devised a cross-modality point cloud registration framework anchored
in feature filtering and local-global optimization to tackle the challenging
task of cross-modality point cloud registration.

  * •

We introduced a local-to-global optimization process for cross-modality
registration, significantly enhancing the preliminary accuracy derived from
feature filtering.

  * •

We fully leverage the advantages of deep learning and traditional optimization
for cross-modality registration and achieve the state-of-the-art with an
improvement from 40.59% to 75.74%.

##  II RELATED WORKS

###  II-A Conventional Optimization Methods

The Iterative Closest Point (ICP) [8] is a classical method in point cloud
registration. Its fundamental premise revolves around iteratively determining
the best rigid transformation between two point clouds, thereby minimizing
their point-to-point distances. While ICP is computationally efficient and
concise, its reliance on initial pose estimates and its sensitivity to
outliers pose challenges in cross-modality registration. Variants of the ICP
algorithm attempt to enhance its performance from multiple perspectives. For
example, TriCP [9] introduces a trimming rate to effectively select
corresponding portions from two datasets for ICP registration, addressing the
issue of partial overlaps. CICP [10] aims to register point clouds of
differing densities produced by varied sensors by matching local surface
representations in both source and target point clouds. GO-ICP [11] adopts a
global search strategy rooted in branch-and-bound to achieve global
optimization, avoiding potential local minima. Building on 4PCS [12],
Super4PCS [13] considerably reduces computational demands, offering an
efficient solution for global point cloud registration. However, despite these
advancements, achieving ideal results in cross-modality point cloud
registration remains elusive.

Probabilistic point cloud registration methodologies offer an alternative
research direction, seeking to probabilistically model the deterministic
correspondences found in ICP. These methods typically employ Gaussian Mixture
Models (GMM) to characterize the distribution of point clouds, recasting point
cloud registration as an optimization problem of probability density
functions. GMM [14]stands out as a representative approach, exhibiting
robustness against significant noise and outliers, albeit with relatively
higher computational complexity. FilterReg [15], on the other hand, transforms
the correspondence problem in point set registration into a filtering problem
using Gaussian filtering, thereby achieving efficient registration. Huang et
al. [16] introduced a GMM-based method for cross-modality point cloud
registration. However, its intricate preprocessing steps are not readily
adaptable to large-scale point clouds with partial overlaps.

Beyond strategies based on GMM, several studies have approached the
registration challenge by treating it as a graph matching problem to address
cross-modality discrepancies. CSGM [17] recasts the registration issue as a
graph matching problem. Yet, its limitation lies in the necessity to segment
the point cloud and rely solely on pairwise point matching for graph node
alignment. To address these constraints, GCTR [18] introduced a cross-modality
point cloud registration technique that considers an extended set of
neighboring constraints, reformulating it into a higher-order graph matching
problem. Owing to its inclusion of more constraints, this method exhibited
more robust performance in experiments compared to previous graph-matching
approaches. Nevertheless, the segmentation process of this approach adds
additional computational time, and its performance is intricately tied to
hyperparameters.

###  II-B Deep neural network methods

Recently, the achievements of deep neural networks in three-dimensional
geometry, such as PointNet [19] and DGCNN [20], have propelled advancements in
deep point cloud registration. At the heart of these methods lies the concept
of leveraging deep neural networks to extract features from cross-source point
clouds, either basing registrations on these feature correspondences or
directly regressing transformation matrices from the features themselves.
Feature learning techniques, SpinNet [21] aims to extract robust point
descriptors through tailored neural network designs. However, its reliance on
a voxelization preprocessing step poses challenges in the context of cross-
modality point clouds. D3Feat [22]necessitates the construction of features
based on k-nearest neighbors, but this descriptor tends to falter when faced
with significant density disparities. Beyond these point descriptor-focused
methodologies, several strategies emphasize feature matching. Deep Global
Registration (DGR) [23] devises a UNet architecture for discerning whether a
point pair corresponds. This process reinterprets the feature matching dilemma
as a binary classification task. Transformation learning approaches, as an
alternative line of investigation, directly estimate transformations via
neural networks. FMR [24] introduces a feature metric registration technique,
aligning two point clouds by minimizing their feature metric projection error.
Specifically, FMR first extracts global features from both point clouds,
followed by computing their feature metric projection error. Subsequently, the
Lukas-Kanadle (LK) [25] algorithm is deployed to estimate transformation
increments, leading to the determination of the final transformation.

##  III METHODOLOGY

Figure 1: Overview of the proposed pipeline. The Cross-Modality Feature
Correlation Filtering Module extracts and filters feature-correlated points,
obtaining an initial pose estimation. Key regions identified by The Local
Adaptive Key Region Aggregation Module are then optimized with the Global
Modality Consistency Fusion Optimization Module to achieve the final optimised
registration.

The comprehensive architecture of our proposed method is illustrated in Figure
1, encompassing three integral modules. The Cross-Modality Feature Correlation
Filtering Module operates on the original point clouds, $\mathcal{K}$ and
$\mathcal{L}$. Voxel downsampling is performed to mitigate density
discrepancies, preventing adverse effects on subsequent feature extraction, it
produces isopycnic points, denoted as $\hat{\mathcal{K}}$ and
$\hat{\mathcal{L}}$. Building upon this foundation, the module isolates
isopycnic points with heightened feature confidence and gets the filtered
points, as $\tilde{\mathcal{K}}$ and $\tilde{\mathcal{L}}$. Simultaneously, a
coarse-grained pose transformation estimation $\mathcal{T}_{c}$ is derived via
feature matching techniques. The Local Adaptive Key Region Aggregation Module
identifies prominent keypoints, $\hat{\mathcal{K}}_{key}$, from
$\hat{\mathcal{L}}$, extracting a subset of the point cloud,
$\hat{\mathcal{K}}_{patch}$, which encapsulates key local regions with a
pronounced adaptive nature. The Global Modality Consistency Fusion
Optimization Module fuses the isopycnic point set $\tilde{\mathcal{L}}$,
discerned from the initial module, with the adaptive key local region sub-
point cloud $\hat{\mathcal{K}}_{patch}$ from the secondary module. By
deploying a modality-consistent optimization strategy that transitions from
local nuances to a global perspective, the coarse-grained pose transformation
estimate $\mathcal{T}_{c}$ undergoes meticulous refinement, yielding the
definitive registration outcome $\mathcal{T}_{f}$. The details of each module
will be provided in subsections.

###  III-A The Cross-Modality Feature Correlation Filtering Module

Our Cross-Modality Feature Correlation Filtering Module is mainly inspired by
the GeoTransformer [26]. Operating under identical physical environments, the
geometric position encoding self-attention module of GeoTransformer
effectively extracts geometry transformation-invariant features from point
clouds. This capability robustly handles challenges in cross-modality point
cloud matching, such as outliers, anomalies, and partial overlaps. To
elucidate the methodology, the module encompasses three distinct components:
the construction of Geometric Self-attention, the extraction of features
through the Geometric Transformer, and the subsequent process of feature
matching and selection.

Initially, we use Geometric Self-attention to learn the feature and global
correlation in the geometric space between isopycnic points. The geometric
structure embedding, at its core, aims to utilize consistent angular and
distance relationships present in cross-modality point clouds from the same
scene. For an isopycnic point set ($\hat{\mathcal{K}}$ or
$\hat{\mathcal{L}}$), the geometric structure embedding consists of pair-wise
distance embedding and triplet-wise angular embedding:

$\mathbf{e}_{i,j}=\mathbf{e}_{i,j}^{D}\mathbf{W}^{D}+\max_{x}\left\\{\mathbf{e}_{i,j,x}^{A}\mathbf{W}^{A}\right\\}$
(1)

$\mathbf{W}^{D}$ and $\mathbf{W}^{A}$ are projection matrices for distance and
angular embeddings respectively, $\mathbf{e}_{i,j}$ is the geometric structure
embedding, $\mathbf{e}_{i,j}^{D}$ is the pair-wise distance embedding, and
$\mathbf{e}_{i,j}^{A}$ is the triplet-wise angular embedding.

The pair-wise distance embedding, $\mathbf{e}_{i,j}^{D}$, is calculated as:

$\displaystyle e_{i,j,2k}^{D}$
$\displaystyle=\sin\left(\frac{d_{i,j}/\sigma_{d}}{10000^{2k/d_{t}}}\right)$
(2) $\displaystyle e_{i,j,2k+1}^{D}$
$\displaystyle=\cos\left(\frac{d_{i,j}/\sigma_{d}}{10000^{2k/d_{t}}}\right)$

$d_{i,j}$ represents the Euclidean distance between isopycnic points
$\hat{\mathbf{p}}_{i}$ and $\hat{\mathbf{p}}_{j}$, $\sigma_{d}$ is a
hyperparameter to adjust distance variations, and $d_{t}$ is the
dimensionality of the data. The triplet-wise angular embedding,
$\mathbf{e}_{i,j}^{A}$, is given by:

$\displaystyle e_{i,j,x,2l}^{A}$
$\displaystyle=\sin\left(\frac{\alpha_{i,j}^{x}/\sigma_{a}}{10000^{2l/d_{t}}}\right)$
(3) $\displaystyle e_{i,j,x,2l+1}^{A}$
$\displaystyle=\cos\left(\frac{\alpha_{i,j}^{x}/\sigma_{a}}{10000^{2l/d_{t}}}\right)$

$k$ neighboring isopycnic points are initially chosen for
$\hat{\mathbf{p}}_{i}$, forming the point set $\mathcal{X}_{i}$. For
$\hat{\mathbf{p}}_{x}$ within $\mathcal{X}_{i}$, $\alpha_{i,j}$ is calculated
as: $\alpha_{i,j}^{x}=\angle(\Delta_{x,i},\Delta_{j,i})$, with $\Delta_{i,j}$
defined as $\hat{\mathbf{p}}_{i}-\hat{\mathbf{p}}_{j}$.

In the subsequent process, the Geotransformer[26] network is utilized to
compute self-attention and cross-attention based on geometric structure
embedding. This yields features $\hat{\mathcal{H}}^{\mathcal{K}}$ and
$\hat{\mathcal{H}}^{\mathcal{L}}$ for the isopycnic point sets
$\hat{\mathcal{K}}$ and $\hat{\mathcal{L}}$, respectively.

The final step involves point cloud selection based on their features. First,
$\hat{\mathcal{H}}^{\mathcal{K}}$ and $\hat{\mathcal{H}}^{\mathcal{L}}$ are
normalized onto a unit hypersphere. The Gaussian correlation matrix $S$ is
then computed, with entries $s_{i,j}\in S$ defined as:

$s_{i,j}=\exp\left(-\left\|\hat{\mathbf{h}}_{i}^{\mathcal{K}}-\hat{\mathbf{h}}_{j}^{\mathcal{L}}\right\|_{2}^{2}\right)$
(4)

###  III-B The Local Adaptive Key Region Aggregation Module

The role of the Local Adaptive Key Region Aggregation module is to aggregate
several locally representative point cloud patches from the isopycnic points
to prepare for the global modality consistency fusion optimization. The
extracted local point cloud patches should be representative, dispersed
throughout the point cloud and containing ample local features.

Initially, from the isopycnic point set $\hat{\mathcal{K}}$, we select
dispersed and representative key points within the point cloud. Following the
approach in PVNET[27], we employ the Farthest Point Sampling (FPS) algorithm
to select $n$ key points. Assuming our point cloud consists of $N$ points,
denoted as set $P$, where each point is represented as a vector, and the set
of selected points is $S$. To initialize the set of key points, we calculate
the geometric centroid of the point cloud. For every remaining point $p\in P$,
we compute its minimum distance to all points in set $S$:

$d(p,S)=\min_{s\in S}\|p-s\|_{2}$ (5)

We then select the point with the maximum distance:

$p_{\text{next}}=\arg\max_{p\in P\backslash S}d(p,S)$ (6)

The chosen point $p_{\text{next}}$ is added to the set $S$ and removed from
set $P$, continuing this process until the size of the set reaches $n$. This
results in the key point set $\hat{\mathcal{K}}_{key}$. For accuracy and
efficiency, we adopt $n=8$. After extracting the key points, we employ the
k-nearest neighbors (knn) algorithm to aggregate neighboring isopycnic points
around the key points from $\hat{\mathcal{K}}$ to form the Local Adaptive Key
Region point set $\hat{\mathcal{K}}_{patch}$, which supplements the local
information of the point cloud.

###  III-C The Global Modality Consistency Fusion Optimization Module

Due to discrepancies between training and validation sets, as well as losses
in local information arising from feature extraction results, registration
results from feature-matching methods frequently suffer from reduced accuracy
or even outright failures. It is crucial to impose additional constraints on
the registration results through optimization techniques following cross-
modality feature alignment, in order to enhance both accuracy and stability.
In consideration of this, we have developed an optimization method that
transitions from local adaptive key region matching to global modality
consistency fusion.

The isopycnic point set $\hat{\mathcal{L}}$, processed through Module A,
yields the cross-modality feature-coupled point set $\tilde{\mathcal{L}}$,
representing the point cloud post-feature selection. The isopycnic point set
$\hat{\mathcal{K}}$, processed through Module B, gives the local adaptive key
region point set $\hat{\mathcal{K}}_{patch}$, symbolizing the key point cloud
region containing representative local information in the other modality. The
$\tilde{\mathcal{L}}$ is then matched with each local adaptive key region in
$\hat{\mathcal{K}}_{patch}$ to compute the point-to-plane residuals and
iteratively map to obtain the optimal transformation pose. Specifically, for
every point $a_{i}$ in the nth set of $\hat{\mathcal{K}}_{patch}$, locate the
corresponding plane in the point cloud $\tilde{\mathcal{L}}$ with the shortest
distance, denoted as $b_{j1},b_{j2},b_{j3}$:

$j^{*}(a_{i})=\arg\min_{j}|(a_{i}-b_{j1})\cdot\vec{n}_{j}|$ (7)

where $\vec{n}_{j}$ is the normal vector of $b_{j1},b_{j2},b_{j3}$. For each
point $a_{i}$ and its corresponding plane $j$, compute the point-to-plane
distance residual:

$r_{i}=(T(a_{i})-b_{j1})\cdot\vec{n}_{j}$ (8)

Minimize the distance residuals for all points to their corresponding planes
through solving the least squares problem:

$T_{key,n}=\arg\min_{T}\sum_{i}r_{i}(T)^{2}$ (9)

This provides the optimal modality-consistent transformation $T_{key,n}$
between the nth $\hat{\mathcal{K}}_{patch}$ and the cross-modality feature-
coupled point set $\tilde{\mathcal{L}}$.

After obtaining the local optimal transformations, a global key point least
squares optimization is necessary to integrate local modality-consistent
adjustments. Transform the corresponding key points from the local adaptive
key region point set according to the local transformation estimate $T_{key}$
to get the transformed point set $\hat{\mathcal{K}}_{key}^{\prime}$:

$\hat{\mathcal{K}}_{key}^{\prime}=\\{T_{key,i}\cdot a_{i}\mid
a_{i}\in\hat{\mathcal{K}}_{key}\\}$ (10)

For each corresponding point pair in $\hat{\mathcal{K}}_{key}$ and
$\hat{\mathcal{K}}_{key}^{\prime}$, solve the following least squares problem
to minimize the squared distance error for all points:

$\mathcal{T}_{f}=\arg\min_{T_{key}}\sum_{i=1}^{n}\|T_{key}\cdot
a_{i}-b_{i}\|_{2}^{2}$ (11)

This results in the final optimized transformation $\mathcal{T}_{f}$ through
the local-to-global modality-consistent transformation estimation. We
summarize the proposed method of The Global Modality Consistency Fusion
Optimization in Algorithm 1.

Input : Isopycnic point sets $\hat{\mathcal{K}}$, $\hat{\mathcal{L}}$

Output : Optimal transformation $\mathcal{T}_{f}$

Initialize : Transformed point set $\hat{\mathcal{K}}_{key}^{\prime}$, Point-
to-plane residual $r_{i}$, Transformation estimates $T_{key,n}$

1

2$\tilde{\mathcal{L}}\leftarrow$ Process $\hat{\mathcal{L}}$ through The
Cross-Modality Feature Correlation Filtering Module;

3 $\hat{\mathcal{K}}_{patch}\leftarrow$ Process $\hat{\mathcal{K}}$ through
The Local Adaptive Key Region Aggregation Module;

4

5foreach  _point set $\hat{\mathcal{K}}_{patch,n}$ in
$\hat{\mathcal{K}}_{patch}$_ do

6 foreach  _point $a_{i}$ in $\hat{\mathcal{K}}_{patch,n}$_ do

7 Find plane $b_{j1},b_{j2},b_{j3}$ in $\tilde{\mathcal{L}}$ with minimum
distance to $a_{i}$;

8 Compute the point-to-plane distance residual $r_{i}$;

9

10 end foreach

11 Solve for $T_{key,n}$ to minimize all $r_{i}$;

12

13 end foreach

14

15Transform $\hat{\mathcal{K}}_{key}$ using $T_{key}$ to get
$\hat{\mathcal{K}}_{key}^{\prime}$;

16 foreach  _point pair in $\hat{\mathcal{K}}_{key}$ and
$\hat{\mathcal{K}}_{key}^{\prime}$_ do

17 Solve least squares problem to minimize squared distance error;

18

19 end foreach

20Compute the final transformation $\mathcal{T}_{f}$ using local-to-global
modality-consistent estimation;

21

Algorithm 1 The Global Modality Consistency Fusion Optimization

##  IV EXPERIMENT

###  IV-A Implementation Details

####  IV-A1 Parameters

In the cross-modality feature correlation selection module, the voxel size for
voxel-based subsampling during dense point selection is set to $0.05m$. We
utilized the Adam optimizer [28] to train our network over a span of 40
epochs, employing the 3DMatch[29] dataset. The training parameters included a
batch size of 1, a weight decay set at $10^{-6}$, and an initial learning rate
of $10^{-4}$, which undergoes an exponential decay at a rate of 0.05 with
every passing epoch. Regarding the mutual top-k selection in the point
correspondences filtering, we set the hyper-parameter $k$ : $k$ =1 for 250,
500 and 1000 matches, $k$ =2 for 2500 matches, and $k$ = 3 for 2500 matches.
This configuration helps in regulating the number of point correspondences. In
the local adaptability key region aggregation module, the number of key points
selected for the set $\hat{\mathcal{K}}_{key}$ is $n=8$. The aggregation
radius for gathering neighboring dense points around the key points from the
set $\hat{\mathcal{K}}$ is $d(p,S)_{max}\times 1.5$. All experiments are
conducted on a machine equipped with a single RTX 4090 graphics card and an
Intel Core i5-13600KF CPU.

####  IV-A2 Dataset

The proposed algorithm and baseline methods are evaluated on the 3DCSR dataset
[30]. Point clouds in this dataset originate from three distinct modalities:
LiDAR, Kinect, and camera sensors. Point clouds produced by the LiDAR
equipment are relatively sparse, while the Kinect point clouds, generated by
the Kinect depth camera, are dense and uniform. The third modality data is
constructed from a series of indoor 2D RGB images using the Structure from
Motion (SfM) approach. This dataset provides ground truth transformations for
aligning either LiDAR or SfM geometry with dense Kinect geometry. It
encompasses the most common objects or scenes found in indoor working
environments. In total, the dataset comprises 202 point cloud pairs, with 37
scenes captured by Kinect and RGB cameras, and 165 scenes acquired by LiDAR
and Kinect sensors.

###  IV-B Evaluation Metrics

For rigorous evaluation, we adopt two key metrics to quantify the quality of
registration:

$\displaystyle\operatorname{RE}(\hat{\boldsymbol{R}},\boldsymbol{R})$
$\displaystyle=\frac{180}{\pi}\arccos\left(\frac{1}{2}\left\\{\operatorname{Tr}\left(\hat{\boldsymbol{R}}\boldsymbol{R}^{T}\right)-1\right\\}\right),$
$\displaystyle\mathrm{TE}(\hat{\boldsymbol{t}},\boldsymbol{t})$
$\displaystyle=\|\hat{\boldsymbol{t}}-\boldsymbol{t}\|_{2},$

where $\operatorname{RE}$ represents the geodesic distance within $SO(3)$ and
$\mathrm{TE}$ signifies the Euclidean distance in $R^{3}$. These metrics
effectively evaluate the discrepancies in rotation and translation between the
estimated outcome $(\hat{R},\hat{t})$ and the established ground truth
$(R,t)$.

###  IV-C Performance

For all methods, we conducted 10 independent experiments to assess their
average performance and recall rates. The registration recall rate is
calculated as the ratio of the number of point cloud pairs with Rotation Error
(RE) less than 15∘ and a Translation Error (TE) less than 0.3m to the total
number of pairs. Consistent with some literature, such as [31], when
evaluating average performance, we only consider point cloud pairs that were
successfully recalled. This is due to the fact that pairs that fail to be
recalled deviate significantly from the baseline data, rendering their
performance metrics potentially unreliable.

The quantitative results are shown in Table I. In addition to the latest
cross-source registration methods, performance tests of many other homomodal
point cloud registration benchmarks are also reported. Our method
significantly outperforms the current state-of-the-art method, GCC, in recall
rate, increasing from 40.59% to 75.74%. TE and RE are slightly higher than the
current lowest method because they are calculated only based on successfully
recalled samples.

It can be observed that among conventional optimization methods, RANSAC[32],
ICP[8], and its variants like TrICP[9], CICP[10], PICP[33], and Super4PCS[13],
do not show significant advantages in recall rate and estimation error. The
graph matching-based GCTR[18] has an even lower recall rate, while methods
based on Gaussian Mixture Model (GMM), such as FilterReg[15], demonstrate
relatively better recall rates and moderate estimation errors. Among deep
neural network-based methods, apart from IDAM[34], DGR[23], and FMR[24] all
exhibit higher-than-average recall rates and relatively lower estimation
errors compared to conventional optimization methods. It’s noteworthy that the
avant-garde cross-modality point cloud registration technique, GCC[31],
eclipses the DGR method, which harnesses deep neural network feature mapping,
in recall metrics, setting a new benchmark. Nonetheless, its sub-50% recall
rate underscores the inherent challenges plaguing the domain of cross-modality
point cloud registration. This reflects the immense challenges in
generalization for the current cross-modality point cloud registration
problem. Existing methods still face significant hurdles in addressing the
generalization of cross-modality point cloud registration. Our method offers a
substantial improvement in generalization, achieving a recall rate of 75.74%.
Furthermore, while maintaining a high recall rate, our method also retains a
relatively low level of estimation error compared to current methods,
indicating its advantages in both generalization and accuracy.

TABLE I: Quantitative comparisons on the 3DCSR dataset. Method | Recall | TE | RE
---|---|---|---
ICP[8] | 24.3 | 0.38 | 5.71
RANSAC[32] | 3.47 | 0.13 | 8.30
TrICP[9] | 7.92 | 0.18 | 6.40
CICP[10] | 2.48 | 0.28 | 8.28
PICP[33] | 4.45 | 0.29 | 10.85
Super4PCS[13] | 6.93 | 0.24 | 6.38
GCTR[18] | 0.50 | 0.17 | 7.46
GMM[14] | 9.41 | 0.18 | 7.92
FilterReg[15] | 30.96 | 0.10 | 2.45
DGR[23] | 36.60 | 0.04 | 4.26
IDAM[34] | 1.98 | 0.13 | 11.37
FMR[24] | 17.80 | 0.10 | 4.66
GCC[31] | 40.59 | 0.06 | 2.21
Ours | 75.74 | 0.09 | 2.85

###  IV-D Ablations

To analyze the efficacy of the proposed local-global optimization process, we
present an ablation study in Table II. Specifically, Feature Filtering (FF)
represents the cross-modality feature association filtering module, Local-
Global Optimization (LOGO) embodies the combined optimization workflow of the
local adaptability key region aggregation module and the global modality
consistency fusion optimization module, while Global Optimization (GO) denotes
a module that encompasses solely global optimization, serving as a replacement
for LOGO. The results indicate that both GO and LOGO further enhance the
relatively high-precision initial pose estimation derived from the FF module,
and the improvement of our LOGO is much more pronounced. Besides, in
comparison to all existing approaches, FF with deep learning methods exhibits
significant potential for enhancing the processing capability of cross-
modality point clouds. However, it remains a coarse registration method with
regard to the specific challenge of cross-modality point cloud alignment and
experiments show that our Local-Global optimization method can accomplish fine
registration on this basis and yield a further enhanced performance
improvements. These findings validate the effectiveness of the local-global
optimization procedure in the context of cross-modality point cloud
registration.

###  IV-E Application

Figure 2: An application of FF-LOGO

To demonstrate the practical application value of FF-LOGO in cross-modality
point cloud registration, we deployed the algorithm on a bipedal wheeled robot
for cross-modality localization tests. As illustrated in Figure 2, we
initially constructed a high-precision point cloud map using a LIDAR scanner.
Subsequently, point clouds generated in real-time from the stereo camera
equipped on the wheeled robot were registered with the high-quality LIDAR
point clouds to find the accurate pose of our robot. Experimental results
validate the robustness and high accuracy of our approach, with very few
instances of registration failure and a localization error of less than 10mm.
FF-LOGO holds significant potential for many robotic tasks such as
localization, point cloud completion, and registration for cross-modality
scenarios.

TABLE II: Ablation study on GO and LOGO FF | GO | LOGO | Recall(%)
---|---|---|---
✓ |  |  | 61.88
✓ | ✓ |  | 65.34
✓ |  | ✓ | 75.74

##  V CONCLUSION

In this paper, we introduced a novel framework combining feature filtering and
local-global optimization, resulting in robust and accurate registration. Our
method fully leverages the advantages of deep learning and traditional
optimization, achieving a significant improvement on registration accuracy, as
evidenced by a substantial increase in the recall rate compared to state-of-
the-art methods on the 3DCSR dataset. In future, we will explore the potential
of our method for general point cloud registration.

## References

  * [1] K. Li, J. Yang, Y.-K. Lai, and D. Guo, “Robust non-rigid registration with reweighted position and transformation sparsity,” _IEEE Transactions on Visualization and Computer Graphics_ , p. 2255–2269, Jun 2019. [Online]. Available: http://dx.doi.org/10.1109/tvcg.2018.2832136
  * [2] W. Lu, G. Wan, Y. Zhou, X. Fu, P. Yuan, and S. Song, “Deepicp: An end-to-end deep neural network for 3d point cloud registration.” in _2019 IEEE/CVF International Conference on Computer Vision (ICCV)_ , Oct 2019. [Online]. Available: http://dx.doi.org/10.1109/iccv.2019.00010
  * [3] V. Ferrari, N. Cattari, U. Fontana, and F. Cutolo, “Parallax free registration for augmented reality opticalsee-through displays in the peripersonal space,” _IEEE Transactions on Visualization and Computer Graphics_ , vol. 28, no. 3, p. 1608–1618, Mar 2022. [Online]. Available: http://dx.doi.org/10.1109/tvcg.2020.3021534
  * [4] D. Cattaneo, M. Vaghi, and A. Valada, “Lcdnet: Deep loop closure detection and point cloud registration for lidar slam,” _IEEE Transactions on Robotics_ , p. 2074–2093, Aug 2022. [Online]. Available: http://dx.doi.org/10.1109/tro.2022.3150683
  * [5] F. Pomerleau, F. Colas, and R. Siegwart, “A review of point cloud registration algorithms for mobile robotics,” _Foundations and Trends in Robotics_ , p. 1–104, Jan 2015. [Online]. Available: http://dx.doi.org/10.1561/2300000035
  * [6] X. Huang, G. Mei, and J. Zhang, “Cross-source point cloud registration: Challenges, progress and prospects,” _Neurocomputing_ , p. 126383, 2023.
  * [7] A. Avetisyan, M. Dahnert, A. Dai, M. Savva, A. X. Chang, and M. NieBner, “Scan2cad: Learning cad model alignment in rgb-d scans,” in _2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_ , Jun 2019. [Online]. Available: http://dx.doi.org/10.1109/cvpr.2019.00272
  * [8] P. J. Besl and N. D. McKay, “Method for registration of 3-d shapes,” in _Sensor fusion IV: control paradigms and data structures_ , vol. 1611\. Spie, 1992, pp. 586–606.
  * [9] D. Chetverikov, D. Stepanov, and P. Krsek, “Robust euclidean alignment of 3d point sets: the trimmed iterative closest point algorithm,” _Image and Vision Computing_ , p. 299–309, Mar 2005. [Online]. Available: http://dx.doi.org/10.1016/j.imavis.2004.05.007
  * [10] M. L. Tazir, T. Gokhool, P. Checchin, L. Malaterre, and L. Trassoudaine, “Cicp: Cluster iterative closest point for sparse–dense point cloud registration,” _Robotics and Autonomous Systems_ , vol. 108, pp. 66–86, 2018\.
  * [11] J. Yang, H. Li, D. Campbell, and Y. Jia, “Go-icp: A globally optimal solution to 3d icp point-set registration,” _IEEE Transactions on Pattern Analysis and Machine Intelligence_ , p. 2241–2254, Nov 2016. [Online]. Available: http://dx.doi.org/10.1109/tpami.2015.2513405
  * [12] D. Aiger, N. J. Mitra, and D. Cohen-Or, “4-points congruent sets for robust pairwise surface registration,” in _ACM SIGGRAPH 2008 papers_ , 2008, pp. 1–10.
  * [13] N. Mellado, D. Aiger, and N. J. Mitra, “Super 4pcs fast global pointcloud registration via smart indexing,” _Computer Graphics Forum_ , p. 205–215, Aug 2014\. [Online]. Available: http://dx.doi.org/10.1111/cgf.12446
  * [14] B. Jian and B. C. Vemuri, “Robust point set registration using gaussian mixture models,” _IEEE transactions on pattern analysis and machine intelligence_ , vol. 33, no. 8, pp. 1633–1645, 2010.
  * [15] W. Gao and R. Tedrake, “Filterreg: Robust and efficient probabilistic point-set registration using gaussian filter and twist parameterization,” in _2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_ , Jun 2019. [Online]. Available: http://dx.doi.org/10.1109/cvpr.2019.01135
  * [16] X. Huang, J. Zhang, Q. Wu, L. Fan, and C. Yuan, “A coarse-to-fine algorithm for registration in 3d street-view cross-source point clouds,” _arXiv: Computer Vision and Pattern Recognition,arXiv: Computer Vision and Pattern Recognition_ , Oct 2016\.
  * [17] X. Huang, J. Zhang, L. Fan, Q. Wu, and C. Yuan, “A systematic approach for cross-source point cloud registration by preserving macro and micro structures,” _IEEE Transactions on Image Processing_ , p. 3261–3276, Jul 2017. [Online]. Available: http://dx.doi.org/10.1109/tip.2017.2695888
  * [18] X. Huang, L. Fan, Q. Wu, J. Zhang, and C. Yuan, “Fast registration for cross-source point clouds by using weak regional affinity and pixel-wise refinement,” _arXiv: Computer Vision and Pattern Recognition,arXiv: Computer Vision and Pattern Recognition_ , Mar 2019.
  * [19] R. Q. Charles, H. Su, M. Kaichun, and L. J. Guibas, “Pointnet: Deep learning on point sets for 3d classification and segmentation,” in _2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , Jul 2017\. [Online]. Available: http://dx.doi.org/10.1109/cvpr.2017.16
  * [20] Y. Wang, Y. Sun, Z. Liu, S. E. Sarma, M. M. Bronstein, and J. M. Solomon, “Dynamic graph cnn for learning on point clouds,” _ACM Transactions on Graphics_ , p. 1–12, Oct 2019. [Online]. Available: http://dx.doi.org/10.1145/3326362
  * [21] S. Ao, Q. Hu, B. Yang, A. Markham, and Y. Guo, “Spinnet: Learning a general surface descriptor for 3d point cloud registration,” in _2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_ , Jun 2021\. [Online]. Available: http://dx.doi.org/10.1109/cvpr46437.2021.01158
  * [22] X. Bai, Z. Luo, L. Zhou, H. Fu, L. Quan, and C.-L. Tai, “D3feat: Joint learning of dense detection and description of 3d local features,” in _2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_ , Jun 2020\. [Online]. Available: http://dx.doi.org/10.1109/cvpr42600.2020.00639
  * [23] C. Choy, W. Dong, and V. Koltun, “Deep global registration.” in _2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_ , Jun 2020. [Online]. Available: http://dx.doi.org/10.1109/cvpr42600.2020.00259
  * [24] X. Huang, G. Mei, and J. Zhang, “Feature-metric registration: A fast semi-supervised approach for robust point cloud registration without correspondences,” in _2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)_ , Jun 2020. [Online]. Available: http://dx.doi.org/10.1109/cvpr42600.2020.01138
  * [25] B. Lucas and T. Kanade, “An iterative image registration technique with an application to stereo vision,” Aug 1981.
  * [26] Z. Qin, H. Yu, C. Wang, Y. Guo, Y. Peng, and K. Xu, “Geometric transformer for fast and robust point cloud registration,” in _Proceedings of the IEEE/CVF conference on computer vision and pattern recognition_ , 2022, pp. 11 143–11 152.
  * [27] S. Peng, Y. Liu, Q. Huang, X. Zhou, and H. Bao, “Pvnet: Pixel-wise voting network for 6dof pose estimation,” in _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , 2019, pp. 4561–4570.
  * [28] D. Kingma and J. Ba, “Adam: A method for stochastic optimization,” _arXiv: Learning,arXiv: Learning_ , Dec 2014.
  * [29] A. Zeng, S. Song, M. Niessner, M. Fisher, J. Xiao, and T. Funkhouser, “3dmatch: Learning local geometric descriptors from rgb-d reconstructions,” in _2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , Jul 2017. [Online]. Available: http://dx.doi.org/10.1109/cvpr.2017.29
  * [30] X. Huang, G. Mei, J. Zhang, and R. Abbas, “A comprehensive survey on point cloud registration,” _arXiv preprint arXiv:2103.02690_ , 2021.
  * [31] M. Zhao, X. Huang, J. Jiang, L. Mou, D.-M. Yan, and L. Ma, “Accurate registration of cross-modality geometry via consistent clustering,” _IEEE Transactions on Visualization and Computer Graphics_ , 2023.
  * [32] M. A. Fischler and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” _Communications of the ACM_ , vol. 24, no. 6, pp. 381–395, 1981.
  * [33] I. Jubran, A. Maalouf, R. Kimmel, and D. Feldman, “Provably approximated point cloud registration,” in _Proceedings of the IEEE/CVF International Conference on Computer Vision_ , 2021, pp. 13 269–13 278.
  * [34] J. Li, C. Zhang, Z. Xu, H. Zhou, and C. Zhang, “Iterative distance-aware similarity matrix convolution with mutual-supervised point elimination for efficient point cloud registration,” in _Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part XXIV 16_. Springer, 2020, pp. 378–394.


# The Extreme Energy Events experiment: an overview of the telescopes
performance.

M.Abbrescia  C.Avanzini  L.Baldini Ferroli  L.Baldini  G.Batignani
M.Battaglieri  S.Boi  E.Bossini  F.Carnesecchi  A.Chiavassa  C.Cicalo
L.Cifarelli  F.Coccetti  E.Coccia  A.Corvaglia  D.De Gruttola  S.De Pasquale
F.L.Fabbri  V.Frolov  L.Galante  P.Galeotti  M.Garbini  G.Gemme  I.Gnesi
S.Grazzi  C.Gustavino  D.Hatzifotiadou  P.La Rocca  G.Mandaglio  O.Maragoto
Rodriguez  G.Maron  M.N.Mazziotta  S.Miozzi  R.Nania  F.Noferini  F.Nozzoli
F.Palmonari  M.Panareo  M.P.Panetta  R.Paoletti  W.Park  C.Pellegrino
L.Perasso  F.Pilo  G.Piragino  S.Pisano  F.Riggi  G.C.Righini  C.Ripoli
M.Rizzi  G.Sartorelli  E.Scapparone  M.Schioppa  A.Scribano  M.Selvi  S.Serci
S.Squarcia  M.Taiuti  G.Terreni  A.Trifirò  M.Trimarchi  M.C.Vistoli  L.Votano
M.C.S.Williams  L.Zheng  A.Zichichi  R.Zuyeuski

###### Abstract

The muon telescopes of the Extreme Energy Events (EEE) experiment are based on
Multigap Resistive Plate Chambers (MRPC). The EEE network is composed, so far,
of 53 telescopes, each made of three MRPC detectors; it is organized in
clusters and single telescope stations distributed all over the Italian
territory and installed in High Schools, covering an area larger than $3\times
10^{5}$ km2. The study of Extensive Air Showers (EAS), that is one of the goal
of the project, requires excellent performance in terms of time and spatial
resolution, efficiency, tracking capability and long term stability. The data
from two recent coordinated data taking periods, named Run 2 and Run 3, have
been used to measure these quantities and the results are here reported,
together with a comparison with expectations and with the results from a beam
test performed in 2006 at CERN.

##  1 Introduction

The Extreme Energy Events (EEE) experiment [1] is a project by Centro Fermi
(Museo Storico della Fisica e Centro Studi e Ricerche "Enrico Fermi") [2], in
collaboration with INFN (Istituto Nazionale di Fisica Nucleare), CERN
(European Council for Nuclear Research) and MIUR (the Italian Ministry of
Education, University and Research). EEE is designed to study Cosmic Rays (CR)
and CR-related phenomena, via a synchronous sparse network of 53 tracking
detectors, deployed over an area covering more than 10 degrees in latitude and
11 in longitude, corresponding to more than 3 $\times$ $10^{5}$ km2. The
observatory is being upgraded regularly: 6 new stations have been installed
within the end of 2017, leading to a 10$\%$ increase in the number of
telescopes.
The EEE network is composed both by clusters and stand-alone stations; the
result is a sparse network where each detection site is located at distances
ranging from 15 m to several km from the one nearby. Each station is made of
three Multigap Resistive Plate Chambers (MRPC), a CR dedicated version of the
detector successfully used for Time Of Flight (TOF) systems and tracking
detectors in high energy physics experiments at colliders (examples are the
TOF system [4] of the ALICE experiment [5] at LHC and of the STAR experiment
at RHIC [6]). Data collected by each station are sent to the CNAF center [7],
the computing facility of the INFN, where they are stored, reconstructed and
made available for analysis. The experiment has completed its Run 3 in June
2017; the whole data set collected since fall 2014 has already exceeded 50
billions of muon track candidates.
The topology of the EEE network allows to measure time-correlated events at
distances never addressed before. Telescopes placed in the same city can
detect individual EAS [8], whereas telescopes located hundreds of kilometers
apart can, in principle, detect the coincidence between two different
correlated air showers, for which a few interesting events were found.
The EEE network can also address the local properties of the CR flux and its
space weather-correlated features [10, 11], CR flux anisotropies in the sub-
TeV energy region [12] and also phenomena related to the upward-going particle
flux [13].
The EEE project has also a strong outreach impact: 47 detectors are installed
in High Schools, where students and teachers actively participate to the data
taking activities, taking care of the telescope operation and maintenance.
Researchers coordinate and supervise activities, providing support during
detectors construction, installation and operation. Students and teachers are
introduced through seminars, lectures and master-classes, to the scientific
research community, with the opportunity of understanding how a real
experiment works, from the infrastructure development to the data acquisition,
analysis and publications of scientific results.
The EEE network commenced its operational activity in 2004 with a set of pilot
sites in 7 Italian cities. In 2017 the observatory has grown up by a factor
almost 8 in terms of number of telescopes. The EEE network is the largest and
long-living MRPC-based system, with 53 sites instrumented and more than 12
years of data taking. The unconventional working sites, mainly school
buildings with non-professional electrical lines, non-controlled environmental
parameters and heterogeneous maintenance conditions, are a unique test field
for checking the robustness, the ageing and the long-lasting performance of
the MRPC technology for particle tracking and timing determination. In
addition to the schools already hosting a telescope, 54 more institutes joined
the project despite not being equipped with the detector; all the students
contribute to the experiment by monitoring the telescopes performance and
analyzing the available data.

##  2 MRPC for the EEE telescopes

The chambers composing the EEE telescopes are MRPC detectors specifically
designed for combining good tracking and timing capabilities, low construction
costs and easy assembly procedures. Since the students of each participating
school are directly involved in the construction of their own detectors, it is
therefore important that the materials used are easy to find, safe and simple
to assemble. The detector structure (Fig. 1) consists of 6 gas gaps obtained
by stacking glass sheets, with voltage applied only to the external ones, and
leaving the inner ones floating.

Figure 1: MRPC inner structure.

The cathode and the anode consist of two glasses (160 cm $\times$ 85 cm, 1.9
mm thick) treated with resistive paint (5-20 M$\Omega$/$\Box$) connected to
high voltage, the space between them being divided into the six narrow gaps
(300 $\mu$m) by 5 intermediate glass sheets (158 cm $\times$ 82 cm, 1.1 mm
thick); inner-glass spacing is assured through a weave made with fishing line.
Anode and cathode are also in contact, on the outer surfaces, with a sheet of
Mylar (175 cm $\times$ 86 cm in dimensions) stretched on a vetronite panel of
equal area on whose external surface 24 copper strips are laid out (180 cm
$\times$ 2.5 cm spaced by 7 mm), to collect the signals induced by particles.
Two rigid composite honeycomb panels (180 cm $\times$ 90 cm) are used to
assure good mechanical stability to the whole structure, which is enclosed in
a gas-tight aluminum box (220 cm $\times$ 110 cm of external dimensions, 192
cm $\times$ 92 cm inside). A schematic top view of a chamber is shown in Fig.
2. The gas inlets and outlets, and the high voltage connectors are located at
the ends of the longer sides, while the front-end (FEA) boards for the read-
out of the strip signals are placed on the short sides.
Chambers are filled with a gas mixture consisting of a 98/2 mixture of R134a
(C2F4H2) and SF6, at a continuous flow of 2 l/h and atmospheric pressure. High
voltage to the chambers, typically in the 18-20 kV range, is provided by a set
of DC/DC converters, with output voltage roughly a factor 2000 with respect to
the driving low voltage (LV). Stand-alone LV power supply units, both
commercial or custom engineered by the EEE Collaboration, provide the LV to
the DC-DC converters. The core unit of the DC-DC converters are the EMCO
Q-series, both positive and negative, with a 10 kV full scale output. The HV
stability declared by the manifacturer is $\pm$10% at full load (50 $\mu$A).
The typical working voltage is 8-9 kV, thus very close to the full scale.

Figure 2: Top view of a MRPC chamber, showing the 24 copper strips, the 2 FEA
at the edges of the chamber and the connectors where 2 DC/DC converters
providing the HV (top left in blu and bottom right in red) are plugged in.

The aforementioned 24 copper strips that collect the signal, provide two-
dimensional information when a cosmic muon crosses the chamber; in our
reference system:

  * •

the $y$ coordinate is determined by the strip on which the signal is induced;

  * •

the $x$ coordinate is determined by measuring the difference between the
arrival time of the signal at the two ends of the strip.

FEA cards (2 for each chamber) incorporate the ultrafast and low power NINO
ASIC amplifier/discriminator specifically designed for MRPC operation [14].
Three MRPC chambers assembled in a telescope are shown in Fig. 3.

Figure 3: One EEE Project telescope located at Liceo Classico Massimo
D’Azeglio in Turin, composed of three MRPC chambers.

The trigger logic consists in a six-fold coincidence of the OR signals from
the FEA cards (corresponding to a triple coincidence of both ends of the
chambers), whose signals are combined in a VME custom made trigger module. The
arrival times of the signals are measured using two commercial TDCs (CAEN
V1190 - 64 and 128 ch - 100 ps bin). Synchronization between telescopes is
guaranteed by a GPS unit that provides the event time stamp with precision of
the order of 40 ns. Data acquisition, monitoring and control are managed by a
LabVIEW based program.

###  2.1 The track reconstruction algorithm

Data reconstruction is centrally managed at CNAF. Raw data are first processed
to calibrate the telescope. Each readout channel has a time offset which
slowly drifts in time, mainly in relation with environmental temperature
variations. The drift is slow and does not affect a single run, whose
approximate duration is typically around half an hour. Every signal induced on
a strip generates two time measurements, $t_{l}$ or $t_{r}$, corresponding to
arrival time of the signal to the edges of the chambers conventionally
labelled as "right" and "left". The calibration is performed for each strip:
the $t_{l_{i}}-t_{r_{i}}$ distribution of the i-th strip is used to calculate
the mean value $\overline{t_{l_{i}}-t_{r_{i}}}$ for that strip. The mean is
then subtracted to measurements $t_{l_{i}}-t_{r_{i}}$, so that the corrected
mean value is set to zero. In this way all time differences on each chamber
are equalized. Once the calibration is done, the corrected time values on one
strip are paired to form a hit point.
As already pointed out, transversal coordinate is given by the strip number,
while the longitudinal coordinate is given by the difference in the arrival
time of the signal to the two chamber edges. A time value is also assigned to
the hit, computed as the arithmetic mean of $t_{l}$ and $t_{r}$ and thus
independent from the hit position. Cuts are then applied to exclude non
physical hits by constraining their longitudinal position: the hit is rejected
if $t_{l}$ and $t_{r}$ give an $x$ coordinate larger than 79 cm on one of the
two sides wrt. the center of the strip (i.e. we require the hit to be inside
the active volume). After all hits are reconstructed, clusters are defined by
grouping adjacent hits, if present. Hits (tagged 1 and 2) are clusterized if
the following requirements are met:

  * •

hits are on adjacent strips

  * •

the differences $\Delta t_{1}-\Delta t_{2}$, where $\Delta
t_{1,2}=t_{l1,2}-t_{r1,2}$, is below 2 ns

  * •

the hit time difference $t_{h1}-t_{h2}$, where
$t_{h1,2}=\frac{t_{l1,2}+t_{r1,2}}{2}$, is below 2 ns

The time associated to the cluster is the smallest one. Finally, track
reconstruction is performed. A linear fit of the clusters found in the three
chambers is performed and the corresponding $\chi^{2}$ is computed. All
possible cluster combinations are used and ordered by their $\chi^{2}$. The
track candidates are defined by iteratively selecting the lowest $\chi^{2}$
and removing the corresponding clusters, continuing up to the point when the
whole set of available clusters has been assigned to a track. At the end a set
of tracks with no hits in common is defined and transferred to the output file
for analysis. The track selection for the measurements presented in this paper
is done by requiring $\chi^{2}$ $<$ 5 and rejecting events with more than 1
track. A $\chi^{2}$ distribution before any cut is applied, for tracks
collected by the EEE station labelled TORI-03, is shown in Fig. 4. The track
multiplicity distribution for events with a $\chi^{2}$ < 5 is shown in Fig. 5.

Figure 4: $\chi^{2}$ distribution for one of the EEE telescopes (TORI-03,
located in Piedmont) before any cut is applied. A zoom in the range $\chi^{2}$
= [0-20] is included.

Figure 5: Track multiplicity distribution of one of the EEE telescopes
(SALE-01, located in Campania); the applied cut is $\chi^{2}$ $<$ 5 in this
case.

Some interesting statistics from the four coordinated runs taken so far are
listed in table 1. Few considerations are due. The number of tracks wrt. the
effective data taking period increased together with the number of telescopes
included in the data taking. The slight decrease of the purity (candidate
tracks/triggers) in Run 3 is due to the inclusion of few telescopes not yet
optimized in Run 3 and well-performing in Run 4, that started in October 2017.

Table 1: Statistics from the four coordinated runs. The number of active telescopes in Pilot Run, Run 1, Run 2 and Run 3, is respectively 15, 28, 38 and 46. The purity is calculated as candidate tracks/triggers. | Pilot Run | Run 1 | Run 2 | Run 3 |
---|---|---|---|---|---
starting date | $27/10/2014$ | $27/02/2015$ | $07/11/2015$ | $01/11/2016$ |
ending date | $14/11/2014$ | $30/04/2015$ | $20/05/2016$ | $31/05/2017$ |
number of days | $19$ | $63$ | $196$ | $212$ |
tracks/day (M) | $\sim 27$ | $\sim 53$ | $\sim 69$ | $\sim 85$ |
purity (%) | $75$ | $84$ | $83$ | $80$ |

The study of the detector performance (described in the next session) has been
carried out by selecting a data sample from Run 2 and the recent Run 3. The
whole EEE network has been used in the present analysis.

##  3 Performance

In the next paragraphs the strategy to measure time and spatial resolution
will be described. A sample of about 8 billion tracks over 31 billions
collected during the Run 2 and Run 3 was used. Time resolution was derived
analysing a sample of events collected in Run2 by telecopes TORI-03 (located
in Piedmont) and PISA-01 (located in Tuscany). The main feature of the two
telescopes is the fact that they were equipped with a dedicated board which
distributed a common clock to the two TDC modules equipping each telescope.
This prevented the slow shifts between the two internal TDCs clock, which
could spoil the measured time resolution. In Run 3 the same clock distribution
card was installed in all EEE telescopes allowing to asses the time resolution
of all telescopes and compare the results with Run 2. A wider data sample from
46 telescopes has been used to evaluate spatial resolution. Telescope network
time and spatial resolution results of the network are presented in paragraphs
3.1 and 3.2. Results of an efficiency measurement, performed without the need
of an external detector are shown in paragraph 3.3. The last paragraph of this
section (3.4) reports a study on the long term stability of the network, in
terms of some quantities like tracking, multiplicity, trigger rate and time of
flight.

###  3.1 Time resolution

The study of the time resolution $\sigma_{t}$ has been performed by measuring
the time information on the upper and lower chambers and using these values to
determine the expected time on the middle chamber; this value is then compared
with the hit time measured on the middle chamber. The width of the obtained
distribution is proportional to the time resolution of the telescope. Time
residuals used for the measurement of the time resolution are therefore
defined as:

$\Delta t=\frac{t_{top}+t_{bot}}{2}-t_{mid}$ (3.1)

where $t_{top}$, $t_{mid}$, $t_{bot}$ are the time values for single or
clustered hits, as appropriate.

####  3.1.1 Results from RUN 2

The $\Delta t$ distribution for TORI-03 (Run 2 data) is shown Fig. 6; the
distribution is fitted with a gaussian function whose $\sigma_{\Delta t}$ =
269 ps. Assuming that the three chambers have similar timing performances,
this implies a time resolution $\sigma_{t}$ for the single chamber
$\sigma_{t}$ = $\sigma_{\Delta t}/\sqrt{\frac{3}{2}}$ = 221 ps. A similar
analysis performed for PISA-01 gave a $\sigma_{t}$ = 270 ps result. It is
worth noting that the time slewing (TS) correction, explained in details in
the next paragraph, is not applied in this case, while is included the
analysis performed on Run 3.

Figure 6: $\Delta t$ distribution for one of the EEE telescopes (TORI-03),
showing the gaussian fit and the time resolution $\sigma_{t}$ = 221 ps. The
data used in this case are from Run 2 and the time slewing (TS) correction is
not applied.

####  3.1.2 Results from RUN 3

The readout electronics used in the EEE project [14] measures time using so-
called leading edge discriminators (whose threshold can be chosen in a range
[0,1] V and was optimized by setting the value at 500 mV in all FEA) coupled
to TDC. The time when the signal becomes lower than the threshold is instead
calledtrailing edge. The Time Over Threshold (TOT) corresponds to the time
difference between the times of the trailing and leading edges and is the time
during which the signal remains over the threshold of the signal
discriminator. The hit time depends on the signal amplitude, whose measure is
roughly given by the TOT; its jitter can be corrected in order to extract the
correct hit time (TS correction). The correction (performed on each chamber)
makes use of the correlation between TOT and $t$-$t_{exp}$, the difference
between the measured time $t$ on a specific chamber and the time expected
$t_{exp}$ on the same chamber, determined by considering the other two
chambers as reference. The procedure for TS correction is standard and can be
found in [15]. An example of the mean time vs. TOT distribution for one
chamber of one of the telescopes of the EEE network is shown in Fig. 7. Each
point of this distribution represents the $i-th$ mean value $t_{i,TOT}$ of the
$i-th$ bin of the profile histogram; these points are used to correct the
measured time values $t$ ($t_{corr}$ = $t$ \- $t_{i,TOT}$). A linear
interpolation is performed to get the mean value of $t$-$t_{exp}$ when TOT is
between two bins.

Figure 7: Correlation between TOT and the difference between the measured time
and the time expected on the concerned chamber. The correction to be applied
to each hit time is obtained from this distribution (for each single chamber).
The distribution of one chamber of the telescope BOLO-01 (located in Emilia
Romagna region) is shown here as an example.

Figure 8: Time distributions for the telescopes: TORI-04, BOLO-03, PATE-01 and
TREV-01 (respectively located in Piedmont, Emilia Romagna, Sicily and Veneto),
measured with data taken in Run 3; the distribution and the time resolution
before and after TS correction are shown.

Figure 9: Time resolution measured with data taken in Run 3, for 33
telescopes; the average time resolution is given by the gaussian fit and is
$\sigma_{t}$ = 238 ps.

Once the correction is determined, it is applied to each hit time and a new
time distribution is built by using the corrected time $t_{corr}$, that can be
used to measure the time resolution. Some examples are shown in Fig. 8, where
the distributions before and after the TS correction are visible. The
measurement has been performed on all the telescopes of the network and a
$\approx$$20\%$ improvement is obtained once the correction is applied.
Depending on the telescope the time resolution ranges between 140 and 380 ps.
The different values of time resolution for different telescopes can depend on
three factors: missing optimization of the detector working point, possible
inhomogeneities in MRPC construction, possible not optimal calibration for
some strips. The first factor is also related to the dependence of the working
point on pressure and temperature; the relative correction is not performed at
the moment, but it will be done in Run 4.. The other two factors should be
less relevant, as the building procedure is robust and tests are periodically
performed, as well as the calibration procedure. A distribution obtained with
the values of time resolution from 33 telescopes of the network is shown in
Fig. 9. A gaussian fit gives an average time resolution $\sigma_{t}$ = 238 ps,
with a sigma of 40 ps. This resolution is within expectations and totally
compatible with Run 2 results and with EEE specifications. It can be compared
with the value measured at the beam tests performed in 2006 at CERN [3] of 142
ps without TS correction and $\approx$100 ps with correction and $t_{0}$
subtraction; the smaller value is explained by the fact that at a beam-test
conditions are well controlled, with a focused, monochromatic and collinear
beam monitored with a set of MultiWire Proportional Chambers (MWPC) and
scintillators. The working points optimization for the next data taking is
expected to improve time resolution.

###  3.2 Spatial resolution

Spatial resolution is obtained by studying the distributions of the particle
impact points in the three MRPC. It has been evaluated by measuring the
spatial information on the upper and lower chambers and by using these values
to determine the expected position on the middle chamber, both in the $xz$ and
$yz$ planes ($z$ being the coordinate orthogonal to the chamber plane). This
value is then compared with the hit measured on the middle chamber. The
residuals used to measure space resolution are therefore defined as:

$\Delta x,y=\frac{x,y_{top}+x,y_{bot}}{2}-x,y_{mid}$ (3.2)

Assuming the same space resolution in the three chambers, the space resolution
along the strip (longitudinal resolution) of a single chamber can be
calculated as $\sigma_{x}=\sigma_{\Delta x}/\sqrt{\frac{3}{2}}$ and along the
short side (transverse resolution) as $\sigma_{y}=\sigma_{\Delta
y}/\sqrt{\frac{3}{2}}$.

####  3.2.1 _Longitudinal spatial resolution_

The two signal arrival times, $t_{right}$ and $t_{left}$, are related to the
$x_{i}$ coordinate of the hit, to the chamber lenght $L$ and to the signal
velocity along the strip $v_{drift}$ by the following relation:

$t_{right}=\Big{(}\frac{L}{2}-x_{i}\Big{)}\frac{1}{v_{drift}}~{}~{}~{}~{}~{}~{}~{}~{}~{}\textnormal{and}~{}~{}~{}~{}~{}~{}~{}t_{left}=\Big{(}\frac{L}{2}+x_{i}\Big{)}\frac{1}{v_{drift}}$
(3.3)

Therefore the $x$ position is evaluated as an average from both equations, by
the difference of the two times:

$x_{i}=\frac{t_{left}-t_{right}}{2}~{}v_{drift}$ (3.4)

where $v_{drift}$ has been assumed to be 15.8 cm/ns.

Figure 10: Longitudinal spatial resolution measured with data taken in Run 2
and Run 3 with 46 telescopes of the EEE network.

A sample of 2.7 (3.5) billions candidate tracks collected in 30 days from 41
(46) telescopes in Run 2 (Run 3) has been used for this measurement. For each
telescope the distribution $\mathit{\Delta}$$x$ (see eq. 3.2) has been plotted
and used to derive $\sigma_{x}$, with the same strategy already applied to
determine the time resolution. The comparison between the $\sigma_{x}$
distributions from Run 2 and Run 3 are shown in Fig. 10. The result from a
gaussian fit gives an average longitudinal resolution of:
$\sigma_{x_{Run2}}=1.48\pm 0.04$ cm and $\sigma_{x_{Run3}}=1.49\pm 0.03$ cm.
The two results are in agreement, showing the stability of the network across
the two runs. The longitudinal spatial resolution, measured at the beam test
performed in 2006 at CERN previously mentioned, is 0.84 cm; the discrepancy
with the measurement reported here is due to a set of missing uncertainty
sources and different conditions wrt. beam tests (in a similar way as already
explained in Sec. 3.1.2).

####  3.2.2 _Transverse spatial resolution_

The expected transverse spatial resolution is derived considering the pitch of
the strips (3.2 cm), $\sigma_{y_{exp}}\sim$ pitch/$\sqrt{12}$ = 0.92 cm.

Figure 11: Transverse spatial resolution measured with data taken in Run 2 and
Run 3 for 46 telescopes of the EEE network.

The spatial resolution in the $y$ direction was measured using the same data
samples used to estimate the longitudinal resolution. For each telescope the
distribution $\mathit{\Delta}$$y$ (see eq. 3.2) has been plotted and used to
derive $\sigma_{y}$, applying the same strategy used for time resolution
evaluation. The distributions for Run 2 and Run 3 are reported in Fig. 11. The
average resolutions is $\sigma_{y}=0.92\pm 0.01$ cm for both Run 2 and Run 3,
in very good agreement with the expectations.

###  3.3 Efficiency

Efficiency curves as a function of the applied voltage have been measured both
at CERN, immediately after chamber construction, and after telescopes
installation at schools; in most cases these curves have been obtained using
scintillator detectors, employed as external trigger, and with additional
electronics.
Later on, during data acquisition runs, the MRPC efficiency has been measured
without using any additional detector, by using a slightly modified version of
the reconstruction code. This method allows to check periodically the
detectors performance and provides efficiency values, useful for all analysis.

####  3.3.1 _High Voltage stability_

The high voltage (HV) applied to an MRPC, or generally to a RPC-based
detector, is a sensitive parameter for all applications involving absolute
particle flux measurements or relative measurements performed over a long time
period. The working point of the detector is ideally fixed within the
efficiency plateau region, 300-400 V beyond the knee of the efficiency curve
and at the lowest allowed value, in order to limit the chamber spurious
counting rate, which usually ranges between 10 and 1000 kHz. Note that any HV
fluctuation beyond 300-400 V (due for instance to changes in temperature and
pressure) can move the working point of the chamber in the region left to the
knee, where even a few tens of Volt variation corresponds to a significant
change in efficiency. An optimal choice of the working point of the EEE
telescope is therefore fundamental to allow the EEE telescopes to be sensitive
to phenomena involving a few percent particle flux variations, such as solar
activity surveys and search for very rare events.
Indeed since the EEE telescope trigger logic selects events detected by the
three MRPC planes, the whole telescope efficiency is $\epsilon_{telescope}$ =
$\epsilon_{t}\times\epsilon_{m}\times\epsilon_{b}$, the product of the
efficiencies of the top, middle and bottom chambers respectively. Therefore
the identification of secondary muons flux variations is strongly affected by
the single MRPC efficiency fluctuations. Assuming the three efficiencies being
roughly equal to a common value $\epsilon$, a small single chamber efficiency
fluctuation $d\epsilon$ reflects in the telescope efficiency with a
fluctuation (at the first order)
$\approx\mathrm{3}\epsilon^{2}\,\mathrm{d}\epsilon\approx$ 2.7$\%$, in case of
$\epsilon=$0.95 and d$\epsilon\sim$1$\%$. The typical flux variations
connected to a Coronal Mass Ejection on the Sun span from 1-2$\%$ to 6-7$\%$,
thus setting the maximum allowed efficiency fluctuation to be well below
1$\%$.
The searches for rare events are even more challenging. The detection
efficiency of an EAS by a telescope cluster, composed by $n$ telescopes, is
proportional to $\epsilon^{3n}$. The search for long distance correlations
between EASs requires the coincidences between 2 clusters (at least 2
telescope each), setting the efficiency for such observations to
$\epsilon^{4n}$. By considering $\epsilon=$0.95 one obtains as the overall
efficiency for these events $\approx$54$\%$.
Temperature and pressure are independent sources of instability for an RPC-
based detector, as they affect the mean free path of the charges in the gas
volume and thus the detector response [16]. To mitigate the variation, the EEE
collaboration adopted two strategies. The temperature variations are reduced
by conditioning the rooms where the telescopes are installed, or an
"effective" voltage $HV_{eff}$, as described in [17], is used. It is defined
as :

$HV_{eff}=HV\frac{p_{0}}{p}\frac{T}{T_{0}}$ (3.5)

where standard pressure and temperature are set in our case to $p_{0}$ = 1000
mb and $T_{0}$=298.15 $K$.

####  3.3.2 _Using the outer chambers as a trigger_

The efficiency measurements, whose results are reported here, have been
performed by changing from the standard 3-chambers operations to a 2-fold
coincidence, excluding the chamber under test from the trigger. The two
chambers in the trigger are also used for tracking and for selecting events
with acceptable values of 1/$\beta$; in particular the 1/$\beta$ distribution
is fitted with a gaussian and events are accepted if the 1/$\beta$ value is
inside $\pm$ 0.7 from the mean value. Once a track is defined, the procedure
requires to check if a hit is present on the chamber under test within a
distance of 7 cm wrt. the expected (calculated) position. An HV scan of the
chamber excluded from the trigger is performed, collecting about 150000 events
per step. An example of the results of these measurements for the middle MPRC
of 9 EEE telescopes is shown in Fig. 12. During the measurements atmospheric
pressure $p$ and temperature $T$ were recorded, so efficiency is plotted vs.
$HV_{eff}$ (see eq. 3.5 in the previous paragraph). As shown in Fig. 12, all
MRPC show a similar behavior, with efficiencies reaching almost $100\%$ for an
applied voltage larger than 18 kV.

Figure 12: Efficiency vs. applied HV (corrected for standard $p$ and $T$) of
the middle MRPC of 9 EEE telescopes. The red arrow indicates the usual value
chosen as working point.

Figure 13: Distribution of the efficiency obtained at the plateau (corrected
for standard $p$ and $T$) of the middle MRPC for 31 EEE telescopes. An
efficiency better than 90% is reached by 77% of the network.

This method was applied to the middle chamber of the EEE telescopes, but can
be used to measure the efficiency of all the MRPC of a telescope by simply
changing the trigger pattern, with the additional care of checking if the
predicted hit position lies inside the fiducial area of the chamber under
test. A distribution of efficiency values at the plateau from 31 telescopes
(middle chamber) obtained from a three parameters sigmoid function fit to each
telescope efficiency curve is shown in Fig. 13 [17]. The fit parameters are
the efficiency at plateau, the High Voltage at $50\%$ of plateau and the slope
of the curve at flush. The average efficiency of the telescope network is
around 93%, compatible with EEE specs and with results of the beam test
performed in 2006 at CERN [3]. An efficiency better than 90% is reached by 77%
of the network, corresponding to 24 telescopes out of 31. The cause of
inefficiency for some telescopes can be related to dead strips and/or MRPC
ageing. The efficiency strip by strip for two telescopes of the network, as an
example, is shown in Fig. 14; the plot shows the efficiency spatial uniformity
in the telescopes involved in this measurement. Possible lowering of the
efficiency for some strips (taken into account in the reconstruction) are
signalled thanks to this detailed measurement.

Figure 14: Efficiency vs. strip for 2 EEE telescopes (located in Emilia
Romagna region and Sardinia.

###  3.4 Long term stability

Long term performance stability is not easy to achieve with detectors hosted
in schools, often far away from the nearest technical support. For telescope
monitoring purposes an automatic Data Quality Monitor (DQM) has been created.
For each file transferred to CNAF a set of parameters and rates are computed
and published online.

(a) $\chi^{2}$

(b) DAQ rate

(c) Multiplicity

(d) Reconstruction efficiency

(e) Time of Flight

(f) Track rate

Figure 15: Run 2 trending plot for 5 EEE stations. Points at zero represent
days when the telescope was not operational.

Daily report are also automatically generated, illustrating the evolution of
the parameters over the last 48 hours. DQM allows for a fast reaction in case
one station deviates from the standard behavior. Using the DQM and full
reconstruction outputs, it is also possible to extend such trending plots to
longer periods. As an example, trends for a selection of relevant quantities
are reported in Fig. 15 for some telescopes of the EEE network:

  1. 1.

$\chi^{2}$: average tracks $\chi^{2}$;

  2. 2.

_DAQ rate_ : raw acquisition rate;

  3. 3.

_Multiplicity_ : average number of hits on the three chambers for each event;

  4. 4.

_Reconstruction efficiency_ : percentage of raw events where at least one
track candidate has been found;

  5. 5.

_Time of Flight_ : average tracks TOF between top and bottom chambers;

  6. 6.

_Track rate_ : rate of events with at least one candidate track.

(a)

(b)

(c)

(d)

Figure 16: Average and per chamber hit multiplicity of SAVO-02, BOLO-01,
GROS-01 and TORI-03 (located respectively in Liguria region, Emilia Romagna
region, Tuscany and Piedmont); a sample from Run 2 data has been used.

(a) $\chi^{2}$

(b) DAQ rate

(c) Multiplicity

(d) Reconstruction efficiency

(e) Time of Flight

(f) Track rate

Figure 17: Run 3 trending plots for 9 stations. Points at zero represent days
when the telescope was not operational.

Data sample used in this case roughly covers 4.5 months of Run 2 for the the
five EEE telescopes with the best “live" time (time of active data taking).
$\chi^{2}$ and TOF together can be used to check the quality of the
reconstructed tracks. Mean TOF values may be different for each station since
distance between chambers are not the same for all installations. $\chi^{2}$
is computed from the best (lowest $\chi^{2}$) tracks in each event, if at
least one hit on each chamber has been recorded. Note that these rates are
sensitive to fluctuations in efficiency and noise rate of the detector, with
the reconstruction efficiency used as cross-check. Hit multiplicity is a key
parameter, because is extremely sensitive to gas and HV instabilities. Hit
multiplicity is also available in the DQM for each chamber independently, and
the average and the single chamber multiplicity for some of the telescopes of
Fig. 15 are shown in Fig. 16.
Deviations from the standard trending provides important warnings for the
identification of problems and their solution. They might be due to cables not
correctly plugged-in, malfunctioning of parts of the electronics, gas bottle
exhausted. A long term stability study has been performed on 2 months out of
Run 3 dataset and reported in Fig. 17, showing the same quantities of Fig. 15
for a subset of 9 stations. These plots are also useful to identify issues
affecting a specific telescope for a limited period of time. For instance
correlation between sudden multiplicity increases and drops in track
reconstruction efficiency and track rate is clearly evident.

##  4 Conclusions

The network of cosmic muon telescopes of the EEE Project, based on MRPC
technology and covering about 106 km2 across the Italian territory, has been
successfully operated in the last years. More than 50 billion tracks have been
collected by the network, during three data taking from 2014 to 2017. The
observatory has grown up by a factor almost 8 in terms of number of telescopes
wrt. 2007 and the EEE network is currently the largest and long-living MRPC-
based telescopes network, with 53 active sites and more than 12 years of data
taking. The unconventional working sites offer a unique check of the
robustness, the ageing and the long-lasting performance of the MRPC technology
for particle tracking and timing determination. The results of the analysis on
the performance of the network are fully compatible with the EEE requirements
in terms of efficiency ($\sim$93%), time resolution (238 ps) and spatial
resolution (1.5 cm and 0.9 cm respectively for longitudinal and transverse
direction). The good performance of the network allowed several analysis to be
performed and published. Among them: search coincidences between near
telescopes [8], study the muon flux decrease due solar events [10][11], study
of cosmic muon anisotropy at sub-TeV scale [12], study of muon decay into up-
going events [13], search long distance correlations between EAS [9]. At the
moment the EEE Collaboration is focusing on further improvements of the
performance in terms of duty cycle and optimization of the working points of
the telescopes.

## References

  * [1] _Progetto "La Scienza nelle Scuole" - EEE: Extreme Energy Events, Società Italiana di Fisica (Bologna)_ , _A. Zichichi_ 3 May 2004; 2nd edition, 1 April 2005; 3rd edition, 20 April 2012
  * [2] _http://www.centrofermi.it/EEE_
  * [3] _Performance of a six gap MRPC built for large area coverage_ _M.Abbrescia et al._ Nuclear Instruments and Methods in Phys.Research A593 (2008) 263 - 268
  * [4] _ALICE Collaboration_ , Addendum to TOF Technical Design Report, 490 CERN/LHCC (2002) 016
  * [5] _Insights from the ALICE quark-gluon coloured world at the LHC_ _L. Cifarelli et al._ RIVISTA DEL NUOVO CIMENTO Vol. 39, N. 10 (2016) 497-545
  * [6] _A single Time-of-Flight tray based on multigap resistive plate chambers for the STAR experiment at RHIC_ _B.Bonner et al._ , Nuclear Instruments and Methods in Physics Research Section A 508 (2003) 181-184, Issues 1-2
  * [7] _www.cnaf.infn.it/annual-report_ ISSN 2283-5490
  * [8] _First detection of extensive air showers with the EEE experiment_ _M.Abbrescia et al._ , Nuovo Cim. B125 (2010) 243
  * [9] _Search for long distance correlations between extensive air showers detected by the EEE network_ _M.Abbrescia et al._ , Eur. Phys. J. Plus (2018) 133: 34
  * [10] _Observation of the February 2011 Forbush decrease by the EEE telescopes_ _M.Abbrescia et al._ , Eur. Phys. J. Plus (2011) 126: 61
  * [11] _The EEE experiment project: status and first physics results_ _M.Abbrescia et al._ , Eur. Phys. J. Plus (2013) 128: 62
  * [12] _Looking at the sub-TeV sky with cosmic muons detected in the EEE MRPC telescopes_ _M.Abbrescia et al._ , Eur.Phys.J.Plus 130 (2015) 187
  * [13] _A study of upward going particles with the Extreme Energy Events telescopes_ _M. Abbrescia et al._ , Nucl. Instr. and Meth. A 816 (2016) 142-148
  * [14] _NINO: an ultra-fast and low-power front-end amplifier/discriminator ASIC designed for the multigap resistive plate chamber_ _F.Anghinolfi et al._ , Nuclear Instruments and Methods in Phys.Research A533 (2004) 183
  * [15] _Results from a large sample of MRPC-strip prototypes for the ALICE TOF detector_ _A. Akindinov et al._ Nuclear Instruments and Methods in Physics Research A 532 (2004) 611-621
  * [16] _Resistive plate chambers performances at low pressure_ _M. Abbrescia, et al._ , Nucl. Instr. and Meth. A 394 (1997) 341
  * [17] _Cosmic ray tests of double-gap resistive plate chambers for the CMS experiment_ _M. Abbrescia et al._ , Nuclear Instruments and Methods in Physics Research A 550  (2005) 116-126