Michaël Clément
email: michael.clement@parisdescartes.fr

Camille Kurtz

Laurent Wendling

Fuzzy Directional Enlacement Landscapes

Spatial relations between objects represented in images are of high importance in various application domains related to pattern recognition and computer vision. By definition, most relations are vague, ambiguous and difficult to formalize precisely by humans. The issue of describing complex spatial configurations, where objects can be imbricated in each other, is addressed in this article. A novel spatial relation, called enlacement, is presented and designed using a directional fuzzy landscape approach. We propose a generic fuzzy model that allows to visualize and evaluate complex enlacement configurations between crisp objects, with directional granularity. The interest and the behavior of this approach is highlighted on several characteristic examples.

Introduction

The spatial organization of objects is fundamental to increase the understanding of the perception of similarity between scenes or situations. Despite the fact that humans seem capable of apprehending spatial configurations, in many cases it is exceedingly difficult to quantitatively define these relations, mainly because they are highly prone to subjectivity. Standard all-or-nothing mathematical relations are clearly not suitable, and the interest of fuzzy relations was initially suggested by Freeman in the 70s [START_REF] Freeman | The Modelling of Spatial Relations[END_REF], since they allow to take imprecision into account. Over the last few decades, numerous works were proposed on the analysis of spatial relationships in various domains, ranging from shape recognition to computer vision, with the main purpose of describing the relative positioning of objects in images [START_REF] Bloch | Fuzzy spatial relationships for image processing and interpretation: A review[END_REF]. These approaches provide a set of interesting features able to describe efficiently most of spatial situations. However, some configurations remain challenging to describe without ambiguities, especially when the objects are imbricated, or composed of multiple connected components. In this context, we propose to study new relations dedicated to the imbrication of objects.

This article is organized as follows. Sec. 2 presents related works to our approach. Sec. 3 recalls the model of directional enlacement, proposed in [START_REF] Clément | Directional Enlacement Histograms for the Description of Complex Spatial Configurations between Objects[END_REF] for the description of complex spatial configurations. From the latter, we propose in Sec. 4 a generic model relying on fuzzy landscapes that allows to evaluate relative enlacement configurations between crisp objects, with directional granularity. Sec. 5 presents experimental results on different illustrative examples that allow to highlight the behavior and the interest of this model. Sec. 6 provides conclusions and perspectives.

In the domain of spatial relations, two major research axes can be distinguished in the literature, based on two dual concepts: the one of spatial relationship and that of relative position. On the one hand, it is possible to formulate a fuzzy evaluation of a spatial relation (for example "to the left of ") for two objects, in order to describe their relative position. The fuzzy landscape model is a widely used method for providing this type of assessments [START_REF] Bloch | Fuzzy Relative Position between Objects in Image Processing: A Morphological Approach[END_REF]. This approach relies on the fuzzy modeling of a given spatial relation, directly in the image space, using morphological operators. Applications of this model can be found in various domains such as spatial reasoning in medical images [START_REF] Colliot | Integration of fuzzy spatial relations in deformable models -Application to brain MRI segmentation[END_REF] or the recognition of handwriting [START_REF] Delaye | Learning of fuzzy spatial relations between handwritten patterns[END_REF]. On the other hand, the location of an object with regards to another can be modeled by a quantitative representation, in the form of a relative position descriptor. Different spatial relations can be assessed from this representation and the associated descriptors can be integrated in pattern recognition systems to match similar spatial configurations. Among the various relative position descriptors, the histograms of forces [START_REF] Matsakis | A New Way to Represent the Relative Position between Areal Objects[END_REF] are widely used due to their ability to process pairwise information following a set of directions. They are applied in different works, such as the linguistic description of spatial relations [START_REF] Matsakis | Linguistic description of relative positions in images[END_REF] or image retrieval [START_REF] Clément | Bags of Spatial Relations and Shapes Features for Structural Object Description[END_REF]. To summarize, fuzzy landscapes consist in determining the region of space matching a specific spatial relation, and relative position descriptors consist in characterizing the position of an object with regards to another, by combining different spatial features into a standalone descriptor.

Although these two types of approaches allow to interpret many spatial relations between objects, they usually fail at properly describing more complex spatial configurations, in particular when objects are concave, or composed of multiple connected components [START_REF] Bloch | On the Ternary Spatial Relation "Between[END_REF]. A typical complex spatial relation is the "surrounded by" relation, which was first studied by Rosenfeld [START_REF] Rosenfeld | Degree of adjacency or surroundedness[END_REF] and deepened by Vanegas [START_REF] Vanegas | A fuzzy definition of the spatial relation "surround" -Application to complex shapes[END_REF] with a dedicated approach based on fuzzy landscapes. Another specific spatial relation is "between". This relation has been studied in details in [START_REF] Bloch | On the Ternary Spatial Relation "Between[END_REF], involving definitions based on convex hulls and specific morphological operators. Applications of this spatial configuration for the analysis of histological images have been proposed by [START_REF] Loménie | Point set morphological filtering and semantic spatial configuration modeling: Application to microscopic image and bio-structure analysis[END_REF]. Work has also been done to characterize the "alignment" and "parallelism" of objects in satellite images [START_REF] Vanegas | Alignment and parallelism for the description of high-resolution remote sensing images[END_REF]. Recent works introduced the φ-descriptor [START_REF] Matsakis | Introducing the Φ-Descriptor -A Most Versatile Relative Position Descriptor[END_REF][START_REF] Matsakis | Fuzzy Models of Topological Relationships Based on the PHI-Descriptor[END_REF], which is a powerful generic framework to assess any spatial relation from a set of specific operators, inspired by Allen intervals [START_REF] Allen | Maintaining knowledge about temporal intervals[END_REF]. This descriptor can determine if two objects are imbricated or not, but it is not able to measure the depth of imbrication (such as, for instance, when two spirals are interlaced).

In this context, recent works [START_REF] Clément | Directional Enlacement Histograms for the Description of Complex Spatial Configurations between Objects[END_REF] introduced both enlacement and interlacement descriptors, from the relative position point of view, in order to obtain a robust modeling of the imbricated parts of objects. Based on this model, in this article we propose to tackle the dual point of view, by considering fuzzy enlacement landscapes instead of enlacement descriptors. The goal of fuzzy enlacement landscapes is to visualize and evaluate these spatial configurations directly in the image space, by considering the concavities of the objects in a directional fashion.

In this section, we present the model used to describe the relative enlacement of objects. This model was initially introduced in [START_REF] Clément | Directional Enlacement Histograms for the Description of Complex Spatial Configurations between Objects[END_REF], mostly from the point of view of the relative position descriptors. Here, we recall the intuitive idea behind what is intended with the term enlacement, and we provide some useful definitions and notations for this model.

A two-dimensional object A of the Euclidean space is defined by its characteristic function f A : R 2 → R. This generic definition allows to handle both crisp and fuzzy objects. Let θ ∈ R be an orientation angle, and ρ ∈ R a distance from the origin. We define the oriented line of angle θ at the altitude ρ by the non-finite set ∆ (θ,ρ) = {e iθ (t + iρ), t ∈ R}. The subset A ∩ ∆ (θ,ρ) represents a one-dimensional slice of the object A, also called a longitudinal cut. In the case of crisp objects, such a longitudinal cut of A is either empty (the oriented line does not cross the object) or composed of a finite number of segments. In the general case, a longitudinal cut of A along the line ∆ (θ,ρ) can be defined as:

f (θ,ρ) A : R -→ R t -→ f A (e iθ (t + iρ)). (1)
Let (A, B) be a couple of objects. The goal is to describe how A is enlaced by B. The intuitive idea is therefore to capture the occurrences of points of A being between points of B. In order to determine such occurrences, objects are handled in a one-dimensional case, using longitudinal cuts along oriented lines. For a given oriented line ∆ (θ,ρ) , the idea is to combine the quantity of object A (represented by f (θ,ρ) A

) located simultaneously before and after object B (represented by f (θ,ρ) B

). Let f and g be two bounded measurable functions with compact support from R to R. The enlacement of f with regards to g is defined as:

E(f, g) = +∞ -∞ g(x) +∞ x f (y) +∞ y g(z) dz dy dx. (2)
The scalar value E(f

(θ,ρ) A , f (θ,ρ) B
) represents the enlacement of A by B along the oriented line ∆ (θ,ρ) . For crisp objects (i.e., each point is either 0 or 1), it corresponds to the total number of ordered triplets of points on the oriented line, which can be seen as arguments to put in favor of the proposition "A is enlaced by B" in the direction θ. Algorithmically, this value can be derived by an appropriate distribution of segments lengths along the longitudinal cuts of both objects (see [START_REF] Clément | Directional Enlacement Histograms for the Description of Complex Spatial Configurations between Objects[END_REF] for more details).

The set of all parallel lines {∆ (θ,ρ) , ρ ∈ R} in the direction θ slices the objects into sets of longitudinal cut functions. To measure the global enlacement of an object with regards to another in this direction, we aggregate the onedimensional enlacement values obtained for each of these longitudinal cuts.

The enlacement of A by B in direction θ is defined by:

E AB (θ) = 1 A 1 B 1 +∞ -∞ E(f (θ,ρ) A , f (θ,ρ) B ) dρ, (3)
where A 1 and B 1 denote the areas of A and B. This normalization allows to achieve scale invariance. In the binary case, this definition corresponds to a number of triplets of points to put in favor of "A is enlaced by B" along the longitudinal cuts in this direction. Intuitively, it can be interpreted as the quantity of B traversed while sliding the object A in the direction θ, with regards to the quantity of B located on the opposite direction.

In [START_REF] Clément | Directional Enlacement Histograms for the Description of Complex Spatial Configurations between Objects[END_REF] the enlacement model E AB was considered from the point of view of the relative position descriptors by building a directional enlacement histogram, allowing to characterize how an object A is enlaced by another object B. In the next section, we involve this model in a novel evaluation point of view based on a fuzzy approach that allows to evaluate enlacement configurations directly in the image space, with directional granularity.

Fuzzy Enlacement Landscapes

We present here how to extend the directional enlacement model to evaluate the enlacement of objects in the image space from a local point of view, inspired by the works of Bloch [START_REF] Bloch | Fuzzy Relative Position between Objects in Image Processing: A Morphological Approach[END_REF] on fuzzy landscapes for classical spatial relations.

Definition

A fuzzy enlacement landscape of an object A should be a representation of the region of space that is enlaced by A. Since the initial enlacement model is essentially directional, we also propose to define directional enlacement landscapes. Let A be a crisp object (i.e., represented as f A : R 2 → {0, 1}). In a given direction θ, for a point outside of A located at (ρ, t) coordinates in the rotated frame, its local enlacement value can be defined as:

E A (θ)(ρ, t) = 1 A 1 +∞ t f (θ,ρ) A (x) dx t -∞ f (θ,ρ) A (x) dx. (4)
Therefore, E A (θ) can be seen as a landscape representing the local enlacement values of the points outside of the object A. This image can be normalized into the [0, 1] range of values in order to be interpreted as a fuzzy set, which we call a Fuzzy Directional Enlacement Landscape (Fuzz-DEL) of the object:

µ A E (θ)(ρ, t) = E A (θ)(ρ, t) max ρ,t E A (θ)(ρ, t) . ( 5
)
Such a landscape allows to assess and visualize to which degree each point is enlaced by the object A in a fixed direction θ. It is interesting to note that the non-zero values of this landscape are necessarily located inside the object's concavities. This is particularly interesting from an algorithmic point of view, since it allows to restrict the computation to points located in the convex hull of A (and outside of A). Another point to highlight is that enlacement landscapes are symmetric, with period π (i.e., µ A

E (θ + π) = µ A E (θ)). (a) Object A (b) µ A E ( π 2 , 0) (c) µ A E ( π 2 , π 6 ) (d) µ A E ( π 2 , π 3 )
Fig. 1: Fuzzy directional enlacement landscapes of a crisp object A, with a fixed direction θ and an increasing width ω. In (b, c and d), A is outlined in white.

Since µ A E (θ) is focused on a single direction, we propose to aggregate such fuzzy landscapes across multiple orientation angles. Let θ ∈ [0, π] be an orientation angle and ω ∈ [0, π] a width parameter. The Fuzz-DEL on the interval

[θ -ω 2 , θ + ω 2 ]
is defined as follows:

µ A E (θ, ω)(ρ, t) = 1 ω θ+ ω 2 θ-ω 2 µ A E (α)(ρ, t) dα, (6)
where θ represents the direction on which the fuzzy landscape is focused, while ω controls the width of the interval, allowing to measure either a narrow direction or a more global one. In particular, the landscape that aggregates all directions is denoted by

µ A E = µ A E ( π 2 , π).
In order to illustrate such definitions, Fig. 1 and2 show the Fuzz-DELs obtained for two different objects. On the one hand, Fig. 1 illustrates the impact of the width parameter ω for a given vertical direction (θ = π 2 ). Note that the landscape would be identical for the opposite vertical direction (θ = 3π

2 ) because of symmetry. We can observe the zero-valued points in the center of the object for ω = 0, representing the fact that these points are not enlaced vertically by A. This can be interpreted by the idea that if another object was located here, it would be able to move in the vertical direction without crossing the other object (i.e., the object could slide downwards). We also observe that when ω increases, the fuzzy landscape progressively gets smoother, taking into account a wider range of directions. On the other hand, Fig. 2 shows enlacement landscapes on another object for different directions θ (with a fixed width ω = π 3 ). From these examples, one can note how a Fuzz-DEL allows to capture the object directional concavities. In the horizontal direction (θ = 0), the local enlacement values are relatively high, and the values are higher the deeper we get inside the "snaked" shape. In the vertical direction (θ = π 2 ), the Fuzz-DEL is mostly empty, except on some small concavities.

Fuzzy Evaluation

In the previous definitions, a reference object A is considered, and different Fuzz-DELs can be derived from it. These fuzzy landscapes allow to visualize the

(a) Object A (b) µ A E (0, π 3 ) (c) µ A E ( π 4 , π 3 ) (d) µ A E ( π 2 , π 3 )
Fig. 2: Fuzzy directional enlacement landscapes of a crisp object A, with a fixed width ω and for different directions θ. In (b, c and d), A is outlined in white.

interaction area of A. In the following, we show how to exploit these landscapes to evaluate to which degree a target object B is enlaced by the reference object A, using classical fuzzy operators. Let µ A and µ B be two fuzzy sets over R 2 . A typical way to evaluate how µ B matches with µ A is the necessity-possibility measure. The necessity N and possibility Π can be respectively defined as follows:

Π(µ A , µ B ) = sup x,y t(µ A (x, y), µ B (x, y)), (7)
N (µ A , µ B ) = inf x,y T (µ A (x, y), 1 -µ B (x, y)), (8)
where t is a fuzzy intersection (t-norm) and T is a fuzzy union (t-conorm). For the rest of this article, the min and max operators are chosen for t-norm and t-conorm respectively, but other fuzzy operators could be considered.

In our context, this fuzzy matching measure can be applied to evaluate how a target object B (represented by its membership function µ B ) matches with a Fuzz-DEL µ A E (θ, ω) of a reference object A. The necessity-possibility interval [N (µ A E (θ, ω), µ B ), Π(µ A E (θ, ω), µ B )] constitutes a fuzzy evaluation of how B is enlaced by A in direction θ, with the necessity being a pessimist point of view, while the possibility represents an optimist point of view. The mean value M (µ A E (θ, ω), µ B ) can also be considered. This evaluation strategy will be further studied in the upcoming experiments.

Experimental Results

We present different illustrative examples to highlight the interest of our approach. These experiments are organized around two main applications. The first one is to evaluate the specific relation "surrounded by". As mentioned previously, this relation can be considered as a particular case that can be derived from the directional enlacement model. The second application is to evaluate the spatial relation "enlaced by" in a more generic sense, in particular when the reference object has multiple degrees of concavities. We also propose some preliminary results on interlacement landscapes.

Surrounding

The "surrounded by" relation is easily apprehended by human perception, but is particularly challenging to evaluate quantitatively. It is usually modeled by the "all directions" point of view, i.e., an object surrounds another object if it is located in all directions. In the following, we adopt the same insight, but we adapt it to the enlacement model: an object is surrounded if it is enlaced by the other object in all directions. Fig. 3 presents characteristic examples of surrounding configurations that we assessed using the proposed fuzzy evaluation strategy. In each image, the reference object A is in gray and the target object B is the white circle.

For this application, we propose a specific way to apply our approach. The target object B is projected into a Fuzz-DEL of A, and further normalized as a fuzzy set. Such a projection is defined as:

µ AB E (θ, ω) = min ρ,t (µ A E (θ, ω)(ρ, t), µ B (ρ, t)) max ρ,t µ A E (θ, ω)(ρ, t) . ( 9
)
Then, the necessity N (µ AB E (θ, ω), µ B ) and possibility Π(µ AB E (θ, ω), µ B ) evaluations are performed for different values of θ ∈ [0, π]. This results in informative directional necessity and possibility profiles, which can be also then exploited to derive a global evaluation of how B is surrounded by A. For the rest of this study, we fixed ω to a low value of π 36 (5 degrees) to take into account different directions individually, while smoothing out some discretization issues. Following the "all directions" point of view, this global evaluation can be obtained with the following:

N AB S = 1 π π 0 N (µ AB E (θ, ω), µ B ) dθ, (10)
Π AB S = 1 π π 0 Π(µ AB E (θ, ω), µ B ) dθ. (11)
Fig. 4 shows the directional necessity and possibility profiles obtained for the configurations of Fig. 3. In situation (a), the object is only partially surrounded. Both the pessimist and possibility evaluations agree that the reference object A is surrounded in the vertical directions, but not in the horizontal directions. The gradual transition of the situation is captured along the diagonal directions. The object is also partially surrounded in situation (b), where half of the surrounding circle has been cut out. In situation (c), small parts were added preventing the object to leave without crossing the surrounding object, and therefore the optimist point of view is 1 while the pessimist one oscillates but is never zero. Finally, evaluations tend to agree that the object is surrounded in situation (d).

The optimist point of view is always 1, yet it takes into account that the object Table 1: Fuzzy surrounding evaluations (necessity-possibility intervals and mean values) obtained for the configurations of Fig. 3 and Fig. 5. could escape by crossing a small portion of the surrounding object, resulting in low pessimist evaluations for the vertical directions.

(b) Segmented image (c) µ A E (d) µ A E (0, π 6 ) (e) µ A E ( π 3 , π 12 ) (f) µ A E ( 3π 4 , π 6
To complement these results, Table 1 presents the surrounding necessitypossibility intervals [N AB S , Π AB S ], to evaluate the global surrounding of the target objects of Fig. 3. For comparison purposes, we also present the results of the approach of [START_REF] Vanegas | A fuzzy definition of the spatial relation "surround" -Application to complex shapes[END_REF], which is also based on a fuzzy landscape framework, but dedicated to surrounding relation. It is based on a specific fuzzy landscape, considering only the visible concavities of the reference object. We also present the results obtained by [START_REF] Clément | Directional Enlacement Histograms for the Description of Complex Spatial Configurations between Objects[END_REF] with the initial enlacement descriptors. Considering the fact that surrounding evaluations are highly subjective, our goal here is not to argue that an approach is better than another, but to illustrate the proposed Fuzz-DELs can provide interesting point of views regarding this surrounding spatial relation.

To show the potential of our approach on real data, we evaluated the "surrounded by" relation on geographical objects extracted from a satellite image (Fig. 5 (a)). This image1 represents the Bassin d'Arcachon (France) and has been acquired by the Formosat-2 satellite. The image was segmented to produce a 3-class image (Fig. 5 (b)) composed of an island enclosed into the bay (reference object A) and the land coast (target object B). For illustrative purposes, Fig. 5 (c-f) present the Fuzz-DELs of the bay object for different directions θ and widths ω. In particular, (c) shows the overall landscape µ A E that aggregates all directions, and (e) shows the direction where the target object is the least enlaced (i.e., for θ = π 3 ). The related directional necessity and possibility profiles are shown in Fig. 6, and the respective fuzzy surrounding evaluations [N AB S , Π AB S ] are reported in Table 1.

Global enlacement

To pursue our study and to go further the surrounding spatial relation, we consider in a more generic sense the spatial relation "enlaced by", in particular when the reference object has multiple degrees of concavities. Fig. 7 (a) presents a complex spatial configuration involving a spiral and different target objects enclosed into it, from the center of the spiral to its "tail". The spiral is the reference object A, and we consider here its Fuzz-DEL µ A E that aggregates all directions. From this landscape (Fig. 7 (b)), we can observe the decreasing pattern (from white pixels to dark gray pixels) as we shift away from the center of the spiral. To assess this behavior, Fig. 7 (c) presents the intervals [N ( µ A E , µ B ), Π( µ A E , µ B )] measuring the global enlacement for the different target objects inside the spiral. Note that other surrounding approaches cannot take into account the depth within the spiral. For instance, the approach of [START_REF] Vanegas | A fuzzy definition of the spatial relation "surround" -Application to complex shapes[END_REF] provides the same evaluations for the green, blue, yellow and pink objects (i.e., around 0.50), because it does not consider the reference object as a whole, but only looks at the visible concavities from the target object.

Towards Fuzzy Interlacement Landscapes

We also propose some preliminary results on interlacement landscapes. The term interlacement is intended as a mutual enlacement of two objects. If we aggregate all directions, a fuzzy interlacement landscape between two objects A and B can be obtained by: µ AB I = µ A E + µ B E . Fig. 8 shows the fuzzy interlacement landscapes obtained for two illustrative images, which have been respectively segmented into 3 classes. The first landscape is obtained from an image of a zebra whose coat features an alternating stripes pattern. We can observe the high interlacement values concentrated in the center of the animal's coat. The second landscape is obtained from a ASTER satellite image2 covering a large delta river. Notice that the interlacement is mainly located around the ramifications between the river and the mangrove. Such interlacement visualization could be useful for instance for ecological landscape monitoring.

Conclusion

We introduced a generic fuzzy model for the evaluation of complex spatial configurations of binary objects represented in images. In particular, we focused on the enlacement spatial relation, which can be considered as a generalization of the notions of surrounding and imbrication of objects. Based on the directional enlacement model [START_REF] Clément | Directional Enlacement Histograms for the Description of Complex Spatial Configurations between Objects[END_REF], our proposed evaluation approach exploits the concept of fuzzy landscapes to assess the enlacement of objects in the image space from a local point of view. An experimental study carried out on different illustrative examples highlighted the interest of this model to evaluate complex spatial relations. In future works, we plan to further study how to exploit fuzzy interlacement landscapes, in particular with overlapping objects. We also plan to extend the model by integrating a measure of spacing in interlacement configurations, allowing to better take into account the distance between the objects.

Fig. 3 :

 3 Fig. 3: Examples of typical surrounding configurations (gray: reference object A; white: target object B).

Fig. 4 :

 4 Fig. 4: Directional necessity, possibility and mean profiles measuring the surrounding configurations of Fig. 3.

)Fig. 5 :Fig. 6 :

 56 Fig. 5: Applicative example of a complex surrounding configuration. The satellite image represents the Bassin d'Arcachon (France). (b) Object A is gray and object B is white. (c-f) A is outlined in white and B is outlined in red.

  77, 0.89] • (green) [0.58, 0.63] • (blue) [0.53, 0.56] • (yellow) [0.33, 0.34] • (purple) [0.33, 0.35] • (cyan) [0.00, 0.08] (c) Necessity-possibility intervals

Fig. 7 :

 7 Fig. 7: Fuzzy enlacement landscape of a spiral (reference object A) and evaluation for different target objects inside the spiral (represented in different colors).

Fig. 8 :

 8 Fig. 8: Examples of fuzzy interlacement landscapes (mapped into a "heat" color scale) obtained for different images (in (b), white: object A; gray: object B).

Thanks to the CNES agency and the Kalideos project (http://kalideos.cnes.fr/).

U.S./Japan ASTER Science Team, NASA/GSFC/METI/ERSDAC/JAROS.


Adélaïde Lerebours
email: adelaide.lerebours@univ-lr.fr

Samuel Robson

Colin Sharpe

Jim T Smith

Subtle effects of radiation on embryo development of the 3-spined stickleback

Keywords: radiation, fish, embryo

The Chernobyl and Fukushima nuclear power plant (NPP) accidents that occurred in 1986 and 2011 respectively have led to many years of chronic radiation exposure of wildlife. However, controversies remain on the dose threshold above which an impact on animal health occurs. Fish have been highly exposed immediately after both accidents in freshwater systems around Chernobyl and in freshwater and marine systems around Fukushima. The dose levels decreased during the years after the accidents, however, little is known about the effects of environmental low doses of radiation on fish health. The present laboratory study assesses the effects of an environmentally relevant dose range of radiation (0.1, 1 and 10 mGy/day) on early life stages of the 3-spined stickleback, Gasterosteus aculeatus.

The cardiac physiology and developmental features (head width, diameter, area) of high exposed embryos (10 mGy/day) showed no significant change when compared to controls.

Embryos exposed to the medium and high dose were slower to hatch than the controls (between 166 and 195 hours post-fertilization). After 10 days of exposure (at 240 hours post-fertilization), larvae exposed to the high dose displayed comparable growth to controls. High-throughput sequence analysis of transcriptional changes at this time point revealed no significant changes in gene regulation compared to controls regardless of exposure conditions. Our results suggest that exposure of fish embryos to environmental radiation elicits subtle delays in hatching times, but does not impair the overall growth and physiology, nor the gene expression patterns in the recently hatched larvae.

Introduction

Serious nuclear accidents at both the Chernobyl Nuclear Power Plant (NPP) in April 1986 and the Fukushima NPP in March 2011 led to high levels of radiation exposure to wildlife. After the Chernobyl accident, the dose to fish found in the cooling pond was estimated at 10 mGy/day [START_REF] Kryshev | Modelling the Accidental Radioactive Contamination and Assessment of Doses to Biota in the Chernobyl NPP's Cooling Pond[END_REF] and then rapidly declined due to the decrease of short life radionuclides and sedimentation processes [START_REF]Chernobyl -Catastrophe and Consequences[END_REF] .

Three decades after the Chernobyl NPP accident, the main radionuclides of concern are 90 Sr (a β emitter) and 137 Cs (a β and γ emitter) due to their long radioactive half-life (28 and 30 years respectively). Transuranium radioelements are also of concern due to their long radioactive halflife and high energetic alpha particle emission. However, their contribution to the total dose to fish at Chernobyl is very low [START_REF] Lerebours | Impact of Environmental Radiation on the Health and Reproductive Status of Fish from Chernobyl[END_REF] . In a highly contaminated lake called Glubokoye, located near the Chernobyl NPP, the total dose rate to perch (Perca fluviatilis) and roach (Rutilus rutilus) 30 years after the accident was up to 16 and 14 Gy/h respectively (less than 0.4 mGy/day) [START_REF] Lerebours | Impact of Environmental Radiation on the Health and Reproductive Status of Fish from Chernobyl[END_REF] . 32 P is a radioisotope of 14.26 days half-life that emits β particles of high energy (1.7 MeV) whose track length is a few millimetres in water. A β-particle directly ionizes molecules by the removal of an electron, whereas  particles (and X-ray) ionize molecules by generating a series of fast electrons (effectively β particles) after first hitting molecules, therefore, the use of a βemitter is relevant to assess the effect of environmental radiation. In order to assess the effects of ionising radiation exposure on fish embryos under laboratory conditions, [START_REF] Dobin | STAR: Ultrafast Universal RNA-Seq Aligner[END_REF] P was selected due to its short half-life minimising the radioactive waste and its high energy β particles. 32 P is used in research laboratories, medical procedures and industry that may lead to discharge into freshwater systems. The Krasnoyarsk Mining and Chemical Industrial Complex in Russia discharged significant amounts of [START_REF] Dobin | STAR: Ultrafast Universal RNA-Seq Aligner[END_REF] P in the Yenisei river that were found to have accumulated in fish, with [START_REF] Dobin | STAR: Ultrafast Universal RNA-Seq Aligner[END_REF] P activities of 2.2 Bq/L in water and 2900 Bq/kg in fish found at 200 km from the industrial site [START_REF] Vakulovskii | 32 P Accumulation in Fish in the Enisei River and Reconstruction of the Irradiation Dose to the Public[END_REF] . In the Columbia River contaminated by the cooling water from the Handford plutonium reactors, the estimated level of [START_REF] Dobin | STAR: Ultrafast Universal RNA-Seq Aligner[END_REF] P in water between 1950 and 1971 varied from 0.1 to 7.7 Bq/L 5 and the activity of [START_REF] Dobin | STAR: Ultrafast Universal RNA-Seq Aligner[END_REF] P in fish was varied from 0.7 x 10 3 to 22 x 10 3 Bq/kg between 1962 and 1964 [START_REF] Honstead | The Uptake and Retention of 32 P and 65 Zn from the Consumption of Columbia River Fish[END_REF] . Waterborne uptake of [START_REF] Dobin | STAR: Ultrafast Universal RNA-Seq Aligner[END_REF] P was found to be negligible as compared to uptake via the dietary route in fish [START_REF] Winpenny | The Uptake of Radioactive Phosphorus by Brown Trout (Salmo Trutta L.) from Water and Food[END_REF][START_REF] Smith | A Review and Model Assessment of 32P and 33P Uptake to Biota in Freshwater Systems[END_REF] . The 3-spined stickleback (Gasterosteus aculeatus) is a vertebrate model used in laboratory settings to assess the mechanistic effects of pollutants and in field surveys using multi-biomarker approaches [START_REF] Katsiadaki | The Potential of the Three-Spined Stickleback (Gasterosteus Aculeatus L.) as a Combined Biomarker for Oestrogens and Androgens in European Waters[END_REF][START_REF] Sanchez | Biomarker Responses in Wild Three-Spined Stickleback (Gasterosteus Aculeatus L.) as a Useful Tool for Freshwater Biomonitoring: A Multiparametric Approach[END_REF] . The early stages of fish embryonic development are sensitive to ionising radiation [START_REF] Simon | Investigating the Embryo/Larval Toxic and Genotoxic Effects of γ Irradiation on Zebrafish Eggs[END_REF] .

Numerous studies describe the effects of acute exposure to radiation on fish embryos.

However, much less is known about the effects of low doses of radiation in the environmental range of 0.1 to 10 mGy/day. Importantly, results from the literature on the effects of low doses on organism health differ [START_REF] Smith | Field Evidence of Significant Effects of Radiation on Wildlife at Chronic Low Dose Rates Is Weak and Often Misleading. A Comment on "Is Non-Human Species Radiosensitivity in the Lab a Good Indicator of That in the Field? Making the Comparison More Robust" by Beaugelin-Seiller et Al[END_REF] . For instance, whilst some studies did not find evidence of radiation effects on populations of aquatic invertebrates 13 , fish [START_REF] Lerebours | Impact of Environmental Radiation on the Health and Reproductive Status of Fish from Chernobyl[END_REF] or mammals [START_REF] Deryabina | Long-Term Census Data Reveal Abundant Wildlife Populations at Chernobyl[END_REF] at Chernobyl, others found adverse effects of radiation on the abundance of invertebrates [START_REF] Moller | Reduced Abundance of Insects and Spiders Linked to Radiation at Chernobyl 20 Years after the Accident[END_REF] , birds [START_REF] Møller | Species Richness and Abundance of Forest Birds in Relation to Radiation at Chernobyl[END_REF] and mammals [START_REF] Møller | Assessing Effects of Radiation on Abundance of Mammals and Predator-Prey Interactions in Chernobyl Using Tracks in the Snow[END_REF] at Chernobyl and Fukushima. Thus, the dose at which significant damage to wildlife populations occurs remains an open question [START_REF] Smith | Field Evidence of Significant Effects of Radiation on Wildlife at Chronic Low Dose Rates Is Weak and Often Misleading. A Comment on "Is Non-Human Species Radiosensitivity in the Lab a Good Indicator of That in the Field? Making the Comparison More Robust" by Beaugelin-Seiller et Al[END_REF] .

Several studies have previously examined the effects of high doses of radiation (approximately 1000-fold above the environmental range) on the morphology of fish embryos. Exposure to acute dose of radiation induced various morphological abnormalities in embryos of zebrafish (Danio rerio) 18192021 , mangrove killifish (Kryptolebias marmoratus) [START_REF] Rhee | Gamma Irradiation-Induced Oxidative Stress and Developmental Impairment in the Hermaphroditic Fish, Kryptolebias Marmoratus Embryo[END_REF] and medaka (Oryzias latipes) [START_REF] Hyodo-Taguchi | Vertebral Malformations in Medaka (Teleost Fish) after Exposure to Tritiated Water in the Embryonic Stage[END_REF] .

Numerous authors studied the effects of exposure to high doses of radiation on the hatching success of embryos but the results differed according to the type and nature of exposure. No difference in the percentage of embryos that hatched was observed in medaka embryos exposed to 35.42 mGy/h of tritiated water [START_REF] Hyodo-Taguchi | Vertebral Malformations in Medaka (Teleost Fish) after Exposure to Tritiated Water in the Embryonic Stage[END_REF] and in zebrafish embryos exposed to 0.01 and 0.05 Gy of γ radiation [START_REF] Hu | Developmental Toxicity and Oxidative Stress Induced by Gamma Irradiation in Zebrafish Embryos[END_REF] . However, other studies found significant effects on the hatching success. The percentage of zebrafish embryos that hatched decreased significantly after exposure to a total dose range of 0.1 -10 Gy [START_REF] Hu | Developmental Toxicity and Oxidative Stress Induced by Gamma Irradiation in Zebrafish Embryos[END_REF][START_REF] Kumar | Effects of Gamma Radiation on the Early Developmental Stages of Zebrafish (Danio Rerio)[END_REF] , and to a dose rate range of 0.3 -2 Gy/day of γ radiation [START_REF] Pereira | Genotoxicity of Acute and Chronic Gamma-Irradiation on Zebrafish Cells and Consequences for Embryo Development[END_REF] . The percentage of mangrove killifish embryos that hatched decreased significantly after exposure to a total dose range of 2.5 -10 Gy [START_REF] Rhee | Gamma Irradiation-Induced Oxidative Stress and Developmental Impairment in the Hermaphroditic Fish, Kryptolebias Marmoratus Embryo[END_REF] . The hatching time is significantly delayed as compared to controls in zebrafish embryos exposed to a dose range of 0.1 -10 Gy 24 and a dose rate range of 0.3 -2 Gy/day of γ radiation [START_REF] Pereira | Genotoxicity of Acute and Chronic Gamma-Irradiation on Zebrafish Cells and Consequences for Embryo Development[END_REF] . However, whilst many studies have examined the effects of high doses of radiation on hatching, fewer studies have examined hatching processes after exposure to lower doses, and no clear patterns of such dose effects has been observed. An acceleration of hatching was observed in zebrafish embryos exposed to a γ radiation dose of 10 and 1000 mGy/day, but no change was recorded after exposure to 1 and 100 mGy/day [START_REF] Pereira | Genotoxicity of Acute and Chronic Gamma-Irradiation on Zebrafish Cells and Consequences for Embryo Development[END_REF] . Hatching process appears to depend on the embryonic stage of exposure with some authors finding an acceleration of hatching in embryos exposed from 3 hpf (blastula stage) but not from 24 hpf (segmentation stage) to 1-1000 mGy/day of radiation [START_REF] Simon | Investigating the Embryo/Larval Toxic and Genotoxic Effects of γ Irradiation on Zebrafish Eggs[END_REF] .

Several studies investigated the effects of high doses of radiation on the cardiac physiology of fish embryos. Studies reported no effect [START_REF] Zhao | Developmental Toxicity and Apoptosis in Zebrafish Embryos Induced by Low-Dose γ-Ray Irradiation[END_REF] or a decreased heart rate [START_REF] Si | Toxic Effects of 56Fe Ion Radiation on the Zebrafish (Danio Rerio) Embryonic Development[END_REF] in zebrafish embryos. To our knowledge, no studies in the literature have yet described the heart physiology of embryos exposed to environmentally relevant doses of radiation.

Several recent studies explored the effects of short-term exposure to radiation (from a few seconds to 96 hrs) on the transcriptional response of embryos. Gene expression changes were described in zebrafish embryos exposed to a total dose of 10 mGy to 100 mGy during 11 to 110 secs respectively (dose rate: 79.2 Gy/day), and the number of the differentially expressed genes was positively correlated to the dose [START_REF] Zhao | Developmental Toxicity and Apoptosis in Zebrafish Embryos Induced by Low-Dose γ-Ray Irradiation[END_REF] . Transcriptional response of genes involved in apoptosis [START_REF] Si | Toxic Effects of 56Fe Ion Radiation on the Zebrafish (Danio Rerio) Embryonic Development[END_REF] and DNA damage repair mechanisms [START_REF] Si | Toxic Effects of 56Fe Ion Radiation on the Zebrafish (Danio Rerio) Embryonic Development[END_REF][START_REF] Arcanjo | Tritiated Water Exposure Disrupts Myofibril Structure and Induces Mis-Regulation of Eye Opacity and DNA Repair Genes in Zebrafish Early Life Stages[END_REF] were changed in zebrafish embryos exposed to 0.5 -4 Gy of 56 Fe ion irradiation (Si et al. 2017) [START_REF] Si | Toxic Effects of 56Fe Ion Radiation on the Zebrafish (Danio Rerio) Embryonic Development[END_REF] or 9.6 and 96 mGy/day of  radiation [START_REF] Arcanjo | Tritiated Water Exposure Disrupts Myofibril Structure and Induces Mis-Regulation of Eye Opacity and DNA Repair Genes in Zebrafish Early Life Stages[END_REF] .

The present study is one of the few to assess of the effects of very low doses of radiation on fish embryo development under laboratory conditions, combining both high throughput molecular and biometric analyses. The aim was to investigate whether exposure to environmental low doses of radiation induces developmental, physiological and transcriptional changes in stickleback embryos.

Methods

Fish maintenance

Adult sticklebacks were kept in artificial reproduction conditions in order to generate the embryos for in vitro fertilization. The artificial water composition and experimental conditions were selected according to the OECD guideline for the testing of chemicals (CaCl 2 : 294, MgSO 4 : 123, NaHCO 3 : 65, KCl: 6 mg/L, pH = 7.5, T°C = 19°C, photoperiod: 16h light/8h dark) [START_REF] Lehninger | Principles of Biochemistry[END_REF] . Four distinct couples were used to generate the embryos. The fertilization procedure was performed according to the protocol described in the OECD guideline for the testing of chemicals (test number 236). In total, 54 embryos were used for monitoring growth and physiology (27 controls and 27 exposed to the high dose), 108 for recording the hatching success (27 for each of the four exposure conditions), 104 for next generation sequencing (NGS) analyses (Table S3) and 36 to check [START_REF] Dobin | STAR: Ultrafast Universal RNA-Seq Aligner[END_REF] P uptake in the chorion, prolarvae and larvae (Table S2).

Three hours after fertilization, each embryo was placed in an individual glass tube and waterborne exposed to 3 mL of a radioactive solution of 0.1, 1 and 10 mGy/day (or 4, 40 and 400 Gy/h) using a solution of adenosine triphosphate labelled on the gamma phosphate group with 32 P (PerkinElmer). The final concentration of ATP in control, low and medium experimental tubes was adjusted to 1.1 x 10 -5 μM by addition of stable ATP. This ATP concentration is negligible as compared to the concentration found in a typical cell of 5 mM 27 . The doses encompass the chronic low (L) (0.1 mGy/day) and medium (M) (1 mGy/day) doses encountered in the environment at Chernobyl 30 years after the accident, and the initial high dose (H) to fish after the accident (10 mGy/day). These doses span the Environmental Agency (EA) guidance level of 40 Gy/h (0.96 mGy/day) described in the radiological impacts on non-human species report of the EA in 2011 [START_REF]Radiological impacts on non-human species. UK EPRTM nuclear power plant[END_REF] . Control embryos were kept in clean artificial water. 2.5 mL of the water was renewed every 3 days. The embryos were exposed for 10 days and euthanized according to schedule 1 of the Home Office Licence (ASPA, 1986) [START_REF]Guidance on the Operation of the Animals (Scientific Procedures) Act[END_REF] using tricaine methanesulfonate (Sigma).

Dose calculation and monitoring

Dose at the centre of the hemisphere was calculated from data in Berger (1971) [START_REF] Berger | Distribution of Absorbed Doses around Point Sources of Electrons and Beta Particles in Water and Other Media[END_REF] (Figure S1). Activity of 32 P was measured using a HIDEX 300SL liquid scintillation counter and associated MikroWin 2000 software (Version 4.43).

Developmental and physiological measurements

The morphological parameters were measured using a Zeiss axiozoom microscope and the Zen Pro software. The physiological parameter was measured using an optical microscope. The growth of embryos was recorded at 4 dpf (days post-fertilization) by measuring the diameter (mm), area (mm 2 ) and eye distance (mm). The hatching rate was calculated as the proportion of fish that hatched to the total number of fish from the same condition for each observation time.

The cardiac physiology was assessed at 6 dpf by counting the heart beat rate (beats/min). The growth of larvae was recorded at 10 dpf by measuring the length (mm) and head width (mm) of the larvae through the glass tubes.

Next generation sequencing (NGS)

Differential expression analysis was conducted using NGS. For each of the 4 conditions (control, low dose, medium dose and high dose), 3 biological replicates of pools of 4 to 10 embryos aged of 10 days were used for NGS analyses (Table S3). Total RNAs were extracted using the High Pure RNA Tissue kit (Roche Diagnostics Ltd, West Sussex, U.K.) according to the manufacturer's instructions. RNA quality and integrity were evaluated using a bioanalyzer (Agilent, Santa Clara, USA). RNA integrity numbers ranged from 7.4 to 9.5 and showed low RNA degradation rates. NGS libraries for each pool were generated using the Illumina TruSeq mRNA library kit following the manufacturer's instructions. Libraries were sequenced using the Illumina HiSeq 2500 analyser, generating 125 base, paired-end sequences from libraries yielding an average of 33.4  5.2 M paired reads per sample (Table S4). Quality control of raw fastq reads was conducted using fastQC (bioinformatics.babraham.ac.uk/projects/fastqc/). Reads were trimmed using the Trim Galore script to remove adapter sequences and low quality sequence tails (bioinformatics.babraham.ac.uk/projects/trim_galore/). Trimmed reads were mapped against the BROAD S1 Gasterosteus aculeatus 3-spined stickleback genome from Ensembl 30 using the STAR universal RNA seq aligner [START_REF] Kersey | Ensembl Genomes 2018: An Integrated Omics Infrastructure for Non-Vertebrate Species[END_REF] with parameters '--outSAMmultNmax 300'. Reads that mapped uniquely to the genome in a proper pair with mapping quality score greater that 20 were used in downstream analyses.

Differential expression analyses

Differential expression analyses were conducted using the DESeq2 package [START_REF] Love | Moderated Estimation of Fold Change and Dispersion for RNA-Seq Data with DESeq2[END_REF] in R. Gene models were taken from Ensembl version 82 [START_REF] Kersey | Ensembl Genomes 2018: An Integrated Omics Infrastructure for Non-Vertebrate Species[END_REF] , and read counts over unique genes were quantified using the "summarizeOverlaps()" function in the GenomicAlignments package [START_REF] Lawrence | Software for Computing and Annotating Genomic Ranges[END_REF] using mode "Union". Raw read counts were normalised using the regularised log transformation in DEseq2 for visualisation (Figure S2). P values were adjusted for multiple testing by using the Benjamini and Hochberg correction [START_REF] Benjamini | Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing[END_REF] . To account for potential confounding effects of lineage due to a systematic difference in the pooling for replicate 3 compared to replicates 1 and 2 (Table S3), lineage was included as a covariate in the analysis. Significant differentially expressed genes were identified based on a fold-change of 2-fold or greater (up-or down-regulated) and an adjusted p-value less than 0.05. To avoid over-representing differential expression in lowabundance genes, significant genes were further filtered to remove those whose normalised expression was less than 1 for both the exposed and control groups. Gene ontology analysis was conducted using the clusterProfiler package [START_REF] Yu | ClusterProfiler: An R Package for Comparing Biological Themes Among Gene Clusters[END_REF] .

Statistical analyses

Statistical analyses were performed using R version 3.1.2. After satisfying the assumptions of the normal distribution of the residuals, linear models were used to assess the potential differences. If the normality of the residuals wasn't respected a Kruskal-Wallis rank test was applied. A Fisher exact test was applied to assess any difference between hatching success at different times post-fertilization. When significant, post-hoc tests were performed and a Bonferroni correction of the α error was applied.

Results

Dose monitoring

The mean activity of 32 P solutions measured during the 10 days exposure experiment were 0.7 ± 0.2, 27 ± 3, 253 ± 24 and 2588 ± 199 Bq/mL (n = 12) (Table S1) and in accordance with the targeted activity of 2500, 250, 25 and 0 Bq/mL respectively, in each glass tube. After 3 days of exposure, the activities measured in the chorion were 1 ± 0 Bq for controls and low exposure conditions, and 3 ± 2 and 42 ± 11 Bq for the medium and high exposure conditions (mean ± SD, n = 3). The activities measured in dechorionated embryos were 1 ± 0 Bq for control, low and medium exposure conditions and 3 ± 2 Bq for the high exposure condition (mean ± SD, n = 3).

After 9 days of exposure, the activities measured in the larvae were 1 ± 0 for control, low and medium exposure conditions and 2 ± 0 Bq for the high exposure condition (mean ± SD, n = 3) (Table S2).

Developmental and physiological parameters

Radiation exposure to 10 mGy/day did not significantly affect the growth of embryos. After 4 days, exposed embryos were equivalent in size. The diameter, surface and head width of exposed embryos were 1.46 ± 0.01 mm, 1.68 ± 0.02 mm 2 and 0.85 ± 0.03 mm respectively. These measures did not significantly differ from controls (diameter: 1.46 ± 0.01 mm, p = 0.65, area:

1.67 ± 0.02 mm 2 , p = 0.64 and eye distance: 0.85 ± 0.03 mm, p = 0.17) (Table 1). After 6 days, the cardiac physiology of exposed embryos was not disturbed by exposure to radiation. The mean heart beats rate of exposed embryos were equal to 163.2 ± 12 beats/min and did not significantly differ from controls (150.0 ± 3.1 beats/min, p = 0.22) (Table 1). After 10 days, the development between exposed and control larvae remained similar. The length of exposed larvae was 5.98 ± 0.06 mm and their head width 0.82 ± 0.01 mm. These values did not significantly differ from controls (length: 5.99 ± 0.05 mm, p = 0.88 and head width: 0. 81 ± 0.01 mm, p = 0.48) (Table 1).

During the hatching process, embryos exposed to 1 (M) and 10 (H) mGy/day were slower to hatch at 170 hpf (hours post-fertilization), with 22% and 24% of the embryos respectively displaying a delay in hatching (p = 0.014 and p = 0.010 respectively) (Figure 1). At 174 hpf, the embryos exposed to the H condition reached 90% of hatching (HT 90 ) [169-176], 6 hours later than the controls that hatched at 168 hpf [164-169] (based on 95% confidence interval overlap) (Figure 2). There was no delay observed for the embryos exposed to L (HT 90 : 171 hpf [168-173]) and M (HT 90 : 172 hpf [166-175]) conditions as compared to the controls (Figure 2). Eventually, at 195 hpf, no significant difference in hatching success was observed between conditions (p = 0.058) (Figure 1) and the hatching percentage reached 100% [88-100] for the control embryos and 92%; 96% and 93% for the embryos exposed to 0.1 (L), 1 (M) and 10 (H) mGy/day conditions respectively (Figure 1).

Differential expression analysis

Analysis of the NGS data quality identified these data as showing excellent base calling qualities and post-filtering mapping rates of approximately 90% were seen throughout (Table S4). Following gene abundance identification, principal component analysis identified little difference between the dosage treatments in these data (Figure 3). A batch effect, resulting from the parentage of individuals pooled in the different replicates was found (Table S3). This batch effect was incorporated into the model for differential expression analysis.

Differential expression analysis was performed to identify genes whose expression was significantly deregulated following radiation exposure by comparing each of the three dosed treatments against a control treatment as described. No significant change in gene expression was observed, with only a single gene showing significant differential expression in the low dosage after filtering (Figure S2).

Data availability

The RNA sequencing data can be obtained from ArrayExpress (https://www.ebi.ac.uk/arrayexpress/) with the accession number E-MTAB-7872.

Discussion

In the present study, embryo mortality was below 12% in each condition, in the range of what is considered as normal in studies using zebrafish embryos. In the literature, zebrafish embryos survival was reduced after exposures to higher doses such as 100 mGy [START_REF] Zhao | Developmental Toxicity and Apoptosis in Zebrafish Embryos Induced by Low-Dose γ-Ray Irradiation[END_REF] and after 2 and 4 Gy of exposure to 56 Fe 20 .

During the hatching process, embryos exposed to 1 mGy/day (M) and 10 mGy/day (H) conditions displayed reduced hatching successes, by 22 and 24% respectively. No change was observed in embryos exposed to the lowest dose 0.1 mGy/day (L). At the end of the hatching process, no significant difference on the hatching success of embryos was noticed between controls and exposure conditions with percentages reaching 92% (L), 96% (M) and 93% (H).

Exposure to different dose and nature of radiation can accelerate hatching. For instance, zebrafish embryos exposed to 9.6 mGy/h for 65h [START_REF] Yu | ClusterProfiler: An R Package for Comparing Biological Themes Among Gene Clusters[END_REF] , 0.3 to 2 Gy/day 18 , 1-1000 mGy/day [START_REF] Simon | Investigating the Embryo/Larval Toxic and Genotoxic Effects of γ Irradiation on Zebrafish Eggs[END_REF] and to an X-ray dose of 25 mGy 37 hatched earlier than control embryos. The embryonic stage at which radiation exposure occurs, appears to have consequences on the hatching sensitivity of embryos.

For instance, mangrove killifish embryos displayed a higher sensitivity when exposed at an early stage to 2.5, 5, 7.5, and 10 Gy of γ radiation. In addition, the hatching success was significantly decreased in embryos that were exposed early (10.5 hpf) for all doses [START_REF] Rhee | Gamma Irradiation-Induced Oxidative Stress and Developmental Impairment in the Hermaphroditic Fish, Kryptolebias Marmoratus Embryo[END_REF] .

Other experiments showed that exposure to radiation induced a delay in hatching. Exposure to an X-ray dose above 25 mGy delayed hatching zebrafish embryos 38 During hatching, biochemical and behavioural process are synchronised to destroy the chorion 41 . Proteolytic enzymes and embryos movement contribute to the chorion disruption to allow hatching. Hatching may be delayed because of potential changes induced by radiation to those enzymes, as evidenced by studies on the effects of copper on rainbow trout eggs 41 . The delay could also reflect a protective response to stress where the chorion would protect the embryos from external hazard. A similar delay has been reported in zebrafish embryos exposed to metals 42,[START_REF] Fraysse | Development of a Zebrafish 4-Day Embryo-Larval Bioassay to Assess Toxicity of Chemicals[END_REF] . The present data suggest that a delay in hatching is a good indicator of exposure to environmental low dose of radiation in laboratory settings, which is in agreement with the study by Bourrachot et al (2008) 39 that uses waterborne 233 U. A developmental delay of maturing fish eggs has also been observed in organism exposed in their natural environment. A delay of oocyte growth has been evidenced in perch exposed to a total dose rate of 10-16 µGy/h (0.2-0.4 mGy/day) in exposed lakes at Chernobyl, 30 years after the accident, and was correlated to the radiation dose [START_REF] Lerebours | Impact of Environmental Radiation on the Health and Reproductive Status of Fish from Chernobyl[END_REF] . The precise mechanism by which radiation induces this delay is unknown. At the molecular level, a recent study found that transcriptional response of genes involved in the circadian clock was modulated in zebrafish larvae (at 96 hpf) exposed to 0.4 and 4 mGy/h of tritiated water [START_REF] Arcanjo | Tritiated Water Exposure Disrupts Myofibril Structure and Induces Mis-Regulation of Eye Opacity and DNA Repair Genes in Zebrafish Early Life Stages[END_REF] .

In the present study, radiation exposure to 10 mGy/day did not significantly affect the growth of embryos (no difference of diameter, area and eye distance at 4 dpf) and larvae (no difference of head width and length at 10 dpf) respectively. Similarly, no deformity (short tail, spinal curve, absence of pigment, failed hatching) and no length difference as compared to controls was observed in embryos exposed to 9.6 mGy/h [START_REF] Hurem | The Effects of Copper on the Morphological and Functional Development of Zebrafish Embryos[END_REF] . A recent environmental study found that the length and Fulton condition index of perch and roach were similar between lakes, in addition, no malformation of gonads and oocytes was recorded revealing that fish were in good health in general [START_REF] Lerebours | Impact of Environmental Radiation on the Health and Reproductive Status of Fish from Chernobyl[END_REF] . Other studies found a tail detachment in zebrafish exposed to 20 µg/L of 233 U but not in embryos exposed to 100 µg/L of 233 U and a decrease of the body length for both exposures 39 . A reduction of body length was also found in zebrafish embryos exposed to high dose of radiation (1 -10 Gy) 40,[START_REF] Kumar | Effects of Gamma Radiation on the Early Developmental Stages of Zebrafish (Danio Rerio)[END_REF] . Exposure to a γ radiation dose of 0.3 to 2 Gy/day induced morphological abnormalities (tail atrophia and trunk axis malformations) in zebrafish embryos [START_REF] Pereira | Genotoxicity of Acute and Chronic Gamma-Irradiation on Zebrafish Cells and Consequences for Embryo Development[END_REF] . Using an acute dose of radiation, deformities (including spinal curvature, pericardial cyst enlargement and thoracic cavity variation) were noticed from 0.1 Gy, and hatching was reduced from 0.05 Gy [START_REF] Zhao | Developmental Toxicity and Apoptosis in Zebrafish Embryos Induced by Low-Dose γ-Ray Irradiation[END_REF] .

Malformations such as tail deformity, pericardial edema and spinal curve were found to increase in zebrafish embryos exposed to 2 and 4 Gy of 56 Fe ion irradiation [START_REF] Si | Toxic Effects of 56Fe Ion Radiation on the Zebrafish (Danio Rerio) Embryonic Development[END_REF] and 0.01 to 1 Gy of γ radiation [START_REF] Hu | Developmental Toxicity and Oxidative Stress Induced by Gamma Irradiation in Zebrafish Embryos[END_REF] . Pericardial and yolk sac edema, curved notochord and thin caudal fin were observed in the hermaphroditic fish embryos exposed to a total dose range of 2.5 -10 Gy of γ radiation [START_REF] Rhee | Gamma Irradiation-Induced Oxidative Stress and Developmental Impairment in the Hermaphroditic Fish, Kryptolebias Marmoratus Embryo[END_REF] .

Vertebral malformations were reported in medaka embryos exposed to 35.42 mGy/h of tritiated water [START_REF] Hyodo-Taguchi | Vertebral Malformations in Medaka (Teleost Fish) after Exposure to Tritiated Water in the Embryonic Stage[END_REF] . Only a few studies have looked at the head development. Freeman et al. ( 2014) 40 found that exposure to high dose of radiation (10 Gy) reduced eye diameter and head length. However, this dose is higher than the environmental dose range used in the present study.

The physiology of 6 dpf embryos exposed to 10 mGy/day was not changed as compared to controls based on the heart beats count. This is in agreement with a few previous studies that did not observed any change in zebrafish embryos exposed to a total dose of 10 to 100 mGy for 10.9 s to 109 s respectively (dose rate of 79.2 Gy/day) [START_REF] Zhao | Developmental Toxicity and Apoptosis in Zebrafish Embryos Induced by Low-Dose γ-Ray Irradiation[END_REF] or after exposure to 2 Gy of 56 Fe ion irradiation (dose rate: 0.5 Gy/min) [START_REF] Si | Toxic Effects of 56Fe Ion Radiation on the Zebrafish (Danio Rerio) Embryonic Development[END_REF] . The present work represents one of the rare studies that have assessed this physiological criterion at environmental low doses.

Interestingly, no significant transcriptional changes were observed in 10 dpf larvae after exposure to all dose levels. This may be a result of genes involved in protective mechanisms already being activated before the larval stage to compensate for the negative effects of radiation exposure, but returning to normal levels in later stages of development. In a recent transcriptomic study assessing the effects of tritiated water on zebrafish embryos, it was suggested that the onset of an early protective mechanism against oxidative stress may not be observed at the larval stage of development (96 hpf) [START_REF] Arcanjo | Tritiated Water Exposure Disrupts Myofibril Structure and Induces Mis-Regulation of Eye Opacity and DNA Repair Genes in Zebrafish Early Life Stages[END_REF] . Indeed, antioxidant defence mechanisms that are activated in embryos may lead to a decrease in lipid peroxidation [START_REF] Hurem | The Effects of Copper on the Morphological and Functional Development of Zebrafish Embryos[END_REF] and a reduction in DNA damage [START_REF] Gagnaire | External Gamma Irradiation-Induced Effects in Early-Life Stages of Zebrafish, Danio Rerio[END_REF] .

Another hypothesis is that the environmental doses used in the present study may be too low for eliciting a differential gene expression change. The basal gene transcriptional levels may be sufficient for the larvae to account for the effects of radiation. Results from the literature indicate a change in gene expression for higher exposure. Kumar et al (2017) [START_REF] Kumar | Effects of Gamma Radiation on the Early Developmental Stages of Zebrafish (Danio Rerio)[END_REF] found that exposure to 5

Gy of radiation induced transcriptional changes of sox genes involved in development. The expression of genes seemed dependent on the embryonic stage of development and the dose level. Transcriptional changes of genes involved in antioxidant defence were found in early stage zebrafish embryos exposed to low doses, but not to high doses. These gene transcriptional levels were unchanged at a later stage for both exposure conditions [START_REF] Arcanjo | Tritiated Water Exposure Disrupts Myofibril Structure and Induces Mis-Regulation of Eye Opacity and DNA Repair Genes in Zebrafish Early Life Stages[END_REF] . The environmental doses used in the present study and currently existing at Chernobyl may be too low to induce a significant oxidative stress [START_REF] Fuller | Does Chernobyl-Derived Radiation Impact the Developmental Stability of Asellus Aquaticus 30 Years On?[END_REF] and subsequent DNA damage. No genotoxic effect was evidenced as measured by micronuclei in erythrocytes of perch, roach 3 and catfish 46 exposed to environmental radiation at Chernobyl.

These data suggest that low levels of radiation exposure have a negligible effect on gene expression profiles and embryo growth and physiology but result in subtle delays to hatching times that does not affect the final numbers of fish that hatched. The current levels of environmental radiation at NPP sites are therefore unlikely to negatively impact embryonic development of future offspring. These results support the findings from a previous large-scale environmental study that found a delay in the maturation of perch eggs, and that fish were otherwise in good general health [START_REF] Lerebours | Impact of Environmental Radiation on the Health and Reproductive Status of Fish from Chernobyl[END_REF] . Moreover, these results corroborate other environmental studies led at Chernobyl on aquatic macro-invertebrate development and physiology [START_REF] Fuller | Does Chernobyl-Derived Radiation Impact the Developmental Stability of Asellus Aquaticus 30 Years On?[END_REF][START_REF] Fuller | Reproduction in the Freshwater Crustacean Asellus Aquaticus along a Gradient of Radionuclide Contamination at Chernobyl[END_REF] . Finally, this laboratory study is important as it provides environmentally relevant data to refine the current thresholds for which an effect is observed. 10 mGy/day or 2500 Bq/mL see Figure S1 for the dose calculation) renewed every 3 days (mean ± SD, n = 3). Measurements were performed using a HIDEX liquid scintillation counter.

Day

Figure 1 .

 1 Figure 1. Hatching success of embryos exposed to control, Low (0.1 mGy/day), Medium (1

Figure 2 .

 2 Figure 2. Time necessary to reach 90% of hatching for embryos exposed to control, Low (0.1

Figure 3 .

 3 Figure 3. Principal component analysis showing the distribution of the 12 samples according to

Figure 1

 1 Figure 1.

Figure S2 .Figure S3 .

 S2S3 Figure S2. MvA plots for the DeSeq2-based differential expression analysis for a) low exposure,

Table 1 .

 1 Bourrachot, S.; Simon, O.; Gilbin, R. The Effects of Waterborne Uranium on the Hatching Success, Development, and Survival of Early Life Stages of Zebrafish (Danio Rerio). Morphological and physiological parameters recorded on 4 and 6 dpf embryos and 10 dpf larvae (mean ± SEM, n =27).

	Induces Reprotoxic Effects Accompanied by Genomic Instability in Zebrafish (Danio
	Rerio) Embryos. Environmental Research 2017, 159, 564-578.
	(38) Miyachi, Y.; Kanao, T.; Okamoto, T. Marked Depression of Time Interval between
	Fertilization Period and Hatching Period Following Exposure to Low-Dose X-Rays in
	Zebrafish. Environmental Research 2003, 93 (2), 216-219.
	(39) Aquatic Toxicology 2008, 90 (1), 29-36.
	(40) Freeman, J. L.; Weber, G. J.; Peterson, S. M.; Nie, L. H. Embryonic Ionizing Radiation
	Exposure Results in Expression Alterations of Genes Associated with Cardiovascular and
	Neurological Development, Function, and Disease and Modified Cardiovascular Function
	in Zebrafish. Frontiers in Genetics 2014, 5.
	(41) Westernhagen, H.; Dethlefsen, V.; Cameron, P.; Berg, J.; Fürstenberg, G. Developmental
	Defects in Pelagic Fish Embryos from the Western Baltic. Helgoländer
	Meeresuntersuchungen 1988, 42 (1), 13-36.

Table 1 .

 1

	Morphological and	Exposure condition
	physiological parameters	Control	10 mGy/day
	Embryos 4 dpf
	Diameter (mm)	1.46 ± 0.01	1.46 ± 0.01
	Area (mm 2 )	1.67 ± 0.02	1.68 ± 0.02
	Eye distance (mm)	0.91 ± 0.02	0.85 ± 0.03
	Embryos 6 dpf
	Heart beats (beats/min)	150.0 ± 3.1	163.2 ± 12
	Larvae 10 dpf
	Head width (mm)	0.81 ± 0.01	0.82 ± 0.01
	Length (mm)	5.99 ± 0.05	5.98 ± 0.06

Table S2 .

 S2 Table showing the[START_REF] Dobin | STAR: Ultrafast Universal RNA-Seq Aligner[END_REF] P activity measured in the chorion and the dechorionated embryos after 3 days of exposure to control, medium and high dose (mean ± SD, n = 3) and in ("unique") or multiple distinct loci ("multihits"). or multihits, the total number of hits and the number of distinct reads are shown in brackets. Reads were filtered to keep only those mapping uniquely in a proper pair with quality greater than 20 for downstream analyses.

		Activity (Bq/mL)
	0 SampleName	Control 0.6 ± 0.1 22.6 ± 0.5 229.0 ± 6.8 Low Medium NumReads Trimmed Unique	High 2714.3 ± 155.3 Multihits	Filtered	Mapped
	3	0.8 ± 0.1 28.3 ± 1.2 251.5 ± 5.4	2533.9 ± 31.3
	6	0.6 ± 0.1 31.4 ± 1.2 290.0 ± 3.2	2781.9 ± 14.7
	9	0.8 ± 0.4 26.4 ± 0.1 240.0 ± 1.4	2320.5 ± 19.8

Acknowledgments

Authors are grateful to Neil Fuller and Graham Malyon for their help with fish maintenance. This work was completed as part of the TREE (Transfer-Exposure-Effects) consortium under the RATE programme (Radioactivity and the Environment), funded by the Environment Agency and Radioactive Waste Management Ltd (NERC grant NE/L000393/1).

Supplemental Information.

Table S1. Table showing the 32 P activity measured for each exposure solutions (corresponding to the control, low: 0.1 mGy/day or 25 Bq/mL; medium: 1 mGy/day or 250 Bq/mL and high dose: the larvae after 9 days of exposure to control, medium and high dose (mean ± SD, n = 3).

Measurements were performed using a HIDEX liquid scintillation counter.

Tissue

Activity (Bq)


Local Enlacement Histograms for Historical Drop Caps Style Recognition

This article focuses on the specific issue of drop caps image recognition in the context of cultural heritage preservation. Due to their heterogeneity and their weakly structured properties, these historical images represent challenging data. An important aspect in the recognition process of drop caps is their background styles, which can be considered as discriminative features to identify both the printer and the period. Most existing methods for style recognition are based on low-level features such as color or texture properties. In this article, we present a novel framework for the recognition of drop caps style based on features of higher levels. We propose to capture the spatial structure carried by these images using relative position descriptors modeling the enlacement between local cells of pixel layers obtained from a document segmentation step. Such descriptors are then exploited in an efficient bag-of-features learning procedure. Experimental results obtained on a dataset of historical drop caps images highlight the interest of this approach, and in particular the benefit of considering spatial information.

I. INTRODUCTION

The cultural heritage of Europe is a unique public good that represents our collective memory, and constitutes a solid basis for the development of the industries relying on digital contents. In this paper, we deal with the problem of cultural heritage preservation, focusing on collections of heterogeneous and weakly structured documents. Such complex data raise both the information research issue and the navigation problem among these corpus. More specifically, this work focuses on historical images of ornamental letters, called drop caps or lettrines. As illustrated on the first row of Fig. 1, drop caps images are usually made up of the following main characteristics: the letter, the color of the letter and the background patterns around the letter. In general, such background patterns can be categorized into different classes, which are illustrated on the second row of Fig. 1: hatchings, dotted, and decorative patterns (with either black or white letters). An important step in the indexing process of drop caps consists in annotating these different background styles, as they are used by historians to retrieve similar looking drop caps, to identify the printer and the period.

In this article, we propose a new method to describe and classify historical drop caps images according to their background styles (independently from the letter). To this end, the rest of this article is organized as follows. In section II, we give an overview of related works and of our contributions. The first step of our approach consists in a segmentation strategy based on Zipf law to decompose drop caps into three layers of information in the images. This procedure is presented in section III. Then, we introduce in section IV how to describe such layers using local enlacement histograms and following a bags-of-features strategy. Experimental results attesting of the performance of this approach will be found in section V. Conclusion and perspectives are given in section VI.

II. RELATED WORK

The automated analysis of graphical drop caps is a promising step towards the digitalization of historical books and manuscripts. Indeed, such information can be used to date historically, to authenticate, and to characterize books by identifying the differences between analyzed historical drop caps. In order to enrich drop caps semantically, by adding meta-data or semantic annotations, many works proposed to describe, to classify and to compare them using some statistical or structural signatures. This context therefore encompasses the ongoing development of content-based image retrieval (CBIR) systems for historical drop caps [START_REF] Jouili | NAVIDOMASS: structural-based approaches towards handling historical documents[END_REF]. The development of such image retrieval systems is complex, since these historical drop caps present a large variety and wide range of models and styles, and because the images contain a lot of information (e.g. texture, letter, and decorated background).

In order to cope with the complexity of these images, the authors of [START_REF] Naegel | Combining Shape Descriptors and Component-tree for Recognition of Ancient Graphical Drop Caps[END_REF], [START_REF] Naegel | A Document binarization method based on connected operators[END_REF] proposed an original binarization method based on connected operators which enable to extract relevant document objects by means of the component-tree structure. This work allowed for an efficient shape-based classification of the image connected components, focusing in particular on detecting and recognizing the letters. However, the main drawback of this approach is the necessity to choose the color of foreground or background, while drop caps could have either a white or black letter on a white or black background.

To deal with this limitation, Coustaty et al. [START_REF] Coustaty | Towards historical document indexing: Extraction of drop cap letters[END_REF] proposed a method for the decomposition of drop cap letters by extracting the information contained in the images into several layers (i.e. segmenting the letter and the elements from its background).

Michaël Clément ; Mickaël Coustaty ; Camille Kurtz ; Laurent Wendling

The Meyer decomposition allows used to filter out the noise, to extract the spatial frequencies of drop cap images, and to segment them into separate layers (shape, texture, and noise layers). Then, the use of Zipf law on the most frequent gray level patterns of the shape layer ensured the detection of large homogeneous regions, which often contain the letter.

In parallel of this document analysis context, bags-offeatures strategies have attracted numerous research attentions in the computer vision community for object recognition and image classification tasks [START_REF] Everingham | The Pascal Visual Object Classes (VOC) Challenge[END_REF]. The approach was notably adapted to historical drop caps images, to recognize styles of strokes [START_REF] Nguyen | Bags of Strokes Based Approach for Classification and Indexing of Drop Caps[END_REF] as well as letters and background styles in [START_REF] Coustaty | Graph matching versus bag of graph: A comparative study for lettrines recognition[END_REF], [START_REF] Mehri | A bottom-up method using texture features and a graph-based representation for lettrine recognition and classification[END_REF], in combination with graph-based representations.

In the field of symbol recognition, the works of [START_REF] Santosh | Integrating vocabulary clustering with spatial relations for symbol recognition[END_REF], [START_REF] Santosh | BoR: Bag-of-Relations for Symbol Retrieval[END_REF] introduced bags-of-relations (BoR), an original way to produce vocabularies of spatial relations. The approach was applied on a well-controlled set of visual primitives specific to the application domain (e.g., circles, corners or extremities of symbols). A generalization of the bags-of-relations approach was proposed in [START_REF] Clément | Bags of Spatial Relations and Shapes Features for Structural Object Description[END_REF] using Force Histograms [START_REF] Matsakis | A new way to represent the relative position between areal objects[END_REF]. These works illustrated the interest of considering spatial relations descriptors into the bags-of-features framework. A new relative position descriptor was recently proposed in [START_REF] Clément | Directional Enlacement Histograms for the Description of Complex Spatial Configurations between Objects[END_REF], and illustrated notably the interest of considering enlacement and interlacement configurations to classify the style of drop caps images. However, the descriptors were applied globally on the whole images, which does not allow to capture distinctive patterns depicted in drop caps at a more local scale.

In the present work, we propose to further explore this idea of exploiting spatial relations to recognize the background styles of historical drop caps. Our contributions are to consider enlacement histograms across local cells (instead of evaluating the images globally) in combination with the Zipf decomposition strategy, and to exploit this characteristic spatial information into a bags-of-features framework.

III. DROP CAPS DECOMPOSITION

As stated before, graphical drop caps are composed of three main layers of information which need to be extracted while their content can be white or black. Based on the results presented in [START_REF] Coustaty | Towards historical document indexing: Extraction of drop cap letters[END_REF], we decided to use a Zipf law segmentation process in order to extract three layer of information and to analyze the spatial configuration. In this section, we present the employed approach to decompose drop cap images into meaningful layers of pixels representing respectively homogeneous regions, outline and details (H, O and D).

Zipf law [START_REF] Zipf | Human Behavior and the Principle of Least Effort[END_REF] is an empirical law relying on a power law. It relies on the idea that in phenomena figured by a set of topologically organized symbols, the distribution of the occurrence numbers of n-tuples named patterns is organized in such a way that the frequencies of the patterns M 1 , M 2 ...M n , noted N 1 , N 2 ...N n , are in relation with the rank of these symbols when sorted with respect to their occurrence frequencies. The following relation holds: where the number of occurrences of the pattern with rank i is represented by N σ (i), k is a constant linked to the length of the symbol sequence studied, and a a constant that characterizes the value of the exponent. Even if the relation is not linear, a simple transformation step leads to a linear relation between the logarithm of N σ and the logarithm of the rank. Finally, the value of the exponent a can be easily estimated by the leading coefficient of the regression line approximating the experimental points of the 2D graph (log 10 (i), log 10 (N σ (i))), with i varying from 1 to n.

N σ (i) = k × i a (1)
In our context of drop caps image, the patterns considered are all the possible gray level patterns of size 3 × 3 which can appear in an image. As the images we are dealing with in this study are mostly binary, we decided to keep only 3 gray levels. This step is essential to build a realistic Zipf curve associated with a drop cap (as by keeping all the 256 gray levels available would lead to patterns with very low frequencies without any meaning). More details about this step can be found in [START_REF] Coustaty | Towards historical document indexing: Extraction of drop cap letters[END_REF]. The obtained graph, presented in Fig. 2 is called Zipf graph. The approximation of the graph is made using the least square method on the experimental points. As a matter of fact, we can see that the curve cannot be reasonably modeled by a straight line. Nevertheless, we can observe that three different linear segments can be extracted to model the curve. Then, according to the frequency of the pattern, we can distinguish three sets of patterns for which the Zipf law holds.

In Fig. 3, we show for different drop caps images the associated decompositions into three layers according to the Zipf curve. We can find an interpretation to these layers. The first set (black layer) which is associated with the left part of the curve, corresponds to the most frequent patterns. It usually corresponds to flat regions with homogeneous intensity values. The second set (red layer), associated with the middle part of the curve, seem to correspond to outline regions, where a lot of transitions between dark and light pixels can be found in the image. Finally, the right part of the curve (green layer), which corresponds to the third layer, can be interpreted as details of an image, i.e. the least frequent patterns. As a result, for each drop cap image we obtain a decomposition into three In the following, we propose to keep all of these three levels of information, and to encode the pairwise spatial organization between them to describe the content of drop caps images. In particular, this allows to retain small details such as very thin contours or small dots, which are characteristic of certain background styles.

IV. LOCAL ENLACEMENT LEARNING

In this section, we propose a way to describe the complex content of drop caps images by considering the spatial organization of layers of pixels at a local scale. For this purpose, we first present enlacement histograms, which are spatial relations descriptors allowing to characterize how two objects are imbricated in each other. Then, we show how to incorporate such descriptors into a bags-of-features framework to recognize drop caps styles.

A. Enlacement histograms

We briefly present the model used to describe the relative enlacement of objects, which was initially introduced in [START_REF] Clément | Directional Enlacement Histograms for the Description of Complex Spatial Configurations between Objects[END_REF].

Two-dimensional objects of the plane are considered, where an object A is defined by its characteristic function f A : R 2 → R. This generic definition allows to handle complex objects composed of multiple connected components (for instance in the binary case, an object can be a set of pixels). We represent the oriented line of angle θ at the altitude ρ by the non-finite set ∆ (θ,ρ) = {e iθ (t + iρ), t ∈ R}. The subset A ∩ ∆ (θ,ρ) represents a one-dimensional slice of the object A, also called a longitudinal cut. In the case of crisp objects, such a longitudinal cut of A is either empty (the oriented line does not cross the object) or composed of a finite number of segments. In the general case of real-valued objects, a longitudinal cut of A along the line ∆ (θ,ρ) is defined as:

f (θ,ρ) A : R -→ R t -→ f A (e iθ (t + iρ)). ( 2
)
The goal is to describe how an object A is enlaced by another object B. The idea is to capture the occurrences of points of A being between points of B. To determine such occurrences, the objects are handled in a one-dimensional case, using longitudinal cuts. For a given oriented line ∆ (θ,ρ) , we seek to combine the quantity of object A (represented by f (θ,ρ) A

) located simultaneously before and after object B (represented by f (θ,ρ) B

). Let f and g be two bounded measurable functions with compact support from R to R. The enlacement of f with regards to g is defined as:

E(f, g) = +∞ -∞ g(x) +∞ x f (y) +∞ y g(z) dz dy dx. (3)
The scalar value E(f

(θ,ρ) A , f (θ,ρ) B
) represents to which degree A is enlaced by B along the oriented line ∆ (θ,ρ) . For crisp objects (i.e., each point is either 0 or 1), this corresponds to the total number of ordered triplets of points (b i , a k , b j ), i < k < j, which can be seen as arguments to put in favor of the proposition "A is enlaced by B" in direction θ. Algorithmically, this value can be derived by an appropriate distribution of segments lengths along the longitudinal cuts of both objects (see [START_REF] Clément | Directional Enlacement Histograms for the Description of Complex Spatial Configurations between Objects[END_REF] for more details).

To further measure the global enlacement of two objects in direction θ, we aggregate the one-dimensional enlacement values obtained for all parallel lines {∆ (θ,ρ) , ρ ∈ R}. The enlacement of A by B in direction θ is therefore defined by:

E AB (θ) = 1 A 1 B 1 +∞ -∞ E(f (θ,ρ) A , f (θ,ρ) B ) dρ, (4)
where A 1 and B 1 denote the respective areas of the objects. This normalization factor allows to achieve invariance with regards to scaling transformations. Then, the computation of E AB along a set of k discrete directions in [0, π] yields a circular histogram describing the enlacement of A by B. Note that both histograms E AB and E BA must be considered to fully describe the spatial configuration.

B. Learning by Bags-of-Enlacement

We present how to extend the bags-of-relations approach to work with the Zipf segmentation results, using enlacement histograms as features. The approach is inspired by traditional bags-of-features strategies usually applied with local image descriptors (such as SIFT or HOG).

A given training image is first segmented using the Zipf decomposition approach which was presented previously. We therefore obtain three binary layers of the image, representing respectively homogeneous regions, outline and details (H, O and D). Then, the images corresponding to the three possible couples of layers are considered, denoted by HO, HD and OD in the following. Each of these images is split into local, nonoverlapping square cells of size 32 × 32. For a drop cap image of size 200 × 200, this results in about 36 × 3 = 108 cells (i.e., 36 blocks for each of the three couples of layers). For each of these cells, we compute the two enlacement histograms E AB and E BA between the two binary objects represented in the current layer (i.e., for a local cell of HO for example, A and B correspond to homogeneous and outline pixels respectively). As these two histograms are complementary to describe the spatial configuration, they are concatenated into a single feature vector describing the local enlacement between the two layers of a given cell.

We then apply the K-Means clustering algorithm [START_REF] Macqueen | Some Methods for Classification and Analysis of Multivariate Observations[END_REF] to regroup enlacement descriptors into similar clusters, therefore building a spatial vocabulary of local enlacement configurations. We perform distinct clusterings of enlacement histograms, one for each couple of layers. That is, for a vocabulary of size K, we perform three independent clusterings with the descriptors coming from couples of layers HO, HD and OD respectively. We therefore produce a total of K × 3 vocabulary words corresponding to similar local enlacement configurations between the different layers of the Zipf decomposition. For visualization purposes, some examples of local enlacement words obtained for the HO layers (homogeneous regions and outline) are presented in Fig. 4. We can notice how very distinctive drop caps patterns are captured by these spatial vocabulary words.

Following this vocabulary building procedure, we then apply a pooling step which consists in representing each image by a distribution of each vocabulary word it is composed of. In this work, we applied a soft encoding strategy [START_REF] Gemert | Visual Word Ambiguity[END_REF] that allows to take into account the distance of the descriptors to the built clusters. For a given image, the soft assignment value for the vocabulary work w k is given by:

z k = 1 n n i=1 K σ (f i , w k ) (5)
where {f i } n i=1 denote the set of descriptors of the image (i.e., its set of enlacement histograms across the local cells), and where K σ is the Gaussian kernel:

K σ (x 1 , x 2 ) = exp - ||x 1 -x 2 || 2 2σ 2 , ( 6
)
with σ allowing to control the smoothness of assignments. The image is finally described by the feature vector z = [z 1 , . . . , z K ] summarizing the soft assignment values for the K vocabulary words. As for vocabulary building, this encoding procedure is followed independently for each couple of layers HO, HD and OD. We therefore obtain three codebooks corresponding different layers of information in the images. Finally, style recognition of test images can be performed by using any supervised classifier trained on a given codebook, or on a combination of multiple ones (by concatenating the feature vectors of the different codebooks).

V. EXPERIMENTAL VALIDATIONS

In this section, we report experimental results obtained for recognition of drop cap styles with our approach, and we compare these results with relevant baselines.

A. Dataset

The dataset used in the following experiments is a set of 636 images of historical drop caps. These images were classified by historians into three classes, each class representing a different background styles (independently from the letter): hatchings (253 images), dotted (214 images) and decorative (169 images). The decorative class is composed of various patterns, with notably several inversed images (i.e., dark letter and outline over light background, and conversely). To maintain homogeneity in the dataset, all images were downsampled to a maximum size of 200 × 200.

B. Experimental Protocol

First, the images of the dataset are segmented following the Zipf decomposition strategy presented in section III. For a given image, we obtain three layers of decomposition (H, O and D) which are combined into the couples of layers HO, HD and OD, and split into local cells of size 32 × 32. Then, we compute the enlacement histograms for each of these cells. All enlacement histograms are computed onto a set of 32 discrete directions, equally separated along the [0, π] interval. When concatenating E AB and E BA , this translates into descriptors of size 64. Following this indexing phase, we obtain a total of 21503 descriptors over the entire dataset.

The dataset is then split into a training set representing 25% of its total size (159 training images), while the remaining 75% is used for testing. The bags-of-enlacement (BoE) approach is applied on training images for all possible combinations of couples of layers, and for different vocabulary sizes (i.e., the value of K for K-Means clustering). For soft encoding (see Eq. 5 and 6), we used an adaptive Gaussian kernel K σ where σ was fixed according to the mean of the pairwise Euclidean distances between the training enlacement features and their associated vocabulary words.

The resulting codebooks are then fed to SVM classifiers [START_REF] Cortes | Support-Vector Networks[END_REF] to recognize the background styles of the corresponding drop caps images. In these experiments, we used linear SVMs following a one-versus-all strategy for multiclass classification. The soft-margin hyperparameter of SVMs was optimized by performing grid search on the training set, following a 5-fold cross validation. Different SVM kernels were tried (Gaussian and χ 2 ) but they did not seem to improve the classification results, while greatly increasing the computation times.

To better assess the robustness of the approach, this classification procedure is repeated 10 times with different randomly chosen training sets (each time preserving the distribution of the different classes). We evaluate the classification results using the accuracy score for each run, and we report the average scores over all runs.

C. Experimental Results

Table I reports the average classification accuracy scores obtained for all the possible combinations of layers from the Zipf decomposition, and for different vocabulary sizes in the bags-of-enlacement approach. The first three lines correspond to the individual couples of layers DH, OH and OD, each of them being composed of independent vocabularies of K words. The following lines denote combinations of these couples of layers, obtained by concatenating their respective codebooks before SVM training (and therefore increasing the dimensionality of the representations).

From these results, we can observe the overall stability of the accuracy scores across the 10 random training runs, attesting of the generalization capacity of the proposed learning approach. Altogether, the recognition results seem to increase as we combine more couples of layers, the best results being obtained for the full combination DH+OH+OD. This suggests that all three layers of information can be useful to characterize the different background patterns represented in drop caps images. Regarding the vocabulary sizes, we can also observe that the recognition results remain particularly stable across the tested values of 100, 200 and 500. This suggests that most spatial information is contained in a small number of vocabulary words.

D. Comparative Study

As our approach is composed of two main parts (Zipf decomposition for segmentation, and bags-of-enlacement for recognition), we propose baseline comparisons on these two aspects. For Zipf decomposition, we compare the results to the same bags-of-enlacement approach but applied directly on Otsu binarizations of drop caps images. For bags-ofenlacement, we compare our results to classical HOG features [START_REF] Dalal | Histograms of Oriented Gradients for Human Detection[END_REF] extracted from the base gray-level drop cap images. The same non-overlapping cells of size 32×32 that were used for local enlacement descriptors are considered. These features are then pooled into a similar bags-of-features framework with soft encoding. In the following comparative results, BoE-Zipf indicates our proposed approach (bags-of-enlacement over the Zipf decomposition) with an initial vocabulary size of K = 100, and with all couples of layers combined (DH+OH+OD), therefore comprising a total of 300 spatial words. For comparability purposes, BoE-Otsu and HOG comparisons are therefore performed with K = 300 vocabulary words, and following the same classification protocol. Fig. 5 shows the precision-recall curves obtained for the proposed comparative baselines. In the context of this drop caps style recognition application, these results confirm the interest of considering local enlacement descriptors based on the spatial configuration of pixel layers, instead of gradientbased features which are classically used in object recognition tasks (i.e., BoE vs HOG). We can also observe that the Zipf decomposition seem to perform slightly better than Otsu thresholding of images. This suggests that this method allows to better extract the complex patterns depicted in these historical drop caps. To better grasp the relative performance of these comparative methods, Fig. 6 also shows the respective confusion matrices, allowing to evaluate the performance on a class-by-class basis. We can remark that our approach seem to recognize hatchings relatively well, which are indeed directional alternating patterns that are efficiently characterized by enlacement histograms.

VI. CONCLUSION

In this article, we proposed an approach for the recognition of historical drop caps images, focusing in particular on their background styles, independently from the letters. To this end, we used a segmentation strategy based on Zipf law to extract meaningful pixel layers in the images. These layers of pixels are described across local cells using relative position descriptors called enlacement histograms. Such descriptors are then learned with a bags-of-features strategy in order to classify the images. Experimental validations on a dataset of drop caps images showed the interest of (1) using the Zipf decomposition strategy as opposed to a standard binarization; and (2) considering enlacement histograms as local descriptors instead of standard gradient-based features.

In future works, we plan to extend this approach by increasing the size and the variety of this drop caps dataset. In collaboration with historians, the goal would be to characterize a more diverse range of background patterns according to historical preservation needs. Another perspective of this research would be to study how to refine the produced spatial vocabularies, for instance by putting an emphasis on most relevant words, and by labeling them with semantic annotations.

Fig. 1 :

 1 Fig. 1: Illustrative examples of drop caps (first row) and of different background styles for the same letter (second row).

Fig. 2 :

 2 Fig. 2: Example of a drop cap image along its Zipf plot. In blue are indicated the different 3 × 3 patterns sorted by appearance frequencies in the image. In red is the corresponding Zipf law, which can be separated into 3 linear parts.

Fig. 3 :

 3 Fig. 3: Examples of Zipf decompositions of drop cap images. The first row shows drop caps from the different background styles (from left to right: hatchings, dotted and decorative). The second row shows their corresponding Zipf decompositions into three layers (in black: homogeneous layer H; in red: outline layer O; in green: details layer D).

Fig. 4 :

 4 Fig.4: Illustrative examples of local enlacement configurations obtained for the HO layers (homogeneous regions in white and outline in gray). For each of the four illustrative clusters, the centroid of the cluster is shown, alongside with some corresponding local cells that are attached to this centroid. Clustering was performed for a vocabulary size of K = 100, and with E AB and E BA concatenated into a single descriptor (shown here on separate curves for the sake of visualization).

Fig. 5 :

 5 Fig.5: Interpolated precision-recall curves obtained for our method (BoE and Zipf) and for the considered comparative baselines (Otsu thresholding instead of Zipf, and standard HOG bags-of-features).

Fig. 6 :

 6 Fig. 6: Average confusion matrices obtained for our proposed method and for the considered comparative baselines.

TABLE I :

 I Average classification accuracy scores obtained for the recognition of drop caps styles, for different combinations of layers issued from the Zipf decomposition, and for different vocabulary sizes.

	Layers / K	100	200	500
	DH	79.81 ± 2.15	80.04 ± 1.63	80.00 ± 1.55
	OD	80.69 ± 1.82	80.96 ± 1.88	81.30 ± 1.62
	OH	80.96 ± 1.83	81.03 ± 1.68	81.43 ± 1.64
	DH+OH	81.49 ± 1.87	81.70 ± 1.62	81.43 ± 1.38
	OH+OD	82.68 ± 1.62	82.68 ± 1.65	82.49 ± 1.99
	DH+OD	84.84 ± 1.35	83.98 ± 2.39	84.53 ± 1.56
	DH+OH+OD	85.07 ± 2.05	84.32 ± 2.33	85.26 ± 1.10