Anatole Chessel
email: achessel@ifremer.fr

Abdesslam Benzinou
email: benzinou@enib.frfcao@irisa.fr

R Fablet
email: rfablet@ifremer.fr

S Pujolle

F Cao

2D Image-based reconstruction of shape deformation of biological structures using a variational level-set representation

Keywords: shape matching, accretionary morphogenesis, level-set, inverse problem

come

2D Image-based reconstruction of shape deformation of biological structures using a level-set representation

Ronan Fablet, Sylvain Pujolle

Introduction and problem statement

A number of biological structures, for instance corals, seashells, fish otoliths 1 , tree trunks or vertebrae grow according to an accretionary process. In other words, they can be viewed as a succession of three-dimensional concentric layers (with respect to an initial core). The composition of these layers, in terms of crystalline organization and chemical features, vary according to endogenous and exogenous factors [START_REF] Panfili | Manual of Fish Sclerochronology[END_REF]. Often, the accretionary process is associated with a periodic, mainly daily or seasonal, scheme, such that the observation of these biological structures in an observation plane going through the initial core depict concentric ring patterns, also called grwoth marks, as illustrated in Fig. 1. These characteristics provide the basis for exploiting these structures as biological archives to define environmental proxies (e.g., for instance to reconstruct temperature and salinity sequences) [START_REF] Chauvaud | The shell of the Great Scallop Pecten maximus as a tool for high frequency paleoenvironmental reconstruction[END_REF] or to reconstruct individual life traits (e.g., individual age and growth information or migration paths) [START_REF] Fablet | Unsupervised bayesian reconstruction of individual life histories chronologies from otolith signatures: case study of Sr:Ca transects of eel (anguilla anguilla) otoliths[END_REF]. To further stress the key importance of these biological structures in marine 1 Fish otoliths are calcified structures present in fish inner ears ecology, it can be pointed out for instance that several millions of fish otoliths are analyzed each year for fisheries management. New computational tools [START_REF] Fablet | Semi-local extraction of ring structures in images of biological hard tissues: application to the bayesian interpretation of fish otoliths for age and growth estimation[END_REF][START_REF] Fablet | Unsupervised bayesian reconstruction of individual life histories chronologies from otolith signatures: case study of Sr:Ca transects of eel (anguilla anguilla) otoliths[END_REF] are sought to improve the understanding, the modeling and the decoding of these biological archives. Their shape characteristics have been extensively exploited [START_REF] Campana | Stock discrimination using otolith shape analysis[END_REF]. Though the presence of internal growth rings provide the mean for back-tracking the temporal evolution of the shape from the core to the outline, the actual analysis and reconstruction of this morphogenesis sequence have not been investigated. From an image processing perspective, the reconstruction of the morphogenesis of the considered biological structures within an observation plane2 can be viewed as the reconstruction of the shape deformation from the initial circular core to the observed outline as illustrated in Fig. 1. Mathematically-sound solutions [START_REF] Caselles | Histogram modification via partial differential equations[END_REF][START_REF] Younès | Optimal matching between shapes via elastic deformations[END_REF] have been proposed to determine the deformation path between any two shapes. The direct application of these schemes would however first require extracting the internal growth rings. Whereas the detection of the growth center and the detection of the external shape may be automated [START_REF] Cao | Automatic morphological detection of otolith nucleus[END_REF], the automated extraction of internal growth rings is a particularly complex task due to the presence of blind areas and so-called subjective contours [START_REF] Guillaud | Autonomous agents for edge detection and continuity perception on otolith images[END_REF][START_REF] Fablet | Semi-local extraction of ring structures in images of biological hard tissues: application to the bayesian interpretation of fish otoliths for age and growth estimation[END_REF]. Image orientations, i.e. the local orientations of image structures [START_REF] Chessel | Interpolation of orientation: an axiomatic approach[END_REF], however locally convey relevant information on the shape of the growth rings, since they can be viewed as estimations of the local growth directions. Consequently, we state the reconstruction of the accretionary growth sequence as the computation of the deformation shape between the initial core and the outline such that any intermediary shape should be normal to local image orientations.

To this end, we adopt a level-set setting to model the accretionnary growth process. Coupling a priori constraints on shape regularity and image-based information in terms of local shape orientation, the considered issue resorts to a variational level-set interpolation. This paper is organized as follows. Section 2 details the proposed variational framework. Minimization issue are described in Section 3. Experiments and concluding remarks are reported in Sections 4 and 5.

Proposed approach

Level-set setting

As suggested in the seminal work of Thompson [START_REF] Thompson | On growth and form[END_REF], we adopt a level-set setting to represent the accretionary growth process. It comes to introduce a potential function U defined over R 2 such that the shape Γ t (U ) of the considered biological structure within a given observation plane at time t is given by the level set of U :

Γ t (U ) = {p ∈ R 2 such that U (p) = f (t)} ( 1
)
where f is a strictly monotonic continuous function. Given U , the sequence of level sets

{Γ t (U )} [0,T ]
represents the evolution of the shape from time 0 to time T. This representation conforms to the classical assumption that accretionary growth is locally normal to the shape. The growth increment at any point p is indeed inversely proportional to ∇U (p), which is, by definition, normal in p to

f(t0) f(0) x Otolith image f(t) f(t1)
Figure 2: Level-set representation of the accretionary growth process: the evolution of the shape is described by a potential function U , such that the growth shape at time t is given by level-line

Γ t (U ) = {p ∈ R 2 such that U (p) = f (t)
} with f a continuous and strictly monotonic function.

level-set Γ U (p) (U ).
Let us stress that this level-set representation is generic. Convex as well as non-convex shapes are represented. Besides, secondary growth centers could also be taken into account, though this point is not investigated in this paper.

Geometric priors and orientation-based constraints

Given an image of the considered biological structure in a given observation plane, our goal is to reconstruct the potential function U associated with the underlying accretionary growth. Let us stress that the proposed level-set representation provides a relevant framework to solve for the inverse problem, since it intrinsically conveys the key geometric properties of the accretionary growth: concentricity and local parallelism of the successive level-sets. Besides, as shown below, the considered biological structure(the orientation field is visualized via its field line using LIC [START_REF] Cabral | Imaging vector field using line integral convolution[END_REF]).

minimization issue.

Formally, we assume that we are given with some boundary conditions as illustrated in Fig. 2.2.a: at least the shapes at times 0 and T, but additional constraints can be considered such as internal partial or complete growth rings. These conditions are stated as a set of points or curves for which the potential value is known. Let us denote by B this point set and G B the associated potential values. Solving for the reconstruction of U is then stated as the computation of its extension from B to the whole domain R 2 .

In addition, the image conveys relevant local geometric information in terms of orientations of the ring structures. Formally, we assume that an orientation field normal to local growth orientations is provided as illustrated in Fig. 2.2.b. The interpolation of level-set representation U is then be constrained to be locally tangent to this orientation field. A first solution consists in considering orientation field ω = ∇I ⊥ /|∇I| with I the image intensity. Obviously, for low gradient values, the computation of the orientation is highly noisy. However, the module of the image gradient can be considered as a meaningful relevance weight [START_REF] Odobez | Separation of moving regions from background in an image sequence acquired with a mobile camera[END_REF]. Hence, a confidence map α is defined as g(|∇I|),

where g is a continuous stepwise function rescaled between 0 and 1. A second solution resorts to computing the orientation field as the AMLE (Absolutely Minimizing Lipschitz Extension) of the orientations normal to the gradient measures selected by a thresholded Canny-Deriche edge filter [START_REF] Chessel | Interpolation of orientation: an axiomatic approach[END_REF][START_REF] Deriche | Using canny's criteria to derive a recursively implemented optimal edge detector[END_REF]. As shown in [START_REF] Chessel | Interpolation of orientation: an axiomatic approach[END_REF], this procedure guarantees to extract smooth orientation field, which is expected to better constrain the reconstruction of the 2D morphogenesis. Let us denote by ω the provided orientation field and α the associated local confidence map. When using AMLE orientation fields, confidence map α is set to one.

Given boundary constraints {B, G B } and orientation constraints {ω, α}, the extension of U to the whole domain R 2 is defined as the minimization of an energy criterion E:

U = arg min U ∈U (G B ) E(U ), (2)
where U(G B ) is the set of the functions from R 2 to R whose restriction to B is G B . Energy E(U ) is split into two terms: a regularization term issued from a geometric shape prior and a data-driven term setting orientation-based constraints,

E(U ) = (1 -γ)E R (U ) + γE O (U ), (3)
where γ is a weighting factor balancing the relative influence of each term.

The chosen regularity criterion resorts to minimizing the perimeter of any growth shape Γ t (U ).

Hence, E R (U ) is defined as the sum over all level-sets of the unity function:

E R (U ) = t∈[0,T ] p∈Γt(U ) 1 (4)
The second energy term evaluates how the reconstructed growth shapes conform to local growth orientations ω. Any shape Γ t (U ) is expected to be normal to orientation field ω. Given that Γ t (U ) is a level-line of U , this is equivalent to the orthogonality between growth directions ∇U/|∇U | and orientations ω along Γ t (U ). Therefore, summing over all level-lines of U , E O (U ) is defined as

E O (U ) = t∈[0,T ] p∈Γt(U ) α(p) • ρ ∇U (p) |∇U (p)| , ω(p) (5)
where ρ is an error function. In order to account for outliers, a robust function is exploited [START_REF] Huber | Robust Statistics[END_REF].

Compared to a classical quadratic term, it ensures the robustness to local incoherences within orientation field w. In the subsequent, ρ is set as ρ(x) = |x|.

Variational framework

The above definition of the energy criterion is issued from the summation over all level-lines of U .

The direct minimization of E(U ) from this formulation is then infeasible since it first implies to extract all level-lines of U . The solution comes from the co-area formula which supplies us with an equivalent computation over R 2 . More precisely, for any function Ψ, the following result applies [START_REF] Lin | Geometric Measure Theory: An Introduction[END_REF]:

t∈[0,T ] p∈Γt(U ) Ψ = p∈R 2 |∇U |Ψ (6)
Norm |∇U |, inherited from the co-area transform, can be viewed as a weight which gives more influence to points where the gradient of the level-set representation is high (conversely, where the growth is slow).

Using the formulations of energy terms E R (U ) and E R O(U ), we resort to the following variational issue:

U = arg min U ∈U (G B ) p∈R 2 (1 -γ) • |∇U | + γ • α • | ∇U, ω | (7)
The reconstruction of the series of growth shapes can then be regarded as a variational interpolation of the potential field U given boundary constraints G B . The minimization to be solved for involve two classical terms that are encountered in the resolution of inverse problems for twodimensional data, for instance in image analysis [START_REF] Rudin | Nonlinear total variation based noise removal algorithms[END_REF]. The first term is as regularization term computed as a function of the norm of the image gradient. Here, we resort to the total variation criterion, widely exploited for image denoising [START_REF] Durand | Reconstruction of wavelet coefficients using total variation minimization[END_REF][START_REF] Rudin | Nonlinear total variation based noise removal algorithms[END_REF]. Contrarily to a quadratic criterion, the minimization of the total variation is associated to an anisotropic diffusion, better accounting for geometric image structures. The second term, often referred as the data-driven term, aims at aligning the orientation field of U to orientation constraints ω. A similar term has been used for the reconstruction of dense orientation fields in fingerprint images within a Markovian and quadratic setting [START_REF] Dass | Markov random field models for directional field and singularity extraction in fingerprint images[END_REF].

Additional constraints

Minimization ( 7) is issued from purely geometric constraints. As level-set representations are contrast invariant (i.e., a contrast change does not affect the geometry of the level-sets but only the indexes of the level-sets) [START_REF] Monasse | Fast computation of a contrast invariant representation[END_REF], additional constraints on U are needed to numerically solve for Eq. [START_REF] Caselles | An axiomatic approach to image interpolation[END_REF]. For instance, if the boundary set is given by the growth center at time 0 and the final shape at time T , solving for Eq.( 7) converges to an unstable solution constant everywhere except at the point corresponding to the growth center.

To account for this issue, a theoretical solution would be that the surface between two successive level-lines Γ t (U ) and Γ t+dt (U ) is constrained by the instantaneous accretionary deposit at time t.

Since the actual instantaneous growth rate is generally unknown, we cannot straightforwardly exploit this constraint. However, setting constraints on the surface between successive level-lines is equivalent to setting constraints on first-order statistics p(U ) of U . In fact, the knowledge of the law of the accretionary deposit comes to set the form of this statistical distribution. Therefore, we choose a prior on p(U ) to impose additional constraints on U . For the sake of simplicity, the uniform distribution has been selected in this work, but other priors might be relevant. Let us stress that changing from one prior to another simply consists in a contrast change.

Hence, the variational interpolation finally comes to solve for min

U ∈U (G B ) p∈R 2 (1 -γ) • |∇U | + γ • α • | ∇U, ω | , (8)
subject to p(U ) is uniform.

Numerical resolution

To solve for the above constrained minimization, we adopt a two-step iterative approach: the first step comes to project the current solution onto the set of level-representations with uniform firstorder statistics. We detail below the unconstrained minimization. To improve the convergence, a multiresolution framework is adopted.

Unconstrained minimization

To solve for the minimization of E with respect to U , Euler-Lagrange equations [START_REF] Aubert | Mathematical problems in image processing[END_REF] provide the expression of the gradient of E. Given that the L1 norm is not derivable in zero, it is approximated as

√ 2 + x 2 .
We let the reader refer to [START_REF] Rudin | Nonlinear total variation based noise removal algorithms[END_REF] for the analysis of the total variation criterion whose gradient is given by:

( 2 R + U 2 x )U xx -2U y U x U 2 xy + ( 2 R + U 2 y )U yy 2 R + ∇U 2 3/2 (9)
Neglecting the variations of the weight α3 , the second term leads to the following gradient:

Ψ(U ) = div    ∇U, ω ω 2 D + ∇U, ω 2 1/2    = div(ω) ∇U, ω 2 D + ∇U, ω 2 1/2 + 2 D ∇∇U • w + ∇ω • ∇U, ω 2 D + ∇U, ω 2 3/2 ( 10
)
where div is the divergence operator, ∇∇U p the Hessian matrix of U at point p, and ∇ω p the gradient matrix (∇w p,x ; ∇w p,y ) with ω p,x and ω p,y the horizontal and vertical component of ω p .

The expression of Ψ(U ) can be compared to PDEs proposed for anisotropic image smoothing which reduces to div( ∇U, ω ω) in the case of the smoothing along a single direction ω [START_REF] Tschumperlé | Fast anisotropic smoothing of multi-valued images using curvature-preserving PDE's[END_REF][START_REF] Weickert | Anisotropic diffusion in image processing[END_REF]. The first term is a weighted version of advection term ∇U, ω . This advection equation corresponds to the transport of a scalar quantity U preserved by a vector field ω, for instance the transport of temperature by wind and currents in meteorology and oceanography. The weighting factor depends on div(ω). If ω is issued from the actual morphogenesis potential function, div(ω) is the curvature of the true (but unknown) successive growth shapes to be reconstructed.

The second term involved in the expression of Ψ(U ) is a weighted version of the diffusion operator along the field lines of ω, ω T ∇∇U w + ω T ∇ω∇U , as proposed in [START_REF] Tschumperlé | Fast anisotropic smoothing of multi-valued images using curvature-preserving PDE's[END_REF] for curvature-based regularization of images. As √ 2 + x 2 is used as a numerical approximation of the L1 norm x ,

| D | << 1.
Therefore, this second term tends to be negligible.

From these considerations, the steady-state corresponding to evolution equation dU/dt = Ψ(U ) reduces to advection equation

div(ω) ∇U, ω = 0. ( 11
)
From this steady-state equation, the existence and the uniqueness (up to a contrast change) of the solution of the considered inverse problem can be derived.

Proposition 1 Let φ be a potential function such that ∇φ = 0 and div(∇φ ⊥ /|∇φ|) = 0. Let ω be the orientation field tangent to the level-lines of Φ.

Let U be a potential function such that ∇U = 0. U is a solution of Eq.11 if and only if it exists a strictly monotonic continuous and derivable function g such that U = g(Φ).

Proof. As ω = ∇φ ⊥ /|∇Φ ⊥ |, div(ω) = 0. Hence, Eq.11 is equivalent to ∇U, ω = 0. As the level-lines of a field U can be defined as the lines tangent to ∇U ⊥ , the latter equation imposes level-lines of U and Φ to be aligned. It then exists a continuous and derivable function g such that U = g(Φ). Given that ∇U = 0 and ∇φ = 0, g is strictly monotonic.

Reciprocally, potential function U = g(Φ), with g a strictly monotonic continuous and derivable function, is a solution of Eq.11 .

This proposition guarantees that, if direction field ω is the direction field of an unknown potential function, the solutions of Eq.11 are transformed versions of this unknown potential function with respect to a contrast change. Note also that this is only valid for a domain on which div(∇φ ⊥ /|∇φ|) = 0. Assuming that only isolated points do not fulfill this condition, this results can be extended to the whole domain by continuity. Condition div(∇φ ⊥ /|∇φ|) = 0 indeed resorts to considering that the curvature of the level-lines is not null. Formally, such an assumption seems reasonable for the studied biological phenomena: they rather involve round or elliptic growth shapes and the formation of growth shapes involving perfect straight lines seems unlikely. From a numerical point of view, numerical unstabilities have however been observed in practice when using directly the gradient-descent issued from Euler-Lagrange equations. These numerical unstabilities may be due to weighting factor div(ω) since growth shapes far from the growth center tend to become locally closer to straight lines. Consequently, to ensure a better numerical resolution, we prefer exploiting an explicit Gauss-Seidel scheme. Given that Eq.11 does not lead to a linear system, the Gauss-Seidel scheme is derived from the discrete version of the considered variational criterion.

Considering a finite difference approximations of |∇U | similar to Markovian setting [START_REF] Geman | Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images[END_REF][START_REF] Mémin | A multigrid approach for hierarchical motion estimation[END_REF], we resort to:

(1γ)

(p,q)∈N ρ R (U p -U q ) + γ p∈R 2 α p • ρ D ( ∇U p , ω p ) , ( 12
)
where N is the four-neighborhood system and (i.e., the neighborhood of a point is given its four western, northern, eastern and southern neighbors in the image). The minimization of the discrete energy involving robust functions is carried out using an iterated reweighted least square (IRLS) scheme, which iterates two steps: the computation of robust weights

β R (p, q) = φ R (U p -U q ) (13)
and

β D (p) = φ D ( ∇U p , ω p ) , (14)
where function φ is the influence function associated with robust estimator ρ computed as φ(x) = ρ (x)/x (these robust weights are low for high residual error, i.e. outliers, and high for low residuals);

and solving for the weighted least square minimization min

U ∈U (G B ) (1 -γ) (p,q)∈N β R (p, q) • |U p -U q | 2 + γ p∈R 2 α p • β D (p) • ∇U p , ω p 2 (15)
given robust weight maps β R and β D . This least square estimation is indeed solved for using a Gauss-Seidel scheme. U p is iteratively updated by explicitly solving for the quadratic minimization [START_REF] Fablet | Semi-local extraction of ring structures in images of biological hard tissues: application to the bayesian interpretation of fish otoliths for age and growth estimation[END_REF] under the assumption that U is constant except at point p. The associated computations based on a centered numerical approximation of ∇U p are detailed in Annex.

Reprojection onto the constrained subspace

The projection of the current solution U onto the set of level-set representation with uniform firstorder statistics can be viewed as an histogram equalization. As histogram equalization can be implemented as a PDE scheme [START_REF] Caselles | Histogram modification via partial differential equations[END_REF], constrained minimization ( 8) could be solved by coupling the PDE issued from the gradient of E to the one proposed in [START_REF] Caselles | Histogram modification via partial differential equations[END_REF]. However, as stressed above, such a PDE-based scheme is numerically unstable and a discrete Gauss-Seidel minimization scheme is preferred. The histogram equalization is applied as a second step after the Gauss-Seidel loop. Given Ũ , the distribution of the potential values p( Ũ is computed as well as their cumulative distribution F ( Ũ ). Aligning F ( Ũ ) to line y = x provides us with a contrast change approximately leading to a uniform distribution p(U ). As stressed previously, this transformation does not modify the geometry of the level lines but only their relative potential values.

Multiresolution minimization

Minimization [START_REF] Caselles | An axiomatic approach to image interpolation[END_REF] is obviously not convex. To ensure a better robustness to the initialization, a multiresolution scheme is used. Given a Gaussian pyramid of the orientation field ω [START_REF] Burt | The pyramid as a structure for efficient computation[END_REF], the multiresolution approach comes to solve for the estimation of the potential function U at successive resolutions, from the coarsest resolution to the finest one. The final estimate at a given resolution serves as the initialization at the next resolution. In practice, Gaussian pyramids with four levels were exploited.

Initialization

The computation of a relevant initialization to the proposed gradient-based multiresolution scheme is important to ensure a fast and relevant convergence. The initialization is delivered by the scalar AMLE (Absolutely Minimizing Lipschitz Extension) of the boundary conditions to the whole domain [START_REF] Caselles | An axiomatic approach to image interpolation[END_REF]. Since the AMLE resorts to the minimization of the L ∞ norm, the AMLE can be viewed as the less smooth interpolation operator among all smooth interpolation operator. The AMLE is implemented as gradient descent ∂U /dt = U ∇∇ where U ∇∇ is the second-order derivative in the direction of the gradient of U . It is shown to converge to the unique AMLE. The key properties of the AMLE is that it is an artifact-free and oscillation-free interpolant actually capable of taking into account isolated boundary points as well as curves.

Results

Extraction of the orientation fields

The proposed approach initially relies on the extraction of orientation field ω. As detailed previously, orientation field ω = ∇I/|∇I| computed from the image gradient ∇I is first investigated. The second solution comes to computing ω as the AMLE of the orientations of the gradient measures selected by a thresholded Canny-Deriche edge filter [START_REF] Chessel | Interpolation of orientation: an axiomatic approach[END_REF][START_REF] Deriche | Using canny's criteria to derive a recursively implemented optimal edge detector[END_REF]. Fig. 4 reports the orientation fields issued from these two schemes for the image depicted in Fig. 1. These orientation fields are visualized via their field lines, using Line Integral Convolution (LIC) [START_REF] Cabral | Imaging vector field using line integral convolution[END_REF]. As expected, orientation field ω = ∇I/|∇I| is not globally coherent and only orientation information along image contours may be meaningful. On the contrary, the AMLE orientation field is much smoother. It conveys relevant geometric cues, which are expected to better constrain the reconstruction of the 2D morphogenesis.

Examples of reconstruction of the series of growth shapes

To illustrate the different steps of our approach, we first display the reconstruction of the series of growth shape for the pollock otolith image previously depicted in Fig. 1. The results of the reconstructions of the morphogenesis associated with the orientation fields issued from the image gradient and the AMLE scheme are compared in Fig. 5. Besides, reconstructions issued for two different configurations of boundary constraints G B : the first example only involves the position of the growth center, whereas the growth center as well as the first translucent ring is given in the second example. Parameters γ, R and D are respectively set to 0.6, 0.1 and 0.1 for the first case and to 0.9, 0.1 and 0.1 for the latter. Equally sampled level lines {Γ t (U )} superimposed to the otolith image are reported. Due to the weaker coherence of the gradient-based orientation field, the minimization of the variational criterion does not lead to very regular level lines in that case.

If only the growth center is provided, such orientation information is not sufficient to reconstruct relevant growth shapes, especially for the first two rings. The additional boundary constraint given as the first bright ring permits to greatly improve the reconstruction of the series of growth shape.

The results issued from the AMLE orientation field clearly depict more regular shapes which fit to the internal otolith structures. In addition, the two boundary constraints lead to very similar results: few differences can be observed and mainly occur in the ventral lobe (left part) of the first translucent ring. Concerning computational time, the proposed scheme is implemented as a C code under linux and runs in about half a minute for a 500x1000 image.

To further illustrate the role of the two energy terms involved in the proposed variational formulation, results are reported for the two configurations processed in Fig. 6 and Fig. 7 setting γ to 0 and 1. If only the regularization term is exploited, the reconstruction of the shapes only relies on the geometric prior set in terms of shape regularity and can be viewed as a shape matching example [START_REF] Caselles | Histogram modification via partial differential equations[END_REF][START_REF] Younès | Optimal matching between shapes via elastic deformations[END_REF]. Such prior does not however permit to reconstruct relevant shape deformations if only the growth center and the otolith outline is provided. The quality of the reconstruction clearly improves if additional boundary constraints are added. While results reported using the AMLE orientation field appear very similar for γ = 1 (Fig. 7) and γ = 0.9 (Fig. 5). It is however preferable to impose some minimum regularity (i.e., γ < 1) in order to deal with potential local incoherences of the AMLE orientation field. This is indeed further illustrated when the gradient orientation-field are used, since the minimization of the variational criterion with γ = 1 does not lead to a meaningful configuration even if the first translucent ring is provided (Fig. 7). Practically, a trade-off has to be achieved between regularity and conformity to the orientation field.

With a view to further investigating this aspect, experiments are carried out for synthetic data.

The synthetic image is created as follows. For the otolith image depicted in Fig. 1, the boundary constraints defined by the set of all translucent rings were exploited to extract a sequence of otolith shapes using only the regularization term (i.e., γ = 0). The values of potential function U are then converted to intensity using a modulated sinusoidal mapping to generate an image depicting a sequence of dark and bright rings. This image is corrupted by a centered Gaussian noise with a standard deviation of 10. This test image is associated with a reference potential function U GT which can be used as a reference for performing a quantitative evaluation. Such a quantitative evaluation is reported in Fig. 8. Both the performances of the variational setting combined to gradient-based and AMLE orientation fields were evaluated as a function of the weighting factor γ.

These results further stress that the AMLE scheme is more robust and more stable. As confirmed empirically for real images, γ values between [0.8, 1[ correspond to the best trade-off between regularity and conformity to orientation data.

To further illustrate the flexibility of the proposed scheme, an example of reconstruction of the growth shapes is carried out using additional constraints given as annotated segments of an internal ring (Fig. 9). This example demonstrates the capability of the proposed variational scheme to take such constraints into account in order to improve the reconstruction of the shapes compared to the results reported above.

Experiments for three other fish species, namely plaice (Pleuronectes platessa), cod (Gadhus morua) and hake (Merluiccius merluccius), as well as the section of a tree trunk, are presented in Fig. 10) and Fig. 11). Obviously, better results are recovered for the plaice otolith and the section of a tree trunk, which involves the clearest structure. The results reported for the whiting (Gadhus morua) and cod (Merlangius merlangus) otoliths demonstrate that we are also capable of approximately recovering the complex and non-uniform evolution of such shapes from lower-contrasted images.

Discussion

We have proposed a scheme aimed at reconstructing from an image the evolution of the shape of biological structures involving accretionary growth process. Its key feature is a level-set representation, which intrinsically accounts for the major characteristics of the accretionary growth process.

From purely geometric criteria on shape regularity and on local orientation coherence with respect to the observed image, a variational formulation is derived. The associated minimization is efficiently solved for within a discrete robust multiresolution framework. Reported results on synthetic and real data provides a validation of the proposed approach. In particular, it demonstrates that AMLE orientation fields should be preferred to the orientation of image gradient since it conveys more relevant geometric information on image structures than image gradients.

Future work will investigate several refinements and extensions of the present work. Whereas uniformity constraints set to the distribution of potential function U are exploited to solve for minimization [START_REF] Caselles | An axiomatic approach to image interpolation[END_REF], other constraints more closely related to growth dynamics (for instance, a mean growth model) might also be exploited. New regularization term E R (U ) may also be developed to encode a priori knowledge on shape statistics, for instance using an exemplar-based setting [START_REF] Cremers | Statistical shape knowledge in variational motion segmentation[END_REF]. 3D morphogenesis reconstruction may also be investigated as an extension of this work from the joint analysis of several observation planes. This contribution also provides the basis for the development of improved pre-processing (for instance, orientation-based image filtering) and information extraction (growth axis, growth rings) tools [START_REF] Chessel | Orientation interpolation and applications[END_REF] for the considered biological images.

In the field of marine ecology, new issues can also be investigated in terms of understanding and modeling of biocalcification and accretionary growth process.

Appendix: potential update

The local update of potential U at point p to solve for Eq.15 relies on a centered gradient approximation and is computed as:

U p =
(1γ) q∈Np β R (p, q) • U q + γ q∈N H p β D (q)ω q,x A p,q , ω q + γ q∈N V p β D (q)ω q,y B p,q , ω q

(1γ)

q∈Np β R (p, q) + γ q∈N H p β D (q)ω 2 q,x + γ q∈N V p β D (q)ω 2 q,y (16)
where N p comprises the four neighbors of p, N H p its two horizontal neighbors and N H p its two vertical ones. ω q,x and ω q,y are respectively the horizontal and vertical component of vector ω q .

Vector A p,q for point p = (i, j) and its horizontal neighbor q = (i, j + k), k = ∓1, is defined as

U i,j+2k , ( -1)
k+1 2 (U i+1,j+k -U i-1,j+k ) t . Similarly, vector B p,q for point p = (i, j) and its vertical neighbor q = (i + k, j), k = ∓1, is defined as U i,j+2k , (-

Figure 1 :

 1 Figure 1: Illustration of the goal of the paper: image of a pollock otolith in a given observation

10 such a representationbFigure 3 :

 103 Figure 3: Geometric priors and orientation-based information exploited to constrain the recon-

Figure 4 :

 4 Figure 4: Examples of extracted growth orientation fields from local image orientations for the image

k+1 2 (.Figure 6 :

 26 Figure 6: Reconstruction of the series of growth shapes for the pollock (Pollachius pollachius) otolith

Figure 10 :

 10 Figure 10: Reconstruction of the series of growth shapes for three examples of fish otoliths: a

Figure 11 :

 11 Figure 11: Reconstruction of the series of growth shapes of the section of a tree trunk: original

In the subsequent, the term "observation plane" will only refer to an observation plane containing the initial core of the analyzed biological structure

It should be stressed that this confidence map is actually exploited only with orientation fields computed from image gradients.


Krien Nathalie

Fleury-Bahi Ghozlane

Rommel Delphine

Coquet Marie

Deledalle Aurore

Lemée Colin

Mercier Denis

Navarro Oscar

No Sea, no Flood Risk: How Importance Granted to the Sea Influences Flood Risk Perception in the particular case of the Guadeloupe Island, Caribbean Sea

Keywords: risk perception, relation to the sea, identity, risk culture, qualitative study

This article focuses on the importance of the coastal dimension of the living area, assuming that even if individuals have a risk culture, flooding by the sea is not always considered as a risk. Starting from the premise that, even if they have a risk culture, not everyone on the coastline considers his/her living area as a coastal one, we expect that those who do will more easily talk about flood risk perception on it. Indeed, through interviews analysis made in Guadeloupe Island in the Caribbean Sea, we highlighted the fact that having a risk culture is not enough for perceiving flood risk. If respondents have actually a risk culture, most of them don't consider flooding phenomenon as a real risk. It is not a priority for them. We demonstrate here that flood risk perception requires to perceive the coastal dimension of the living area, which is not the case of the most part of respondents. Those who perceive it are those with activities directly linked with the sea. They consider the sea as a part of their living area and not only its delimitation. Therefore, in areas where the sea is too current for being visible, risk culture is not focused on the sea except for people with activities linked with it.

Introduction

Caribbean tourism has really grown since only few decades [START_REF] Wong | Caribbean Island Tourism: Pathway to Continued Colonial Servitude[END_REF]. Hence uninhabited coastal areas are building up to answer this growing pressure. This anthropisation on coastal areas considerably increases stakes on such places exposed to natural hazards relating to the presence of the sea. During a long time, managers tried to contain hazards seeking to fix the coastline.

Considered as safe, even places the nearest to the sea has been urbanized. Protecting works can eventually reduce coastal hazards consequences. But, at the same time, urbanization increases 1 LPPL (Laboratoire de Psychologie des Pays de la Loire), UPRES EA 4638 -Université de Nantes (France) 2 LETG-Géolittomer (Littoral -Environnement -Télédétection -Géomatique), UMR6554 -Université de Nantes (France) stakes on concerned areas more and more exposed to the sea because of the rising sea level (Church and White, 2006) and the increase of storms' frequency [START_REF] Meur-Ferec | DE LA DYNAMIQUE NATURELLE À LA GESTION INTÉGRÉE DE L'ESPACE LITTORAL : UN ITINÉRAIRE DE GÉOGRAPHE[END_REF][START_REF] Miossec | Les littoraux entre nature et aménagement: le plus de campus en un seul livre[END_REF]. The importance of humans and properties exposed to coastal hazards has never been so important.

Coastal areas have never been so vulnerable, so risky.

Flood risk perception

Risk is a subjective construction about damages probability of occurrence [START_REF] Terpstra | The perception of flood risk and water nuisance[END_REF]). Here we are interested in the specific risk of flooding by the sea on coastal areas and most especially in how risky is the situation according to concerned people (Lopez- [START_REF] Lopez-Vazquez | Risk perception, stress and coping strategies in two catastrophe risk situations[END_REF][START_REF] Lupton | Risk and Sociocultural Theory: New Directions and Perspectives[END_REF]. In other words, we are interested in how they perceive flood risk (Chauvin, 2014;[START_REF] Slovic | Perception of risk[END_REF]: how dangerous such phenomenon could be, according to individuals exposed to it. To perceive flood risk or not, depends on a wide range of elements. In particular it depends on what constitutes a risk to individuals. In this way it depends on their risk culture. Furthermore risk perception depends on the importance granted to potentially risky factors in the way an area is perceived.

Risk culture and flood risk perception

For a part, risk perception is influenced by cultural markers that allows to indicate what is a risk and what is not for individuals in concerned area. It evolves according to the risky dimension granted by people and community to phenomena. We can talk about "risk culture" when the concerned population agreed to consider some phenomena existence in its living area as risks (Castro and Batel, 2007;[START_REF] Douglas | Risk and culture: an essay on the selection of technological and environmental dangers[END_REF][START_REF] González-Riancho | Storm surge resilience and the Sendai Framework: Risk perception, intention to prepare and enhanced collaboration along the German North Sea coast[END_REF]Pidgeon et al., 2003).

However, each culture does not consider the same phenomena as the risky ones (Adams, 2013). It depends on the importance granted by individuals to each potentially risky phenomenon they are exposed to, and how they assess the seriousness and the occurrence probability of these phenomena on the concerned area.

Living area perception and risk

With regards to the flood risk perception, previous research highlighted the influence of distance to the sea on it. The most people consider they live near the sea, the more they consider their living area as exposed to flooding phenomenon. (Afanador Franco et al., 2006;[START_REF] Vazquez | Volcanic Risk Exposure, Feelings of Insecurity, Stress, and Coping Strategies in México 1[END_REF][START_REF] Michel-Guillou | Inhabitants of coastal municipalities facing coastal risks: understanding the desire to stay[END_REF][START_REF] O'neill | The Impact of Perceived Flood Exposure on Flood-Risk Perception: The Role of Distance: Flood-Risk Perception: The Role of Distance[END_REF][START_REF] Zhang | Hazard Proximity or Risk Perception? Evaluating Effects of Natural and Technological Hazards on Housing Values[END_REF]. To a lesser extent, the importance of the coastal dimension of the living area has also been approached. In a quantitative survey, researchers have shown that the more individuals considered their living area as terrestrial rather than coastal, the less they considered the existence of coastal phenomena such as marine erosion/flooding by the sea (N. [START_REF] Krien | Relationships between representations of living areas and of coastal risks: explnation and mapping[END_REF]. Thus, floods by sea perception seems to be correlated with the importance of the coastal dimension of living area.

Beyond the dichotomy coastal/terrestrial of living area, the importance granted to the sea by individuals (to identify that particular space as their personal use of it) influences the importance granted to every element associate with the sea, including flooding phenomenon.

Aims of the study

According to research regarding the relation between risk culture and flood risk perception, the more some phenomenon can have disastrous consequences and the more frequently it can happen, the more it should be considered as a risky one. It has already been acknowledged that previous experiences of the phenomenon can considerably influence risk perception (Barnett and Breakwell, 2001;[START_REF] Ohman | Previous Experiences and Risk Perception: The Role of Transference[END_REF][START_REF] Sun | Climate Change Risk Perception in Taiwan: Correlation with Individual and Societal Factors[END_REF]. According to this, we can suppose that phenomena considered as risky ones would be the most dangerous ones in the past and would have a great probability of occurrence. Then, our first aim will be to determine if people living in a particular coastal area exposed to flooding by the sea have a risk culture and, if it's the case, what they consider as risks, and finally, if they consider flooding by the sea as a risk.

Furthermore, based on previous works about the links between living area perception and risk perception, it seems that the more the people give importance to the coastal dimension of their living area, the more they consider flooding by sea as an important phenomenon on this area (a phenomenon they have to take into account and to deal with) and a risky one. But why some people grant a great importance to the coastal dimension when some people don't? According to [START_REF] Proshansky | Place-identity: Physical world socialization of the self[END_REF], the meaning given to an area depends on the identity of who has given it. Thus the more individuals give importance to the sea when they describe themselves (as sea or coastal people), the more they should give importance to the coastal dimension of their living area description and so the more they should give some credit and some importance to the existence of flood risk in this area. Our second aim will be to determine if everyone on the coastline considers his/her living area as a coastal one. We expect that if some don't, those who do will describe their living area mentioning the coast and/or reporting activities related to the sea, and they will more consider flood by the sea on this area as important and risky phenomenon. Such findings would demonstrate the existence of different profiles of individuals exposed to the risk of flooding by the sea, depending on the relationship they maintain with the coastal dimension of their living environment. This would highlight a new vulnerability factor.

To perceive flooding by sea as a risk involves first to be in a place where such phenomenon could be relevant. That means to be in a place potentially exposed to such phenomenon. That's why we decided to locate this study on coastal areas considered by scientists as exposed to flooding by the sea. In some coastal spaces most people attach great importance to the coastal dimension of their living area [START_REF] Michel-Guillou | Inhabitants of coastal municipalities facing coastal risks: understanding the desire to stay[END_REF]. In such places it could be difficult to verify our second assumption. But it might not be the case everywhere. Identity is built through similarities and differences [START_REF] Kuhn | An empirical investigation in self-attitudes[END_REF]. For people living in a place where sea is everywhere, like in a small Island, everyone in their direct environment lives "near the sea". In this context we expect that people will give less consideration to the coastal dimension of their living area, especially those who have never left this place.

Method

Participants

For our survey, we had an interest in a place surrounded by the sea: the Guadeloupe Island named "Grande-Terre" (Caribbean Sea). It is only 586 km² in circumference. This place is often exposed to hurricanes and affected by floods (Krien et al., 2015;[START_REF] Zahibo | Statistical analysis of cyclone hazard for Guadeloupe, Lesser Antilles[END_REF]. Furthermore, in 2013, agriculture, marine and fishing sectors represented 5% of the guadeloupean employment (INSEE 4 ), which is very low for a coastal area. Because of the volcanic island topography, most important cities are on the coastline. We focused on two particular municipalities considered by scientists as exposed to flood risk (according to historical and cartographic data about flood risk): Pointe à Pitre and Sainte Anne. On the one hand Pointe à Pitre consists in the economic center of the island, it is built in the very south-west of Grande-Terre at the mouth of the Rivière Salée. It is built for a part on a polder and includes many building and social housing. In the other hand, Sainte Anne consists in a touristic area in the south coast of Grande-Terre. It includes mostly single-storey houses or with one floor. In this municipality activities focuses mainly on the down-town beach or near it.

Material

To verify our assumptions, we decided to explore the people's point of view with a qualitative approach. So we established an individual interview guide covering several themes: where they lived in the past, description of their actual home, of their actual neighborhood and municipality of residence (general aspects, the advantages and disadvantages), activities practised on the municipality and the risk perception of flooding by the sea.

Procedure

Using our interview guide, we conducted semi-structured interviews with people living in the municipality of Pointe à Pitre and Sainte Anne during the spring 2017. In Pointe à Pitre 14 interviews were conducted (these were 3 women and 11 men, with an average age of 50 years). In Sainte Anne 16 interviews were conducted (these were 7 women and 9 men, with an average age of 61 years). All in all, we met 30 people for an average duration of 40 minutes.

Data analysis

Those interviews were recorded and transcribed literally. Transcriptions were then submitted to a manual analysis through a single category matrix. This matrix was built from the themes developed during the interviews. To meet our expectations particular attention has been drawn to three elements: 1/risks mentioned by people (what are these), 2/the coastal dimension of the living area (if this spontaneously mentioned the area or activities related to the sea), and 3/flooding by sea phenomena on the living area (is it considered as a possibility and as a risk or not). Then all speeches were fragmented and classified according to that matrix, finally they were analysed in order to answer our objectives and comparisons were made between interviews5. In this article all speeches, in French, were translated in English6.

Results

Risk culture on studied place

When people describe their living area, in Sainte Anne as in Pointe à Pitre, several phenomena are spontaneously mentioned, presented as dangerous and described as such. They are then associated with some dramatic experiences. The most mentioned phenomena are the cyclones. In Guadeloupe, special importance is given to the cyclone Hugo which happened in 1989: " I saw cyclone Hugo, you can't do anything against that! You can't do anything " (E.19), often associated with the wind: " Even in buildings there are people they hid in their bathtub! It remained that. A few years ago, in 2011, (...) It had rained, it had rained ! So she asked her husband and brother-in-law to come and get them (...). The husband and brother-in-law went to get the lady but the lady wanted her car back and the water was so high they all drowned. (E.21).

Reference is also made to coastal erosion: I used to go to the beach of Sainte Anne when I was young, to park I could walk on ten meters of sand before having access to water. Now I'm parking just two meters of sand, I'm already in the water. (E.06), to the earthquake: " ...I estimate 100,000 victims. And if it's night, half of the population is down. " (E.16), or insecurity: " Difficult life. Very difficult life. (...) Difficult and dangerous: lack of education, lack of many things. It's a world of survival. " (E.05). There seems therefore to be a certain culture of risk in Guadeloupe that concerns phenomena that have already caused human losses in the past such as wind during cyclones, heavy rains, earthquakes and insecurity, or phenomena whose damage remains visible and continues as is the case for beach erosion.

With regard to flooding by the sea, if everyone is talking about it, the subject seems more induced by our questions than spontaneously mentioned by the interviewees. Some report having experienced a similar phenomenon, but it is only associated with material damage: " Boats were found in Victory Place during the cyclone. " (E.11). There is never any question of human losses linked with this phenomenon. When asked about the existence of a risk of flooding by the sea, most individuals express doubt: Honestly, I never thought about that. Then... it never occurred to me. Honestly, I don't know. That depends. Now I'm not a mind reader, so... Ah, frankly, I... it never occurred to me. But then you never know, with nature. (E.01), Or a total rejection of this idea: " The water will drain. But there won't be a water surge. (...) No, we don't have that risk there. Guadeloupe is a blessed country. " (E.07).

The only allusion to a human drama associated with flooding by the sea is through the reference to the tsunami. The speeches then show that this phenomenon is considered as the ultimate danger, almost fantasized: " Because for me personally, the day when there will be a tsunami in Guadeloupe, Guadeloupe will no longer exist. " (E.06). However, if some believe that this could happen, then they are more fatalistic than concerned:

We have that in our heads, but we don't think about that. I make my life! We're done to die.

We're done to live and die. Well, I live my life. Maybe I'll see this and maybe I won't see this. I don't know, I don't know. That's it. Only the good Lord knows that. Anything is possible! We don't know. We don't decide either, we don't know. It's God's decision. When I say God, it's... how to say... it can happen. We don't know that. (E08)

Others even consider that this risk is inconceivable: " No because it is really, it will really be, let say an accident, if you will. Yes, not only exceptional but that will leave no trace behind. " (E.16). Thus, even if there does seem to be a culture of risk in Guadeloupe, the phenomena considered as risky are those which have already, in the past, led to serious consequences (human losses), lasting consequences (disappearance of the beach) and with a high probability of occurrence. Flooding by the sea, on the other hand, has not yet had such serious repercussions. To date, it has not resulted in any loss of life and the water has always ended up being evacuated. This phenomenon is therefore not considered as a risk for most of the interviewees, except in its extreme version: the tsunami.

Nevertheless some people consider flooding by the sea as a phenomenon likely to happen in their living area, but few consider it as a risk, except in its most extreme and therefore most dangerous form. But similar phenomenon having never been lived yet by the population of Guadeloupe, it remains hardly conceivable.

The key role of living area's coastal dimension on flood risk perception

These results demonstrate, once again, the link between the experience of a dramatic phenomenon and the perception of this phenomenon as a risky one. With regard to the flooding by the sea on Pointe à Pitre and Sainte Anne, only a few are considering it. Those who are considering it less as a risk than as a fate to which they have to resign to live with when you live by the sea: " So whether I like it or not I am often enough exposed since across the street it is the sea. " (E.06). When we compare these speeches with the relationship of individuals to the sea, we see that those who consider flooding by the sea attach a certain importance to the coastal dimension of their living area: " Because I like it, I like living by the sea. " (E.28). When these individuals describe their living area they spontaneously refer to its coastal dimension: " Well, Sainte Anne, compared to other municipalities that I know, it is that we have a beach that is really, that is really in the town. it is the only municipality that I know that is like this. "(E.29), or to activities linking them to the coast and the sea: " We're a family of sailors. It means that we live the sea. The sea is our everyday activity. It is... today not working on the coastline, for me it's something that... unthinkable. " (E.13). Some of these people are fishermen or ship-owners. Otherwise, they are people who have lived, in the past, far from the sea, on the continent, and who have come, among other things, to enjoy the coastal advantages of this new living area (swimming, beach, surfing, etc.). Nevertheless, in most of our interviews, very little reference is made to the coastal dimension of the municipalities studied. Those who speak least about it are people who have always lived on the island and whose work is not directly related to the sea. Among them, some even declare openly: " We don't even use it [The sea], we don't even realize it. She's here, but given the fact that she's so close we don't care. " (E.01). What is then highlighted in particular with regard to the advantages of their living area is the proximity of services: " It is a city where... really organized, where you can find everything. We have everything carried by hand. " (E.02), attachment to the living area: " I like it here. I liked it here at home. It's where I was born, where I grew up. " (E.30), or human relations: " The advantages are that there is conviviality. That means people have an approach that means we live in a community, in solidarity. And that there is mutual aid, there is listening, there is proximity. " (E.07). When it comes to the disadvantages, in addition to the dangers, the people interviewed talk mainly about the unhealthy: " The disadvantages are that there is no lift and I have trouble getting around so it's not easy and for my husband either. And then there's no hot water. " (E.03), or traffic problems: " Traffic problems in Sainte Anne, it blocks every day! Morning and night! " (E.18). The sea seems to be a secondary element of the environment for most respondents, especially those who have always lived by the sea and who do not have a job directly related to this element. Many of them don't even go swimming: " When you're in Guadeloupe, that's it. We don't even care about the sea. Because we're not even going swimming! We're not going swimming! No. Even going to the beaches, we're not going at all. " (E.09). Among those who go, many do not know how to swim: " It's not in the culture of the locals that... they'll teach their children to float and be in the water, yes. Swim, swim 10 feet, no. No, no, it's rare. It's very rare. " (E.06). With regard to flooding by the sea, these people do not allude to it and, when asked, do not see it as a risk:

The water will not rise ! it is that the water will take over, which means that there will be a flush, the water will go down, the water will circulate. But the water will be drained. She'll evacuate. Because it's good soil. The water will drain. But there won't be a water surge. Who means so that people can swim in the water, there is no dog, there is no cat, there is no beef, there is no pig that will drown. No, we don't have that risk right now. Guadeloupe is a blessed country. (E.07).

Thus flooding by the sea is only considered by people who attach a certain importance to the coastal dimension of their living area in the way they conceive and use it.

Discussion

Our first objective concerned risk culture. We assumed that if there is a risk culture on our land, it does not necessarily imply that the phenomenon of flooding by the sea is considered a risky one by the people. Considering the results, it seems that even if the term "risk" seems to be used only to echo the interviewers or the discourse of scientists, there does exist a culture of risk in Guadeloupe (Castro and Batel, 2007). This is based in particular on experiences of past phenomena [START_REF] Kellens | Perception and Communication of Flood Risks: A Systematic Review of Empirical Research: Perception and Communication of Flood Risks[END_REF][START_REF] Van Der Linden | On the relationship between personal experience, affect and risk perception:The case of climate change: Personal experience, affect and risk perception[END_REF]. Indeed phenomena such as cyclones and their violent winds, heavy rains, earthquakes or even insecurity refer to the idea of human losses and are spontaneously associated with the idea of potential threat and therefore risk. However, this risk culture does not concern flooding by the sea phenomenon. According to our results, it seems that, until then, flooding by the sea have never caused human losses and have had little impact on the communes of Pointe à Pitre and Sainte Anne. The sources of dangers envisaged are little, if any, associated with the coastal dimension of the municipalities: they " do not think about it ". Thus, the phenomenon of flooding by the sea is rarely mentioned spontaneously as a phenomenon existing on Pointe à Pitre or Sainte Anne. When this is the case, the speeches are more anecdotal than about human drama. Moreover, our second objective concerned the relationship between the perception of the coastal dimension of the living area and the perception of the risk of flooding by the sea. The interviews conducted in Pointe à Pitre and Sainte Anne highlighted the fact that the sea is rarely mentioned by respondents to describe their living area. The few individuals who describe their living area as coastal are those who work in contact with the sea or those who have already lived far from it. The sea is thus considered as an integral part of their living environment and not as the limit of it. Thus the populations of Pointe à Pitre and Sainte Anne are divided between those who are turned towards the sea (whose living area integrates the coastal dimension of the municipality) and those who are turned towards the land (whose living area does not integrate this coastal dimension). When it comes to the risk of flooding by the sea, these two groups have quite distinct discourses. Individuals facing the sea recognize it as a source of danger and consider themselves exposed to the phenomenon of flooding by the sea. Nevertheless, they remain more fatalistic than concerned about this. People facing the land, on the other hand, have the impression that a tsunami only would have the strength to flood their living place. Then, flood by the sea is seen as possible according to some people and highly, improbable according to others, the tsunami being considered as an ultimate catastrophe against which nothing can be done. Thus, the fact that living on the seashore does not necessarily imply to imagine this space as a coastal one. But those for whom it is the case are more inclined than others to consider the possibility of flooding by the sea on this space.

The relationship between men and their environment is both physical (" objective ") and social (" subjective ") (Berger and Luckmann, 1966). How a space is described largely depends on who describes it (Breakwell, 2001;[START_REF] Stedman | Toward a Social Psychology of Place: Predicting Behavior from Place-Based Cognitions, Attitude, and Identity[END_REF]. Identity is constructed through social relationships and social comparison: by similarization and differentiation [START_REF] Kuhn | An empirical investigation in self-attitudes[END_REF]. But it is also elaborated through the relationship maintained by individuals with their living environment (lived, uses, etc.) [START_REF] Hauge | Identity and Place: A Critical Comparison of Three Identity Theories<SUP>1</SUP&gt[END_REF][START_REF] Proshansky | Place-identity: Physical world socialization of the self[END_REF].

Let us recall that our sample comes from a population mainly made up of islanders all living not far from the sea and having, for some of them, never lived elsewhere than in Guadeloupe. On this small island of Grande-Terre very far from the French-speaking continent, important cities are all coastal.

Thus those who reside in those cities differentiate themselves primarily from those who reside in the countryside. Even though our study areas are seaside municipalities, most of the people build their identity around this " urban "/" rural " comparison. They attach little importance to the coastal dimension of their living area in the way they describe it. They put more emphasis on its urban dimension. Only few identify themselves as living by the sea and even fewer describe themselves as " living the sea " (E.13). This expression is only relevant in opposition to those who do not integrate the sea into their lives. But for people who live on a space where the sea is everywhere, nobody is really far from it. Hence the coastal dimension concerns everyone at first sight. In this context, the coastal dimension of the living environment is only highlighted by professionals specializing in activities directly linked to the sea. Among the others, many do not even use the sea, not even to swim: " It's not in the culture of the locals. " (E.06). Indeed, if there is a risk culture in Guadeloupe, it does not concern the sea because, for most individuals, the coastal dimension of the living environment is too present to be visible. This element no longer makes sense in the way individuals compare their environment to that of others and, by extension, in the way they compare themselves to others. When we look more closely at the question of the phenomenon of flooding by the sea, the same observation comes back. In most interviews this topic is only developed after the interviewer has guided the discussion on this topic.

Even then, for most of the people interviewed, the idea of flood risk from the sea does not make sense. However, there seems to be a difference in the way in which individuals who lives in these coastal areas perceive their living environment as at risk of flooding by the sea or not. In particular, this is due to the fact that the use that is made of this space is not the same for everyone, so the way of understanding it is not the same. Those who make use of the coastal dimension of their living area are more inclined than others to attach some importance to this dimension in the way they describe this space and themselves. They are also more inclined to recognize the advantages and disadvantages associated with this dimension and thus to recognize the existence of the risk of flooding by the sea. Nevertheless, past experience also plays an important role in risk perception. So far, floods by the sea have only caused material damages, while other phenomena have caused human losses. Thus, if the importance given to the sea makes possible to perceive the risk of flooding by the sea, the importance given to this risk will depend essentially on the assessment of its potential gravity in comparison with the other risks envisaged.

To conclude, these results allow us to identify two profiles of individuals living in Guadeloupe in areas considered by scientists to be at risk of flooding by the sea: the individuals we will describe as " facing the sea " and those " back to the sea ". Back to sea individuals represent the majority of the

  .. the roof left, there only remained the bathroom. " (E.27), and with the rains: 5 Made by Nathalie Krien 6 Made by Nathalie Krien 6/13

https://www.insee.fr/fr/statistiques/3294491?sommaire=3294516&q=Activit%C3%A9%20Guadeloupe

population. For them the sea is not included in the delimitation of their living environment. By extension, the associated dangers are not included in their living environment either. Flooding by the sea does not make sense as a phenomenon likely to impact their environment because it has no place there. Individuals turned towards the sea, for their part, attach great importance to the coastal dimension of the island, they integrate the sea into the delimitation of their living space. At the same time, they recognize the dangers of the sea, including flooding, but seem to accept them in sometimes fatalistic ways. This distinction between individuals facing the sea Vs. individuals back to the sea explains, in part, why so many individuals in Guadeloupe, exposed to flooding by the sea according to scientists do not even consider the occurrence of this phenomenon in their living area. It also demonstrates the importance granted to the coastal dimension of an area for the recognition of the latter's exposure to the phenomenon of flooding by the sea. Thus, in these areas if we wish to assess the vulnerability of populations to flooding by the sea or if we want to understand why individuals continue to live in areas exposed to flooding by the sea and if we want to adapt policies and prevention campaigns to the populations to whom they are addressed, the relationship to the sea is therefore a factor that must be taken into account by the authorities in charge of risk management.


Eric Jauvert

Etienne Palleau

Etienne Dague

Laurence Ressier
email: laurence.ressier@insa-toulouse.fr

Directed assembly of living Pseudomonas aeruginosa on PEI patterns fabricated by nanoxerography for statistical AFM bio-experiments

Keywords: directed assembly, Pseudomonas aeruginosa, PEI, atomic force microscopy, assembly, nanoxerography

est destinée au dépôt

Directed assembly of living Pseudomonas aeruginosa on PEI patterns fabricated by nanoxerography for statistical AFM bio-experiments

Introduction

Atomic force microscope (AFM) is a powerful tool in microbiology since it allows topographical, mechanical and chemical characterizations at the nanoscale of biological objects of interest, still evolving in their culture media. However, working on immobilized living microorganisms is one of the main prerequisites of AFM measurements in liquid. Nowadays, realizing this selective assembly is still challenging since the strength of the grafting has to respect a certain balance: it has to be strong enough to maintain biological objects which can be altered or moved by the AFM tip interaction while scanning the surface; but not too aggressive to prevent them from possible denaturation.

Ideally, a technique that allows the immobilization of living biological objects of interest, on pre-defined periodic arrays over large areas of a substrate will help gaining time on the localization of the zone of observation by AFM and collecting statistical data on heterogeneous population in their culture media. For this purpose, several approaches for cell assembly have been developed and can be divided into two main groups: (i) mechanical trapping in topographically patterned or soft substrates (based on a gel matrix [START_REF] De | Immobilization method of yeast cells for intermittent contact mode imaging using the atomic force microscope[END_REF][START_REF] Gad | Method for immobilizing microbial cells on gel surface for dynamic AFM studies[END_REF] , with patterns obtained by lithography [START_REF] Kailas | Immobilizing live bacteria for AFM imaging of cellular processes[END_REF] , through porous membranes [START_REF] Kasas | A method for anchoring round shaped cells for atomic force microscope imaging[END_REF][START_REF] Dufrêne | Direct Probing of the Surface Ultrastructure and Molecular Interactions of Dormant and Germinating Spores ofPhanerochaete chrysosporium[END_REF][START_REF] Francius | Detection, Localization, and Conformational Analysis of Single Polysaccharide Molecules on Live Bacteria[END_REF] , assisted by convective self-assembly 7 ) (ii) immobilization using localized functionalization of a substrate (based on electrostatic interaction [START_REF] Lower | Measuring interfacial and adhesion forces between bacteria and mineral surfaces with biological force microscopy[END_REF][START_REF] Bolshakova | Comparative studies of bacteria with an atomic force microscopy operating in different modes[END_REF][START_REF] Yoshida | ε-Poly-l-lysine: microbial production, biodegradation and application potential[END_REF] , covalent bonds [START_REF] Camesano | Observation of Changes in Bacterial Cell Morphology Using Tapping Mode Atomic Force Microscopy[END_REF][START_REF] Cerf | Nanomechanical Properties of Dead or Alive Single-Patterned Bacteria[END_REF][START_REF] Razatos | Molecular determinants of bacterial adhesion monitored by atomic force microscopy[END_REF] , antibody-antigen linking [START_REF] Rozhok | Methods for Fabricating Microarrays of Motile Bacteria[END_REF] , assisted by convective self-assembly [START_REF] Ressier | Combining Convective/Capillary Deposition and AFM Oxidation Lithography for Close-Packed Directed Assembly of Colloids[END_REF] ). Nevertheless, all these techniques present a least one negative side effect: complexity of implementation, lack of selectivity in assembling, non-versatility or denaturation of assembled micro-organisms. Over the range of available assembly techniques, electrostatic immobilization is very convenient for electrostatically charged microorganism. Most of them are negatively charged and therefore polycations were used t create positively charged substrates. Among them, Poly L Lysine and Polyethylenimine (PEI) films are probably the most largely employed ones since they provide an efficient grafting and are very simple to implement. However, this technique suffers from two main drawbacks: (i) it generates random deposition of studied microorganisms, (ii) polycation chains poorly grafted to the substrate are released in the solution and contaminate the culture environnement [START_REF] Xia | Preparation and characterization of chemically-crosslinked polyethyleneimine films on hydroxylated surfaces for stable bactericidal coatings[END_REF] .

In the present study, we propose a novel approach where biological objects of interest are electrostatically assembled on Polyethylenimine (PEI) patterns pre-fabricated by nanoxerography (EAPPFN). The nanoxerography process consists in electrostatic trapping of PEI chains on negatively charged patterns written on electret thin films by AFM or electrical micro-contact printing [START_REF] Jacobs | Submicrometer Patterning of Charge in Thin-Film Electrets[END_REF] (e-µCP). The potentialities of this approach are evaluated, by applying it to the medical relevant bacterium, Pseudomonas aeruginosa. This bacteria are, indeed, responsible for hospital acquired infections, and able to acquire resistance to all the known antibiotics. In previous studies we studied the effect of antibiotics on the cell wall of this micro organisms but were limitated by the random deposition of the cells. Here, we have investigated if AFM characterizations in culture media can be carried out of bacteria arrays obtained by EAPPFN, checked the viability of assembled bacteria and studied how to control finely the number of bacteria immobilized on each PEI pattern. Such developments are of first interest to generate statistically relevant AFM data, in a reasonable time scale.

Results and discussion

Fabrication of PEI patterns by nanoxerography and characterizations.

Figures 1 illustrates the two-step protocol of nanoxerography used in this work. First, negatively charged patterns of desired geometry were written into a 100 nm thick polymethylmethacrylate (PMMA) spin-coated on 10 16 cm -3 p-doped silicon substrates, by applying negative voltage pulses either to a highly n-doped silicon AFM tip or a micro-structured gold-metallized PolyDiMethylSiloxane (PDMS) stamp (so-called electrical micro-contact printing (e-µCP) process) (Fig. 1a). These two kinds of charge writings are complementary: AFM charge writing is versatile since AFM allows to draw charge patterns of complex geometry in a few minutes and to quantify their surface potential by its derived electrical mode of Kelvin Force Microscopy (KFM). Charge writing by e-µCP is very useful to fabricate, in parallel, hundreds of thousands of charge patterns covering large areas of substrates or to perform repetitive charge writings with the same stamp on various samples, a necessity for future scaling up and automation of the protocol. In the second phase (Fig. 1b), a 10 µl droplet of 0.2% concentrated solution of aqueous Poly(ethyleneimine) (PEI) was incubated on the electrostatically patterned substrates for 90s. The substrates were subsequently immersed in absolute ethanol for 30s, rinsed with pure water and dried under nitrogen, following the two-step protocol previously developed by our group, for aqueous colloidal suspensions [START_REF] Palleau | Coulomb Force Directed Single and Binary Assembly of Nanoparticles from Aqueous Dispersions by AFM Nanoxerography[END_REF] . This second phase led to the selective electrostatic trapping of the cationic PEI polymer chains on charge patterns of opposite polarity thanks to electrophoretic forces. The first one, consisting of a 17 µm large Occitane cross, illustrates the flexibility in the pattern design offered by AFM nanoxerography (Fig. 2a). The KFM image on the left panel reveals that this charge pattern, written using -30 V voltage pulses, presents a surface potential of -1.5 V.

After development in the PEI solution, the AFM topographical image in the middle panel shows that a 1.5 nm thick PEI layer is selectively grafted on the charge pattern, reproducing it very accurately. As expected, this PEI pattern presents a positive surface potential, of +80 mV in this case (right panel). Figure 2b shows similar results for another pattern geometry obtained by e-µCP nanoxerography. In that case, hundreds of 5 µm wide PEI squares were fabricated on a 1 cm² zone. Each PEI square exhibits a 2 nm mean thickness and a surface potential of about +80 mV.

In both cases, it is important to note that PEI patterns fabricated by nanoxerography present a similar surface potential as observed on regular thicker PEI continuous films. This indicates that such PEI patterns, even composed of a limited number of PEI chains, have the same electrostatic trapping capability than thicker PEI films.

Directed assembly of Pseudomonas aeruginosa bacteria on PEI patterns and characterizations.

The directed assembly of negatively charged Pseudomonas aeruginosa on positively charged PEI patterns was performed by incubation a 10 µl droplet of the aqueous bacteria suspension for 10 min, on arrays of PEI patterns similar to the one depicted in Figure 2b, followed by a rinsing in deionized water. The samples were then transferred in a 10 mM phosphate buffered saline (PBS) buffer to avoid denaturating bacteria immobilized on PEI patterns. It is worth noting that it would not be possible to fix directly the negatively charged bacteria on positively charged patterns written on PMMA because the required immersion of bacteria in ethanol would denature them.

Figure 3a presents typical AFM images in buffer medium of Pseudomonas aeruginosa assembled on an array of 5 µm square PEI patterns. Ten bacteria are immobilized on each PEI square, demonstrating the repeatability of the process. Firmly fixed on the patterns, the bacteria can be imaged in contact monde in buffer medium several hours without revealing any damaging or displacement. Figure 3b shows a zoom-in AFM deflection image of bacteria assembled on the PEI pattern marked by a dashed square in Fig 3a . It evidences ten Pseudomonas aeruginosa immobilized on the 5 µm PEI pattern. The mean height of 500 nm measured on the crosssections of the AFM height images is very typical of living Pseudomonas aeruginosa [START_REF] Formosa | Nanoscale analysis of the effects of antibiotics and CX1 on a Pseudomonas aeruginosa multidrug-resistant strain[END_REF][START_REF] Formosa | Nanoscale effects of antibiotics on P. aeruginosa[END_REF] . Force volume mapping experiments performed in buffer medium evidence heterogeneities of Young's modulus within the bacteria (Fig. 3c). Force volume mappings on 200 nm scan in the middle of the five bacteria labelled in Figure 3b allow us to extract, using the Sneddon model 21 , the distribution of Young's modulus for each bacterium. The elasticity values vary from 740 kPa to 967 kPa, in agreement with values usually reported in the literature [START_REF] Formosa | Nanoscale analysis of the effects of antibiotics and CX1 on a Pseudomonas aeruginosa multidrug-resistant strain[END_REF][START_REF] Formosa | Nanoscale effects of antibiotics on P. aeruginosa[END_REF] . These heterogeneities of elasticity from one bacterium to another pointed out by these distributions show the absolute necessity to perform statistical analysis on a large population of micro-organisms to obtain accurate mechanical characteristics. To check if the cell cytoplasmonic membrane of the immobilized bacteria was not damaged by PEI patterns fabricated by nanoxerography, a Livedead® kit was employed (see Materials and methods section for details). Pseudomonas aeruginosa tagged with the LIVEDEAD® cell viability assays, were immobilized by incubation for 30s on three different silicon substrates: one covered by 5 µm square PEI patterns fabricated by e-µCP nanoxerography, one covered by a PEI thick film and a bare one. Figures 4a and4b present typical fluorescence optical microscopy images taken in buffer medium on assemblies of bacteria on the PEI patterns and the PEI film respectively. These images recorded after 20 minutes of incubation, show that a strong proportion of bacteria assembled randomly on the thick PEI film are colored in red, meaning that their cell wall are permeable to Propidium Iodide and thus damaged. On the contrary, all the bacteria selectively assembled on the PEI patterns fabricated by nanoxerography are colored in green confirming that their cell wall is not denatured. Figure 4c quantified the percentage of damaged bacteria as a function of time grafted in the case of the three tested substrates. The rate of damaged bacteria is about 25% after only 25 minutes and strongly increases with time in the case of bacteria immobilized on PEI films. One hour after their immobilization on the continuous PEI film, 40% of the bacteria are damaged. As reported in the literature, PEI films are toxic for bacteria because PEI chains are released back in the solution [START_REF] Xia | Preparation and characterization of chemically-crosslinked polyethyleneimine films on hydroxylated surfaces for stable bactericidal coatings[END_REF] . The rate of damaged bacteria assembled on a silicon wafer, around 10%, is weak and stable with time. It probably corresponds to the naturally dead bacteria in the starting solution.

Similar results are obtained in the case of bacteria assembled on PEI patterns, indicating that PEI patterns are not toxic for bacteria. This observation points out a major advantage of PEI patterns fabricated by nanoxerography: PEI patterns are constituted of a limited amount of PEI chains selectively attached on charge patterns (a negligible amount of PEI is deposited outside the charge pattern), strongly grafted on the substrate by electrostatic interactions, preventing the culture medium from poisoning. Figure 5a presents a first serie of ten PEI patterns fabricated from 5 µm square charge patterns written with decreasing voltage pulses (-80 V, -75 V, -70V, -65 V, -60 V, -50 V, -40 V, -30 V, -20 V, -10 V from the left to the right). The surface potential of such charge patterns varies from -3 V down to -500 mV (from the left to the right). No charge pattern was visible when using -10 V and -20 V voltage pulses indicating that there is a pulse voltage threshold between -20 V and -30 V, in agreement with previous results [START_REF] Ressier | Electrostatic nanopatterning of PMMA by AFM charge writing for directed nano-assembly[END_REF] . The development by incubation of a PEI solution conducts to 2 nm thick PEI patterns, independently of the surface potential of charge patterns (between -3 V and -1.15 V). All these PEI patterns present a surface potential of +80 mV. No PEI grafting was observed on the -0.770 V charge pattern revealing that the electric field generated by this charge pattern was not strong enough to trap PEI chains. This evidences the existence of a threshold of surface potential of charge patterns (around -1 V) for effective PEI grafting. A more precise analysis of topographical AFM images of PEI patterns reveals a significant decrease of the roughness of PEI patterns with increasing in absolute value the surface potential of charge patterns. This indicates that the density of grafted PEI chains increases with the surface potential of charge patterns in absolute value. Similar results were reported on directed assembly of charged colloidal nanoparticles by AFM nanoxerography [START_REF] Ressier | How to Control AFM Nanoxerography for the Templated Monolayered Assembly of 2 nm Colloidal Gold Nanoparticles[END_REF][START_REF] Palleau | Quantification of the electrostatic forces involved in the directed assembly of colloidal nanoparticles by AFM nanoxerography[END_REF] where an increase of the surface potential led to an increase of NP density on charge patterns.

Here, the increasing surface potential in absolute value, i.e. increasing electric field, generated by charge patterns allows more PEI chains to be assembled on charge patterns while a second layer of PEI molecules cannot be grafted on the first one because of induced electrostatic repulsion between each layer. Figure 5b illustrates a second serie of ten PEI patterns fabricated from square charge patterns of various sizes ranging from 5 µm down to 500 nm (from the left to the right) by 500 nm step. As expected, whatever the initial dimension of the charge pattern, the thicknesses of obtained PEI patterns are homogeneous and are about 2 nm. Their surface potentials are constant around +80 mV; the observed smaller values for the 1 µm and 500 nm pattern come from the average effect artefact inherent to KFM measurements [START_REF] Charrier | Real versus Measured Surface Potentials in Scanning Kelvin Probe Microscopy[END_REF][START_REF] Jacobs | Resolution and contrast in Kelvin probe force microscopy[END_REF][START_REF] Palleau | Numerical simulations for a quantitative analysis of AFM electrostatic nanopatterning on PMMA by Kelvin force microscopy[END_REF] . Pseudomonas aeruginosa bacteria were then assembled on twenty series of PEI patterns similar to the ones depicted in Figure 5. Figure 6 reports the mean number of bacteria immobilized per PEI pattern while varying independently the surface potential of charge patterns (red square symbols) and their lateral size (blue disk symbols). The number of bacteria fixed per pattern increases with the surface potential in absolute value of the charge patterns. As previously mentioned, the increasing surface potential in absolute value of the charge patterns leads to an increasing density of PEI chains grafted on charge patterns which creates more anchoring points for bacteria. On the other side, we observed that the mean number of bacteria assembled per pattern increases with the lateral size of the PEI patterns. The reason for this fine control of the bacteria number per pattern is purely geometrical: once grafted, a single micron sized bacteria do not leave sufficient room for others to be grafted on the same pattern. The fine tuning of any of these two parameters allows adjusting the mean number of trapped bacteria immobilized per PEI pattern down to one single bacteria, as illustrated in the inset of Figure 6.

Conclusion

We presented a novel approach to tackle a major prerequisite of AFM characterizations of living micro-organisms in their culture media: their immobilization on pre-defined areas of a substrate. This approach consists in electrostatic immobilization of biological objects of interest on PEI patterns fabricated by electrostatic trapping of PEI chains on charge patterns written on electret thin films by AFM or e-µCP. As a proof of concept, we validated it using a common opportunistic pathogen, Pseudomonas aeruginosa. The flexibility of nanoxerography allowed us to design PEI patterns with various geometry, size and density of PEI chains. Obtained PEI patterns, only 2 nm thick, present a constant positive surface potential similar to that of continuous PEI thick films. But, contrary to these ones, the strong and selective grafting of a limited amount of PEI chains prevents micro-organisms immobilized on these PEI patterns from poisoning. We demonstrated that the number of bacteria immobilized on each PEI pattern can be controlled down to unity by either tuning the lateral size or the surface potential of charge patterns. This approach allows user-friendly AFM characterizations in buffer medium on large populations of bacteria without any denaturation of these ones. Most of all, it opens a generic route for electrostatically assembling any biological objects of interest and statistically characterize them by AFM in culture media without denaturation.

Materials and methods

Charge writing.

Charge writing was performed under ambient conditions by applying 1 ms negative voltage pulses at a frequency of 50 Hz to a highly n-doped silicon AFM tip (AFM charge writing) or a 1 cm × 1 cm micro-structured gold-metallized PDMS stamp (e-µCP charge writing), while the substrates were grounded. The amplitude of the pulses was varied from -20 V to -80 V. These specific writing conditions are reliable and reproducible, causing no tip, no stamp and/or sample damage at the high voltages used, as demonstrated previously [START_REF] Ressier | Electrostatic nanopatterning of PMMA by AFM charge writing for directed nano-assembly[END_REF] . After the charge writing step, the surface potential of the charge patterns was systematically measured in air by the electrical derived mode of amplitude modulation Kelvin Force Microscopy (KFM).

Growth of Pseudomonas aeruginosa bacteria.

The Pseudomonas aeruginosa ATCC 27853 used in this work were kindly provided by Raphael Duval from SRSMC, Nancy. Pseudomonas aeruginosa cultures were conducted at 35°C in Mueller Hinton media (difco, 275730-500 g) during 24 hours in static conditions. Bacteria at their stationary phase of growth were used. 1mL of media at a 10 8 cells/mL concentration was collected and centrifuged at 5000 rpm during 10 min. Supernatant was then removed and replaced by 1 mL of deionized water. This washing step was repeated 3 times.

AFM characterizations.

AFM images and force spectroscopy on the bacteria assembled on PEI patterns were all carried out in buffer medium in contact mode using an ICON from Bruker, equipped with a Nanoscope V controller. Si 3 N 4 AFM probes (MLCT manufactured by Veeco Instruments), presenting a pyramidal tip, with an opening angle of 35° were used for all the experiments. Their cantilever spring constants were systematically measured using the thermal tune method. They ranged from 10 to 30 pN/nm. The maximum force applied to the cells was limited to 1 nN in order to probe the cell wall elasticity (Young's Modulus) and not the cell turgor pressure that is made at higher loading forces [START_REF] Arnoldi | Bacterial turgor pressure can be measured by atomic force microscopy[END_REF][START_REF] Yao | Atomic force microscopy and theoretical considerations of surface properties and turgor pressures of bacteria[END_REF] . The topography and surface potential of PEI patterns were determined by AFM imaging in tapping mode and KFM mapping under ambient conditions.

Figure 1 .

 1 Figure 1. Schematics of the fabrication of PEI patterns by nanoxerography: charge writing by AFM or electrical micro-contact printing (e-µCP), (b) development by incubation in an aqueous PEI solution.

Figure 2

 2 Figure 2 shows examples of PEI patterns fabricated by AFM and e-µCP nanoxerography.

Figure 2 .

 2 Figure 2. (a) Occitane cross-shaped PEI pattern fabricated by AFM nanoxerography and (b) array of 5 µm square PEI patterns fabricated by e-µCP nanoxerography. In each case, KFM surface potential images of the charge patterns written on a PMMA thin film are presented on the left panel, AFM height images and KFM images of the PEI patterns obtained after development are shown on the middle and the right panels respectively. Representative sections are systematically shown under each image. Note that a larger view by optical microscopy of the array of PEI squares is provided in inset of the AFM height image presented on the middle panel of (b).

Figure 3 .

 3 Figure 3. (a) AFM height image (left) and deflection error image (right) in buffer medium of Pseudomonas aeruginosa assembled on an array of 5µm square PEI patterns similar to the one presented in Fig. 2b, (b) deflection error image of ten Pseudomonas aeruginosa assembled on the square PEI pattern marked by a dashed square on (a), with height profiles of the five bacteria labelled on the deflection error image, (c) Young's modulus force volume mapping in buffer medium of the area observed in (b) with Young's modulus histograms of the five bacteria labelled in (b).

Figure 4 .

 4 Figure 4. (a) Fluorescence microscopy image in buffer medium of Pseudomonas aeruginosa tagged with the Livedead® kit 20 minutes after their assembly on an array of 5 µm square PEI patterns similar to the one presented in Figure 2b (left) and on a continuous thick PEI film (right), (b) Percentage of damaged bacteria as a function of time when assembled on a bare silicon (Si) substrate, a PEI film and PEI patterns.

Figure 5 .

 5 Figure 5. Fabrication of PEI patterns by AFM nanoxerography using charge patterns of (a) decreasing surface potentials and (b) decreasing lateral sizes (from the left to the right). Data reported are KFM surface potential images and associated sections of the charge patterns (top), AFM height images and associated sections of the PEI patterns after development (middle) and KFM images and associated sections of the PEI patterns (bottom).

Figure 6 .

 6 Figure 6. Evolution of the mean number of bacteria assembled per PEI pattern with the lateral size (blue disk symbols) or the absolute value of the surface potential of the charge patterns (red square symbols). An AFM deflection image in buffer medium of an array of single Pseudomonas aeruginosa bacteria immobilized on 1 µm PEI patterns is shown in the inset.

Fluorescence optical microscopy characterizations using a Livedead ® assay

In order to test the viability of Pseudomonas aeruginosa bacteria immobilized on PEI patterns fabricated by nanoxerography, PEI thick film and bare silicon substrate, the bacteria were tagged using a Livedead ® kit, purchased from life Technologies XXX. This kit was composed of two fluorophores: (i) Cyto®9 (green) which enters the cytoplasmic membrane of any bacteria and (ii) propidium iodide (red) which penetrates the cytoplasmic membrane only if bacteria cannot control anymore osmotic flows. Observations in buffer medium by fluorescence optical microscopy of bacteria immobilized on these three substrates allowed us to quantify the percentage of damaged (red colored) and non-damaged (green colored) bacteria.