Q Remy

Y A Gallant

Matthieu Renaud

Prospects on high-energy source searches based on pattern recognition Object detection in the H.E.S.S. Galactic Plane Survey

Keywords: Gamma rays: Sources, TeV: supernova remnants, Methods: data analysis 15 remnants (SNRs), composite SNRs, and γ-ray binaries. The

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The H.E.S.S. Galactic Plane Survey (HGPS, H.E.S.S. Collaboration, 2018f) represents the one of the most sensitive surveys of the Galactic plane (-110 • < l < 65 • , |b| ≤ 3 • ) in the very high energy (VHE) γ-ray domain (0.1-100 TeV). The 5 HGPS source catalogue includes 64 sources detected with the HGPS analysis pipeline and 14 additional sources analysed independently. The latter have been excluded from the HGPS source detection and analysis pipeline because of their complexity, and include in particular sources in the Galactic Cen-10 tre region (H.E.S.S. Collaboration, 2005Collaboration, , 2016Collaboration, , 2018b) ) and sources with shell-like morphologies (H.E.S.S. [START_REF] Collaboration | A new SNR with TeV shell-type morphology: HESS J1731-347[END_REF]Collaboration, , 2018d,e,c,a),e,c,a).

The HGPS catalog differentiates four classes of identified sources: pulsar wind nebulae (PWNe), (shell-type) supernova SNR class includes both well-resolved shell-type SNRs and unresolved VHE sources, or sources with unclear morphology, for which the association of the VHE emission with a SNR is highly probable (as in the case of W28, W49B and G353.6-0.7). PWNe refer to plerionic objects with no observed shell, or to resolved plerionic components in composite SNRs, which consist of a PWN inside an SNR shell. HGPS sources classified as composites refer to VHE sources which are spatially coincident with a known composite SNR, but which are not sufficiently well-resolved to distinguish between the PWN and the SNR shell as the origin of the VHE emission (H.E.S.S. Collaboration, 2018f).

The source detection procedure applied to the H.E.S.S. GPS is based on iterative template fitting. Starting with an empirical model of the diffuse background emission, the most significant γ-ray excesses have been iteratively fitted with two-dimensional symmetric Gaussian components by means of a maximum-likelihood estimation (H.E.S.S. Collaboration, 2018f). The last step of the HGPS catalogue pipeline consists in merging the overlapping Gaussian components, not clearly resolved as separate emission peaks, into single sources. Such an approach presents two major drawbacks: on the technical side, the convergence of the iterative scheme is time consuming, especially as the computation time greatly increases with the number of objects and the associated confusion; on the physics side, the morphological description of an extended γray source is limited by the simplistic template in use. In particular, as Gaussian morphology is imposed, a search for shell-like source has been conducted independently (H.E.S.S. Collaboration, 2018a). Such an approach limits the capability to detect complex-shape or nested sources, and could induce a selection bias in further population studies.

In this paper we propose an alternative object detection approach, complementary to the iterative template-fitting method.

We have investigated blind search methods for VHE γ-ray source detection based on well-known and widely used image processing and pattern recognition techniques. Our goal is to build in a short amount of computational time a list of potentially valuable objects without prior case-specific morphological assumptions. This list of objects could be used to:

-provide seed source candidates with robust guess on their position and morphological parameters to be tested by conventional analysis pipelines and/or dedicated analyses using template-fitting approach (as done for the Fermi-LAT point-source catalogues Fermi- LAT Collaboration, 2017, but generalized to extended sources);

-give a detailed description of the sub-structures in complex regions that would ease multi-wavelength (MW) association search and so help firmly identify multiple nested sources;

-evaluate potential valuable targets to support additional observation proposals, in particular toward source candidates below the significance threshold at the sensitivity of current observations that could be confirmed as sources by deeper surveys.

In the following we show that Hough circle transform can be used to detect objects with partial circular symmetry regardless of a shell-like or Gaussian-like morphology. We have tested the robustness and the efficiency of the algorithm to reconstruct the position and extent of simulated sources and to detect the firmly identified sources in the HGPS catalogue. We also investigate how the morphological parameters of the detected objects can be used to differentiate the various source populations in the HGPS. We discuss on the identification of new source candidates based on such morphological classification, and/or supported by spatial coincidence search in MW catalogues.

The paper is structured as follows: In Sect. 2 we present the data and catalogues used; In Sect. 3 we describe the detection algorithm based on Hough circle transform, the parameters derived in order to classify the detected objects, and the association procedure. In Sect. 4 we discuss the tests on bootstrap simulations. In Sect. 5, we present the list of objects found in the HGPS maps compared to the catalogued sources; In Sect. 6, we discuss the identification of the objects based on the morphological classification and MW coincidence search; In Sect. 7 we briefly summarize the results and discuss possible future studies. In supplements, the production of the simulated skies is detailed in Appendix A; potential improvements of the algorithm are discussed in Appendix B; and additional tables and 95 figures are given in Appendix C.

Data

H.E.S.S. Galactic Plane Survey (HGPS) maps

We have used significance and flux maps of the HGPS survey1 presented in H.E.S.S. Collaboration (2018f). Pixels of the 100 significance maps contain the values of the statistical significance of the γ-ray excess in the sense of [START_REF] Li | Analysis methods for results in gamma-ray astronomy[END_REF] within a given correlation radius R corr . The background level is estimated by counting the number of photons in OFF-regions, bearing in mind that the large-scale emission from the Galaxy 105 is not taken into account in this computation. The value of a given pixel in the flux maps corresponds to the integrated flux above 1 TeV of a potential source centered on the pixel and fully enclosed within the correlation radius of the map, assuming a power-law spectrum with a spectral index of 2.3 (see Eq. 110 2 to 4 in H.E.S.S. Collaboration, 2018f, for more details).

Catalogues

In order to associate the objects detected by our algorithm to known sources at various wavelengths, we have made use of the following catalogues: 115 -The HGPS source catalogue, containing 78 sources of VHE γ-rays (H.E.S.S. Collaboration, 2018f). The majority of the HGPS sources are spatially coincident with known sources at other wavelengths that could potentially account for the production of γ-rays at VHE energies but 120 only 40% of the HGPS sources could be firmly identified. Among the 31 firmly identified sources there are 12 PWNe, 8 SNRs, 8 composite SNRs (where both the interior PWN and SNR shell may contribute to the emission) and 3 high-energy binary systems. Most of the so-called 125 unidentified sources are associated with multiple objects but one cannot pinpoint the precise origin of the VHE emission because of the source confusion induced by the relatively broad point-spread function (PSF) of VHE γray observations compared to those in other domains. The 130 unassociated sources could emit exclusively in the VHE domain (truly dark sources) or may have been missed at other (radio, X-ray) wavelengths. If so, they would require either a more sophisticated MW association procedure or deeper observations.

135

-the gamma-cat package2 (version 0.1, July 2018) which provides a collection of data and catalogues for VHE γray astronomy. .

-the SNRcat3 , including Galactic SNRs and PWNe [START_REF] Ferrand | A census of high-energy observations of Galactic supernova remnants[END_REF]. The list of SNRs with their 140 basic physical properties is based on the Catalogue of Galactic SNRs by [START_REF] Green | A catalogue of 294 Galactic supernova remnants[END_REF] and on the list of Galactic SNRs Interacting with Molecular Clouds maintained by Bing Jiang4 . Entries have also been cross-checked with the Pulsar Wind Nebula catalogue [START_REF] Kaspi | Isolated neutron stars[END_REF] and

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the SGR/AXP catalogue from the McGill Pulsar Group [START_REF] Olausen | The McGill Magnetar Catalog[END_REF]. This catalogue is updated regularly, we used the same version as that considered in the HGPS catalogue (from Oct 10, 2015).

-the Fermi-LAT eight-year source catalog5 (4FGL v19,

150
The Fermi-LAT collaboration, 2019) based on eight years of data in the 100 MeV -1 TeV range. SNRs and significance with respect to various diffuse emission models to suggest these are the GeV counterparts, and 14 additional candidates which may also be related to known radio-emitting SNRs.

Methods 170

Object detection in Hough space

We have applied the object detection algorithm to significance maps with R corr = 0.1 • from the HGPS survey and bootstrap simulations. We have performed a single scan of the large region of the sky covered by the HGPS in order to detect poten-175 tial VHE γ-ray sources in a uniform and automated way. In the following sub-sections we detail the algorithm step by step.

Pre-processing

The goal of the pre-processing is to extract a sparse description of the relevant structures in the image that can be used to compute the Hough transform efficiently. In practice it consists in applying an edge detection operator, such as the Canny filter [START_REF] Canny | A computational approach to edge detection[END_REF].

The edge detection procedure is described as follows: First we smooth the significance image by applying a convolution with a Gaussian kernel (σ = 0.09 • = 4.5 pixels). Then we use the Sobel-Feldman operator8 [START_REF] Sobel | An isotropic 3x3 image gradient operator Presentation at Stanford A.I[END_REF] to compute an approximation of the image gradient. For an image I, the Sobel-Feldman operator returns a value for the first derivative in the horizontal direction (G x ) and the vertical direction (G y ) as :

G x = I *           -1 0 1 -2 0 2 -1 0 1           , G y = I *           -1 -2 -1 0 0 0 1 2 1           (1)
At each point in the image, the gradient magnitude is then de-

rived as G = G 2
x + G 2 y , and the gradient direction as θ = arctan(G y /G x ). The gradient magnitude provide thick edges of the structures so a non-maximum suppression is applied to obtain 1-pixel thin edges. These first steps are performed following the implementation of the Canny filter in scikit-image python package9 while the subsequent steps differ. Then we filter the thin edges using conditions on both gradient and significance values. We mask the thin edges where gradient magnitude is lower than its 86.6 percentile value (∼ 1.5σ for a Gaussian distribution). The significance maps are filtered by hysteresis thresholding with a high threshold of 4.5σ and a low threshold of 1σ (pixels between these two thresholds are masked only if they are not connected to a pixel above the high threshold). Contrary to the hard threshold usually applied in VHE γ-ray studies for source detection (as in the HGPS procedure), a hysteresis thresholding better preserves the global spatial coherence of the extended excess even if the whole structure is not strictly above the hard threshold. In order to exploit the information of the significance maps with R corr = 0.1 • and R corr = 0.2 • we combine their respective hysteresis masks with an or condition. The boolean mask (named "blob mask") associating the gradient and significance filters is shown in Fig 1 andA.24 (third panel) for one of the simulated maps. Finally, we removed the small edges of less than 3 pixels long. The final result is a boolean mask (named "edge mask") highlighting the sharp edges of the significance map, as illustrated in Fig. 1 andA.24.

The structure of the gradient associated to the diffuse background has a latitudinal symmetry centred on the Galactic Plane, while the sources can be seen as spherical perturbations to this background gradient. In order to improve the contrast between the source and the diffuse structures we applied a longitudinal thickening to the edge mask: for each pixel in the edge mask we extend the mask by one pixel (i.e. 0.02 • ) along the longitude axis, so that the sources appear on average thicker than the diffuse structures, which often already appears as longitudinal features. This simple step reduces the weight of diffuse structure compared to sources in Hough space, and should reduce the false detections triggered by the diffuse background (particularly toward the dense clouds of the Central Molecular Zone in the vicinity of the Galactic Center, see second line of Fig. 6).

Finding local maxima in Hough space

The classical Hough transform is meant to identify lines in an image, and was introduced by Hough (1959) to detect particle trajectories in bubble chamber images. The generalized Hough transform proposed by [START_REF] Duda | Use of the hough transformation to detect lines and curves in pictures[END_REF] extends the principle to any analytically defined shapes, usually circles or ellipses. More recent implementations generalize the concept to arbitrary complex shapes by performing template matching [START_REF] Ballard | Generalizing the hough transform to detect arbitrary shapes[END_REF]. For our purpose a simple Hough circle transform can be used to indifferently detect sources with point-like, Gaussian-like or shell-like morphologies.

For a circle transform the Hough space is represented by a 3D accumulator matrix in longitude, latitude, radius. The accumulator resolution is set to 0.04 • in longitude-latitude and 0.01 • in radius. We fix the minimal radius to 0.1 • , to match the minimal correlation radius of the significance maps used. These choices limit the computational time to less than 5 minutes to process the whole HGPS region, without limiting the sampling precision which remains lower than the H.E.S.S. angular resolution.

In practice for each point of the edge mask, (l i , b i ), and for each radius sampled, R i , we can define a circle, C(l i , b i , R i ), in the Hough space. So the values of the accumulator matrix, HA(l, b, R), (initially zeros) are incremented toward the pixels where the circle passes through:

HA(l C , b C , R i )+=1 ∀(l C , b C ) ∈ C.
The angle sampling used to compute the circles is limited to 1 • . We normalize the accumulator values by the angle sampling dimension, so the value of the accumulator can be assimilated to a fraction of the circle circumference in the original space. In the following, we will refer to this parameter as the circularity of the object. Once the accumulator matrix is built the next step is to find its local maximum. To do so we select only the pixels that are at maximum within a 3D sliding window of 0.3 • ×0.3 • ×0.5 • in longitude-latitude-radius or 0.5 • ×0.5 • ×0.5 • if their radius is larger than 0.25 • (we use two window sizes to scan different structure scales). We discard objects with circularity lower than 0.6 or 0.5 if their radius is larger than 0.25 • (so the detected objects are at least half-circular). We also discard objects with radius lower than 0.25 • if the significance at their center is not larger than 3σ in significance maps with R corr = 0.1 • or R corr = 0.2 • . Finally we remove potential duplicates with both inter-center distance and radius difference lower than 0.1 • . The position of a local maximum in the Hough space gives the centre and the radius of the object in the original space.

The different threshold values introduced here and previously in Sect. 3.1.1 have been empirically optimized in order to maximize the fraction of the simulated sources which are well-reconstructed, given the association criterion introduced in Sect 3.3. We have also ensured to maintain the fraction of 275 detected objects associated to a simulated source higher than about 30% in average (or similarly the detected objects to significant sources ratio lower than about three, see discussion in Sect. 6.1).

The resulting list of objects provides a discrete and 280 parametrised view of the pertinent structures in the data that is easier to interpret and analyse than the continuous values of a significance map. However the detected objects cannot be directly interpreted as sources. In order to identify the most valuable candidates, that could warrant a dedicated analysis, several 285 approaches are possible: distinguish the sub-structures from the main objects, guess the source type by comparing its morphological parameters to well-identified sources, and find possible associations at other wavelengths. We further discuss these issues in Sect. 6. 290

Classification based on morphological parameters

Determining a class of objects that can be assimilated to a known source population is a well-suited problem for machinelearning techniques. Classification requires a parameter space in which the different populations can be isolated. We introduce 295 the following set of morphological parameters:

-the radius given by the third coordinate in the Hough accumulator space;

-significance at central pixel of the object (in the map with R corr = 0.1 • );

300

-the circularity given by the Hough accumulator value;

-the Pearson correlation coefficient (PCC or Pearson-R) of a 5-point radial profile in flux: for each object we have integrated the flux map (with R corr = 0.1 • ) in 5 rings of equal area between the center of the object and its radius; 305 -a morphology flag, the Pearson-R coefficient of the radial profile in flux is used to distinguish 3 types of structures:

Peak ≡ PCC < -1/3, Flat ≡ |PCC| < 1/3, Cavity ≡ PCC > 1/3;
310 -a nesting flag: for each pair of objects C of radius R and R sub , we calculate their inter-center distance, d, and define 5 overlapping configurations : 0 1.3 1.7 2.3 3.0 3.9 5.1 6.7 8 First row, left: Significance map derived using the Adaptive Ring Background method as in the HGPS (R corr = 0.1 • ). Second row, left: Gradient of the significance map derived using Sobel operator. Third row, left: Blob mask given by thresholding the significance and gradient values (as described in Sect. 3.1.1). Fourth row, left: Significance map at R corr = 0.1 • (same as first row but in grey-scale) with the Edge mask obtained after applying the Canny filter overlaid in red. Second row, right: objects detected in Hough space. Third row, right: Detected objects associated to simulated sources using criterion on inter-center distance and surface overlap as described in Sect. 3.3. Note that we test for associations regardless of the expected TS values. Fourth row, right : Simulated sources, the dotted circles correspond to the outer radii of radial shells, the plain circles correspond to the sigma of radial Gaussians, point sources are shown as crosses. Light and dark blue colors correspond to sources with an expected TS value below and above 30, respectively.

Class 0 ≡ C(R) : d > R + R sub , ∀ C(R sub ), Class 1 ≡ C(R) : ∃ C(R sub ) | d R+R sub , R sub R, 315 Class 2 ≡ C(R sub ) : ∃ C(R) | d R + R sub , R sub < R, Class 3 ≡ C(R sub ) : ∃ C(R) | d R, R sub < R, Class 4 ≡ C(R sub ) : ∃ C(R) | d R -R sub , R sub < R.
In the following, Class 0 and 1 are defined as main objects; Class 0 objects are non-overlapping, while Class 1 are large 320 objects partially overlapping with smaller ones. These smaller objects are considered as sub-structures, and are of Class 2, 3 or 4 depending on the inter-center distance to the main object.

From a basic point-of-view, the pertinence of a Gaussianlike object with R < 0.2 • can be filtered by threshold conditions in significance at its center, the pertinence of a shell-like object can be filtered by threshold conditions in circularity and Pearson-R. The unresolved objects should reach minimal radius and maximal circularity. The potential of automated object classification and source population identification on this basis is further discussed in Sect. 6. We will present simple classification schemes based on the comparison of detected objects with well-identified H.E.S.S. sources in the parameter space introduced here.

Catalogue cross-matches

In order to associate the detected objects with the known sources we test for spatial coincidence using two criteria based on inter-center distance and surface overlap. For each object we search for known sources within an inter-distance: d c < 0.1 + 0.3 × R ob ject and we report only the source maximizing the surface overlap fraction, defined as:

SF overlap = S object ∩ S source S object ∪ S source . (2)
We choose to report only the strongest positional coincidence in order to limit the possible associations for extended objects.

As the objects are detected on significance maps with a correlation radius of R corr = 0.1 • , we can not compare directly their radius (and so their surface) to those of known sources (simulated or catalogued). So for each known source we introduce an effective radius as R eff = R 2 source + R 2 corr . We define R source as the outer radius for shell-like sources, the 1σ width for Gaussian-like sources, the radius for disk-like sources, and zero for point-like sources.

In the following we set SF overlap > 0.3 as association criterion. We also enforce that each source can be associated to only one object and conversely. This association criterion is used to estimate the fraction of simulated sources associated to a detected object (reconstruction fraction, see Sect. 4), and the fraction of objects associated to a known source (association fraction, see Sect. 6).

We have tested associations with the HGPS catalog sources and their Gaussian components separately. Correlations in position and radius of detected objects with HGPS sources are further discussed in Sect. 5. Additionally, based on the information provided by the 4FGL, SNRcat and Fermi-LAT SNR catalogues, we report on possible MW associations for each object.

Tests on simulations

Simulated datasets

We have performed a bootstrap of the sources catalogued in the HGPS survey. We produced 10 sky realisations, each one including 100 sources, a model for hadronic background emission and a toy-model for diffuse Galactic background emission. Details on the production of the simulated flux, counts, exposure and final significance maps are given in Appendix A. We did not intend to produce a realistic model for the various components of the diffuse Galactic emission, instead we used a simplistic toy-model that we can tweak in order to test how the source reconstruction is affected by an increase of the diffuse background level. To do so, we arbitrarily tweaked the contrast in flux between the source and the diffuse background with one parameter. The contrast parameter C ism has been set to 0.1 in the minimal case and 0.3 for a stronger diffuse emission. In order to test the systematics related to background estimation, we produced significance maps using the exact simulated background model (noted SBG in figures) or through the adaptive ring background method as defined in the HGPS (noted as ARBG in figures). We show in Fig. 2 the H.E.S.S. significance map and 10 simulated ARBG significance maps in the minimal diffuse emission case (C ism = 0.1). We illustrate the application of the method on one of the simulated sky in Fig. 1 andA.24

Object detection performance

By design the detection algorithm will find more structures than there are sources. So its performance depends on the capability in reconstructing the sources correctly, among the substructures. We define the reconstruction fraction as the fraction of simulated sources associated to detected objects using the procedure introduced in Sect. 3.3. The association criterion based on inter-center distance and surface overlap are strong enough to ensure a close match in position and extension between the simulated sources and detected objects (as shown in Fig. 3). The differences in the longitude, latitude and radius have a mean value compatible with zero with a root-meansquare dispersion (rms) lower than 0.05 • . The difference in radius increases with radius, but the absolute relative error is mostly stable around its average value of ∼15%.

The detectability of γ-ray sources is usually expressed in terms of their statistical significance. For each simulated source we can estimate their expected test statistic (TS) as the loglikelihood ratio between the exact simulated model and the same model excluding the source. In Fig. 4 we show that the reconstruction fraction of simulated sources increases with their expected TS, and exceeds 70% above TS> 30. Fig. 4 also shows that the use of the adaptive ring background rather than the perfect simulated background in the significance map calculation changes the reconstruction fraction by only a few percent, even when we considered a higher diffuse background level (Fig. C.26).

In order to quantify the effect of the source confusion on the source reconstruction capabilities, we plot in Fig. 5 the reconstruction fraction as a function of the nearest neighbour distance of the simulated source, d nn . The reconstruction fraction progressively increases from 40% to 80% for sources closer than 1 • . For the closest sources the low fraction is primarily explained by the source confusion while the effect of the diffuse background level is secondary. For sources with d nn larger than 1 • and with an expected TS> 30 the reconstruction fraction is

Gaussian

Point-like Shell

Figure 3: Positional correlations between detected objects and simulated sources -The left and middle panels give the differences in longitude and latitude, respectively. The right panel shows the absolute relative error on radius. Note that the effective radii, R eff given in the right panel are the quadratic sum of the simulate radii and the 0.1 • correlation radius of the significance map used to determine the Hough circle radii, so their values can be readily compared. In each panel the mean and standard deviation values are given by the plain and dotted black lines, respectively. The colors correspond to the morphological models used for the simulated sources. Note that we generated the simulated source sample from the detected source distribution and we did not extrapolate the distribution to include sources with lower flux, so the effect of source confusion is potentially underestimated. The reconstruc-425 tion fraction will likely be lower for the low TS values (see the two first bins of Fig 5).

Application to the HGPS survey

The object detection procedure was applied on the publicly available HGPS significance map with a correlation radius of For each object associated to a HGPS source we flag its type according to the HGPS identification (PWN, composite, SNR or binary). However, we have differentiated two sub-classes 445 of SNRs based on the information provided by the gammacat. We reduce the so-called SNR class to only resolved shelllike SNRs (HESS J0852-463, HESS J1442-624, HESS J1534-571, HESS J1713-397 and HESS J1731-347), while the SNR-MC class includes unresolved HGPS-SNRs (HESS J1718-374, 450 HESS J1911+090), and sources coincident with a radio SNR or associated to a Molecular Cloud (HESS J1800-240, HESS J1801-233). This differentiation is essential for accurate morphological classification. It should be also noted that the "composite" type in the HGPS refers to sources for which the angular 455 resolution does not allow for a separation of the PWN from the SNR shell, so that formally one cannot discriminate between the PWN and the shell as the dominant source of the VHE emission (H.E.S.S. Collaboration, 2018f). Nonetheless, the VHE PWN population study (H. E. S. S. Collaboration, 2018) con-460 siders most of these VHE sources to be PWNe based on physics arguments. The HGPS sources morphologically classified as composites would then mostly be younger and more compact PWNe than those firmly identified as PWNe.

In Fig. 8 we show the reconstruction fraction for the different 465 source types catalogued in the HGPS. All the shell-type SNRs catalogued (based on dedicated analyses) are associated to at least one object. In Fig. 9 we show the significance maps, their gradients and the edge masks used in the detection procedure toward the 5 well-resolved SNR shells in the HGPS. We found 470 a good agreement in position and radius between the HGPS sources and the main objects detected, as shown in the first and last rows of Fig. 9.

The position and size correlations between the detected objects and the HGPS sources are shown in Fig. 10. This figure demonstrates the excellent reconstruction in longitude and latitude. The error on the position given by the inter-center distance is 0.03 • on average with a standard deviation of 0.04 • . By construction we cannot find objects with radius lower than 0.1 • as we set the minimal radius in Hough space to the correlation radius of the significance map. We compare the detected radii with R eff given as the quadratic sum of the catalogued radii and the 0.1 • correlation radius. Most of the objects present a reasonably good correlation in radius within 20% error, even though we note a systematic trend toward lower detected radii for sources larger than 0.2 • in radius. These differences can be explained because the Hough transform tends to decompose a source in more sub-structures than the HGPS Gaussian components.

The HGPS components not associated to detected objects generally belong to one of the following cases:

-Large Gaussian components may be decomposed in several sub-structures in the object list so there is no exact match (as seen in Fig. 7 for HESS J1843-033).

-Large Gaussian components associated to a smooth gradient are not seen because the edge detection imposes to preserve only sharp gradients (as seen in Fig. 6 for HESS J1837-069). Thus, the object detection procedure is less sensitive to the diffuse background and to extended/faint PWNe.

-The 0.15 • limitation in the separation of objects with similar radius does not allow one to detect very close point-like sources; as an example, HESS J1745-290 in the Galactic center region is detected but not HESS J1746-285. In that case only the most prominent source is detected (because of a sharper significance gradient). This issue could be addressed by using another complementary technique, such as the object detection based on wavelet decomposition which is very efficient at isolating very close-by point-like objects from one another and from the underlying background [START_REF] Starck | Structure detection in low intensity X-ray images[END_REF][START_REF] Schmitt | Poisson denoising on the sphere: application to the Fermi gamma ray space telescope[END_REF].

In Fig. 16 we represent the detected objects in three morphological parameter spaces. The distributions of the different source types tend to indicate that they are separable using our set of parameters. For example, sources identified as composites or binaries are close to the maximum circularity (unity) and the minimal radius (0.1 • ), while those identified as PWNe have mostly lower circularity and larger radius (see left panel). The well-resolved shell-type SNRs are clearly separated from all the other identified source populations by their Pearson-R (see middle panel). We also note that sources detected by the HGPS pipeline (which exclude well-resolved SNRs and several unidentified sources) populate a more restricted fraction of the parameter space than the detected objects. The HGPS detection procedure, based on an iterative detection of Gaussian components, does lead to a selection bias that can explain such a difference. However, due to the uncertain nature of detected objects, a fraction of the parameter space would correspond to spurious detection associated with sub-structures or background. In the following we discuss this issue and how we could identify the 530 most valuable objects.

6. Discussion on the objects identification 6.1. Disclaimer: not all detected objects are sources By design the object detection algorithm will find much more objects than there are sources, but this is expected for a preliminary list of seeds. For example, the latest Fermi-LAT point source catalogues (4FGL or the preliminary FL8Y) contain about 5 000 sources while their initial detection step provides more than 13 000 objects (The Fermi-LAT collaboration, 2019). According to our HGPS bootstrap simulations, we detect about 540 3.5 times more objects than simulated sources with an expected TS of 30 (or 3 times more if we consider sources with TS> 10). In our case the main problem is that we have to deal mostly with nested extended objects. Among the nested objects, many will be internal sub-structures of the same source and not nec-545 essarily unrelated sources. Among the isolated objects, even if our detection procedure is by construction more sensitive to sources than background, several objects will be spurious detections triggered by statistical fluctuations or background structures from the Galactic large-scale emission.

550

We performed tests on simulations containing only noise and given the hysteresis threshold imposed on the significance maps we found on average only 8 fake objects detected per simulated sky (compared to about 250 detected on each baseline simulations containing 100 sources), so pure noise is marginal in the 555 fraction of spurious detections. Additionally we produced significance maps without and with diffuse Galactic background for two different flux levels. For 100 sources simulated per sky we found on average 253 objects for the case without Galactic background, 224 for the minimal background case, and 265 560 when increasing the Galactic background flux by a factor of 3. According to Fig. 5 and 11, the reconstruction and association fractions tend to decrease when the diffuse Galactic background level increases, but only by 5% on average.

In Fig. 13 we show that the unassociated objects are mostly located at the edge of the simulated sources and have radii smaller than those of their parent sources. Moreover the number of unassociated objects decreases with the distance to simulated sources. The fraction of unassociated objects beyond ∼ 8-radius away from the sources matches the average false detection rate of the noise-only simulations. So we expect that the spurious detections are mostly bad reconstructions due to source confusion or irrelevant sub-structures within, or large and faint wings of, extended sources.

In order to minimize the spurious detections we can filter the objects as to maximize the association fraction to simulated sources or MW-catalogues without impairing the reconstruction fraction. To do so we can adjust the minimal thresholds on circularity or significance as defined in the Sect. 3.1.2. Alternatively we can focus on a subset of objects: isolate the main ones from their sub-structures; select objects that share similar morphological parameters to the firmly identified sources; or search only for objects with a MW-association in at least one wavelength. In the following, we aim to classify and filter the objects in order to narrow down the list to the most valuable ones for further dedicated MW analyses and deeper VHE observations.

Candidate selection maximizing association fraction

We can flag valuable objects by searching for a MWcoincidence. The selection can be further improved by identifying a subset of objects that maximize the ratio between the association fraction and the probability of coincidence by chance.

In order to quantify the fraction of coincidence by chance we have evaluated the association fraction to MW-catalogues of a randomized list of 10 000 objects. This list is obtained by bootstrapping the list of objects detected on the HGPS map, so the density of objects in longitudes, latitudes and radius are preserved (those quantities are independently drawn). In Fig. 14 we show the MW-association fraction to at least one of the sources from the 4FGL, SNRcat, or SC1 catalogues for the randomized list and the original one. Despite the large number of sources referenced in those catalogues the association fraction in the randomized list do not exceed few percent while the association fraction in the original one is about 10 times larger in average. This ratio can be further improved by selecting a subset of objects that show an enhanced association fraction. As shown in Fig. 11 the fraction of detected objects associated to a simulated source increases with the circularity (i.e. the fraction of the object circumference that triggered the detection). Note also that the condition we imposed to discard objects with circularity lower than 0.6 if their radius is lower than 0.25 • (see Sect. 3) improves the association fraction at low circularity. The shape of this cut could be improved, but we prefer to avoid complex cuts by hand. The cut could be directly inferred from simulations in a more automated way using machine learning, and this also holds for the other parametric filters we chose for the source candidate identification. This is a wide topic to explore so we prefer to defer these refinements to future implementations. In Fig. 12 we show the fraction of detected objects associated with catalogued sources in the HGPS and/or at other wavelengths. We observe the same trend with an increasing association fraction with circularity. Figure 13: Distance of the detected objects from simulated sources -Top: Distribution of the associated (blue) and unassociated objects (black), the quantity on the horizontal axis is the distance of the object to the nearest simulated source in unit of source radius, d NN /R NN , and the quantity on the vertical axis is the ratio of the object radius to the source radius, R ob ject /R NN . We show the results for the ARBG case (see Sect. 4.1). Bottom: Anti-cumulative distribution of the unassociated objects with object-source distance (number of objects above a given value of d NN /R NN per 100 source simulated). The dotted line is the average fake detections rate of noise-only simulations.

Based on these observations we propose as valuable candidates a subset of objects with a circularity larger than 0.95 and associated to at least one source in the 4FGL, SNRcat or SC1 catalogues10 (but not catalogued in the HPGS). The 5 candidates resulting from this selection are shown in Fig. 15. The content of this subset list is given in table C.2. We note that the Fermi-LAT source coincident with HC 57 candidate is catalogued as a pulsar (4FGL J1112.1-6108). The candidate HC 56 is in coincidence with a plerionic composite SNR source (G291.0-0.1) and a Fermi-LAT plusar (4FGL J1111.8-6039). The candidate HC 69 is in coincidence with a plerionic composite SNR source (G308.8-0.1) and a Fermi-LAT plusar (4FGL J1341.7-6216). Similarly the objects with circularity close to the unity that are associated to a HGPS source correspond mostly to small-size sources referenced as composites.

SNR-like object identification

In the simplistic object classification previously introduced, most of the well-known shell-like SNRs are identified as class 1 cavities (HESS J0852-463, HESS J1534-571, HESS J1713-397). In the parameter space that we defined, this class of objects corresponds to a main object with several nested substructures associated and with a radial profile exhibiting a We select only objects with a circularity larger than 0.95 and coincident with a catalogued source in radio or GeV γ-ray wavelength (SF overlap > 0.3), but which are not catalogued in the HGPS. The detected objects are given as orange circles, blue squares are Fermi-LAT sources from the 4FGL list; yellow items correspond to radio sources given by the SNRcat; magenta items correspond to extended Fermi-LAT sources from the SC1.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Radius Pearson-R coefficient larger than 1/3. Note that the two other known shell-like SNRs, namely HESS J1442-624 and HESS J1731-347, are classified as flat rather than cavities because the Pearson-R coefficient of the radial profile is close to zero as shown in Fig. 16. Given their smaller size, the contrast between the outer ring and the inner part of the shell is less obvious (see Fig. 9). Filtering the list of detected objects to keep only class 1 cavities associated with a catalogued source results in 7 SNRlike candidates as shown in Fig. 17. In Fig. 18 we display maps of the significance, and the edge mask centered on these objects. Details on their properties are given in Table C.3.

Among these 7 SNR-like objects, 4 of them are already catalogued as unidentified sources in the HGPS (HGPSC 059 component of HESS J1809-193, J1800-240, J1852-000 and J1912+101, H.E.S.S. Collaboration, 2018f), while 3 are found towards a (discarded) large HGPS structure (HGPSC 015 and HGPSC 051). In the HGPSC 015 region, we distinguish two objects : one (HC 76) coincident with a radio SNR (G312.4-0.4) and one (HC 73) with a Fermi-LAT extended source, both showing a reasonably good match in radius with their potential counterparts (as illustrated in the two first rows of Fig. 18).

In the HGPSC 051 region, we report one object coincident with a radio SNR (G359.0-0.9) in the close vicinity of HESS J1745-303. Among the objects associated to unidentified HGPS sources, HESS J1912+101 has already been identified as a SNR candidate due to its shell-like morphology (H.E.S.S. Collaboration, 2018a), and J1800-240 is potentially associated to the SNR W28 [START_REF] Aharonian | Discovery of very high energy gamma-ray emission coincident with molecular clouds in the W 28 (G6.4-0.1) field[END_REF]. Interestingly in the W28 region the shell-like object is associated to the SNR while its substructures are associated to the surrounding HGPS sources.

Four candidates show no evidence for association with a SNRcat source (including HESS J1912+101, see third row of Fig. 18). Two candidates show partial matches, that is the main object is not coincident with a known shell but at least one of its nested sub-structures is coincident with a catalogued source in both radio and GeV γ-ray domains. Note that our MW-coincidence search is only based on catalogued sources, more information could be collected by looking directly at the MW images in order to propose additional observations in case of the presence of a potential, uncatalogued, counterpart. We stress that focusing on Class 1 Cavities objects limits the results to SNR candidates for which the sub-structures are resolved. Less restrictive constraints could result in more candidates. For example, one of the sub-structures of the unidentified source HESS J1843-033, flagged as class 0, is coincident with G28.6-0.1 and can be considered as a poorly resolved SNR candidate (see the last row of Fig. 7).

Conclusion and perspectives

Analysis products

We provide the full list of objects detected on the HGPS significance map together with several short lists for convenience:

-list of the objects associated with the HGPS sources (providing a detailed description of their sub-structures)

-list of non-HGPS objects with MW coincidences (which could be further studied in dedicated analyses)

-list of high-circularity candidates (see Sect. 6.2)

700

-list of SNR-like candidates (see Sect. 6.3)

In addition to the object positions (in longitude and latitude), these lists contain the morphological information defined in Sect. 3.2 and the possible association given by the catalogue cross-match described in Sect. 3.3. All these lists are available 705 in FITS format in the paper data on the editor page. A description of the FITS file columns is provided in Table C.1 in Appendix. Some examples of FITS file contents are provided in Tables C.2 and C.3 (see Sects. 6.2 and 6.3).

Summary and future works 710

We have shown that using pattern recognition techniques we can extract pertinent structural information from the HGPS significance maps and detect objects with partial spherical symmetry without assuming a morphological template (e.g. point-like, Gaussian-like, or shell-like). In the approach proposed, sparse 715 structural information is extracted using a edge detection operator. We then apply a Hough circle transform and detect a collection of objects as local maxima in Hough space. On the basis of morphological parameters we can characterize different object classes. Morphological classification and comparison with 720 known source populations allow one to constrain the nature of the detected objects. In particular we have shown that the well-resolved shell-type SNRs catalogued in the HGPS can be isolated from the other source types with simple classification rules (Main-object with sub-structures and Pearson-R larger 725 than 1/3). By extension, we can identify new source candidates that share the characteristics of the well-known sources. Moreover, catalogue cross-matches indicate that several detected objects not catalogued in the HGPS are spatially coincident with MW counterparts. Those are more likely to not be coincidence 730 by chance when considering objects with higher circularity.

We have presented a prospective study on the use of pattern recognition and classification techniques to detect source-like objects in the VHE γ-ray sky and identify new valuable source candidates. We have no doubt about the potential of this ap-735 proach, but there is still a lot to explore as shown by the various perspectives discussed throughout this paper. We list other possible technical improvements in Appendix B. Future developments and prospects will be discussed within the H.E.S.S. Collaboration and the CTA Consortium. Meanwhile, we warmly 740 welcome collaboration with anyone interested in writing up follow-up proposals for deeper MW observations and/or in carrying out dedicated analyses with the existing MW archival data towards the most valuable objects presented here, in particular those not catalogued in the HGPS.

one Gaussian corresponding to the averaged source given in the HGPS because we do not have the information on the flux of its Gaussian components. This is not an issue as the random re-sampling of the sources will naturally create multiple nested sources. For simplicity the shells are generated with an unique width fixed to 20% of the inner radius. We simulated shell-like, Gaussian-like and point-like sources using the spatial models implemented in the Gammapy v0.1 Python package [START_REF] Deil | Gammapy -A prototype for the CTA science tools[END_REF]. The flux map of each source is given by the spatial model (whose integral equals one) times the integrated flux from the bootstrapped catalogue.

Figure 1 :

 1 Figure1: Objects detection and association -These figures illustrate the application of the method to a simulated sky (see Sect. 4 and appendix Appendix A). First row, left: Significance map derived using the Adaptive Ring Background method as in the HGPS (R corr = 0.1 • ). Second row, left: Gradient of the significance map derived using Sobel operator. Third row, left: Blob mask given by thresholding the significance and gradient values (as described in Sect. 3.1.1). Fourth row, left: Significance map at R corr = 0.1 • (same as first row but in grey-scale) with the Edge mask obtained after applying the Canny filter overlaid in red. Second row, right: objects detected in Hough space. Third row, right: Detected objects associated to simulated sources using criterion on inter-center distance and surface overlap as described in Sect. 3.3. Note that we test for associations regardless of the expected TS values. Fourth row, right : Simulated sources, the dotted circles correspond to the outer radii of radial shells, the plain circles correspond to the sigma of radial Gaussians, point sources are shown as crosses. Light and dark blue colors correspond to sources with an expected TS value below and above 30, respectively.

Figure 2 :

 2 Figure 2: Significance maps sample -Top row: Significance map from the HGPS survey. Other rows: Significance maps for 10 simulated skies, each one including 100 sources and a toy-model for background emission (with C ism = 0.1, see Appendix A). In all panels, significance maps are derived using the Adaptive Ring Background method with R corr = 0.1 • . We display only |l| < 50 • but simulations have the same coverage as the HGPS survey.

Figure 4 :Figure 5 :

 45 Figure 4: Reconstruction fraction as a function of the expected TS -Top: Histogram of the number of simulated sources within bins in expected TS values. Bottom: Fraction of simulated sources associated to a detected object in the same bins in expected TS values. Magenta and blue bars correspond to objects detected as Hough circles in the significance map derived using simulated background (SBG) and through the adaptive ring background method (ARBG), respectively.

  Fig 6and 7. Following the cross-match procedure described in Sect. 3.3, 72 objects are coincident with a HGPS source within the inter-center distance limit (d c < 0.1 + 0.3 × R ob ject ) and 64 also match the association criterion based on surface overlap (SF overlap > 0.3). Similarly, we have 74 objects close to a HGPS 440

Figure 6 :

 6 Figure 6: H.E.S.S. sources as seen through edge detection and Hough circles -Left column: Significance maps (R corr = 0.1 • ) and catalogued source components from the HGPS (circles correspond to the sizes of the Gaussian components if available or to the source radii otherwise, squares indicate point-like sources; the source given in the panel title appears in white and the others in grey). Middle column: Edge masks obtained after applying the Canny filter. Right column: Significance maps (same as the left column but in grey-scale) and objects detected; dashed circles denote cavities or flat regions, plain circles represent peaks; blue circles flag isolated objects (class 0), orange circles main-objects associated with sub-structures (class 1), and other colors correspond to the sub-structures (green, red, purple for class 2, 3, 4 respectively). Further information on classification flags is given in Sect. 3.2.

Figure 7 :Figure 8 :

 78 Figure 7: Comparison between catalogued sources and detected objects -Left column: Significance maps (R corr = 0.1• ) and catalogued source components from the HGPS (same description as first column of Fig.6). Middle column: Significance maps (R corr = 0.1 • ) and MW catalogued sources; blue squares are Fermi-LAT sources from the 4FGL list; yellow items correspond to radio sources given by the SNRcat, circles give the radii when available, dotted circles correspond to SNRs[START_REF] Ferrand | A census of high-energy observations of Galactic supernova remnants[END_REF]; magenta items correspond to extended Fermi-LAT sources from the SC1 (Fermi-LAT Collaboration, 2016b). Right column: Significance maps and objects detected (same description as the last column of Fig.6).

Figure 9 :

 9 Figure 9: Identification of the resolved shell-like SNRs -First row: Significance map with R corr = 0.1 • and catalogued sources from the HGPS. Second row: edge mask obtained after applying the Canny filter. Third row: Significance map with R corr =0.1 • (same as first row but in grey-scale) and objects associated with the procedure described in Sec. 3.3 (associations are unique so the eventual nested sub-structures related to those objects are not displayed here, but they are shown in Fig. C.28).

Figure 10 :Figure 11 :

 1011 Figure10: Positional correlations between detected objects and HGPS sources -The left, middle, and right panels give the correlations in longitude, latitude and radius, respectively. Note that the effective radii,R eff , given in the right panel are the quadratic sum of the catalogued radii and the 0.1 • correlation radius of the significance map used to determine the Hough circle radii, so their values can be readily compared. In each panel the mean and standard deviation values are given by the plain and dotted black lines, respectively. The colors correspond to the object types as given in the HGPS, except that we have differentiated the SNR-Molecular Cloud (MC) from the shell-type SNRs based on the information provided in the gamma-cat (see Sect. 5).

Figure 12 :

 12 Figure 12: Association fraction (catalogues) -Top: Histogram of the number of sources within bins in circularity. Bottom: Fraction of detected objects associated to a catalogued source in the same bins in circularity. Blue bars correspond to associations with the HGPS source or their Gaussian components. Green bars correspond to Multi-wavelength associations from the 4FGL, SNRcat or SC1 source catalogues.

Figure 15 :

 15 Figure 14: Multi-wavelength association fraction and coincidence by chance -Top: Histogram of the number of objects within bins in longitude, latitude and radius (from left to right). Bottom: Fraction of objects associated to a 4FGL, SNRcat or SC1 source in the same bins. Black bars correspond to the list of objects detected in the HGPS significance map, and grey bars correspond to a randomized list generated by bootstrapping of the original list.

Figure 16 :Figure 17 :Figure 18 :

 161718 Figure16: Morphological parameters of the objects detected in the HGPS observations -For each object we display the circularity versus radius (left), the Pearson-R of the radial profile versus radius (middle) and the Pearson-R versus the circularity (right). The colors correspond to the object type as given in the HGPS or gamma-cat (for the SNR-MC case). Black points correspond to detected objects with no HGPS counterpart (such that SF overlap < 0.3)

  Figure A.19: Average background noise parameter -Top: Estimation of B/A according to Eq. A.4 using the N excess , F excess and N OFF of the sources fitted in the HGPS catalog. The grey line correspond to a slope equal to the average B/A ratio per pixel. Bottom: Relative error on the average B/A value.

FigureFigureFigure

  Figure A.21: Simulated sky maps ( -First row: Count map. Second row: Exposure map normalized by its maximum value. Third row: Toy-model for the background emission used in the simulation. Fourth row: Background emission derived using the adaptive ring background method (R corr = 0.1 • ). The example displayed correspond to the first simulated sky in Fig. 2 (second row)

Figure A. 24 :

 24 Figure A.24: Edge detection on simulated significance map -First row: Significance map derived using the Adaptive Ring Background method as in the HGPS (R corr = 0.1 • ). Second row: Gradient of the significance map derived using Sobel operator. Third row: Blob mask given by thresholding the significance and gradient values (as described in Sect. 3.1.1). Fourth row: Significance map at R corr = 0.1 • (same as first row but in grey-scale) with the Edge mask obtained after applying the Canny filter overlaid in red.

Figure A. 25 :

 25 Figure A.25: Comparison of detected objects with simulated sources -In all panels the underlying map is the same significance as that shown in Fig. A.24, derived using the Adaptive Ring Background method as in the HGPS (R corr = 0.1 • ). First row: Simulated sources, the dotted circles correspond to the outer radii of radial shells, the plain circles correspond to the sigma of radial Gaussians, point sources are shown as crosses. Light and dark blue colors correspond to sources with an expected TS value below and above 30, respectively. Second row: objects detected in Hough space. Third row: Detected objects associated to simulated sources using criterion on inter-center distance and surface overlap as described in Sect. 3.3. Note that we test for associations regardless of the expected TS values.

Figure

  Figure C.28: Objects detected in the HGPS significance map -Black contours correspond to the edge mask and red circles to the objects detected in Hough space.

Table C .

 C 2: List of candidates based on high-circularity filter and MW-coincidence search (seeSect. 6.2)

		Name	HC 43			HC 56		HC 57		HC 115		HC 258
		GLON	-93.01			-68.97			-68.81		-39.41			0.63
	Latitude [deg]	GLAT Radius Circularity SigCenter Name GLON GLAT	-0.97 0.16 0.98 10.51 HC 73 -48.27 0.19	-0.01 0.14 1 3.19 Table C.3: List of the SNR-like candidates (see Sect. 6.3) -0.53 0.14 1 4.40 HC 76 HC 249 HC 282 HC 303 -47.65 -0.97 6.35 11.43 -0.25 -0.87 -0.13 -0.29	-0.01 0.11 1 4.09	HC 403 33.23 -0.15		2.27 0.12 1 4.19 HC 450 44.47 -0.17
		NestFlag Radius	0.27	3		0.29	0		0.31		0 0.38		0.33	0	0.21		0 0.42
	TypeMorph Circularity SigCenter	0.56 0.27 55	Peak	50	0.55 1.37	Peak 45	0.61 3.18	40	Peak 0.55 0.30	35	0.72 5.27	Peak 30	0.64 2.63	25	Peak 0.8 3.50	20
		PearsonR NestFlag	1	-0.99		1	-0.99		1		-0.98 1		1	-0.95	1		-0.97 1
	HGPS Region TypeMorph	Cavity	Cavity			Cavity	Cavity	Cavity		Cavity		Cavity
	PearsonR HGPS Object HGPS Region	0.53			0.54			0.61		0.90	0.48 HESS J1809-193 HESS J1852-000 HESS J1912+101 0.86 0.54
	HGPS Otype HGPS Object												HESS J1852-000 HESS J1912+101
	HGPS Radius HGPS Otype													Unid		Unid
	HGPS Dist HGPS Radius													0.28		0.49
	HGPS Dist HGPS SFoverlap HGPS SFoverlap													0.12 0.46		0.04 0.70
	HGPSG Object HGPSG Object						HGPSC 051			HGPSC 059	HGPSC 090
	HGPSG Otype HGPSG Otype						Discarded Large		Source Multi	Source Single
	HGPSG Radius HGPSG Radius							0.40				0.30		0.28
	HGPSG Dist HGPSG Dist HGPSG SFoverlap							0.02 0.57				0.01 0.90		0.12 0.46
	HGPSG SFoverlap SNRCAT Object			G312.4-0.4	G359.0-0.9	G6.4-0.1
	SNRCAT Object G267.0-1.0 SNRCAT Otype		G291.0-0.1 shell	shell		shell		G308.8-0.1
	SNRCAT Otype filled-centre plerionic composite SNRCAT Radius 0.32 0.19		0.40		plerionic composite
	SNRCAT Radius SNRCAT Dist SNRCAT SFoverlap		0.		0.15 0.53	0.12		0.06 0.48		0.1 0.70			0.2
	SNRCAT Dist SC1 Object SNR311.5-00.3 0.04			0.07	SNR358.5-00.9			SNR011.4-00.1
	SNRCAT SFoverlap SC1 Otype Not an SNR 0.41			0.5	Not an SNR			0.26 Marginally Classified
	SC1 Object SC1 Radius	0.30			SNR291.0-00.1 2.09				0.
	SC1 Otype SC1 Dist SC1 SFoverlap	0.04 0.74			Classified	0.13 0.02				0.17 0.09
	SC1 Radius FL8Y Object		0. 4FGL J1411.5-6133									4FGL J1913.3+1019
	SC1 Dist FL8Y Otype				PSR	0.11										PSR
	SC1 SFoverlap FL8Y Dist					0.25		0.1								0.15
	FL8Y Object FL8Y SFoverlap			4FGL J1111.8-6039 4FGL J1112.1-6108 4FGL J1341.7-6216 4FGL J1511.2-5803 0.12 0.06
	FL8Y Otype					PSR				PSR			PSR
		FL8Y Dist					0.10				0.05			0.05			0.06
	FL8Y SFoverlap					0.29				0.52			0.55			0.51
									27

available online at: https://www.mpi-hd.mpg.de/hfm/HESS/hgps/

http://gamma-cat.readthedocs.io/

http://snrcat.physics.umanitoba.ca/

http://astronomy.nju.edu.cn/ ~ygchen/others/bjiang/ interSNR6.htm

https://fermi.gsfc.nasa.gov/ssc/data/access/lat/8yr_ catalog/

https://fermi.gsfc.nasa.gov/ssc/data/analysis/software/ aux/4fgl/Galactic_Diffuse_Emission_Model_for_the_4FGL_ Catalog_Analysis.pdf

https://fermi.gsfc.nasa.gov/ssc/data/access/lat/1st_ SNR_catalog/

https://www.researchgate.net/publication/239398674_An_ Isotropic_3_3_Image_Gradient_Operator

for further details see https://scikit-image.org/docs/dev/api/ skimage.feature.html?highlight=feature\%20canny#skimage. feature.canny

These catalogues contain objects which belong to the two most representative TeV source classes, namely plerions (PWNe) and SNR shells. Nevertheless, these are certainly incomplete and other TeV emitters such as gamma-ray binaries or stellar clusters would thus be absent from our list of valuable candidates.

Acknowledgements

The authors acknowledge the Centre National de la Recherche Scientifique and the Institut National de Physique Nucléaire et de Physique des Particules in France, and the Max-Planck-Institut für Kernphysik in Germany for their support to this project. We thank the anonymous referee for his/her valuable comments.

Appendix A.1. Bootstrap simulations

We performed a bootstrap of the sources catalogued in the 870 HGPS survey. We generated 10 sky realisations, each one including 100 sources. Their latitude, longitude and radius are randomly and independently picked up among the catalogued value. The spatial distribution of the sources is preserved if the longitude and latitude distributions are independent. The ra-875 dius is given either by the source size column when available or by the R 70 column otherwise. For a given radius, we use the same flux (column Flux map if available) and the same spatial model than catalogued so the surface brightness and the source population distributions are preserved. However for sources 880 composed of multiple Gaussian components we generated only Appendix A.2. Toy-model for background emission and exposure maps

At VHE energies, the γ-ray flux from resolved sources dominates the total emission observed but a large scale diffuse emission is still detected [START_REF] Abdo | A Measurement of the Spatial Distribution of Diffuse TeV Gamma-Ray Emission from the Galactic Plane with Milagro[END_REF] H. E. S. S. Collaboration, 2014). The nature of this emission is assumed to be a mixture of γ rays from unresolved sources and γ rays of interstellar origin. The latter are indirectly produced by the interaction of cosmic ray protons with the interstellar gas (production and decay of neutral pions), and by energy losses of cosmic ray electrons and positrons via Bremsstrahlung and inverse-Compton scattering on radiation fields (see Fermi- LAT Collaboration, 2012; H. E. S. S. Collaboration, 2014;Fermi-LAT Collaboration, 2016a, and reference therein). We did not intend to produce a realistic model for the various components of the background emission, instead we used a toy-model that simply mimic a fake contribution from the interstellar γ rays and the instrumental noise. The flux of the toy-model, F Toy-BG , is define as

with F GC = 1.65 × 10 -12 /[π(R corr /d pixel ) 2 ] cm -2 s -1 pixel -1 , the HGPS flux at the Galactic center weighted by the surface ratio between the correlation kernel of the HGPS flux map and the pixel size d pixel .

In order to imprint a shape to the diffuse Galactic emission from the interstellar medium, we used the dust optical depth at 353 GHz (τ 353 from Planck Collaboration, 2016), normalized by its maximum value, τ norm 353 = τ 353 /τ max 353 . Note that the emission from large dust grains and the γ-ray emission from CR interaction with molecular clouds are both dependent on the gas column density so they share many structural similarities. However the dust optical depth per gas nucleon also depends on the grain properties that change across the gas phases and the Galaxy while the γ-ray emissivity per gas nucleon independently varies with energy and Galactocentric radius. So formally the dust emission cannot be used to linearly trace the gas column density and precisely model the shape of the γray emission of interstellar origin. Nevertheless we use this template parametrisation for simplicity as we only need to test how the source reconstruction is affected by an increase in the diffuse background level. To do so we arbitrarily tweaked the contrast in flux between the source and the diffuse background with one parameter. The contrast parameter C ism has been set to 0.1 in the minimal case, which is about the ratio in flux on 930 the HGPS map between the pixels at the Galactic center and the surrounding ones toward the central molecular zone clouds. We also considered a case where C ism =0.3 for a stronger diffuse background emission.

The isotropic term, C iso , implicitly assumes that the instrumental noise (hadron background) is proportional to the exposure which is not exactly the case. With such an approximation, we can write the OFF counts as:

with B the background count rate, t the observation time and 935 Expo = At the exposure for the instrument acceptance A. As N OFF is integrated within a radius R spec , we have to normalize by the surface ratio between the integration radius and the pixel size,

Then the normalisation factor C iso is proportional to the ratio B/A, that can be estimated using the information on the sources fitted in the HGPS catalogue. Indeed the excess counts are expressed as:

so combining the two previous equations we have:

with N excess , F excess and N OFF given in the HGPS catalog as the 940 columns named Excess RSpec Model, Flux Map RSpec Total, and Background RSpec, respectively. We get an average B/A ratio per pixel: B/A = 5.01 × 10 -15 cm -2 s -1 pixel -1 (see Fig.

A .19). Then we have the normalization factor C iso 0.24.

In the limit case where N OFF N excess , the significance of the excess can be expressed as σ excess = N excess / √ N OFF . By combining this relation with the Eq. A.3 into Eq. A.4 we can write:

Note that we can also derive an average B/A from this equation 945 and the value found is consistent with the previous one even if we approximate the significance.

The HGPS sensitivity map is defined as the minimal flux in cm -2 s -1 within a correlation radius R corr required to detect a source with a significance of 5. Thus, according to Eq. A.5, we can define the simulated exposure map in cm 2 s as :

The same exposure map has been used for all the simulations. In Fig . A.20 we checked that the exposure estimated for each source in the catalogue using Eq. A.5 and the simulated expo-950 sure map at each source location are consistent.

Appendix A.3. Count and significance maps

The simulated flux maps of the sources and of the background have been multiplied by the exposure map and convolved by a Gaussian kernel of 0.06 • in order to mimic the instrument point-spread-function. We then applied Poisson noise to get the simulated counts.

The significance maps have been derived using the same formalism as that of the HGPS survey. The excess counts N excess within an ON region are defined as

with N ON the counts in the ON region, N OFF the counts in the OFF region, and α the background normalization factor defined as the ratio of the integral acceptances in the ON/OFF regions: α = ξ ON /ξ OFF . The significance has then been calculated using Eq. ( 17) from [START_REF] Li | Analysis methods for results in gamma-ray astronomy[END_REF]:

The ON region is defined as a disk of radius R corr (correlation radius). We produced maps with R corr = 0.1 • and 0.2 • . The OFF counts are determined either from the expected counts of the simulated background or from the adaptive ring background method. In the first case the OFF region is the same as the ON region since we have a perfect knowledge of the OFF counts. In the second case we proceed in a similar way as that developed in the HGPS. For each pixel, the OFF region is defined as a concentric ring with inner radius of 2 times R corr and a variable outer radius chosen to minimize the difference to a target α value fixed to 0.02. By comparison the default geometric α of the HGPS analysis is about 0.01 (surface ratio between ON/OFF regions) After producing a first significance map we define an exclusion region in order to mask the significant pixels from the OFF region. Then the background is re-evaluated in each pixel using the masked adaptive ring, and the significance map is updated. This iterative procedure is repeated three times (after that the limited change in the exclusion mask no longer affects the final results).

The exclusion mask is derived by hysteresis thresholding on the significance maps with a high threshold of 4.5σ and a low threshold of 1σ. Note that this step differs from the HGPS procedure where a hard threshold at 5σ is used and the mask is then uniformly extended by 0.3 • beyond the 5σ contours. The mask obtained by hysteresis thresholding better preserves the structure of the excess.

In Fig.

A.21 we show the counts, exposure and background maps for one of the simulated skies. In Fig . A.22 simulated significance maps derived from the exact background and through the adaptive ring background method, together with their difference, are presented. In the edge detection procedure we filter these significance maps using the information of the maps with R corr = 0.1 • and R corr = 0.2 • by combining their respective hysteresis mask with an or condition. An example of filtered significance map for a simulated sky is shown in

Appendix B. Possible technical improvements

On the background removal: Using the gradient information to extract only sparse structural information and detect only sharp edges in the data allow us in principle to filter most of the diffuse structures associated to the interstellar background. It should be further tested on the on-going simulations of the Galactic Plane Survey which will be conducted by the next generation of imaging atmospheric Cherenkov telescopes (IACTs), namely the Cherenkov Telescope Array (CTA) [START_REF] Actis | Design concepts for the Cherenkov Telescope Array CTA: an advanced facility for ground-based high-energy gamma-ray astronomy[END_REF]CTA Consortium, 2017). CTA will probe lower energies with a higher sensitivity and better angular resolution so that the contribution of diffuse Galactic emission will be larger and hence, more refinement may be necessary to filter the diffuse background. The filters applied to the edge mask can enhance the response of the algorithm to sources against background.

On the object detection:

In complement to object detection based on the Hough transform, we could use the Wavelet transform. Both Wavelet-based and Hough-based detections can be used to generate a list of seeds in a short amount of time that can be further tested in dedicated analyses or catalogue pipelines using the templatefitting approach. According to our tests, a good agreement in position and radius is found between the two detection methods for small-size objects resolved in Hough space. The wavelets-based detection presents a clear advantage for dissociating point-like/small-size objects in close vicinity. The Hough-based detection presents a huge advantage for extended objects, in particular SNR-like objects for which the shell is not entirely above the noise level. It would be interesting to further test the complementarity of these two methods in the framework of the CTA simulations, in order to help in the preparation of the future catalogue pipeline.

On the object classification and identification:

We have shown that the different types of well-identified sources can be separated within a set of morphological parameters using simple linear classification rules. More sophisticated machine-learning techniques like support vector machines [START_REF] Cortes | Support-vector networks[END_REF] could be used to define the classification rules automatically. In our study, we have used the well-identified HGPS sources to define a training sample and find new source candidates that share similar characteristics. In a more general way we could use unsupervised machine-learning techniques as clustering algorithms to identify different classes of objects and identify them to known source populations only a posteriori. This could help dissociate sources from spurious detections or find new types of VHEemitting sources (not represented in any training sample). Of course the more object classes we want to separate, the higher the dimension of the parameter space should be. For instance, we could improve the classification of the different source types by including their spectral index and their variability.

On the multi-wavelength associations:

In order to firmly confirm the nature of these objects, dedicated MW analyses, including spectral fitting, are necessary. We 1050 postpone this work for future follow-up studies. As MW catalogues are not exhaustive, deep mining into MW archival data is essential to find potentially relevant counterparts that have remained below the detection threshold of catalogues. Given the number of available surveys from radio to γ-rays, collecting all 1055 these data is a complicated and time-consuming task. Moreover cross-matching all these surveys is far from being straightforward given the large diversity in the instrumental performances and characteristics in terms of calibration, resolution, field-ofview and so on. In order to address this important issue, a new 1060 automated algorithm is being developed by J. Devin and M. Renaud. In the future, it could be used in order to further look for MW coincidences toward the most interesting source candidates flagged by the morphological classifier, especially those which do not show any catalogued counterpart.


Yanis Roussel

Audrey Giraud-Gatineau

Marie-Therese Jimeno

Jean-Marc Rolain

Christine Zandotti

Philippe Colson

Didier Raoult
email: didier.raoult@gmail.com

Marie-Thérèse Jimeno

SARS-CoV-2: fear versus data

Keywords: COVID-19, coronavirus, SARS-CoV-2

Introduction

Coronaviridae represent a very important family of animal and human viruses (1; 2) that circulated permanently. These four common human coronaviruses (HKU1, NL63, OC43, E229) represent between 10 to 20% of respiratory infections worldwide and are present in all continents (3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14) (Table 3). Mortality is poorly assessed, but it is clear that there are chronic carriers as well as asymptomatic carriers. There are even two studies, one carried out by our team showing that there are as many asymptomatic carriers as symptomatic patients, and a second carried out in Ghana that shows that the number of asymptomatic carriers was not significantly different from the number of symptomatic carriers (3; 9). Since then, three epidemic episodes of emerging coronaviruses have been reported. The first, the SARS virus, has had very little impact on global morbidity and mortality since there have been more than 8000 recognized cases and 774 deaths (15; 16). The second, MERS-Coronavirus, remained localized in Saudi Arabia, with a small epidemic of mainly nosocomial infections in South Korea [START_REF] Zaki | Isolation of a novel coronavirus from a man with pneumonia in Saudi Arabia [published correction appears[END_REF]. The MERS-Coronavirus, like SARS, have highlighted the major danger of nosocomial transmission to healthcare personnel who must absolutely be preserved in these epidemics [START_REF] Hui | Middle East respiratory syndrome coronavirus: risk factors and determinants of primary, household, and nosocomial transmission[END_REF]. Finally, SARS-CoV-2 that appeared in December has expanded and has now affected more than 90,000 people worldwide (2; 19; 20). However, there is a significant number of cases only in the Far East so far. It is incontestably contagious since the example of a quasiexperimental study on the Diamond Princess cruise-ship that showed that if one locked up infected patients with uninfected patients, uninfected patients very quickly become infected in a confined world, and thus more 700 cases were diagnosed on this cruise-ship [START_REF] Rocklöv | COVID-19 outbreak on the Diamond Princess cruise ship: estimating the epidemic potential and effectiveness of public health countermeasures[END_REF]. However, commonlycirculating coronaviruses remain globally very predominant in the global situation because of their global distribution and their non-negligible mortality (22; 14). In this study, we wanted to share the experience of a reference laboratory representing around 1% of serious and diagnosed forms of respiratory infections, particularly seasonal, in France. This will allow evaluating the relative mortality of different human coronaviruses presented in hospitals in Marseille, compared to that of the Chinese coronavirus as it has appeared for the moment in countries with the same economic development, including France.

Materiel and methods

Assistance Publique -Hôpitaux de Marseille (AP-HM) is administrating all public hospitals in Marseille, France, including four university hospitals: La Timone hospital, Conception Hospital, North Hospital and South hospital, corresponding to 3,400 beds and 125,000 admissions each year [START_REF] Abat | Real-Time Microbiology Laboratory Surveillance System to Detect Abnormal Events and Emerging Infections, Marseille, France[END_REF]. IHU Méditerranée Infection diagnosis laboratory is testing all samples from AP-HM in which respiratory viruses are suspected. The diagnosis is performed through molecular biology analysis. The results are monitored by a weekly automated surveillance system in IHU Méditerranée Infection, coupled to a laboratory information system (Nexlabs) [START_REF] Abat | Real-Time Microbiology Laboratory Surveillance System to Detect Abnormal Events and Emerging Infections, Marseille, France[END_REF]. SARS-CoV-2 epidemiological data were obtained through an online platform gathering data from public agencies [START_REF]INSEE, 594 000 personnes décédées en France en 2016, pour un quart d'entre elles à leur domicile[END_REF]. Statistical analyses were performed by using BiostatGV online-software.

Results

In 2016, a total of 594 000 people deceased in France, among which 59,2% deceased in a care establishment (25). In 2016, a total of 2854 patients deceased in AP-HM hospitals. We can therefore estimate that each year, around 0,8% of people that deceased in care establishments in France died in AP-HM. This estimate allows us to have an idea of the number of peoples affected by a pathogen in France according to the number of people who died each year at the AP-HM.

From January, 1 st 2013 to December, 31th 2019, 21 662 samples were tested by the AP-HM diagnosis laboratory. Among these, 770 samples were positive for coronavirus, of which 8 died (Mortality rate: 1%). Among identified coronaviruses, 63 were identified as Coronavirus HKU1 (1 died, Mortality rate 1.6%), 74 were identified as Coronavirus NL63 (2 died, Mortality rate 2.7%), 92 as Coronavirus E229

(1 died, Mortality rate 1.1%) and 160 as Coronavirus OC43 (4 died, mortality rate 2.5%). 381

Coronavirus, diagnosed before 2017, were not assigned to any of these four strains (Table 1).

We performed systematic testing (molecular biology) in the context of SARS-CoV-2 from January During the same period, IHU Méditerranée Infection has been the regional center for the detection of the novel coronavirus SARS-CoV-2. A total of 596 analyses were performed on suspect patients since the emergence of the novel pathogen, among which 4 were positive to the SARS-CoV-2, and 709 were performed on French returnees from the Hubei province, all negative.

Until the 2 nd of March 2020, a total of 90 307 patients were tested positive to SARS-CoV-2 in the world, among which 3086 died (mortality rate 3,4%). Including OECD countries only, 7476 patients were tested positive to SARS-CoV-2, among which 96 died (Mortality rate 1.3%) (Table 2). In France, 191 people were tested positive, 3 died (Mortality rate 1,6%).

  , 1 st 2020 to March, 2nd 2020, 7059 samples from patients presenting viral infections symptoms were tested by AP-HM diagnosis laboratory. Among them, 543 samples were positive to Coronavirus with 2 deaths (Mortality rate: 0,36%): 277 were positive to Coronavirus HKU1, 146 Coronavirus NL63, 77 to Coronavirus OC43, and 43 to Coronavirus 229E. No SARS-CoV-2 have been identified among these samples. One patient died with Coronavirus OC43 (Mortality rate 1,3%) and 1 patient died with Coronavirus HKU1 (Mortality rate 0,36%). No patients died with Coronavirus NL63 and E229 during this period.

Table 1 :

 1 Results for AP-HM diagnosis laboratory 234

		Agent		Location	Confirmed cases	Deaths	Rate
		Coronavirus*
		Coronavirus OC43			160	4	0,0250
		Coronavirus NL63	AP-HM, Marseille, France	74	2	0,0270
		Coronavirus HKU1			63	1	0,0159
		Coronavirus E229			92	1	0,0109
		Coronavirus**
		Coronavirus OC43			77	1	0,0130
		Coronavirus NL63	AP-HM, Marseille, France	146	0	0
		Coronavirus HKU1			277	1	0,0036
		Coronavirus E229			43	0	0
		* From 2013-01-01 to 2019-12-31
		** From 2020-01-01 to 2020-03-02
	235	Table 2: SARS-CoV-2 international epidemiological situation (OECD countries)
	236	Consulted on 03 march 2020, 9.00 GMT
		Countries	Confirmed cases	Deaths	Rate
		Germany		157	0	0,0%
		Australia		30	1	3,3%
		Austria		18	0	0,0%
		Belgium		8	0	0,0%
		Canada		24	0	0,0%
		South Korea	4335	28	0,6%
		Denmark		4	0	0,0%
		Spain		123	0	0,0%
		Estonia		1	0	0,0%
		United States		100	6	6,0%
		Finland		7	0	0,0%
		France		191	3	1,6%
		Greece		7	0	0,0%

We compared the mortality rate of Coronavirus SARS-CoV-2 in OECD countries (1,3%) with the mortality rate of common coronaviruses identified in AP-HM patients (0,8%) from January 1st, 2013 to March 2nd, 2020. We performed a χ2 test on these values. The p-value was 0.11 (not significant).

Discussion

In this work, we highlight that the mortality of common Coronavirus infections is of 0.8% in France. This is to be compared with the mortality of the SARS-CoV-2 in the European or American developed countries of comparable economic level, which is of 1,3% (Table 2). If our extrapolation of deaths in AP-HM is true, in metropolitan France this would represent 543 / 0.8 * 100 = 67,875 cases of patients hospitalized with a respiratory infection with common coronaviruses in two months, almost as much as SARS-CoV-2 in the world. In fact, mortality from respiratory infections is extremely dependent on the quality of care and access to care, and severe forms have a better prognosis in countries with superior medical infrastructures. Under these conditions, there does not seem to be a significant difference in the mortality of Coronavirus SARS-CoV-2 in OECD countries with an economic level comparable to that of common coronaviruses (χ 2 test p=0.11). Of course, the major flaw in this study is that the percentage of death attributable to the virus is not determined, but this is the case for all of the studies reporting respiratory virus infections, including those of SARS-CoV-2. Indeed, viral infections are ecosystem infections where the outcome depends on the inoculums and the surrounding microbiota [START_REF] Edouard | The nasopharyngeal microbiota in patients with viral respiratory tract infections is enriched in bacterial pathogens[END_REF]. Thus, certain bacteria seem to be associated with symptomatic manifestations, such as Streptococcus pneumoniae, Haemophilus influenzae, and Staphylococcus aureus, which are known to be the bacteria causing an excess of mortality due to secondary infection. Finally, seasonality, geographic location, heat, humidity are co-factors, as are age, gender and underlying pathologies.

Under these conditions and all other things being equal, the disease with SARS-CoV-2 cannot be described as being statistically more severe than that linked to currently circulating other coronaviruses .

Finally, in particular in OECD countries, the SARS-CoV-2 does not seem to be particularly deadlier than other circulating viruses. In addition to coronaviruses, there are [START_REF] De Wit | SARS and MERS: recent insights into emerging coronaviruses[END_REF] [START_REF] Gbd | Global, regional, and national age-sex-specific mortality and life expectancy, 1950-2017: a systematic analysis for the Global Burden of Disease Study 2017[END_REF]. There is little chance that the emergence of SARS-CoV-2 could change this statistic significantly. Fear could have a larger impact than the virus itself: a first case of suicide motivated by the fear of SARS-COV-2 has been reported in India [START_REF] Goyal | Fear of COVID 2019: First suicidal case in India ![END_REF].

In addition, coronaviruses that have rarely been tested systematically around the world may persist in the pharynx of asymptomatic people being a potential source of population immunity [START_REF] Raoult | Coronavirus infections: Epidemiological, clinical and immunological features and hypotheses[END_REF].

Furthermore, it should be noted that in systematic studies that have been carried out for other coronaviruses (but not yet for SARS-CoV-2), the percentage of asymptomatic carriers is equal or even higher as compared to symptomatic patients. We may soon have the same data for SARS-CoV-2, which will further reduce the relative risk associated with this specific pathology.

Declarations