Julien Rabin
email: rabin@cmla.ens-cachan.fr

Julie Delon
email: delon@telecom-paristech.fr

Yann Gousseau
email: gousseau@telecom-paristech.fr

Artefact-free Color and Contrast Modification

Keywords: contrast modification, color transfer, contrast adjustment, contrast equalization, histogram specification, optimal transportation, image regularization, artefact-free

This work is concerned with the modification of the gray level or color distribution of digital images. A common drawback of classical methods aiming at such modifications is the revealing of artefacts or the attenuation of details and textures.

In this work we propose a generic filtering method enabling, given the original image and the radiometrically corrected one, to suppress artefacts while preserving details. The approach relies on the key observation that artefacts correspond to spatial irregularity of the so-called transportation map, defined as the difference between the original and the corrected image. The proposed method draws on the non-local Yaroslavsky filter to regularize the transportation map. The efficiency of the method is shown on various radiometric modifications: contrast equalization, midway histogram, color enhancement and color transfer. A comparison with related approaches is also provided.

I. INTRODUCTION

A PPLYING contrast changes to digital images is one of the most elementary tool for image enhancement. Such changes may be obtained by applying a prescribed function to the gray values of images, as in contrast stretching or Gamma correction, or by prescribing the histogram of the resulting image, as in histogram equalization or specification from an example image [START_REF] Bovik | Handbook of Image and Video Processing (Communications, Networking and Multimedia)[END_REF]. Such operations are characterized by the way they affect the histogram of an image and may be seen as modifications of their gray level distribution. These techniques extend to color images by considering a luminance channel, as in Gamma correction, or by working on each color channel separately. The prescription of the three-dimensional color distribution is more satisfying because it avoids the creation of false colors, but is also more involved. Actually, a nice theoretical framework enabling to merge the gray level and color cases is the one of optimal transportation, also known as the Monge-Kantorovich problem [START_REF] Villani | Topics in optimal transportation[END_REF], as we will briefly recall in this paper. When the resulting color histogram is prescribed by a target image, one speaks of color transfer. Various approaches to this task are proposed in [START_REF] Reinhard | Color transfer between images[END_REF], [START_REF] Morovic | Accurate 3d image colour histogram transformation[END_REF], [START_REF] Pitié | Automated colour grading using colour distribution transfer[END_REF], [START_REF] Tai | Local color transfer via probabilistic segmentation by expectation-maximization[END_REF].

Applications of contrast or color changes are of course extremely numerous. With the popularization of digital photography, these techniques have became immensely popular through the use of various "curves" in image editing software. Early uses of contrast equalization are the enhancement of medical images [START_REF] Selzer | The use of computers to improve biomedical image quality[END_REF] and the normalization of texture for analysis purposes [START_REF] Rosenfeld | Visual texture analysis[END_REF]. In a related direction, the construction of midway histograms [START_REF] Delon | Midway image equalization[END_REF], [START_REF] Papadakis | A variational model for histogram transfer of color images[END_REF] is useful for the comparison of two images of the same scene. More recently, extensive campaigns of old movies digitization have claimed for the development of contrast modification techniques to correct flicker [START_REF] Delon | Movie and video scale-time equalization application to flicker reduction[END_REF], [START_REF] Delon | Stabilization of flicker-like effects in image sequences through local contrast correction[END_REF]. Similar techniques are commonly used in the post-production industry [START_REF] Haro | Visual acuity in day for night[END_REF], [START_REF] Bertalmío | Perceptual color correction through variational techniques[END_REF]. Another field of increasing industrial interest in which contrast changes play a central role is the one of imaging in bad climatic conditions, see e.g. [START_REF] Narasimhan | Vision and the atmosphere[END_REF]. Color modification or transfer is also useful for a wide range of applications: aquatic robot inspection [START_REF] Torres-Méndez | Color correction of underwater images for aquatic robot inspection[END_REF], space image colorization [START_REF] Lipowezky | Grayscale aerial and space image colorization using texture classification[END_REF], enhancement of painting images, etc.

A common drawback of most methods aiming at modifying the contrast or color content of images is their strong tendency to create visual artefacts. Indeed, when increasing the contrast, parasite structures that were barely visible become prominent. Most noticeable is the enhancement of noise and compression scheme patterns, such as "block effect" due to the JPEG standard. In the other direction, contrast reduction or color transfer may yield detail loss and texture washing. A last artefact is particularly noticeable in the case of color transfer and appears when the proportions of colors are very different between images. The goal of this paper is to propose a universal approach to remove those artefacts. This approach can be used as a post-processing for many classical image modification tasks, such as contrast and color transfer, movie restoration, gammut mapping, High Dynamic Range (HDR) image visualization, etc.

Before proceeding, we now recall some of the approaches that have been proposed in the literature to suppress artefacts due to contrast or color modification. The simplest one is proposed in [START_REF] Pizer | Adaptive histogram equalization and its variations[END_REF] in the context of local histogram modifications, and amounts to limit the modification depending on gradient values. While improving the results in some cases, this approach let most artefacts untouched. In [START_REF] Pitié | Automated colour grading using colour distribution transfer[END_REF], it is proposed to correct color transfer artefacts by using a variational regularization after the transfer. Still in a variational framework, the authors of [START_REF] Papadakis | A variational model for histogram transfer of color images[END_REF] propose a unified formulation containing both color transfer and regularity constraints in a single energy minimization. For the problem of color proportion, a possible approach is to transfer color after having identified some homogeneous regions, as proposed in [START_REF] Abadpour | An efficient PCA-based color transfer method[END_REF], [START_REF] Tai | Local color transfer via probabilistic segmentation by expectation-maximization[END_REF]. A related class of works takes interest in the avoidance of compression artefacts, usually using the properties of the compression scheme, see e.g. [START_REF] Alter | Adapted total variation for artifact free decompression of jpeg images[END_REF].

In this paper, we propose to remove all the artefacts described above by regularizing the transportation map, defined as the image of the differences between the original image and the one after contrast or color modification. Indeed, we will show that all these artefacts may be interpreted as spatial irregularities of this transportation map. In order to regularize this map without introducing blur in the final image, we take inspiration from non-local methods [START_REF] Buades | A review of image denoising algorithms, with a new one[END_REF] that have been proposed for image denoising and more precisely from the Yaroslavsky filter [START_REF] Yaroslavsky | Digital Picture Processing, An Introduction[END_REF]. The transportation map is filtered by averaging pixel values using weights that are computed on the original image, therefore adapting to the geometry of this initial image. It will be shown that artefacts are progressively suppressed by iterating this filtering stage and that the proposed filter generally provides better results than the approaches described in the previous paragraph.

The paper is organized as follows. In Section II the general setting for contrast and color modifications is introduced. The generic approach proposed in this work is given in Section III and experiments are displayed in Section IV. In the appendices, useful facts and results about optimal transportation and powers of stochastic matrices are given.

II. COLOR AND CONTRAST MODIFICATION

In this section, we recall how color and contrast modifications can be applied to images and why they are likely to create visual artefacts.

A. Contrast or color distribution of an image

Let u : Ω → R n be a discrete image, with n = 1 for a gray level image, n = 3 for a color image, and where Ω ⊂ Z 2 is the bounded image domain. Assume that u takes its values in the set {y 1 , . . . , y P } ⊂ R n , then the gray level or color distribution of u is defined as

h u = P i=1 h i δ yi , (1)
where

h i = 1 |Ω| | {x ∈ Ω; u(x) = y i } |.
When n = 1, we denote by H u the cumulative distribution function of h u . The distribution h u is also called the gray level or color histogram of u and H u is called its cumulative histogram.

B. Color and contrast modifications

It is usual to apply simple radiometric transformations to a gray level image in order to improve its contrast and level of details. Such transformations generally consist in an increasing function T , in order to preserve gray level ordering. The image u becomes T (u), and its gray level distribution becomes h T (u) = P i=1 h i δ T (yi) . Particular cases of such transformations are histogram stretching (T (x) = ax + b) or histogram clipping (T (x) = min(β, max(α, x))), used for instance to improve visualization in satellite or medical imaging [START_REF] Selzer | The use of computers to improve biomedical image quality[END_REF]. Another example is the function T (x) = log(1 + x), which is particularly useful to visualize images of Fourier transforms, or high dynamic range images [START_REF] Durand | Fast bilateral filtering for the display of highdynamic-range images[END_REF]. Similar transformations can also be applied to the luminance channel of a color image (see an example of histogram clipping in Figure 1(j)). Note that some other methods have been developed for local contrast enhancement, e.g. making use of the Curvelet transform [START_REF] Stark | Adaptive image contrast enhancement using generalizations of histogram equalization[END_REF], of a variational framework [START_REF] Bertalmío | Perceptual color correction through variational techniques[END_REF], or of a PDE formalism [START_REF] Morel | A PDE formalization of Retinex theory[END_REF].

In some cases, it is useful to assign to an image u a given target distribution f . This amounts to find a mapping T (called contrast or color transfer) such that the distribution of T (u) is equal or at least close to f , i.e. such that h T (u) f.

(2)

Most of the time, the equality cannot be exactly satisfied. For instance, if h u = δ 1 2 (u is a constant image) and f = 1 2 (δ 0 + δ 1 ), there is no mapping T such that the distribution of T (u) is exactly f . T is thus generally chosen so that h T (u) be close to f in some sense.

For n = 1, Equation ( 2) can be satisfied in the sense that the cumulative distribution functions H T (u) and F coincide on the values taken by T (u). This is always possible in the continuous setting (i.e. when F is continuous). Now, if we add the constraint that T is increasing, the solution is given by

T = F -1 • H u , (3)
where

F -1 is defined as F -1 (t) = inf{λ ∈ R; F (λ) ≥ t}.
If f is a constant distribution on the range of u, Equation (3) yields the well known histogram equalization. More generally, if f is the gray level distribution h v of another image v, then T = H -1 v • H u is called histogram specification. These transformations can also be applied to the luminance channel of a color image (an example is displayed in Figure 1(b)). Some variants of this framework have been proposed to apply such equalization locally [START_REF] Pizer | Adaptive histogram equalization and its variations[END_REF], [START_REF] Caselles | Topographic maps and local contrast changes in natural images[END_REF] (see Figure 1(c) and 1(d)), or with a data fidelity term [START_REF] Arici | A histogram modification framework and its application for image contrast enhancement[END_REF].

When n ≥ 2, the interpretation of Equation ( 2) is less clear and the monotonic constraint cannot be used anymore to find an optimal mapping T . A naive solution, proposed in [START_REF] Reinhard | Color transfer between images[END_REF] in the case of color images, consists in applying an affine transformation to the color distribution of u in order to match the mean and variance of the color distribution f . If this elementary solution can be satisfying for cases involving images having similar and simple color distributions, it usually fails in general cases. In order to find a satisfying mapping in the general case, the problem must be seen in the framework of optimal transport, as described in more details in Appendix A. If n = 1, this framework leads to formulas similar to (3) for histogram equalization and specification. If n ≥ 2, however, no analytic formulation can be found for the optimal mapping T . Such mappings can be estimated numerically, for instance by using the simplex algorithm. Most of the time, this estimation leads to expansive computations. In practice, a common approximation is to perform an histogram specification separately on the three channels of the color image (see e.g. [START_REF] Mccollum | Multidimensional histogram equalization and modification[END_REF]). Though, a more satisfying approximation can be computed by estimating iteratively 1-D optimal mappings on random axes, as proposed in [START_REF] Pitié | Automated colour grading using colour distribution transfer[END_REF] and studied in [START_REF] Rabin | Wasserstein Barycenter and its Application to Texture Mixing[END_REF] (an illustration is proposed in Figure 1(m)). The result is fast to compute, although not perfectly optimal in the sense of the Monge-Kantorovich transport problem described in Appendix A.

C. Visual artefacts

As it can be observed from the several examples provided in Figure 1, four major visual artefacts can be caused by contrast or color modifications:

Noise enhancement: this happens if the variance of the noise in u increases after the application of T to u, as illustrated for instance in Figures 1(b) and 2(d) for histogram equalization. Compression artefacts: these artefacts appear when the original image u is the result of some compression scheme (e.g. JPEG) and when pixels with similar colors are mapped to different colors (see e.g. Figure 1(o)). Detail loss: this results from a reduction of contrast between u and T (u), and can be observed for instance on the head of the bird in Figure 1(p). Color proportion inconsistencies: Ideally, the mapping T should be defined in such a way that pixels having similar colors in the original image are mapped to similar colors. However, this is unfeasible if the proportions of colors are very different in the original and the target distributions, as illustrated by Figure 1(q) and 6(i).

Our approach to remove these artefacts relies on the observation that they are all due to spatial irregularities of the transportation map of the image u, defined as T (u) -u. Indeed, when comparing the geometrical information of the transportation map with the one of the original color map (see for instance Figures 6(j) and 6(g)), each of the aforementioned artefacts appears as an irrelevant high frequency feature. As a result, a piece-wise constant transportation map (as displayed for instance in Figure 6(k)) taking into account the geometry of the image will considerably reduce artefacts from color and contrast modification. In this paper, the proposed solution to obtain such a desired transportation map consists in applying a guided edge-preserving filter to the transportation map, using the original image.

III. A NEW REGULARIZATION APPROACH FOR TRANSPORTATION MAPS

Following the observations of the previous section, we propose to spatially filter the transportation map. The solution we chose is inspired from non-local filters [START_REF] Buades | A review of image denoising algorithms, with a new one[END_REF]. This concept has been introduced for image denoising by Yaroslavsky [START_REF] Yaroslavsky | Digital Picture Processing, An Introduction[END_REF]. Similar filters have been independently defined, as SUSAN [START_REF] Smith | SUSAN-A New Approach to Low Level Image Processing[END_REF] or the Bilateral Filter [START_REF] Tomasi | Bilateral filtering for gray and color images[END_REF]. More recently, a somehow radical extension of this approach, the so-called "Non-Local Mean" filter [START_REF] Buades | A review of image denoising algorithms, with a new one[END_REF] has been shown to outperform many approaches to image denoising. In what follows, we will make use of a variant of the Yaroslavsky filter to regularize transportation maps.

A. Transportation Map Regularization

Recall that T (u) is the image after color or contrast modification. In what follows, we write M(u) := T (u) -u for the transportation map of image u. We propose to regularize it thanks to the operator Y u , a weighted average with weights depending on the similarity of pixels in the original image u.

The effect of this operator on an image

v : Ω → R n with n ≥ 1 is defined as Y u (v) : x ∈ Ω → 1 C(x) y ∈ N (x) v(y) • w u (x, y) dy with weights w u (x, y) = e -u(x)-u(y) 2 σ 2 , (4)
where . stands for the Euclidean distance in R n , where

N (x) = x + N (0) ⊂ Ω, with N (0) a spatial neighborhood of 0,
where σ is a tuning parameter of the method and C(x) is the normalization constant C(x) = y∈N (x) w u (x, y)dy .

Observe that if we apply Y u to the image u, we obtain the Yaroslavsky filter [START_REF] Yaroslavsky | Digital Picture Processing, An Introduction[END_REF]. If the weights also decrease as a function of the distance to x, Y u becomes similar to the cross bilateral filter introduced in [START_REF] Eisemann | Flash photography enhancement via intrinsic relighting[END_REF] for flash photographic enhancement.

The regularization of the image T (u), referred to as Transportation Map Regularization (TMR), is then defined as TMR u (T (u)) := u + Y u M(u). Now, observe that this formulation can be divided in two terms:

TMR u (T (u)) = Y u T (u) filtering of image T (u) + u -Y u (u) image detail . (5)
First, the image T (u) is filtered by a non-local operator Y u , following the regularity of the image u. This operation attenuates noise, compression and color proportion artefacts but also the details of the image T (u). The second operation performed by the TMR filter consists in adding the quantity u details = u -Y u (u), which can be considered as details of the original image (e.g. texture and fine structures). We will see in the experimental section that these two steps are very important to obtain a natural rendering of the image.

B. Properties

The previously defined filter has several nice properties which enable us to reduce the visual artefacts described in Section II-C.

First, observe that this filter leaves all the images u + λ, λ ∈ R n , unchanged. Moreover, if the application T consists in a multiplication by a positive constant α, then TMR u (αu

) = αu + (1 -α) • u details . If α > 1
, the transfer T increases the contrast. In that case, the TMR filter reduces the noise contained in the image difference u details . If α < 1 the transfer T decreases the contrast and the TMR filter restore the lost details contained in u details . Last, another interesting aspect of the TMR filter is that the discrete distribution of the regularized image TMR u (T (u)) is contained in the convex hull of the specified distribution of T (u). This property somewhat prevents the creation of false colors which may be caused by the regularization process.

C. Iteration of TMR and convergence study

In practice, more than one iteration of the TMR filter is required to remove all the aforementioned artefacts. The image T (u) after k iterations of the TMR filter can be written as follows: where Y k u refers to the recursive use of the Y u filter. An illustration for histogram equalization is given in Figures 5(b) and 5(a), where the equalized image (Fig. 1(b)) is regularized using respectively one and several iterations of the TMR filter.

TMR k u (T (u)) := Y k u T (u) -u + u ,
The question is then how to choose the right number of iterations k and one may wonder what happens for large values of k. Studying the limit of Y k u when k → ∞ boils down to the study of the limit of the powers of a matrix. Indeed, let us resize the discrete image u into a column vector v of size m. In this setting, the linear filter Y u can be written as an m × m matrix A , whose coefficients are

A i,j = w u (i, j) • 1 j∈N (i) m k=1 w u (i, k) • 1 k∈N (i) , 1 ≤ i, j ≤ m. (6)
In this formulation, i is the index in the vector v of a pixel x in u, and N (i) is the set of indexes in v corresponding to the 2-D neighborhood N (x) in u. If we resize the map T (u) -u into the vector w, then Y k u (T (u)-u) corresponds to the vector A k w. Now, observe that the matrix A is stochastic, i.e. that A i,j ≥ 0, ∀i, j and m j=1 A i,j = 1, ∀i. If we assume that A is primitive, i.e. that A r is strictly positive for some r ∈ N * (and this is clearly true if the neighborhoods N (x) are disks of radius ρ > 1 in Equation ( 4)), the Perron-Frobenius theorem permits to conclude that A k tends toward a stochastic matrix A ∞ when k → +∞, and that all the lines of A ∞ are equal (see Appendix B). This means that the map Y k u (T (u) -u) tends toward a constant image Y ∞ u (T (u) -u). In other words, the limit image TMR ∞ u (T (u)) is only a shift of the image u by a constant color.

The Perron-Frobenius theorem also gives information on the convergence rate of A r towards A ∞ . More precisely, we know that A r -A ∞ behaves as O(|λ| r r m(λ)-1 ), where λ is the eigenvalue of A with the second largest modulus and where m(λ) is the algebraic multiplicity of λ. In practice, |λ| is generally close to 1 for a similarity matrix A, and the resulting convergence rate is quite slow, as it will be confirmed in the experimental section. The aim of the next section is to propose a way to stop automatically the iterations of the filter TMR.

D. Stopping criterion

In order to control the iterations of the TMR filter, we compute at each iteration a convergence map, written C and defined at each pixel as follows:

C(x) = Y k u M u(x) -Y k-1 u M u(x) ,
where . is the average Euclidean norm in R n . We then consider that there is numerical convergence in pixel x when C(x) < t, and the TMR filter is only applied to pixels for which the convergence map is greater than the threshold t. In all experiments, the convergence threshold has been set equal to t = 1 (for n × 8-bit images). In practice, if x is the first pixel to attain this numerical convergence, this boils down to replace the line corresponding to x in matrix A by the same line in the identity matrix. The new matrix A 1 is then iterated until a second pixel attain numerical convergence, and A 1 is then replaced by A 2 , etc.

Observe that each matrix A j is stochastic and such that A k j converges when k → +∞ (see Appendix C for a proof), which implies that a new pixel attains numerical convergence after a finite number k j of iterations. The whole process hence stops once all pixels are in C(x). At the end, if v is the vector corresponding to T (u) -u, we get

v ∞ = A kn-1 n-1 . . . A k1 1 A k0 • v . (7)
Observe that the proposed stopping criterion permits also to save computation time since the iterations of the TMR filter concern fewer and fewer pixels.

IV. EXPERIMENTAL STUDY

This section presents several applications of the TMR filter.

Observe that this filter relies on two different parameters. The most important one is σ, which is used to compute the weighting terms in the computation of the regularized map (Formula (4)). In the following experiments, we have used σ = 10 The second parameter is related to the size of the neighborhood N (x). In experiments, we used disks of radius ρ = 10.

A. Convergence study

This paragraph illustrates the interest of the stopping criterion introduced in Section III-D. Consider the image u of Figure 2(a). This image has a narrow dynamic range, as illustrated by its histogram (Fig. 2(b)). Applying an histogram equalization to u yields an image u eq with a more satisfying dynamic range but also increases the noise level (Fig. 2(d)). Using the stopping criterion proposed in Section III-D, 23 iterations of the TMR filter are required to converge in the sense of [START_REF] Selzer | The use of computers to improve biomedical image quality[END_REF]. This permits to reduce dramatically the noise level while preserving the contrast and details of u (Figs. 2(e) and 2(m)).

The asymptotic behavior of the iterated TMR filter without using this stopping criterion is illustrated by the Figures 2(e) to 2(o). In accordance with the convergence study of Section III-C, we observe that the map Y k u u eq -u) tends toward a constant map Y ∞ u u eq -u) 1 when k increases. The convergence rate is illustrated by Figure 2(c), which plots the values of the norm TMR k u u eq -TMR ∞ u u eq when k increases. As expected, this convergence rate is very slow. This confirms that, while the threshold on the convergence is important in practice, its precise setting is not crucial.

B. Contrast modification

In this section, we investigate different applications of contrast modification to illustrate the interest of the proposed approach. In this context, we propose in Section IV-B3 a comparative study of our scheme with different regularization approaches that have been proposed in the literature. Notice how the artefacts described in Section II-C are present in these examples, in particular the enhancement of both noise and compression artefacts. In each case, the iterated TMR filter permits to remove these artefacts while preserving contrast and restoring details (see e.g. Figure 1(f)).

In Figure 3, a challenging example of contrast modification using both histogram clipping and Gamma correction is given, resulting in an increase of noise level. The result of the iterated TMR filter is illustrated in Figure 3(d), using σ = 4. Observe that our approach limits the noise enhancement and maintains the desired contrast modification. It should be noticed that using σ = 10 (see Figure 3(d)) on this example is not satisfying due to the very poor dynamic of the original image (Fig. 3(a)). This illustrates that the practical choice of the parameter σ may depend on the considered contrast or color modification.

2) Flicker reduction: The proposed regularization scheme can also benefit the restoration of old movies. Figure 4(a) shows three images of a sequence suffering from a strong local flicker (fast and unnatural intensity fluctuations from one frame to the other). This sequence is restored by the local method proposed in [START_REF] Delon | Stabilization of flicker-like effects in image sequences through local contrast correction[END_REF] and the three corresponding restored frames are shown on Figure 4(b). The method manages to harmonize the local contrast in the sequence. However, as we can see, the flicker and film compression are so brutal that several artefacts appear on some parts of the frames (see for instance both heads in the second image and the jacket in the third image in Figure 4(b)). Figure 4(c) shows how these defects are corrected by the iterated TMR filter.

3) Comparison with other regularization approaches: In the following paragraphs, we confront our method with other approaches that have been proposed in the literature to reduce irregularities created by contrast modifications.

Gradient control: The approach of [START_REF] Pizer | Adaptive histogram equalization and its variations[END_REF], that has been proposed to enhance the contrast of medical images, consists in applying local histogram equalizations independently on subparts of an image. We return to the images of Figure 1 to illustrate this point. Figure 1(c) shows an example where the image has been divided into 8-by-8 overlapping tiles. To prevent the noise level to skyrocket (in particular in constant regions), the gradient of the transportation map is restricted to a user-defined interval, which also limits the contrast enhancement. In practice, one can observe that artefacts, if still present, are less noticeable than in the classical histogram equalization (Fig. 1(b)). Figure 1(h) shows that the iterated TMR filter enables to remove the remaining artefacts while preserving the local contrast changes.

Two-scale decomposition technique: Figure 5(b) shows the result of a single iteration of the TMR filter when the mapping T is an histogram equalization (denoted here by the operator EQ) applied to the image u of Figure 1(a). Following [START_REF] Pitié | Automated colour grading using colour distribution transfer[END_REF], the resulting regularized image can be written as TMR u (EQ(u)) = Y u • EQ(u) + u details , where u details = u -Y u (u) is the detail image. This formulation shares similarity with the approach proposed by Durand and Dorsay in [START_REF] Durand | Fast bilateral filtering for the display of highdynamic-range images[END_REF] in a different context for tone mapping (contrast reduction for high dynamic range images). In their framework, the image u is first decomposed into a base layer using the bilateral filter (corresponding here to Y u (u)) and a detail layer u details = u -Y u (u). A contrast reduction is then applied to the base layer, and u details is added to the result to obtain the final image. Figure 5(c) demonstrates that this approach, well suited for dynamic reduction, is not adapted to contrast enhancement, yielding discontinuities in flat regions.

One can see on Figure 5(a) how using iterations of the TMR filter until convergence yields even a better result. It is noticeable that this framework shares some common features with the two-scale decomposition approach of [START_REF] Durand | Fast bilateral filtering for the display of highdynamic-range images[END_REF].

Regraining: Another regularization scheme has been proposed by Kokaram et al. [START_REF] Pitié | Automated colour grading using colour distribution transfer[END_REF] as a post-processing for color transfer and can also be used for contrast modification. This scheme relies on a variational formulation combining two fidelity terms: one depending on the gradient of images and the other one on their gray levels. These two terms are weighted by two spatial-adaptive functions, which depend on the gradient norm of the original image. The result of our implementation of their algorithm on the equalized image EQ(u) is shown on Figure 5(d). Although the visual impact of artefacts is reduced, this method fails to restore completely details, yielding a blurred and "mottled" appearance.

C. Color transfer

This section presents the results of our regularization filter on several color transfer examples (see Section II-B). In all [START_REF] Delon | Stabilization of flicker-like effects in image sequences through local contrast correction[END_REF]. Observe that the contrast is well harmonized over the sequence, but some artefacts related to brutal and local contrast modifications appear. Figure 4(c): The iterated TMR filter permits to remove those artefacts.

(a) Iterated TMR filter on EQ(u) .

(b) One iteration of TMR on EQ(u): Yu • EQ(u) + u details .

(c) Alternative approach: EQ • Yu(u) + u details .

(d) Regraining [START_REF] Pitié | Automated colour grading using colour distribution transfer[END_REF] on EQ(u). these experiments, the raw color transfer is computed thanks to the algorithm proposed in [START_REF] Pitié | Automated colour grading using colour distribution transfer[END_REF], which is both fast and easy to implement.

1) Four examples:

We have already analyzed the color transfer example displayed at the bottom of Figure 1, which exhibits many artefacts (see details given in Figures 1(o), 1(p) and 1(q)). Figure 1(n) shows the result of several iterations of the TMR filter (until the stopping criterion is reached) on this example. As it can be observed on the different zooms, the regularization removes all compression artefacts while restoring fine details in the image and reducing color proportion problems.

Two additional examples of color transfer are proposed in Figure 6. The first one (Fig. 6(a) to 6(f)) illustrates the two-terms decomposition of Equation [START_REF] Pitié | Automated colour grading using colour distribution transfer[END_REF]. Let u denote the original image (Fig. 6(a)) and T (u) the same image after color transfer (Fig. 6(c)), using the color palette of Figure 6(b). Then TMR u (T (u)) (Fig. 6(f)) can be seen as the sum of Y u (T (u)) (Fig. 6(d)), the filtered version of T (u), and u -Y u (u) (Fig. 6(e)), which restores the details of the original image u. In the second example, at the bottom of Figure 6, the colors of Mahana no atua by Gauguin are transferred to the painting Le Déjeuner des Canotiers, by Auguste Renoir. The resulting raw transportation map is shown on Figure 6(j), while Figure 6(k) and 6(l) show respectively the transportation map and the result of the color transfer after several iterations of TMR filter. Among other effects, the annoying color proportions problems (see for instance the blue spots on the white clothes) completely vanish, resulting in a far more plausible image.

A last example is given in Figure 7 to illustrate the versatility of the proposed approach for various color modification techniques. In this example, the image shown in Figure 7(a) is modified using an image editing software (The Gimp) to separately increase both the contrast and the saturation of colors. The result of this operation, along with some artefacts, is visible in Figure 7(b). Again, the proposed method makes it possible to attenuate color blotches and to restore lost details (as can be seen e.g. on the patterns on the roofs in Figure 7(c)).

2) Comparison with other approaches: Two results of the regraining approach [START_REF] Pitié | Automated colour grading using colour distribution transfer[END_REF], respectively on the Renoir/Gauguin experiment and on a Lena/Barbara color transfer, are shown respectively on Figures 8(a) and 8(h). While this variational approach tends to reduce irregularities in the transportation map, it fails at removing severe compression artefacts or inconsistencies in color proportions. As a comparison, the result of the iterated TMR filter on both examples can be seen on Figures 8(b) and 8(i).

Another variational approach has been proposed very recently to transfer color between several images while preserving their geometry [START_REF] Papadakis | A variational model for histogram transfer of color images[END_REF]. This interesting approach enables to perform simultaneously the desired color transfer and its regularization thanks to a unified energy minimization framework, relying on several terms: a quadratic data fidelity term, a color distribution constraint based on cumulative histograms, and a regularization term preserving the geometry of the images. The result of this approach for the Renoir/Gauguin experiment is displayed in Figure 8(c), and for the Lena/Barbara color transfer in Figure 8(j). Observe that the method achieves the transfer without producing strong artefacts. It is interesting to see that some color inconsistencies are still occurring (Figs. 8(c) and 8(j)) which are removed with the iterated TMR filter (Figs. 8(d) and 8(k)).

D. Discussion

Patch-based regularization: Following the idea of the NL-means filter [START_REF] Buades | A review of image denoising algorithms, with a new one[END_REF], one could think of replacing the pixelwise comparisons in the TMR filter by patch comparisons. Indeed, in [START_REF] Buades | A review of image denoising algorithms, with a new one[END_REF], Buades et al. show that using small patches instead of pixels increases the confidence level on the similarity measure between pixels corrupted by noise. In our case, it boils down to replace the weights in Formula (4) by

ŵu (x, y) = exp -z∈ W u(x + z) -u(y + z) 2 nσ 2 ,
where W is a centered square neighborhood defined on the pixel grid, and where n is the size of W . Using patches in our framework does not improve the results (see Figure 9(e) for a comparison). On the contrary, using the same parameter σ, some fine structures are more blurred (along edges or stokes) with this approach, while some artefacts are less regularized (see the compression artefacts around the book title). Indeed, the use of patches tends to increase the similarity between pixels across edges, so that even some contrasted structures are blurred after several iterations. At the same time, the use of patches tends to decrease the similarity of pixels of nonrepetitive structures (see [START_REF] Duval | On the parameter choice for the Non-Local Means[END_REF] for details), which explains that some artefacts remain. While Yaroslavsky filter is less robust than the NL-means for denoising purposes, it is particularly adapted in our case, where the image u is regular. It permits a faster approach and a better preservation of edges.

Median-based regularization:

In some cases, it could be interesting to replace Yaroslavsky filter by a median filter. Indeed, the median filter requires only one parameter (the size of the neighborhood), it does not introduce blur and it is able to remove small objects (for instance salt and pepper noise). In the case of contrast modifications, Formula (5) can be rewritten as

TMR u (T (u)) = Med u T (u) + u -Med u (u) ,
where [Med u (v)](x) is the weighted median of the values v(y) when y spans N (x), with weights wu(x,y) C(x) . Figure 9(d) displays an example of the median based TMR filter. The result presents typical characteristics of median filter approaches, avoiding blurring effects that are inherent to averaging filters, while providing some unsatisfactory piece-wise constant regions.

V. CONCLUSION

In this paper, we have introduced a generic filtering procedure in order to remove the different kinds of artefacts created by radiometric or color modifications. The ability of the proposed TMR filter to deal these artefacts while restoring the fine details of images has been demonstrated on various examples. Several extensions of this work are foreseen. First, notice that the computation time of the TMR operator is similar to those of the Bilateral filter [START_REF] Tomasi | Bilateral filtering for gray and color images[END_REF] or Non-Local means [START_REF] Buades | A review of image denoising algorithms, with a new one[END_REF]. As a consequence, it could directly benefit from several accelerations techniques that have been proposed recently in the literature for those type of filters, as for instance, multiscale approximations [START_REF] Kervrann | Local adaptivity to variable smoothness for exemplar-based image denoising and representation[END_REF], the use of kd-tree structures for fast computation of pixels comparison [START_REF] Adams | Gaussian KD-trees for fast high-dimensional filtering[END_REF], or FFT-based convolutions [START_REF] Darbon | Fast nonlocal filtering applied to electron cryomicroscopy[END_REF]. Second, the whole procedure would also be strengthened by the automatic estimation of the parameters σ and ρ (for instance, by considering the recent work of [START_REF] Duval | On the parameter choice for the Non-Local Means[END_REF]), even if most experiments gives satisfactory results running the same parameter values. In particular, when considering movie restoration, those parameters should be set adaptively, depending on the local motion and the local contrast change. Last, we plan to increase the control of color inconsistencies. Indeed, the approach presented here permits to remove artefacts due to color proportions as long as these are not too extreme. But it cannot completely modify the proportions of colors in the final image. In the case of color transfer, one possible option would be to transfer colors from a precomputed "color palette" [START_REF] Tai | Local color transfer via probabilistic segmentation by expectation-maximization[END_REF], [START_REF] Delon | Automatic color palette[END_REF]. We also believe that the scheme presented in this paper can benefit other applications that color or contrast modifications. One possible framework of application, for which the approach should of course be adapted, is the one of the fusion of panchromatic and multispectral images [START_REF] Ballester | A variational model for p+xs image fusion[END_REF].

(Q k ) i,l Q l,j ≤ m-r l=1 (Q k ) i,l .
Moreover, for each line i ≤ m -r, there exists a rank k 0 such that for all k ≥ k 0 , m-r j=1 (Q k ) i,j < 1. Indeed, the set C of points which have already converged is not isolated in the image.

Step by step, each point outside of C (indexes {r + 1, . . . m} in B) undergoes the influence of at least one point of C (indexes {1, . . . r} in B) after a large enough number of iterations, which implies that for all i ∈ {r + 1, . . . m}, there exists k 0 and j ∈ {1, . . . r} such that R k (i, j) > 0 for k ≥ k 0 .

The index k 0 can be chosen such that this property holds for all i ∈ {1, . . . , m -r}. Since these sequences are decreasing, there exists γ in ]0, 1[ such that for all i and all k > k 0 , m-r j=1 (Q k ) i,j < γ. Thus, for each p ∈ N + * , m-r j=1

(Q pk+k ) i,j = m-r j=1 m-r l=1 (Q pk ) i,l (Q k ) l,j ≤ γ m-r l=1 (Q pk ) i,l < γ p+1 .

It follows that

Fig. 1 .

 1 Fig. 1. Examples of visual artefacts produced by different image processing techniques and the corresponding regularizations. The first row exhibits several images resulting from different contrast enhancement methods applied to the same original image (Fig. 1(a)). The second row shows the corresponding applications of the TMR filter proposed in this paper. The third row shows an example of color transfer (colors of Figure 1(l) are affected to Figure 1(k)). Resulting artefacts are visible on Figure 1(m) and are shown to be removed by the TMR filtering in Figure 1(n). The fourth row shows corresponding details illustrating the various artefacts and their removal. Note: All the images in this paper are much better appreciated when viewed full size from the electronic version of this article. All examples are available at: http:// perso.telecom-paristech.fr/ ∼ delon/ artefact removal html/ .

  Average Euclidean norm of difference ||TMR k u ueq -TMR ∞ u ueq|| as a function of the the number of iterations k. (d) Equalization ueq. (e) TMR 23 u ueq. (f) TMR 10000 u ueq. (g) TMR ∞ u ueq (h) Transportation map ueq -u. (i) Transportation map Y 23 u (ueq -u). (j) Map Y 10000 u (ueq -u). (k) Constant map Y ∞ u (ueq -u).

Fig. 2 .

 2 Fig. 2. Convergence study of the iterated TMR filter. (a) a low dynamic range image u and (b) its gray level histogram; (d) image ueq, obtained by applying an histogram equalization to u, and (l) histogram of ueq; (h) the corresponding transportation map M(u) = u -ueq; (e) to (g) iterations of the TMR filter, with (e) 23 iterations (corresponding to the automatic stopping criterion), (f) 10000 iterations and (g) convergence; (m) to (o) the corresponding gray level histograms; (i) to (k) the corresponding transportation maps. Observe how the 23 iterations chosen by the stopping criterion permit to reduce the noise level while preserving contrast and image details.

4 Fig. 3 .

 43 Fig. 3. Application of the iterated TMR filter for Gamma correction. Figures 3(a) and 3(b): gray-level image and its contrast enhancement via histogram clipping and Gamma correction (with γ set to 1 2 ).Figure 3(c) and 3(d): result of the iterated TMR filter, respectively with σ = 10 and σ = 4.

Figure 3 (

 3 Fig. 3. Application of the iterated TMR filter for Gamma correction. Figures 3(a) and 3(b): gray-level image and its contrast enhancement via histogram clipping and Gamma correction (with γ set to 1 2 ).Figure 3(c) and 3(d): result of the iterated TMR filter, respectively with σ = 10 and σ = 4.

  (a) Three consecutive frames from a movie [Be Kind Rewind, Michel Gondry, 2008], suffering from a strongly localized flicker. (b) Same frames after local flicker reduction [12]. (c) Same frames after local flicker reduction and application of the TMR filter.

Fig. 4 .

 4 Fig. 4. Application of the iterated TMR filter to flicker stabilization.Figure 4(a): a sequence of three images corrupted by flicker (strong and fast local contrast change).Figure 4(b): flicker stabilization results with the method of Delon and Desolneux[START_REF] Delon | Stabilization of flicker-like effects in image sequences through local contrast correction[END_REF]. Observe that the contrast is well harmonized over the sequence, but some artefacts related to brutal and local contrast modifications appear. Figure4(c):The iterated TMR filter permits to remove those artefacts.

Figure 4 (

 4 Fig. 4. Application of the iterated TMR filter to flicker stabilization.Figure 4(a): a sequence of three images corrupted by flicker (strong and fast local contrast change).Figure 4(b): flicker stabilization results with the method of Delon and Desolneux[START_REF] Delon | Stabilization of flicker-like effects in image sequences through local contrast correction[END_REF]. Observe that the contrast is well harmonized over the sequence, but some artefacts related to brutal and local contrast modifications appear. Figure4(c):The iterated TMR filter permits to remove those artefacts.

  Fig. 4. Application of the iterated TMR filter to flicker stabilization.Figure 4(a): a sequence of three images corrupted by flicker (strong and fast local contrast change).Figure 4(b): flicker stabilization results with the method of Delon and Desolneux[START_REF] Delon | Stabilization of flicker-like effects in image sequences through local contrast correction[END_REF]. Observe that the contrast is well harmonized over the sequence, but some artefacts related to brutal and local contrast modifications appear. Figure4(c):The iterated TMR filter permits to remove those artefacts.

Fig. 5 .

 5 Fig.5. Comparison of the iterated TMR filter with other regularization techniques for contrast enhancement. We consider here the image u and its equalization EQ(u) previously shown in Figures.1(a) and 1(b)) respectively. In Figures5(b) and 5(a), we show respectively one and several iterations of the TMR filter. The image u details = u -Yu(u) corresponds to the details extracted in u. One can compare results with a two-scale decomposition method inspired from[START_REF] Durand | Fast bilateral filtering for the display of highdynamic-range images[END_REF] (Fig.5(c)) and with the "regraining" approach of[START_REF] Pitié | Automated colour grading using colour distribution transfer[END_REF] (Fig.5(d)). See Section IV-B3 for details.

  (a) Original image. (b) Target color distribution. (c) Raw color transfer. (d) Filtering of image (c). + (e) Details extraction of (a). = (f) Regularization of (c) with iterated TMR filter. (g) Original image (Auguste Renoir, Le déjeuner des Canotiers, 1881). (h) Target color distribution (Paul Gauguin, Mahana no atua -le jour de Dieu, 1894). (i) Raw color transfer. (j) Raw color transportation map. (k) Regularized color transportation map. (l) Iterated TMR filter.

Fig. 6 .

 6 Fig. 6. Illustration of color transfer regularization with iterated TMR filter. The first row displays (Fig. 6(c)) the result of transferring the colors of Figure 6(b) to Figure6(a). The second row illustrates that the corresponding regularization (Fig.6(f)) is obtained as the addition of the filtering of the raw color transfer (Fig.6(d)) with the details extracted from the original image (Fig.6(e)) where the mean has been changed for visualization purpose. The third row displays (Fig.8(a)) the result of transferring the colors of Figure6(h) to Figure6(g). The result of the proposed iterated TMR regularization is displayed in Figure6(l). One observes that in contrast with Figure6(i), the artefacts due to different color proportions are mostly removed. For illustration, the transportation maps before and after regularization are displayed in Figure6(j) and 6(k) respectively.

Fig. 7 .

 7 Fig. 7. Illustration of image editing correction with iterated TMR filter. In this example, an image 7(a) is edited with an image editing software (The Gimp) for color enhancement (Fig. 7(c)), using global contrast and saturation modification tools. Figure 7(c) displays the result of the proposed approach.

  (a) Color transfer with regraining [5]. (b) Color transfer with our approach. (c) Color transfer with approach of [10]. (d) Iterated TMR filter applied to Fig. 8(c). (e) Original image. (f) Target color distribution. (g) Raw color transfer. (h) Regraining [5] applied to Fig. 8(g). (i) Iterated TMR filter applied to Fig. 8(g). (j) Color transfer with approach of [10]. (k) Iterated TMR filter applied to Fig. 8(j).

Fig. 8 .Fig. 9 .

 89 Fig. 8. Comparative color transfer regularization results with regraining approach of [5] (Figs. 8(a) and 8(h)), iterated TMR filter (Figs. 8(b), 8(d), 8(i) and 8(k)) and variational histogram equalization of [10] (Figs. 8(c) and 8(j)). Original images are shown respectively in Figures 6(g) and 8(e), with the corresponding target color distribution displayed respectively in Figures 6(h) and 8(f). Note: These examples and some other ones are available in full resolution at: http:// perso.telecom-paristech.fr/ ∼ delon/ artefact removal html/ .

Figure 9 (

 9 Fig. 9. Variation around TMR filter based on different edge-preserving filters.Figure 9(c): Yaroslavsky-based filter. Figure 9(d): Median-based filter. Figure 9(e): Non-local Means based filter with 3 × 3 pixels patches comparison. The same number of iterations (10) and the same parameter setting (σ = 10) have been used for each experiment.

  pk ) i,j → p→∞ 0. This property also holds for the whole sequence m-r j=1 (Q k ) i,j since it is decreasing with a subsequence converging to 0. Since all the coefficients of these matrices are positive, we conclude thatQ k → k→∞ 0. Now, notice that R k = k-1 j=0 Q j R = (I -Q) -1 (I -Q k )R (if I -Q was not invertible, then we would have x = 0 such that Qx = x which is impossible since Q k → k→∞ 0). Thus R k → k→∞ (I -Q) -1 R. Finally, B k -→ k→∞ I r 0 r×(m-r) (I -Q) -1 R 0 (m-r)×(m-r).

The limit map can be computed explicitly in our case, see Appendix B.

ACKNOWLEDGMENT

The authors are grateful to acknowledge Adrian Márques for its work on flicker experiments and Nicolas Papadakis for providing his code. The authors would like also to thank Gabriel Peyré for its fruitful comments and discussions. This work has been supported by the French National Research Agency (project ANR-07-BLAN-0235 OTARIE, project ANR-07-JCJC-0048 FREEDOM and ANR-09-CORD-003 CALLISTO).

APPENDIX A LINK WITH OPTIMAL TRANSPORT

This section recalls why color ans contrast transfers can be seen as optimal transportation problems. As described in Section II-B, assigning a given distribution f to an image u boils down to find a mapping T such that h T (u) = f . If such mappings exist, one looks generally for one minimizing the global cost

where . is the Euclidean norm. This problem, first stated by Monge in [START_REF] Monge | Mémoire sur la théorie des déblais et des remblais[END_REF], has generally no solution when h u is discrete. Kantorovich proposed to relax the problem into a more general one, where one looks for a probability distribution π on R n × R n , with marginals h u and f (we write Π(h u , f ) the set of these probability measures, which are called transportation plans). Observe that π can be seen as a multivalued function sending exactly h u onto f . Among all transportation plans in Π(h u , f ), one imposes that π minimizes a global transportation cost

In practice, a satisfying mapping T between h u and f can then be chosen as one approximating the optimal plan π. If we apply this framework to the case n = 1, we find formulas similar to (3) for histogram equalization and specification.

APPENDIX B POWERS OF STOCHASTIC MATRICES

In this section, we recall the Perron-Frobenius theorem as it is stated in [START_REF] Brémaud | Markov chains: Gibbs field, Monte Carlo simulation and queues[END_REF], [START_REF] Seneta | Non-negative Matrices and Markov Chains[END_REF]. Recall that a square matrix A is said to be primitive if there exists q ∈ N * such that A q is strictly positive, in the sense that all coefficients A q i,j are strictly positive.

Theorem 1 (Perron-Frobenius, see [START_REF] Brémaud | Markov chains: Gibbs field, Monte Carlo simulation and queues[END_REF], [START_REF] Seneta | Non-negative Matrices and Markov Chains[END_REF]): Let A be a nonnegative primitive m × m matrix. There exists a real eigenvalue λ 1 with algebraic as well as geometric multiplicity one such that λ 1 > 0, and λ 1 > |λ j | for any other eigenvalue λ j . Moreover, the left eigenvector π 1 and the right eigenvector l 1 associated with λ 1 can be chosen positive and such that π T 1 l 1 = 1. Let λ 2 , λ 3 , . . . λ m be the eigenvalues of A other than λ 1 ordered in such a way that

where m j is the algebraic multiplicity of λ j . Then,

where O(f (r)) represents a function of r such that there exists

βf (r) for all r sufficiently large.

Proof : see [START_REF] Seneta | Non-negative Matrices and Markov Chains[END_REF].

Observe that the matrix A defined in Section III-C is stochastic, which implies that λ 1 = 1 and l 1 = (1, 1, . . . , 1) T . All the lines of A ∞ are thus equal to the left eigenvector π 1 for the eigenvalue 1. Now, if the neighborhood N (0) is symmetric (which implies that i ∈ N (j) if and only if j ∈ N (i)), this left eigenvector is

where exponential weights w u are defined in Formula 4. The limit matrix can thus be computed easily in this case.

APPENDIX C STOCHASTIC MATRICES WITH STOPPING CRITERION

In the following, we show that if A is the matrix defined in Section III-C, and if B is built by replacing some lines in A by the same lines in the identity matrix, then the sequence (B k ) still converges toward a limit matrix B ∞ . This property is a consequence of classical results and the proof is provided for the sake of completeness.

First, observe that there exists a permutation matrix Σ such that B = ΣBΣ -1 can be written

where I r is the identity matrix of size r, 0 r×(m-r) is the null matrix of size r × (m -r), R ∈ M m-r,r (R) and Q ∈ M m-r (R). Since B k = Σ -1 B k Σ, the convergence of the sequence (B k ) will imply the convergence of (B k ), so we assume in the following that B is written as in [START_REF] Delon | Movie and video scale-time equalization application to flicker reduction[END_REF]. Now,

and the study of the sequence (B k ) boils down to the study of the sequence (Q k ).


Y Sawall

 N Phongsuwan

) C Richter

Coral recruitment and recovery after the 2004 Tsunami around the Phi Phi Islands (Krabi Province) and Phuket, Andaman Sea, Thailand

Keywords: recovery, recruitment, corals, tsunami, destruction, tourism

The 2004 tsunami left a discontinuous pattern of destruction in the reefs along Andaman Sea coast of Thailand. Here, a comparative assessment of coral recruitment was carried out to assess differences in recovery between damaged and undamaged sites in near-shore fringing reefs one year and three years after the tsunami. Settlement plates showed high frequencies of coral spat after 4 months (< 17 spat tile -1 ) in both, damaged and undamaged locations. Field surveys carried out 3 years after the tsunami on natural substrate confirmed that tsunami damage did not suppress recruitment in damaged sites relative to no impacted controls. New and stable settlement space along with unabated larval supply supported posttsunami recruit densities up to 7.2 m -2 year -1 . Mean recruit densities were found at the level of post-storm situations with rapid recovery success, suggesting that the duration of disturbance, degree of sorting and, hence, stability of coral rubble is a key determinant of recruitment success. Low regeneration success of some species e.g. branching acroporids and rebounding tourism industry at sites like Patong and partly around the Phi Phi Islands (dense carpets of filamentous algae) led to the assumption of selectivity and eventually to an alternation of the coral community even though live coral cover might be recovered soon.

Introduction

The 26 December 2004 hitting the west coast of Thailand had a much higher impact on land than in the sea (DMCR 2005). During a rapid assessment three weeks after the event, only about 13 % of the coral reefs in the Andaman Sea were found to be highly damaged (>50 % of corals destroyed), while almost 40 % showed no measurable impact by the tsunami (DMCR 2005). The degree of damage on coral reefs was found to be related to exposure to and amplification of the incident wave due to local differences in bathymetry and coastline leading to a localized pattern of destruction [START_REF] Allen | Rapid assessment survey of tsunami-affected reefs of Thailand[END_REF]DMCR 2005). Generally, the highest impact was found between adjacent islands (funneling effect) and in areas with shallow embayments or shallow exposed reefs [START_REF] Phongsuwan | Posttsunami status of coral reefs and other coastal ecosystems on the Andaman Sea Coast of Thailand[END_REF]. Corals were overturned (the massive Porites lutea and table corals such as some Acropora and Montipora spp.), broken (branching species e. g., Acropora spp.) or buried by debris or sediment, while less consolidated colonies slid away with the substrate (DMCR 2005).

So far, there is no precedent in the scientific literature for a coral recovery study after tsunami. Time spans for recovery after other large-scale mechanical disturbances such as tropical storms are highly variable, e. g. from only few years in storm-beaten reefs in Florida [START_REF] Shinn | Coral reef recovery in Florida and Persian Gulf[END_REF]) and Phuket Island [START_REF] Phongsuwan | Recolonization of a coral reef damaged by a storm on Phuket Island, Thailand[END_REF], from few year to several decades in Heron Island, Australia (Woodhead quoted by [START_REF] Pearson | Recovery and recolonization of coral reefs[END_REF][START_REF] Connell | A 30-year study of coral abundance, recruitment, and disturbance at several scales in space and time[END_REF] and Hawaii (Dollar and Tribble 1993), and up to a century in British Honduras [START_REF] Stoddart | Post-hurricane changes on the British Honduras reefs: re-survey of 1972[END_REF]. Other reefs may fail to recover altogether under continued unfavorable combinations of natural and anthropogenic stressors [START_REF] Woodley | Hurricane Allens impact on Jamaican coral reefs[END_REF][START_REF] Woodley | The effects of hurricane Gilbert on coral reefs at Discovery Bay[END_REF][START_REF] Rogers | Permanent 'phase shifts' or reversible declines in coral cover? Lack of recovery of two coral reefs in St. John, US Virgin Islands[END_REF].

Reef recovery is driven by two processes: sexual propagation with re-colonization of freshly exposed substrate by new recruits and asexually, by regeneration of damaged coral colonies or fragments. The success of re-colonization is dependent on larval supply, suitability of substrate as well and competition and predation [START_REF] Pearson | Recovery and recolonization of coral reefs[END_REF]. It is not known at present to what extent the tsunami may have affected any of these factors governing coral recruitment.

On the one hand, the small-scale patchiness of destruction both between and within reefs (DMCR 2005) may allow for an uninterrupted supply of larvae from undamaged to adjacent damaged reefs. On the other hand, the loss of more than half of the colonies in heavily impacted reefs may have rendered reproductive success critically low (Allee effect; [START_REF] Stephens | Consequences of the Allee effect for behavior, ecology and conservation[END_REF], particularly for short range dispersing species. Although connectivity between reefs has been emphasized for many reef organisms at various scales (e.g., [START_REF] Williams | Transport mechanisms and the potential movement of planktonic larvae in the Central Region of the Great Barrier-Reef[END_REF][START_REF] Roberts | Connectivity and management of Caribbean coral reefs[END_REF], self-seeding with a significant fraction of propagules settling within the natal reef has been shown, as well, in studies of larval dispersal [START_REF] Sammarco | The Helix Experiment -differential localized dispersal and recruitment patterns in Great Barrier-Reef corals[END_REF][START_REF] Black | Residence times of neutrally-buoyant matter such as larvae, sewage or nutrients on coral reefs[END_REF][START_REF] Jones | Self-recruitment in a coral reef fish population[END_REF].

The success of re-colonization is also governed by the substrate composition. Well-sorted rubble following tropical cyclones in response to a high number (>1,000) of huge waves, may provide a "killing field" for coral recruits [START_REF] Thongtham | Influence of surface complexity on coral recruitment at Maiton Island, Phuket, Thailand[END_REF]Chansang 1999, Tamelander 2002;[START_REF] Fox | Recovery from blast fishing on coral reefs: a tale of two scales[END_REF]. By contrast, unsorted rubble of various sizes, broken and overturned corals generated by large but few (<10) tsunami waves may provide an interlocking framework, thus enhancing substrate stability and, hence, coral recruitment. These different substrate characteristics need to be considered in the recruitment process, together with the abundance of potential space competitors such as algae, expanding adult coral colonies and bryozoans. In terms of predation, corallivore fishes were rare and herbivore fishes were abundant in "normal densities" before, as well as after the tsunami [START_REF] Allen | Rapid assessment survey of tsunami-affected reefs of Thailand[END_REF].

Generally, the asexual process of regeneration proceeds smoothly, if the lesion is not too large and the coral is healthy [START_REF] Knowlton | Evidence for delayed mortality in hurricanedamaged Jamaican staghorn corals[END_REF][START_REF] Woodley | Hurricane Allens impact on Jamaican coral reefs[END_REF]. For some branching species (e.g., Acropora spp.), mechanical fragmentation and subsequent regeneration is the dominant way of reproduction [START_REF] Highsmith | Reproduction by fragmentation in corals[END_REF], but also massive corals, such as Porites lutea dominating in the Andaman Sea of Thailand, are known for their rapid regeneration after damage [START_REF] Highsmith | Passive colonization and asexual colony multiplication in the massive coral Porites lutea Milne Edwards and Haime[END_REF][START_REF] Phongsuwan | Recolonization of a coral reef damaged by a storm on Phuket Island, Thailand[END_REF][START_REF] Brown | Serial patterns of biodiversity change in corals across shallow reef flats in Ko Phuket, Thailand, due to the effects of local (sedimentation) and regional (climatic) perturbations[END_REF].

The degree of damage determines the favorable mode of recovery, while heavy damage with high coral mortality results in a rather slow recovery process of re-colonization [START_REF] Connell | A 30-year study of coral abundance, recruitment, and disturbance at several scales in space and time[END_REF].

The aim of this study was to assess the recovery of tsunami impacted reefs relative to reefs less affected by destruction. Recruitment success was hypothesized to be high in areas with large areas of freshly exposed solid substrate in spite of a potentially patchy larval supply. Also regeneration was expected to be rapid compared to results of previous studies [START_REF] Phongsuwan | Recolonization of a coral reef damaged by a storm on Phuket Island, Thailand[END_REF][START_REF] Brown | Serial patterns of biodiversity change in corals across shallow reef flats in Ko Phuket, Thailand, due to the effects of local (sedimentation) and regional (climatic) perturbations[END_REF]. The following variables influencing coral recruitment and potential reef recovery were investigated: (1) Recruitment in damaged and undamaged sites, (2) abundance of suitable substrate for planula larvae to settle on, (3) abundance of potential space competitors of coral recruits and (4) survival of damaged corals. Two depths were chosen due to a much higher tsunami impact in the shallow reef (< 4m deep) compared to deeper areas.

The results of this study are discussed in the light of previous storm recovery studies in order to provide a baseline for conservation and management of the tsunami affected areas.

Materials and methods

Study sites

The study was carried out in reefs fringing the island of Phuket as well as the Phi Phi Islands in Phang Nga Bay, which were affected to various degrees by the 2004 tsunami. Two depths were chosen in the context of higher tsunami impact in the shallow reef area (< 4m). The Thai region features a monsoonal climate, where the wet and stormy SW monsoon season is from May to November and the dry season with the calm NE monsoon is from December to April. In 2005 the SW monsoon was exceptionally dry in the beginning (except May) and above-average rainfall occurred during the end of the season (September -November) (Southern Meteorological Center, Thailand). The Andaman Sea is comparatively nutrient rich, due to upwelling and land run-off [START_REF] Janekarn | Coastal and offshore primary production along the west coast of Thailand (Andaman Sea) with notes on physical-chemical variables[END_REF][START_REF] Brown | Seasonal fluctuations in environmental factors and variations in symbiotic algae and chlorophyll pigments in four Indo-Pacific coral species[END_REF]. In spite of growing anthropogenic pressures the coral reefs are still in a fairly good condition [START_REF] Brown | Coral reefs of the Andaman Sea -an integrated perspective[END_REF].

Phi Phi Islands (Krabi Province):

The Phi Phi Islands consist of 6 limestone islands located 40 km southeast of Phuket and about 30 km west of Krabi in Phang Nga Bay, a large shallow bay not deeper than 30 m (Fig. 1). Well developed fringing coral reefs are found on the eastern sides of the islands or in areas protected from SW storms. At most sites, coral grow down to about 8 -10 m depth, but to about 15 -20 m at Ko Phi Phi Lae. The visibility ranges from 5 -25 m. Massive P. lutea, branching Acropora spp., such as A. formosa, A. grandis, A. subulata and A. austera and the tabular A. hyacinthus and A. subulata are the dominant species.

Although the Phi Phi Islands were declared a marine national park in 1983, unrestricted access by the tourism industry has led to the degradation of the surrounding reefs [START_REF] Chou | Status of Southeast Asia coral reefs[END_REF]. There is no sewage treatment plant, only some collecting ponds and it remains unclear, where the wastewater enters the sea. Some of the coral reefs were strongly hit by the tsunami in December 2004 and suffered severe damage, while other areas remained untouched, providing an ideal setting for testing small scale differences (<10 km) in coral recruitment as a function of reef damage.

Seven study sites were chosen, three damaged (marked with a "D" superscript in the following) and four undamaged sites (Fig. 1). Highest tsunami damage occurred at Ko Pai and at Lolana Bay (up to 50 % damage), and at the northern end of Ko Phi Phi Lae (30 -50 % damage) (DMCR 2005).

The remaining study sites Ko Yoong, Leam Tong, Hin Phae and Ko Phi Phi Lae SE were only slightly damaged or completely untouched (DMCR 2005).

Phuket:

Coral reefs are well developed on the west coast in protected bays and on some areas along the southern coast. The study site South Patong in the Southwest of Phuket (Fig. 1) is a tourist hotspot with over 30,000 hotel bedrooms. Corals grow to about 7 m depth and the dominant species are P. lutea, D. heliopora, Millepora sp., H. coerulea, Lobophyllia sp., few branching corals such as A. formosa, few table corals and encrusting corals. About 30 % of waste waters of the city of Patong are untreated and being discharged into the bay only a few hundred meters away from the investigated reef smothering the corals. The visibility is 5 -10 m.

South Patong is the only reef area on Phuket, which was severely impacted by the tsunami (DMCR 2005).

[Insert Fig. 1 about here]

Settlement plates

A settlement experiment was carried out one year after the tsunami to evaluate coral larvae distribution between damaged and undamaged sites and to quantify space-competing algae and fouling organisms. 12 x 12 cm plates were cut from acrylic board (2.5 mm thick), roughened with a metal brush and fixed in triplicates in a vertical position on 1 m iron rods. Six rods were fixed in an upright position for every location and depth (shallow: reef edge ~3 m and deep: lower reef slope ~7 -10 m) resulting in 2 depths x 6 rods x 3 plates = 36 plates per study site. Although acrylic shares the disadvantages of all artificial settlement plate material compared so far in being highly selective for certain taxa [START_REF] Harriott | A comparison of settlement plate types for experiments on the recruitment of scleractinian corals[END_REF] opposed to natural reef substrate (e.g. [START_REF] Morse | Flypapers for coral and other planktonic larvae[END_REF], they are nevertheless useful in detecting differences in coral recruitment in both, space and time.

All the settlement plates were deployed early November 2005. For a given site and depth the triplicate plates of rod number one were replaced after one month, the plates of rod number two after two months, etc., resulting in a time series of settlement of varying exposure period (up to four months, early November 2005 to early March 2006; Tab.1).

After removal, plates were allowed to dry in the sun for 2-3 days for examination with a magnifying glass and stereo microscope. Settlement plates were searched for coral spat and specimens identified to family level according to [START_REF] Babcock | Identification of scleractinian coral recruits from Indo-Pacific reefs[END_REF]. The abundance of fouling organisms (filamentous algae, crustose coralline red algae and sessile fauna such as barnacles, bivalves, bryozoans and spirorbid worms) was recorded on an ordinal scale between 0 (absent) and 5 (replete). Category 5 applied to high densities of filamentous algae featuring long filaments; crustose coralline algae covering most of the plate in thick patches; bryozoans covering more than 40 % of the plate; spirorbid worms in excess of 40 individuals per plate; bivalves and barnacles with more than 25 individuals per plate, respectively.

Statistical analyses were conducted with the software SAS. The data collected on one rod (3 plates) were treated as one replicate. A Poisson regression was carried out since the coral spat densities followed a Poisson distribution. The data set of the four month period was used to assess the effects of three indicator variables (1) "status" (damaged, undamaged), (2) reef "sites" (Ko Yoong, Leam Tong, Hin Phae, Phi Phi Lae SE, Phi Phi Lae N, Ko Pai, Lolana, Patong) and (3) "depth" (shallow, deep) on the response variable "coral spat" density, whereas "sites" were nested within "status". The effects of filamentous and crustose coralline red algae and of fouling organisms (additional indicator variables) on coral spat densities were analyzed in a separate run of Poisson Regression.

To test for differences in coral spat abundances between the two seasons (November -January end of rainy season, January -March dry season) data of the two month period were used and Poisson Regression was applied. The additional indicator variables was "season", however the variable "site" was eliminated, because each site was represented by only two data points (one deep rod, one shallow rod).

The effect of seasonality on algae and fouling organisms was tested with univariate ANOVA using season and depth as fixed factors and the sites were treated as replicates. Levene´s test was applied to test homogeneity of residuals.

Succession over the four month period was analyzed graphically.

[Insert Tab. 1 about here]

Visual census of coral recruits in situ

In this paper, we distinguish between newly settled corals ("coral spat") on settlement plates, and the young corals ("coral recruits") in the field.

Visual census of coral recruits was done one year (January / February 2006) as well as three years (November 2007) after the tsunami in proximity to the settlement plates at all sites, along the reef edge and the lower reef slope in order to quantify the success of coral recruitment. Recruits were counted on natural substrate using a 0.5 x 0.5 m square (0.25 m -2 ) placed at random (n=10) in areas dominated by dead coral substrate and summed up (recruits 2.5 m -2 ). Within the quadrates 0.5 -2.0 cm coral recruits (diameter) were recorded. Visual census with unaided eye allowed undoubted recruit identification only for the genus Pocillopora; all other scleractinians were recorded as "other". Given linear extension rates of >1 cm year -1 even for slow-growing taxa in the area [START_REF] Phongsuwan | Recolonization of a coral reef damaged by a storm on Phuket Island, Thailand[END_REF][START_REF] Scoffin | Patterns and possible environmental controls of skeletogenesis of Porites lutea, South Thailand[END_REF], it was assumed that the bulk of the recruits had settled after the tsunami.

For statistical analyses Levene´s test was applied to test homogeneity of residuals and univariate ANOVA was used to compare recruit abundances. Status and depth were fixed factors and the sites were treated as replicates.

Line intercept transects

Line intercept transects (English et al. 1994) were carried out in January / February 2006 (i.e. one year after the tsunami) to determine live coral cover and the availability of suitable substrate for coral larvae settlement. 20 m transects (n=3) were laid out with a measuring tape along the reef edge and the lower reef slope in proximity to the settlement plates at all sites. The substrate directly under the tape was assigned to the following categories -live coral (LC), dead coral (DC), other organisms (including soft coral, sponges and giant clams), coral rubble (RB), sand (SA), macroalgae and categories recorded to the nearest cm. RB included small pieces of coral skeleton (<10 cm long), while DC was composed of coral skeleton pieces larger than RB, dead patches on coral colonies and entire dead colonies up to few meters in diameter. The respective mean percentage cover of each component was calculated for each location and depth.

Results

Settlement plates

Coral spat

Pocilloporids dominated by far the coral spat on the settlement plates, in spite of the dominance of adult Acroporidae and Poritidae in the reefs. Spat were patchily distributed between the plates, ranging from 0 to 17 spat plate -1 and a total of 394 spat for all plates. Coral spat densities were lower during the first two months of the experiment (November 2005 -January 2006), compared to the last two months (January -March 2006) (Table 3, Fig. 2). There was no detectable difference between damaged and undamaged sites after 4 months. More coral spat were found in the deeper areas; however the difference between the 2 depths varied between damaged and undamaged sites (Table 3) and the high number of coral spat at Ko Yoong deep (Table 2) strongly influenced this result. The high variations in spat abundances between the sites led to site effects at all sites in damaged as well as in undamaged reefs (Table 3, Online Resource 1 shows graphical illustration of spat densities).

Coral recruitment showed a functional response to filamentous algae with highest coral spat densities on plates with intermediate algae cover (Online Resource 2). A positive relationship between crustose coralline red algae and coral spat [START_REF] Morse | Flypapers for coral and other planktonic larvae[END_REF] was not detectable.

[Insert Fig. 2

and Tab. 2 and 3 about here] Algae and fouling organisms

Filamentous and crustose coralline red algae showed a clear seasonality with a higher abundance within the first two months (Fig. 2, ANOVA p<0.001 for both). Depth had no effect on the distribution of filamentous algae (ANOVA p>0.05). However, crustose red algae were significantly more abundant in the shallow reefs (ANOVA p=0.016). There were pronounced differences in algal cover between sites: Lolana D had the highest abundance of filamentous algae followed by Patong D , while the lowest densities were found at Leam Tong and Phi Phi Lae SE (Online Resource 3). Sediment was trapped between the algal filaments of densely covered plates especially in the deeper area of Ko Yoong and Lolana D .

Highest abundances of crustose algae were found at Ko Pai D and Lolana D displaying thick algae crusts on the plates.

Although the abundance of fouling organisms (bryozoans, spirorbid worms, bivalves, barnacles) was generally low, some plates had high abundances of certain groups (e.g., spirorbid worms) and variation was sometimes high on the level of a single rod. Peak abundances were visible in the deeper area of Patong D , where bryozoans (>40 % coverage) and bivalves (9 -15 ind. plate -1 ) showed the highest abundances. Seasonality was not significant, but showed a similar pattern as filamentous and crustose algae (Fig. 2, ANOVA p>0.05). An overgrowth of spat by bryozoans was observed in some cases.

Succession took place following the expected pattern, in which filamentous algae and crustose coralline red algae are the first settlers being than gradually replaced by sessile animals, such as bryozoans and bivalves and finally by corals (Online Resource 4).

Coral recruits on natural substrate

There was a significant increase in coral recruitment between one and three years after the tsunami (ANOVA p=0.016), but no differences between either damaged and undamaged or shallow and deep reefs (ANOVA p>0.05). One year after the tsunami the highest density of recruits was found at Lolana Bay D with more than 6 recruits m -2 in the shallow reef area followed by Leam Tong. Almost 2 yrs later Ko Yoong showed the highest recruit density and Lolana Bay D was situated around the average of all sites (Table 4). Generally, pocilloporids contributed the bulk of the recruits; but variation between sites was very large ranging from 0 % pocilloporids in shallow Hin Phae after 1 yr to 100 % in shallow Leam Tong after 3 yrs (Table 4).

No relationship was visible between the number of spat and the number of recruits for either pocilloporid corals alone or the ensemble of corals. At Ko Yoong, which showed an extremely high abundance of pocilloporids on the plates, the number of recruits was found within the range of other sites (Table 2 and4). Also no connection between recruit densities and algae abundance (on plates) could be found (Online Resource 5).

Additionally to the < 1 year old recruits some older recruits (1 -3 yrs), in particular fast growing Acropora spp. (10 -20 cm in diameter), were observed during the November 2007 survey on tsunami generated dead corals at Lolana Bay D and Patong D .

[Insert Tab. 4 about here]

Substrate composition and survival of damaged corals

Highest LC cover was found at Ko Yoong in the shallow reef (57 %). In five out of eight cases a higher LC cover was found in the shallow area; the opposite situation was observed at Lolana D and Patong D and Hin Phae. The cover by DC was highest in the shallow areas of damaged reefs in particular at Ko Pai D and Lolana D with 59 % largely due to overturned Porites heads. But also the deeper reef areas showed a higher abundance of DC compared to the undamaged sites. In contrast, we found no relation between RB cover and tsunami impact. The only site with high rubble cover was Phi Phi Lae SE deep with 49 %, while the other sites were lying generally between 10 and 20 % at other sites (Fig. 3, Online Resource 6 presentation in numbers). No correlation was found between LC and coral recruit densities.

Many of the overturned or toppled Porites heads survived, showing partial re-growth around the edges.

Branching coral species such as Acropora spp. were severely impacted in some areas; many fragments were dead in the shallow water, particularly on the reef flat. Some fragments on the reef slope survived and showed new outgrowth, unless covered by sand or debris. Dead Acropora table corals were found uprooted in the sand, and toppled over specimens in no direct contact with the sediment were found alive even in an upside down position. New little outgrowths directed to the light could be observed.

[Insert Fig. 3 about here]

Discussion

The densities of coral spat recorded on the settlement tiles as well as the recruit abundances on the natural substrates indicate a successful supply of coral larvae and subsequent recruitment not only in the undamaged but also in the damaged reef areas. Although the predominance of pocilloporids on the settlement plates is likely biased, similar to the overrepresentations found in other settlement plate studies [START_REF] Bak | Distribution, abundance and survival of juvenile hermatypic corals (Scleractinia) and the importance of life-history strategies in the parent coral community[END_REF][START_REF] Harriott | A comparison of settlement plate types for experiments on the recruitment of scleractinian corals[END_REF][START_REF] Dunstan | Spatio-temporal variation in cores recruitment at different scales on Heron Reef, southern Great Barrier Reef[END_REF], the high densities show that these monthly reproducing brooders (Fadlallah 1983) are able to disperse to sites featuring only sparse adult brood stock over a range of several kilometers (cf. Tab. 5).

The high spat densities are reflected also in the densities of coral recruits on natural substrate which increased from an average 3.2 ± 1.6 m -2 in damaged areas and to 4.15 ± 1.3 m -2 after 3 years. While these findings suggest successful recovery, it must be kept in mind that the natural variability in recruitment between years can be pronounced [START_REF] Dunstan | Spatio-temporal variation in cores recruitment at different scales on Heron Reef, southern Great Barrier Reef[END_REF]. These results are lying within the recruit densities found during a 30-year study in the Great Barrier Reef (1.8 -30.3 recruits yr -1 ). The high fluctuation in the GBR was partly attributed to storm events and partly to natural temporal variability, while the recovery success after different storms was found to be strongly influenced by the severity of storm impact [START_REF] Connell | A 30-year study of coral abundance, recruitment, and disturbance at several scales in space and time[END_REF]. At a storm-beaten reef in the Andaman Sea of Thailand high recruitment success was found (17 -19 recruits m -2 , size <5 cm Ø) due to the abundance of solid substrate [START_REF] Phongsuwan | Recolonization of a coral reef damaged by a storm on Phuket Island, Thailand[END_REF]. Nevertheless our results are outstanding compared to another stormshattered reef in the area, where low recruitment success was the consequence of long lasting unconsolidated rubble (2 -4 recruits m -2 , size <5 cm Ø) [START_REF] Thongtham | Influence of surface complexity on coral recruitment at Maiton Island, Phuket, Thailand[END_REF]. This leads to the suggestion that substrate stability plays a decisive role in recovery after large-scale disturbance. In the context of tsunami few but very energetic waves creates a heterogeneous and interlocking framework with coral debris of various forms and sizes, This was typical for reefs strongly hit by the tsunami such as Lolana D and Ko Pai D , where dead corals (59%) provide a solid foundation with a high variation of substrate orientation and surface complexity, which is known to be supportive for larval settlement and survival [START_REF] Pearson | Recovery and recolonization of coral reefs[END_REF][START_REF] Thongtham | Influence of surface complexity on coral recruitment at Maiton Island, Phuket, Thailand[END_REF].

[Insert Tab. 5 about here]

Space competing organisms such as algae and a range of small filter feeders did not seem to have a negative impact on coral spat-and recruit densities leading to the conclusion of a rather high resilience of corals in the Andaman Sea being able to successfully compete with other organisms. This idea is further supported by other studies in this area, in which high recruitment success and regeneration of damaged coral colonies after storms, sediment plumes from dredging, negative sea level anomalies and increased sea surface temperatures were found [START_REF] Phongsuwan | Recolonization of a coral reef damaged by a storm on Phuket Island, Thailand[END_REF][START_REF] Brown | Serial patterns of biodiversity change in corals across shallow reef flats in Ko Phuket, Thailand, due to the effects of local (sedimentation) and regional (climatic) perturbations[END_REF][START_REF] Brown | Constancy and change on shallow reefs around Leam Panwa, Phuket, Thailand over a twenty year period[END_REF]. Additional evidence for the corals ability to persist and / or recover quickly are: (1) high growth rates [START_REF] Phongsuwan | Recolonization of a coral reef damaged by a storm on Phuket Island, Thailand[END_REF][START_REF] Scoffin | Patterns and possible environmental controls of skeletogenesis of Porites lutea, South Thailand[END_REF]), (2) high tolerance for sedimentation and elevated nutrient levels [START_REF] Brown | Coral reefs of the Andaman Sea -an integrated perspective[END_REF]) and (3) preferred spawning during the end of the dry season when algae growth is suppressed as shown in our results of the settlement plates and also found by [START_REF] Chanmethakul | Spawning season of scleractinian corals on Phuket Island[END_REF] and [START_REF] Guest | Seasonal reproduction in equatorial reef corals[END_REF]. Latter might also be a reason for the low contribution of many coral species on the settlement tiles, where plates were removed (March) just after the onset of the spawning period (February).

After demonstrating all the positive features of corals in this region, some weakness in the recovery of branching acroporids was found. In contrast to massive (e.g. Porites lutea, faviids) and table like corals (e.g. Acropora hyacinthus, A. clathrata, Montipora spp.), regeneration by tissue re-sheeting was hardly visible in branching Acropora spp. resulting in high mortality rates. Only few coral fragments were still alive after three years -in spite of its alleged fast fixation [START_REF] Phongsuwan | The use of coral transplantation in the rehabilitation of coral reefs affected by the 2004 tsunami[END_REF] and their naturally high recovery potential [START_REF] Highsmith | Reproduction by fragmentation in corals[END_REF][START_REF] Veron | Corals of Australia and the Indo Pacific[END_REF]. This goes in line with the findings at a reef off Phuket, where recovery of branching acroporids after stress from low sea levels and increased temperature was unsuccessful in contrast to other species [START_REF] Brown | Constancy and change on shallow reefs around Leam Panwa, Phuket, Thailand over a twenty year period[END_REF]. After all, this might lead to selection of coral species not only concerning the regeneration process but consequently also the recruitment diversity. Unfortunately, the recruitment diversity has not been assessed; however the relatively high contribution of pocilloporids and the intermediate numbers of coral recruits support the idea of selectivity. Even though the percentages of live coral cover might be restored, lower diversity in areas with strongly degrading water quality such as Patong and partly around the Phi Phi Islands [START_REF] Chou | Status of Southeast Asia coral reefs[END_REF][START_REF] Yeemin | Status of coral reefs in Southeast Asian countries: Thailand[END_REF]) might be the consequence.

Therefore, higher sensitivity of the coral community can not be ruled out, which leads to a higher vulnerability of a reef ecosystem to natural disturbances e.g. heavy storms. This emphasizes the need of further monitoring activities and the need of effective coastal management to maintain viable conditions for Andaman Sea coral reefs, especially where tourism is growing in great numbers.

Figure Legends

Fig. 1 :

 1 Fig. 1: Map of middle section of the Andaman coast of Thailand (7.57°N -8.60°N) (1a)

Fig. 3 :

 3 Fig. 3: Substrate composition at different sites and depths.

Fig. S2 :

 S2 Fig. S2: Coral spat density vs. filamentous algal density after 4 months. The x-axis

Fig. S4 :

 S4 Fig. S4: Abundance of coral spat, filamentous algae, crustose algae and fouling

Fig. S5 :

 S5 Fig. S5: Coral recruit density vs. abundance of filamentous algae. The x-axis represents

  Experiment design for one study site und depth including the intervals of plate replacements. Exchanged plates (grey).Nov -Dec Dec -Jan Jan -Feb Feb -Coral spat abundances on settlement tiles with an exposure time of 4 months.

  Pocilloporidae [%] Acroporidae [%] Poritidae [%] Tab. 4: Coral recruit abundances on natural substrate. Tab. 5: Abundance of Pocilloporidae adults, spat and recruits. Damaged sites ( D ). No data (n. d.). Adult [% of LC] Spat [no. m -2 ] Recruits [no. m -2 ]

						Jan/Feb 2006							Nov 07
			recruits m	-2	Pocilloporidae m	-2	others m	-2	recruits m	-2	Pocilloporidae m	-2	others m	-2
		shallow	deep	shallow	deep		shallow	deep	shallow	deep	shallow	deep	shallow	deep
	Ko Yoong	2.8	2.8	1.6	1.6		1.2	1.2	7.2	5.6	4.8	3.2	2.4	2.4
	Leam Tong	4.8	3.2	3.6	1.6		1.2	3.2	2.8	4,0	2.8	0.8	0,0	3.2
	Hin Phae		1.2	2.0	0,0	0,0		1.2	1.2	3.2	3.2	1.2	1.2	2,0	2,0
	PPLae SE		2.4	1.6	1.6	0.8		0.8	1.2	6.4	2.4	4,0	0,0	2.4	2.4
	PPLae N D		3.2	3.2	0.4	0.4		2.8	2.8	2.8	4.4	0.8	0.4	2,0	4,0
	Ko Pai D		2.4	1.2	0.8	0.4		1.6	0.8	3.2	4.4	1.6	1.6	1.6	2.8
	Lolana D		6.4	3.2	2.4	0.8		4,0	2.4	4.8	4.8	2.4	0.4	2.4	4.4
	Patong D		4.0	2.0	1.2	0.8		2.8	1.2	6.4	2.4	2.8	0,0	3.6	2.4
	Ko Yoong		10.96			137			1.5
	Leam Tong			1.80			48			1.8
	Hin Phae			0.51			42			0.4
	PPLaeSE			n. d.			25			1.0
	PPLaeN D			n. d.			11			0.4
	Ko Pai	D			0.00			23			0.6
	Lolana D			0.00			16			1.5
	Patong D			0.46			52			1.0
			spat tile -1									others [%]
					3 ± 0.5	81		67		0	17		13	17	6	0
	Patong D	3.3 ± 2.4 0.6 ± 1.1	95		33		0	33		4	17	2	17

[START_REF] Dunstan | Spatio-temporal variation in cores recruitment at different scales on Heron Reef, southern Great Barrier Reef[END_REF][START_REF] Heyward | Natural inducers for coral larval metamorphosis[END_REF][START_REF] Petersen | Innovative substrate tiles to spatially control larval settlement in coral culture[END_REF][START_REF] Mangubhai | Patterns of coral larval settlement on lagoon reefs in the Mombasa Marine National Park and Reserve, Kenya[END_REF]

Acknowledgment

We thank the scientists of Phuket Marine Biological Center (PMBC), in particular Dr. Nalinee Thongtham, Dr. Suree Satapoomin and Dr. Somkiat Khokiattiwong for their advice and logistic support, the technicians at PMBC and Andrew Hewett (Phi Phi Dive Camp) for their field assistance and Gerrit Nanninga for his support throughout the period in Thailand. This work was funded by Deutsche Gesellschaft für Technische Zusammenarbeit (GTZ; PN: 95.3506.3) and ZMT.

1

Tab. 3: Results of Poisson Regression: coral spat dependency on status 2 (damaged/undamaged), depth and site (nested within status), using the 4 month data; 3 effect of season, using 2 month data; effect of algae and fouling organisms on coral spat 4 abundances, using 4 month data. ns (not significant). p<0.05 significant.