Emmanuel Faure

Isabelle S Peter

Eric H Davidson

A New Software Package for Predictive Gene Regulatory Network Modeling and Redesign

Keywords: artificial life, gene networks, genetic analysis, recognition of genes, regulatory elements

. The program GeNeTool computes spatial gene expression patterns based on GRN interactions and thereby allows the direct comparison of predicted and observed spatial expression patterns. GeNeTool also permits in silico exploration of both cis-and trans-perturbations of GRN interactions. Here, we present this program, review briefly its major features and applications, and provide a detailed and accessible tutorial.

experimentally established or synthetically constructed GRNs. Input information that the program is fed from the starting GRNs includes the repertoires of genes included in the GRN, the identities of the regulatory genes to which each gene in the system responds (positively or negatively) according to its genomically encoded cis-regulatory system, and the logic transactions these cis-regulatory systems execute. The input identities and the logic transactions are encoded in GeNeTool as a set of vector equations, which are expressed in Boolean logic such that the output of a gene is 1 if and only if all the necessary input conditions are true, otherwise it's 0.

In successive time intervals, the GeNeTool software computes the output of each gene, sweeping across all spatial domains considered. Thus for all spatial domains defined in the model, the complete set of vector equations is used to compute the genes expressed based on the regulatory inputs in each respective domain. That is, for each gene the output at each temporal step is the predicted consequence of the inputs to which the gene is exposed, but these inputs are themselves the outputs of other genes within the system at prior times. The dynamics are controlled by statements also included in the vector equations that provide the intervals (in real time or merely as a sequence of steps) between the activation of a gene and the activation of its direct target genes. GeNeTool includes fields in the vector equations in which a variety of other input information that is utilized to determine whether the output at a given time and place is 1 or 0, including presence or absence of signaling where this is relevant; location in the spatial domains of the system; and again where relevant, choice of alternative regulatory modules (i.e., in silico, alternative vector equations).

GeNeTool permits the use of the computations of spatial and temporal gene expression, which it performs in many ways. It generates direct graphic comparisons between observed and computed expression patterns, and it generates comparisons revealing the deviations between expression patterns computed under ''normal'' vs. perturbed conditions. Every kind of perturbation can be modeled in GeNeTool including gene product knockdowns, cis-regulatory target site mutations, relative temporal alterations, alteration of the relative positions of spatial domains in the developing system (i.e., of signal availability), and alterations of GRN circuit design.

GeNeTool accommodates many essential features general to the processes of development. The program incorporates and utilizes for its computations input information on all the following: (i) all genes in the system about which there is specific spatial regulatory information; (ii) initial inputs, for example, localized maternal factors; (iii) cis-regulatory results indicating how combinatorial regulatory inputs interact and what these inputs are, and any results that indicate the Boolean logic functions of the cisregulatory modules controlling each gene; (iv) data on use of different cis-regulatory modules at different times; (v) results of all the perturbation data on which the interaction maps of the GRNs are based; (vi) the progressive spatial geometry of the embryonic territories with respect to one another; (vii) signaling interactions, that is, source and targets; (viii) digitized representation of observed spatial expression patterns, which it reserves for automated comparison with the computed spatial patterns of spatial gene expression.

Table 1 is a transformation table that relates specific biological features of the developmental control process to the form of their representation within GeNeTool and summarizes the rationale behind each feature of the computational output of the program. Figure 1 is a screenshot of GeNeTool.

GeNeTool is constructed for maximum flexibility so that diverse geometrical or temporal relations, or any different kind of cis-regulatory control system or gene interaction, can be input, and the consequences studied in silico. As illustrated in the accompanying Supplementary Material (available online at www.liertonline.com/cmb), the interactive graphics used in GeNeTool make it particularly easy to change vector equations for any gene, with respect to the inputs into its cis-regulatory system, the cis-regulatory module it uses in given contexts, the logic operators that characterize its function, or its temporal behavior with respect to its inputs. Similarly, genes can be inserted or added to the system by the simplest operations, and gene interactions can be altered in any desired manner. Thus GeNeTool will have many uses for many different developmental systems.

Three major classes of application can be envisioned. First, GeNeTool can be used to provide a direct test of the completeness and explanatory power of an experimentally determined GRN, and indeed, though critical in importance, completeness and explanatory power of GRNs are otherwise elusive parameters. Thus, if the observed and computed expression patterns through developmental time are largely convergent, the GRN used for construction of the vector equations is causally sufficient, otherwise not, and furthermore what lacunae exist become explicitly evident. Second, GeNeTool can be used to explore in silico the expected effects of given perturbations. These can be 2 FAURE ET AL.

perturbations of cis-regulatory function (site-specific regulatory mutations in silico); perturbations of gene interactions (morpholino treatment or genetic lesions in silico); or redesign of GRN architecture to be carried out by synthetic methods [START_REF] Damle | Synthetic in vivo validation of gene network circuitry[END_REF]. Thus, GeNeTool can be used for network redesign and synthetic reengineering of developmental systems. Both of these classes of application are illustrated in the study of the sea urchin GRN to which GeNeTool was originally applied [START_REF] Peter | Predictive computation of genomic logic processing functions in embryonic development[END_REF].

In the future lies another related application, and that is the use of GeNeTool to analyze and reconstruct evolutionary change in body plans, as such changes are the surviving consequences of the network reengineering that have occurred naturally in deep time in every animal lineage [START_REF] Davidson | Gene regularoty networks and the evolution of animal body plans[END_REF][START_REF] Erwin | The evolution of hierarchucal gene regulatory networks[END_REF].

METHODS

The accompanying online material, available at http://whis.caltech.edu/GeNeTool/GeNeTool.html, consists of a complete primer and tutorial on the use of GeNeTool. Both an overview and detailed instructions and examples are provided for each of the following topics: (1) Downloading and opening GeNeTool, handling models and menus, and exporting results; (2) entering explicit and implicit data from the GRN model; (3) inserting temporal step dynamics into the model; (4) inserting spatial information about the developmental system to be modeled; (5) dealing with signaling interactions; (6) setting initial conditions and other manual inputs; (7) setting responses that are dependent on input levels; and (8) the repertoire of computational functions available in GeNeTool. For examples of application of all the features described in the accompanying material, see [START_REF] Peter | Predictive computation of genomic logic processing functions in embryonic development[END_REF].

Table 1 .

 1 Representation of Biological Features in GeNeTool Software A screenshot of the GeNeTool computation of regulatory gene expression in a particular domain of the sea urchin embryo. The functions illustrated include the Boolean computation of expression or silence of each gene at each 1-hr step in time for a 30-hr developmental process; comparison of computed result with experimental expression data; use of vector equations containing logic statements for each gene (e.g., see the Boolean logic statement for gatae at top). For symbolism and details, see the GeNeTool tutorial available online as Supplementary Material.

	Biological feature	Formal statement	Explanation
	Regulatory gene	Vector equation output, i.e.,	Gene expression is modeled on the
	expression	output of 1 or 0 at each	principle that the outcome of
		time interval	cis-regulatory interactions
			determines presence or absence
			of the regulatory gene product
	Regulatory gene	Input variables in vector	Cis-regulatory inputs to given
	interactions (in	equations	regulatory genes are outputs
	the GRN)		of other regulatory genes in
			the network
	Cis-regulatory logic	Boolean logic operators upon	Captures cis-regulatory logic
		variables in vector	operations given the inputs
		equations	per module
	Cis-regulatory	Vector equations for individual	Vector equation represents the
	modules	modules	invariant regulatory system
			encoded in the DNA of
			each gene
	Module choice	Boolean logic operators that	Captures module choice apparatus
		determine which modular	operating in genes expressed
		vector equations are in effect	in multiple developmental
			conditions
	Spatial domains and	Matrix of domain contiguity/	Captures morphological
	their changing	noncontiguity relationships	interrelations of regulatory state
	geometry in	in developmental time	domains during embryogenesis
	development
	Signaling interactions	Janus function: target genes are	Converts signaling function into
		ON in cells receiving signal,	status of transcriptional
		otherwise turned OFF	regulatory response
	Observed gene	Boolean matrix of observed	Represents expression status of
	expression	gene expression in time/space	each gene through time and
			space as experimentally
			determined
	GRN output	Boolean matrix of computed	Represents expression status of
		gene expression in time/space	each gene through time and
			space as computationally
			generated in dynamic
			Boolean model
	Temporal dynamics	Step time dynamics used to	Computation incorporates real-time
	of gene expression	relate gene interactions to	observations of interval from
	patterns	real-time intervals	activation of an upstream gene
			to activation of its target gene
			(step time)

DISCLOSURE STATEMENT

The authors declare that no competing financial interests exist.

Address correspondence to:

Emmanuel Faure Centre de Recherche en E ´piste´mologie Applique´e Ecole Polytechnique, Centre National de la Recherche Scientifique 57 Rue Lhommond Paris 75005 France E-mail: emmanuel.faure@polytechnique.edu GRN MODELING


Karam Naser
email: karam.naser@univ-nantes.fr

Vincent Ricordel
email: vincent.ricordel@univ-nantes.fr

Patrick Le Callet
email: patrick.lecallet@univ-nantes.fr

Experimenting Texture Similarity Metric STSIM for Intra Prediction Mode Selection and Block Partitiong in HEVC

Keywords:

Textures can often be found in large areas of images and videos. They have different spectral and statistical properties as compared to normal (structural) components. Encoding them with ordinary video coders requires higher bit rate and usually results are unsatisfying in perceived quality. Recently, different perceptual tools have been developed to estimate the perceived quality of textures taken into account models of Human visual system. In this paper, we investigate and discuss the practical usability of one of these tools, namely STSIM, as a distortion function for selecting the intra-prediction mode and block partitioning of texture images in HEVC. We experiment few practical implementations to examine its performance compared to default metrics used by HEVC. Experimental results showed that the perceived quality of the decoded textures has been significantly improved specially for stochastic types of textures

I. INTRODUCTION

Video coding standards, such as HEVC [START_REF] Sullivan | Overview of the high efficiency video coding (hevc) standard[END_REF], aim at representing video signals with a minimum bitrate at a certain distortion level. The typical distortion measure is based on comparing individual pixels values of the original and distorted signals. This kind of measure, however, does not correctly fit our visual perception, in other words, the amount of distortion that it measures does not proportionally reflect the amount of distortion that we perceive. To overcome this problem, many researchers have introduced various Perceptual Distortion metrics in the context of Perceptual Video Coding. These metrics are based on models of Human Visual System (HVS). The details of such metrics and coding techniques can be found in [START_REF] Wu | Perceptual visual signal compression and transmission[END_REF].

In visual perception, the visual signal can be classified into two components, Texture and Structure. Textures represent homogeneous areas of video scenes with coherent statistics, whereas Structures represent rather the semantics of the scene. Textures appear in large areas of video streams. They can appear in different forms such as sand, grass, tree leaves, see waves and others. Estimating the amount perceptual distortion in the compressed textures is highly different from structures. The is because the Human Visual System focuses on the semantic meaning of the texture rather than the exact details of each pixel. This fact has been exploited in some approaches of texture coding where the textures are removed at the encoder side and re-synthesized at the decoder side. The texture can be synthesized with few parameters to give approximately the same perceptual quality. Examples of these approaches can be found in [START_REF] Balle | Models for static and dynamic texture synthesis in image and video compression[END_REF] and [START_REF] Zhang | A parametric framework for video compression using region-based texture models[END_REF].

Perceptual video coding can be implemented in several levels of the coding process. It can be done at a pre-processing level such as removal of high frequency components. It can also be done at the post processing level by optimization the rendering filter. At the encoding level, many other approaches have been developed. Examples of this are Region of Interest (ROI) coding, Rate Quality Optimization, Perceptual Quantization and others. All of these approaches try to optimize the perceptual quality of the decoded videos at a given constraints.

In this paper, we investigate the possible perceptual optimization of texture coding in HEVC framework. We used STSIM [START_REF] Ehmann | Structural texture similarity metrics for image analysis and retrieval[END_REF], as being a perceptual similarity metric designed for textures, for selecting the prediction mode and block partitioning in intra-prediction scheme within a fixed quantization parameter scenario. We implemented this metric and compared its performance with the default metrics in HEVC and also with the well known similarity metric (SSIM).

The rest of the paper is organized as follows: Sec. II gives an overview of HEVC intra-prediction mode and Texture similarity metrics used in this work. Sec. III presents the evaluation procedure we used to analyze each metric. In Sec. IV, the simulation results and discussion is presented with conclusion and possible further research is given in Sec. V.

II. THEORETICAL BACKGROUND

A. Intra-Prediction Scheme in HEVC

HEVC encoder starts by dividing video frames into Coding Tree Units (CTUs). Each CTU contains (M ×M ) Coding Tree Block (CTB) for luminance component and 2 (M/2 × M/2) for chrominance components. The CTB is the basic container of one or multiple Coding Blocks (CB). The encoder assigns first one CB for the CTB and tries encoding different prediction schemes and modes. It chooses the one that minimizes the rate-distortion function. The CB can be partitioned in Quadtree manner to find a better rate-distortion value in a smaller block size.

In intra-prediction scheme, each CB contains either 1 or 4 equal sizes Prediction Blocks (PB). For each PB, the encoder searches for the best prediction mode and partitioning into Transform Blocks (TB). The TB's are converted to a bitstream after applying transform and quantization. In HEVC, there are 35 intra-prediction modes. This include 33 directional prediction, DC prediction and Planer prediction. Due to the high complexity of searching for the best prediction mode and quadtree partitioning, the encoder considers only three most probable modes for its optimization process.

B. Overview of Texture Similarity Metrics

We begin this overview with one simple and effective image quality metric which frequently replaces MSE for different applications. It is known as Structural Similarity Index (SSIM). This metric compares the statistics of two image patches x and y. It is composed of three comparison terms, namely luminance term (I x,y ), contrast term (C x,y ) and structure term (S x,y ). The luminance term compares the mean values of the two patches, where as the contrast term compares the standard deviations of them. The structure term is the cross correlation coefficient between the patches modified with some correction constant. The similarity index between the two patches is calculated as:

q SSIM = (I x,y ) α (C x,y ) β (S x,y ) γ (1)
where α, β and γ are design constants and typically take a value of 1. SSIM has been used for wide range of applications. In [START_REF] Jin | Joint perceptually-based intra prediction and quantization for hevc[END_REF], it has been used in template matching for generating the prediction signal. It has been improved using the Complex Wavelet domain (CW-SSIM) [START_REF] Wang | Translation insensitive image similarity in complex wavelet domain[END_REF] instead of the spatial domain. Similarly, the frequency coefficients in this domain have been perceptually weighted to fit the perceptual properties of human vision [START_REF] Brooks | Structural similarity quality metrics in a coding context: exploring the space of realistic distortions[END_REF].

These metrics, although being useful similarity metrics, may not be reliable similarity metrics for texture images. One of the possible objection is that they allow implicit pixel by pixel comparison inherited in the cross correlation measure of the contrast term. Due to this, an SSIM based approach for texture similarity has been developed. It is known as Structural Texture Similarity Metric (STSIM) [START_REF] Zhao | Structural texture similarity metrics for retrieval applications[END_REF]. This metric compares the statistics of images subbands performing the following steps:

• Subband Decomposition: It uses the Steerable Pyramid Filter [START_REF] Simoncelli | Shiftable multiscale transforms[END_REF] to decompose the image into multiple subbands with different orientations and scales. This decomposition has an interesting property of Shiftability which allows subbands to have constant power against input shifts. • Measure of Statistical differences in Subbands coefficients: For each subband, the luminance and contrast terms are calculated. The structure term is replaced by the correlation terms. The correlation terms account for horizontal and vertical autocorrelation of the subband. STSIM was also improved in [START_REF] Ehmann | Structural texture similarity metrics for image analysis and retrieval[END_REF] by adding the crossband correlation term for comparing the cross correlations coefficients between adjacent bands. • Pooling: The pooling strategy used for STSIM is similar to SSIM except for the cross correlation term. That is, for each subband m, a multiplicative pooling of the similarity terms is calculated:

q m (x, y) = (I m x,y ) 1 4 (C m x,y ) 1 4 C m xy (1, 0) 1 4 C m xy (0, 1) 1 4
where C m xy (1, 0) and C m xy (0, 1) are the horizontal and vertical cross correlation terms respectively. After this, the overall similarity index is calculated by accumulating this term and adding the crossband correlation terms. Let N b equals to the number of subbands and N c is the number of crossband correlations, the similarity index is defined as follows:

q ST SIM = N b q m (x, y) + Nc C mi,ni x,y (0, 0) N b + N c (2)
where this term C mi,ni

x,y (0, 0) is the cross correlation term which compares the cross correlation between the subbands m and n of x and y.

III. PERFORMANCE EVALUATION

We evaluated respectively the use of SSIM and STSIM metrics as distortion measure inside HEVC for texture coding. Since q SSIM and q SST IM assess the similarity between two images with a range between [0, 1], we consider as distortion:

D SSIM = 1 -q SSIM (3)
D ST SIM = 1 -q ST SIM (4)
We replaced the distortion measure in HEVC with these two distortions respectively and evaluated the performances of each of them. The details of the experiments and evaluations are given in the following subsections.

A. Framework and Setup

We used the HEVC Modeling software HM9.0 [START_REF]/WG[END_REF] as a host encoder. We chose the Brodatz texture images from USC Viterbi texture dataset [START_REF]Usc viterbi texture dataset[END_REF] in our experiments. These are 13 textures all in gray level images with dimensions 512x512. We converted these textures into YUV240 format with Y component filled with the textures and padding zeros in U and V components. To evaluate the similarity metrics performance, we encoded these videos by replacing the distortion measure of HM by a scaled version of D SSIM and D ST SIM in Eqn.

(3) and Eqn. (4).

B. Experiments

We experiment using SSIM and STSIM inside the HM encoder as a distortion measure. Since our videos consist of one frame, these metrics were only tested for Intra-Picture prediction scheme. The distortion measure that we replaced with them has an effect at two computation levels:

1) Hadamard Transformed Sum of Absolute Difference (SATD): This metric is used to select the three most probable intra-prediction modes. These modes, as discussed in Sec. II, will be checked by the encoder in order to find the best rate-distortion tradeoff considering also the partitioning of the prediction blocks. 2) Sum of Square Difference (SSD): The encoder uses this metric at several levels. we replaced its use only for the distortion measure of best mode selection in a particular partition of the prediction blocks SSIM an STSIM were used in our experiment to compare patches of textures that correspond to the size of the prediction block. For STSIM, we used the simplified design of the steerable pyramid filter developed in [START_REF] Castleman | Simplified design of steerable[END_REF]. The number of orientations we chose for the frequency decomposition is 2 while the number of scales was varying according to the patch size. We chose the number of scales equals to 2 for the HEVC prediction block sizes of 64x64, 32x32 and 16x16 and 1 for the size of 8x8 and 4x4. the experiments carried out are:

D 2 SSIM = D SSIM * 255 2 * BlockSize D 2 ST SIM = D ST SIM * 255 2 * BlockSize
• Experiment 3: In this experiment, we replaced both SATD and SSD by the corresponding SSIM and STSIM measure used in the two previous experiments. For all of the above experiments, The HM encoder were used to encode the texture videos with different Quantization Parameters (QP). The QP we chose were (22,26,32,36,43,51) to cover a wide range of compression (from fine to coarse compression). We studied the effect of using these metrics on the decoded picture quality. We studied also the effect of using these metrics on the prediction mechanism of HEVC. The results of experiments are given in the next section.

IV. EXPERIMENTAL RESULTS

To show the result of the three experiments on the decoded pictures, we first provide one example of a decoded texture for each of experiments explained before. The effect of using different distortion metrics is not very distinguishable for lightly compressed images, that is why, we show here effect in a very high compression scenario. Fig. 1 shows the effect of replacing SATD with SSIM and STSIM for QP value of 51. It can be seen that replacing SATD with

D 1 SSIM or D 1 ST SIM
reduces the number of DC blocks and enhances slightly the quality of the decoded image. This has very little improvement because in this approach, the new metrics affect only choosing the 3 most probable intra-prediction modes but doesn't decide on neither the mode selection nor the block partition. SSIM or D 2 SSIM increases dramatically the quality of the decoded image. this can be seen in Fig. 2. If we look carefully on the decoded textures. It can be seen that STSIM introduces some artificial lines which were not available in the original image. The reason is that STSIM is rotationally invariant metric. With this property, the prediction signal generated using directional prediction may have little distortion computed by STSIM although it is in a wrong direction as compared to the original image. Texture coded with SSIM can maintain better the directionality of the texture (due to the pixel by pixel comparison inherited in it) in some texture blocks, but the overall quality of the texture coded with STSIM looks more natural.

The effect of replacing both SATD and SSD is not very different from replacing SSD only since replacing SATD has a minor effect on the decoded picture as seen before. One thing can be noticed is that the effect of producing artificial lines in STSIM is more obvious here as the all mode selections doesn't relay on pixel by pixel comparison.

Another example is given in Fig. 4 of replacing SATD and SSD with D 2 SSIM and D 2 ST SIM for a non-directional texture. It can be seen that both SSIM and STSIM reduce the amount of visually noisy blocks. It can also be noticed that reconstructed texture looks more natural when using STSIM as compared to SSIM. That is, for a non-directional texture, STSIM performs very well even though some blocks may be predicted in a wrong direction.

To show the effect of these metrics on all of the used texture dataset, Fig. 5 and6 show the result of coding all textures in third experiment. Looking at these figures, we can draw the same conclusion as before: the quality of the decoded textures increases in using either SSIM or STSIM, textures coded with STSIM look more natural specially for non-directional textures.

To study the effect of each metric on the prediction mechanism of HEVC, we ran the same simulation as before and measured the number of times that the encoder chooses a size of the prediction block in different QP. For our 13 textures, we computed the average value of these numbers and obtained the curves shown in Fig. 7. These curves shows how the encoder works using different distortion metrics.

The first thing that one can notice is the high correlation between the curves of default distortion measure, "SSIM 1"(replacing SATD with D 1 SSIM ) and "STSIM 1" (replacing SATD with D 1 ST SIM ). The reason behind it is that the behavior of the encoder doesn't change very much in these experiments, SATD only affects selecting the best candidates for ratedistortion optimization. This doesn't have a big influence on the decoded pictures as shown before. It can be even proven if you look at the curves of "SSIM 2" and "SSIM Both" and also the curves of "STSIM 2" and "STSIM Both" where "2" here represents replacing SSD by the corresponding distortion measure and "Both" means replacing both SATD and SSD by them. The very high similarity between them indicates that replacing SATD as well as SSD is not very different from replacing SSD alone.

Another observation from these curves is that the encoder tends to use larger prediction blocks for higher compression. By using SSIM or STSIM, the encoder is forced to use more number of smaller blocks to provide better prediction of the signal.

V. CONCLUSION

In this paper, we have studied the possibility of perceptual optimization of HEVC for texture components. We used one recent perceptual texture similarity metric, namely, STSIM, as a distortion function for mode selection and block partitioning in intra-prediction scheme of HEVC. This metric was implemented and compared to a the default metrics used in HEVC and also to SSIM which is as well known similarity metric. Both metrics have shown a significant improvement of the quality of decoded textures specially for high compression range.

The implicit pixel by pixel comparison incorporated in SSIM prevents it from selecting wrong direction in the set of directional prediction modes defined in HEVC as happens with STSIM, but generally, the quality of the decoded textures tends to be better although they might differ more in pixel by pixel comparison. In other word, the non-reference quality of the decoded textures is improved using STSIM. This observation is more accurate for stochastic textures rather than directional textures.

The rate-quality optimization of the used metrics was out of the scope of this paper. This can be done by appropriately selecting the Lagrangian multiplier of the rate-distortion function. This is left for a possible future research.

VI. ACKNOWLEDGEMENT

• Experiment 1 :

 1 We replaced the SATD by the distortion measures of D SSIM and D ST SIM from Eqn. (3) and Eqn. (4). We scaled both of them to match the range of SATD as follows: D 1 SSIM = D SSIM * 255 * BlockSize D 1 ST SIM = D ST SIM * 255 * BlockSize where 255 is the maximum pixel value for 8 bits integer representation. • Experiment 2: Similar to the first Experiment, we replaced the SSD by a scaled version of D SSIM and D ST SIM which are defined as:

Fig. 1 .

 1 Fig. 1. Effect of replacing of SATD with D 1 SSIM and D 1 ST SIM for QP value 51. Top left: original texture, top right: encoded using default distortion function, down left: SSIM instead SATD, down right: STSIM instead of SATD Replacing SSD with D 2SSIM or D 2 SSIM increases dramatically the quality of the decoded image. this can be seen in Fig.2. If we look carefully on the decoded textures. It can be seen that STSIM introduces some artificial lines which were not available in the original image. The reason is that STSIM is rotationally invariant metric. With this property, the prediction signal generated using directional prediction may have little distortion computed by STSIM although it is in a wrong direction as compared to the original image. Texture coded with SSIM can maintain better the directionality of the texture (due to the pixel by pixel comparison inherited in it) in some texture blocks, but the overall quality of the texture coded with STSIM looks more natural.The effect of replacing both SATD and SSD is not very different from replacing SSD only since replacing SATD has a minor effect on the decoded picture as seen before. One

Fig. 2 .

 2 Fig. 2. Effect of replacing SSD with D 2 SSIM and D 2 ST SIM , QP value 51. Top left: Original Image, top right: encoded using default distortion measure, down left: SSIM instead of SSD, down right: STSIM instead of SSD

Fig. 3 .

 3 Fig. 3. Effect of replacing both SATD and SSD with SSIM and STSIM, QP value 51. Top left: Original Image, top right: encoded using default distortion measure, down left: SSIM instead of SATD and SSD, down right: STSIM instead of SATD and SSD

Fig. 4 .

 4 Fig. 4. Effect of replacing both SATD and SSD with SSIM and STSIM, QP value 43. Top left: Original Image, top right: encoded using default distortion measure, down left: SSIM instead of SATD and SSD, down right: STSIM instead of SATD and SSD

Fig. 6 .

 6 Fig. 6. Effect of replacing both SATD and SSD with SSIM and STSIM, QP value 51. First column: original textures, second column: encoded using default distortion measure, third column: SSIM instead of SATD and SSD, forth column: STSIM instead of SATD and SSD

Fig. 7 .

 7 Fig.7. Average number of times of selecting a prediction blocks size as a function of the Quantization parameter. "SSIM 1" and "STSIM 1": replacing SATD with SSIM and STSIM resp., "SSIM 2" and "STSIM 2": replacing SSD with SSIM and STSIM resp., "SSIM Both" and "STSIM Both": replacing both SATD and SSD with SSIM and STSIM resp., horizontal axes: QP, vertical axes: number of time

This work was supported by the Marie Curie Initial Training Network under the PROVISION (PeRceptually Optimizaed VIdeo CompresSION) project.


Yves Denéchère

Regulating a particular form of migration at the European level: the Council of Europe and intercountry

adoptions (1950-1967)

Introduction

As during the Second World War, the postwar period favoured intra-European movements of displaced, refugee, lost, and surviving children. 1 These transfers constituted de facto intra-European movements of people, of which international adoptions were the most successful legal manifestations. The history of these "intercountry adoptions", as they were called at the time, shows that in the 1940s and 1950s, movement within Europe was coupled with a movement from Europe toward the United States. Then from the 1960s onward, an intercontinental movement developed from Asia toward Europe, then another from Latin America toward Europe (very significant in the 1980s) and finally in the 1990s from Africa toward Europe, and new intra-European movements from the East toward the West. 2 The three dimensions indicated in the title of the conference (in Europe, to Europe, from Europe) have thus been well presented in the study of international adoption. Although this is, above all, the creation of a legal parent-child relationship in order to give a family to a child who does not have one (and not the opposite), it could also be considered as a particular form of migration, whether seen as a modern version of traditional circulation of children well studied by anthropologistsor as a solution to demographic, economic, and social problems. 3 Impressive peaks of the number of international adoptions in the 1980s and 1990s strengthened the migratory approach. However their clear drop over the past several years has brought experts back to the question. 4 Here, it is a question of returning to the origins of "intercountry adoptions" and studying how this nascent transnational social phenomenon was seen from the beginning as a particular type of migration which necessitated regulation at the international level. Europe found itself at the centre of the first movements -with the children's home countries and their host countries -how did the Council of Europe, institution created in 1949, take hold of this question and how did it contribute to regulating the phenomenon?

The sources mobilised firstly for this contribution were obviously the archives of the Council of Europe itself. Unfortunately, the Central Archives of the Council of Europe conserved in Strasbourg, in particular Thematic file 105 "Children", could not be consulted. Despite a request sent in due form in July 2014, then a letter addressed to the general secretary, they were inaccessible "because of a lack of personnel and relocation of a part of the archives..." and remain so now. 5 Fortunately, documents produced by the Council of Europe (such as reports, projects, and various committee work) are available for consultation in the Archives of the French Foreign Affairs Ministry (in La Courneuve), particularly the collections "Administrative Conventions and Consular Affairs" and in the archives of the Ministry of Public Health and Population (National Archives).

A -Migrations of Children in Postwar Europe

I -Lost children, sought-after children

In Europe, the demographic results of the Second World War were very different to those of the First because of the great number of civilian victims. Data specific to children are even heavier because they figured, like other categories of the population, among the victims or the survivors.

Added to the orphans of soldiers killed in combat were orphans whose parents were victims of bombings or the concentration and extermination camps of Nazi Germany. There were also hundreds of thousands of children born from rapes or love affairs during invasions, occupations and detentions, left behind in the disorder at the end of the war, and whose fate illustrated the disarray of European societies. 6 The question of the place reserved for children born to Allied soldiers arose very early in occupied Germany. 7 In France, from its creation in April 1945, the High Consulting Committee on Population These reflections wholly illustrate the population policy common in postwar France. The country had to keep all its children, including those born to French mothers and occupying German soldiers or American GIs come to liberate the country: after the war, specialised nurseries took responsibility for Franco-American babies. The number of children born to French mothers and German soldiers under the Occupation from 1940 to 1944 are estimated to have been in the tens of thousands. 10 Those abandoned by their mothers were adopted by French families, particularly thanks to the association La Famille Adoptive Française. It was also called upon to organise the adoption of children coming from Germany after 1945. Born to German mothers and occupying French soldiers, 11 often not recognized by their fathers and abandoned by their mothers under social pressure, several hundred were adopted in France between 1946 and 1950, consituting one of the first large movements of intra-European international adoption. 12 French authorities estimated it necessary to retrieve French children born in Germany and decided, depending on the case, either to bring them back to France to live with their paternal family, or to entrust them to Child Aid Services for placement or adoption. General Koenig, Commander-in-chief of French forces in the French Zone of Occupation Zone (FZO), gave orders to take a census of the children born to French or Allied soldier fathers. The Service of Displaced Persons and Refugees (DPR) was responsible for verifying if the father had acknowledged paternity and if the mother intended to raise or abandon her child. The first question raised was the 8 Tara Zahra, note 1, p.146. 9 Paul-André Rosental, L'intelligence démographique. Sciences et politiques des populations en France (1930-1960) was very wary of international adoptions. Its publication International Child Welfare Review regularly and heatedly mentioned a practice which it did not consider necessary to come to the aid of children in need. 15 International Social Service (ISS) was the international organisation most involved in the reflection on international adoption as a response to the existence of children without parents, while making sure of a certain number of guarantees. 16 Faced with the great distress of numerous children, a surge of international generosity manifested itself to adopt children who had little to no chance of being adopted in their own countries. The Swedish were particularly attentive to this question. Finnish children were adopted in Sweden, then in the 1950s, Swedes working in other European countries adopted children on site from Greece, Yugoslavia, or elsewhere. Of these children, 240 were brought back to Sweden between 1950 and the mid-1960s. 17 Since that time, the country has had one of the highest rates of international adoption. The same phenomenon existed among French expatriates: in 1952, authorities pondered ways to validate acts of adoption of foreign children when the adoptive French families lived abroad. 18 In certain European regions (like in Italy and Greece) the overall economic situation and the absence of fathers killed in the war also gave rise to hordes of children taken in by institutions who were available for adoption at home or in neighbouring countries. In 1954, the artist Josephine Baker, after having adopted two children from Japan, brought little Jari home from one of her tours in Finland and then continued building her "Rainbow tribe". Given great media coverage in France, Belgium and Switzerland particularly, it is very difficult for the historian to evaluate the impact this single experiment had on the development of intercountry adoption. 19 But international adoptions in the 1950s were especially done from European countries toward the United States. In bringing European children across the Atlantic, Americans were often unable to successfully conclude an adoption procedure as home governments had not supplied them with papers. 20 It was to solve this type of problem that the ISS -which had a consulting role in the UN -was led to intervene in adoption cases. It tried hard to meet the requests for information which had been brought before its national offices by collaborating with the social services of the countries of origin. The French branch of the ISS, the Service Social d'Aide aux Emigrants (SSAE) played a large role in the adoptions of German children by American couples garrisoned in France.

In the 1950s, a German mother who abandoned her child at the Youth Office (the German equivalent of welfare services) knew it was likely to be adopted by Americans living in Europe. For those in France, the Youth Office asked the SSAE to enquire on candidates. After a child was placed, the SSAE was once again called upon to establish a report on his integration into his new American family. The intervention of the SSAE was thus strictly social, legal questions were attended to between the German and American governments. 21 It is understood then that in no circumstance did the ISS and its national branches play the role of go-between in the placement of children, rather it had a role of support and help in in facilitating the legality and transparency of procedures. 22 In most cases, the governments themselves, European and American especially, appealed to the ISS. 23 In doing so, the administrators and social worked of the ISS regularly pointed out the inadequacy of national laws and international rules in addition to the poor application of existing legislation. In substance, the ISS position on adoption was clear: "finding adoptive parents for children who particularly needed them and who did not have the possibility to be adopted in their own countries, rather than supplying children to parents who wished to adopt a child from a another country." 24 This was the philosophy of international adoption expressed from the 1920s onward. In concrete terms, the ISS realistically and constructively intervened in intercountry adoptions in order to introduce the best guarantees possible, as much from a legal as a social point of view.

Throughout 1956, ISS offices dealt with 3,500 placements of children in foreign families concerning fifty-four countries. 25 The large number of international adoptions can largely be explained by the enactment of an American law, the Refugee Relief Act of 1953, which provided for the admission of four thousand children to the United States before the end of 1956. 26 In the 1960s, a European couple who went to Greece with thoughts of adopting could do so in a month (statutory time limit in Greece), be entrusted with a child, and obtain a ruling of adoption. This very short period, and its corollary reflection on on both sides, was sometimes detrimental to the child's best interest: a case was reported of a French woman adopting a child, and then returning to France without him after changing her mind . . . 27 Adoptions of Italian children took place in France. The head of Health and Social Affairs of the Maine-et-Loire highlighted the fact that an Italian charity from Turin organised the placement of some children in that département.

But according to Italian authorities, too many French couples easily crossed the border with an

Italian child handed over to them by an institution for abandoned children. Through its consulates in France, Italy then asked the ISS and the SSAE to assure that adoptions of Italian children be carried out lawfully. 28 The great evolution of the 1960s, however, was that from that point onward a movement of adoption developed from Asia toward Europe. Arriving from Lebanon, India, South Korea, and Vietnam, hundreds of children arrived each year in Europe to be adopted in France, Belgium, Germany, the Netherlands and Norway...very few in the United Kingdom, where international adoption was and has remained marginal. As the countries of origin became more and more numerous the countries of Western Europe all more or less became host countries; once a country of origin, Italy became a host country. This evolution of the migratory movements of intercountry In this way, the Social Committee and the Legal Commission initiated work to reflect upon, define and establish statistics on the migratory phenomenon of transnational adoptions. 31 In August 1956 in Germany, the ISS brought its personnel together and drew up a certain number of principles. the UN position "which considered adoption to be one of the important principles in its policy of the protection of childhood." The beginning assessment was clear and well defined the situation of international adoption at the time: "in many countries, the verification of the delivery of passports to emigrating children […] is careless […] and encourages the placements of children from one country to another without the necessary preparation and protections." 32 During the work in Geneva, two directions were explored: first "to increase possibilities for adoption within each country, which would reduce the need for adoption between countries," then to establish "conditions in which intercountry adoption could be carried out […] with the most serious guarantees in cases where it is judged to be necessary and desirable, given that one would expect cases of this type to continue to come up." 33 The first direction entailed a reflection upon adoption in general in each country, which was not always well accepted by governments; the second was to find a modicum of legal harmonisation among governments in order to establish rational bases to confront the unbridled development of a growing phenomenon. The work of these experts resulted in the drawing up of twelve principles, short and very expressive. They stated that the good of the child was the principal element upon which all aspects of adoption should be based. 34 In November 1959, at the UN General Assembly, the international community unanimously adopted the Declaration of the Rights of the Child. Based on the previous great declarations of human rights, the text lists ten great principles so that each child may have "a happy childhood and enjoy for his own good and for the good of society the rights and freedoms herein set forth." Here was a veritable recognition of children's rights, to that point the legal status of children had especially been specified. Adoption was not mentioned, but Principle Six stipulated that the child "shall, wherever possible, grow up in the care and under the responsibility of his parents, and, in any case, in an atmosphere of affection and of moral and material security; a child of tender years shall not, save in exceptional circumstances, be separated from his mother. to the ISS. 36 The group of experts meeting in Geneva in January 1957 had recommended the meeting of an international seminar, whose work could make proposals which the UN would address to governments and the Council of Europe.

II -Drawing up principles

The Social Committee of the Council of Europe, at its Eighth Session (30 November -4 December 1959), after having heard a talk by a UN representative on the problems linked to transnational adoption, decided to contribute to finding solutions. The Council of Europe looked to write a regional convention with model regulations whose principles would apply to member states.

The first measure for the Council of Europe was to an observer to the seminar the group of experts had wished for in 1957, held in Leysin, Switzerland from 22 -31 May 1960. 37 The seminar was organised by the United Nations Technical Assistance Administration as a part of the special programme of social service for Europe, and in collaboration with the Swiss government, the ISS and the IUCW. The seminar was reserved for European participants who, through their experience, could bring a positive contribution to the studies and promote the spread of new ideas in their countries. So that meant social workers dealing with adoption, legal experts, and civil servants. The Council of Europe, the Hague Conference on Private International Law, and the National Catholic Welfare Conference sent observers. 38 The work done in Leysin was based on "two axioms": "1 -Adoption is the best replacement for a biological family[…] 2 -The aim is above all to promote the well-being of the child." The different work groups in Leysin took up the twelve principles formulated by the group of experts in Geneva in 1957 and would propose practically the same text to create a fundamental charter to diffuse and apply. The six first principles related to adoption in general and the last six were proper to intercountry adoption. Principle One focused on adoption's goal: "Adoption is the best replacement for the care given to a child by his parents or his immediate family, on the condition that this adoption be principally founded on the well-being of the child." All possibilities for adoption in the home country must be studied before a foreign placement is considered, "given that it is risky to transplant a child outside of his cultural environment" (Principle Two). According to Principle Three, the adoption of children placed in an institution should be carried out as early as possible. In each country, efforts should be made to find families for physically or mentally disabled children (Principle Four). The fifth principle stated that every parent should be in a position to evaluate the consequences of adoption for his child before consenting to it. The same necessity applied to the adopted child if he was of an age to understand and to make a choice (Principle Six). 39 Out of the last six principles came the statement of the guarantees which should accompany each international adoption. An investigation must absolutely be done into the home of the adopting parents as well as into the child (Principle Seven). This investigation must determine the choice of a child's adoptive family by the child protection agency, particularly by taking religion into account (Principle Eight). The necessity of a placement lasting at least six months in the family before the adoption is clearly confirmed (Principle Nine), which aimed to eradicate the practice of adoption by mandate, in other words an adoption carried out before the adopting parent had even seen the adoptee. The fact of insisting on the necessity of possessing all documents in due form in order to carry out the adoption (Principle Ten) proves that this was a practice which was not always respected. Principle Eleven considered the period between the arrival of a child in a foreign country and his official adoption as one of the most critical regarding the protection of the child. Finally, the best interest of the child also demanded that his adoption be acknowledged in his country of origin (Principle Twelve), which was hardly the case in 1960 as national legislation on the subject varied greatly. 40 As far as the manner in which these principles were applied is concerned, the Leysin meeting recommended the "social casework" method in the different phases of adoption, in reaction to the all too frequent intervention of unqualified people: "their ignorance of social, psychological, and legal elements can have tragic consequences for the children, their biological parents, and their adoptive parents." It was then indicated that a "service of trained casework is vital to inform candidates for adoption and the biological parents of the legal consequences of adoption and to enlighten them about its psychological consequences." The list of recommendations was long. The experts seemed to have foreseen every instance, every difficulty which came up or which could come up in the legal or social domain or the protection of children. The Leysin seminar also produced a draft of a convention, in six titles and sixteen articles, "intended to inspire the authors of a European tool," whose goal would be to "protect the interest of the adopted child, whose well-being is absolutely predominant." [START_REF]Rapport de mission…[END_REF]

III -Toward a European Adoption Convention

As seen above, the main principles of intercountry adoption were unanimously defined in 1957 and 1960. Neither formalised nor inscribed in international law, they were not restrictive for governments, international organisations, or the national associations which handled adoption. The role of the different organs of the Council of Europe were then of paramount importance in moving toward an international text.

In 1960, the Social Committee raised the following point on intercountry adoption: "Such is the problem at hand: that of general inadequacy." It was thus urgent to "go back over the logic de transnational adoption of children in trying to improve it at its different stages." The convention draft of sixteen points established by the experts in Leysin seemed to be an interesting base for writing a convention whose object was to "protect the interest of the adopted child, whose wellbeing is absolutely predominant." [START_REF] Caac | L'adoption des enfants entre pays[END_REF] The Legal Commission insisted that legislation of member states of the Council of Europe be harmonised "in compliance with modern concepts." Legal conflicts brought about by intercountry adoption were indeed very numerous. The main question lay with determining the competent local authority, and so the law to apply, to authorise the adoption and to manage its impacts: was it the law of the adopter's country or that of the adoptee's? [START_REF] Caac Ac 1 | Rapport sur le droit de l'adoption[END_REF] Drawing on this report, the Social Committee decried the lack of precise statistics but considered that from the evidence, "adoptions among member states of the Council of Europe were few compared to the adoptions carried out between European countries and other countries." It affirmed that the problems relative to intercountry adoption were to be put in the wider framework of adoption in general. It noted the very great disparities in national legislation and the impossibility of moving towards uniform regulations or a restrictive convention. So it proposed establishing "a convention only containing a minimum of essential principles" accompanied by recommendations that each member committed to implementing in its legislation. [START_REF] Caac Ac 1 | Conclusions du sous-comité d'experts pour l'adoption des enfants entre pays[END_REF] This option completely suited all the member states, particularly France who did not want a text which was too legally restrictive in order to preserve "pluralism of forms when it has historically existed and meets a pluralism of needs." Reference was of course being made here to the specificity of the two forms of French adoption, with or without a break with the biological parents. [START_REF]Letter from the French Minister of Public Health and Population to the FAM[END_REF] In Recommendation 292 (1961), the consulting Assembly of the Council of Europe, "Considering that adoption exists as a legal institution in all member countries of the Council of Europe, but that national legislation on the subject differs both as to the form and as to the substance of adoption," invited the Committee of Ministers, "should appoint a committee of governmental experts […] to draft a convention which would contain a minimum of essential principles in regard to adoption." [START_REF]Consultative Assembly of the Council of Europe[END_REF] This is what was done starting in 1962: a sub-committee on adoption met regularly and worked on writing a convention draft. It endeavoured to deal with adoption in general whilst always keeping in mind the problems of international adoption. [START_REF] Caac Ac 1 | Réunion d'un groupe de travail du sous-comité pour l'adoption[END_REF] The Hague Conference on Private International Law, which had sent --it too --an observer to Leysin, set to work a special commission which settled upon a draft for a "Convention on International Adoption" in March 1963. It was debated and led to a final document on 7 October 1964 aiming to resolve conflicts of jurisdiction and assure the recognition of granted adoption decisions. The twenty-four articles of the convention "concerning the jurisdiction of authorities, the applicable law and the recognition of decisions on the subject of adoption" concluded 15 November 1965 particularly dealing with the authorities competent to grant adoptions (Article Three), the conditions of social enquiries (Articles Six and Seven), questions of nationality (Article Ten) or adoption bans, for example the age conditions between adopter and adoptee (Article Thirteen). The main principle is that in legal conflicts, the judge applies his own law, meaning most often the law of the host country, except for what concerns the consent of the child's birth parents. [START_REF] Hans Van Loon | Genèse et historique de la Convention du 29 mai 1993[END_REF] After several years of reflection and writing, the European Convention on the Adoption of Children was opened to the signature of Council of Europe members on 24 April 1967. Containing twenty-eight articles organised in four parts, it was the most complete text on adoption to date. [START_REF]Part I: Undertakings and field of application (Articles 1-3); Part II: Essential provisions (Articles 4 -16); Part III: Supplementary provisions; Part IV: Final clauses[END_REF] Its impact was to insure that child protection measures were applied equally to the adoptions of foreign children, whether European or from other countries of origin. To do this, it took the main principles drawn up earlier but cut them back to a minimum so that they would be acceptable for all states which had to integrate them into their own legislation. It also provided an additional list of measures which states were free to implement if they so chose. The three main principles chosen were the following: the adoption must be ordered by an administrative or legal authority, the decision to offer a child up for adoption must be freely accepted by the parents, and the adoption must insure the child's well-being. Signed by eleven countries and ratified by six of them, it went into effect on 26 April 1968; in total, eighteen states ratified the convention and three signed it. 50 The convention then could not settle all cases of international adoption, particularly between the countries of Western and Eastern Europe. Certain countries would then contract bilateral conventions, such as the Franco-Polish Convention of 5 April 1967 which stipulated that the conditions and effects of adoption are those of the adoptee's law and that the forms of adoption are subject to the national law of the adopter, or the Franco-Yugoslav Convention of 18 May 1971 which stipulated that the authorities of both countries have the jurisdiction to grant an adoption. 51

Conclusion

The efforts of the Council of Europe to regulate a complex transnational social reality like international adoption on the European level illustrates how the institution tried to tackle a problem which could hardly find a way forward in the bilateral relationships between governments. On the contrary, the Council of Europe fit within a group of interactions with other international organisations like ISS or the Hague Conference on Private International Law, and made possible the proposition of a general approach to a very unique type of migration.

The COE arrived at the conclusion that a convention was necessary, laying out essential convention was brought up. 52 For their part, Third World nations, countries of origin for international adoption, considered that the convention was written to benefit the European host nations which had put it together. 53 As if in reaction, in La Paz in 1984 Latin American countries drew up a convention on legal conflicts in adoption. It gave jurisdiction to judges of a child's home country applying the laws of their country, except for the criteria aimed at the adopters. 54 In

  and the Family (Haut Comité consultatif de la Population et de la Famille, or HCPF) recommended turning the flows of refugees coming from Germany toward France. During a meeting on 18 May 1945, General de Gaulle asked the HCPF to examine bringing children of all nationalities to France, who were "currently orphaned or isolated in Germany." Immigration proved essential to guarantee 5 Consultation request dated 10 July 2014 and letter to Bjorn Berge, Director of the Cabinet of the COE Secretary General, 11 July; response from Ute Dahremöller, Director General of Administration of the Council of Europe, 25 August 2014. 6 Tara Zahra, note 1, introduction : "Civilization in disarray", p.1-23. 7 Heide Fehrenbach, Race after Hitler. Black Occupation Children in Postwar Germany, Princeton 2007, Chapter 5: "Whose children, theirs or ours? Intercountry adoptions and debates about belonging ".

France's

  recovery. It meant welcoming children who bore promises for the future and to make French citizens out of them to replace those who were lacking due to a low birth rate. For Pierre Pflimlin, Undersecretary of State to the Population, it meant carrying out a veritable "blood transfusion." 8 In April 1946, he specified "that it was no longer only a question of children with French blood in their veins." And adoption could help this regeneration. In nationality law (Ordinance of 19 October 1945), Article 35 stipulated: "The child who was subject to adoptive legitimization (adoption while breaking links with the biological family) acquires French nationality if his adoptive father is French." For simple adoption -(maintaining links with the biological family), Article 55 applied: "The child adopted by a person with French nationality can, until he reaches legal age, declare […] that he claims French nationality." 9

  24 FAM, CAAC, AC 1, No. 3, "Adoption entre pays: rapport d'un groupe d'experts européens, Genève 21-25 janvier 1957), United Nations, 1958, TAA/EG Rep.3, p.3-4. 25 Ibid, p.4 26 Christopher Bagley (ed.), note 15, p.148-149. 27 Camille Olivier, note 21, p.135-136 28 Archives of the Département Maine-et-Loire, 303 W 82, annual activity report of the Department of Social Services --DASS (1968-1969); Jean Foyer Collections, 818 J, Report from the DASS of Maine-et-Loire "les adoptions en Maine-et-Loire" for the years 1967-1969.adoption pushed the Council of Europe to propose a convention.B -The Contribution of the Council of EuropeI -The necessity for inter-institutional dialogueIn 1952, the World Health Organisation (WHO), organised a meeting on adoption in New York with the aim of drawing up universal statutes. Obviously, governments were very reticent to accept guidelines on a practice over which they had exclusive jurisdiction.29 Yet, in transnational adoptions, a minimum amount of harmonisation is necessary to preserve the rights of the children as well as those of the biological and adoptive parents. On the international level, the first reflections of the ISS on this new phenomenon were shared by the UN services concerned and the brand-new Council of Europe (COE), which gathered the main host countries of international adoption in the 1950s and 1960s (Belgium, Denmark, France, Norway, the Netherlands, and Sweden) and also countries of origin (Italy and Greece).30 In the 1950s then, the new European institution started to look into these "intercountry adoptions." Indeed, at the time there existed no regulatory guidelines, no international text which organised and controlled this particular type of migration of thousands of European children, intra-European migration coupled with intercontinental migration. The Committee of Ministers of the Council of Europe, in a special message on 20 May 1954, proclaimed its intention "to study the means of unifying and harmonising the legislation of member states" and wished to receive the suggestions of the consulting Assembly.

  principles as per the respect of the rights of children (in reference to the 1959 UN Declaration of the Rights of the Child). Within the Council of Europe, a long negotiation effort ended in the writing of the European Convention on the Adoption of Children (1967). International adoption was still developing in the 1970s, and this minimalist text quickly became insufficient. Many Council of Europe member states had indeed revised their legislation according to social and legal changes, and certain provisions of the Convention became obsolete. As early as 1977, at the first European conference on family law, the necessary update of the 50 European Convention on the Adoption of Children , Council of Europe, (CETS No. 058), 1967. 51 Hélène Gaudemet-Tallon, Le droit français de l'adoption internationale, Revue Internationale de Droit Comparé, n°42-2 (1990) p.567-597. Caroline Mécary, L'adoption, Paris 2006, p.104-105.

  18 FAM, Administrative Conventions Series (from now on CAAC) AC Volume 1, Box No. 3, Letter from the Justice Minister to the Foreign Affairs Minister, 26 August 1952.19 Josephine Baker adopted twelve children of all colours, origins, religions and nationalities in order to raise them

according to her ideal of universal brotherhood. See Yves Denéchère, note 2, p.56-63. 20 Yves Denéchère, La migration singulière des adoptés dans l'espace euro-américain depuis 1945, AMNIS, 2013, URL : http://amnis.revues.org/1980. 21 Camille Olivier, Adopter un enfant, Paris 1965, p.132-133. 22 Karen A. Balcom, The Traffic in Babies. Cross-border Adoption and the Baby-selling between the United States and Canada 1930-1972, Toronto 2011, p.161-162. 23 Camille Olivier, note 21, p.130-131.

  Then, in accordance with the United Nations' European Office of Technical Assistance, a group of European experts met in Geneva from 21-25 January 1957 to decide what action to take. The fundamental principle which inspired the group's work was that "adoption,

	whatever its form, must have only one objective: the good of the child." This was consistent with
	29 Rachel Gayman, Le problème de l'adoption, Cahiers français d'Informations. Quatre études sur la jeunesse
	socialement inadaptée, No. 283, (1955), p.20-26.
	30 At its creation in May 1949, the COE counted ten member states: Belgium, Denmark, France, Ireland, Italy,

Luxembourg, the Netherlands, Norway, Sweden, and the United Kingdom. Joining later were Greece (1949), Turkey (1949), the Federal Republic of Germany (1950), Iceland (1950), Austria (1956), Cyprus (1961), Switzerland (1963), Malta (1965), and others followed after our period of study. For the history of the institution, see particularly Birte Wassenberg, History of the Council of Europe, Strasbourg 2013. 31 CAAC, AC 1, Box Number Three contains documents on transnational adoption issued by the Council of Europe (1957-1968), particularly several reports on the different steps of the consideration of the transnational adoption question by the COE.

  1988, the Council of Europe's Committee of Experts on Family Law put certain questions on adoption on its working agenda, but a new text was written on an international level as a part of the Hague Conference on Private International Law. This work led to the Hague Convention on Protection of Children and Co-operation in Respect of Intercountry Adoption in May 1993. 55 This convention has generally presided over international adoption in the world since it went into effect (1 May 1995). On a European level, Recommendation 1443 (2000) launched an effort to review and adapt the 1967 convention in order to ensure compliance with the convention of the Hague. This process concluded in 2008. 56 ____________________ 52 Hans van Loon, note 48, p.9-17 53 Maev O'Collins, The influence of Western adoption laws on customary adoption in the Third World, in Philip Bean (ed), Adoption. Essays in Social Policy, Law and Sociology, London 1984, p. 288-304. 54 Francisco J. Pilotti, Intercountry Adoption : A view from Latin America, Child Welfare, n°LXIV-1 (1985), p.25-35. 55 Hans van Loon, note 48, p.9-17 56 European Convention on the Adoption of Children (Revised), Council of Europe, 2008, (CETS No. 202).

Yves Denéchère, Des adoptions d'Etat : les enfants de l'occupation française en Germany, Revue d'Histoire Moderne et Contemporaine, n°57-2, (2010), p.159-179

Foreign Affairs Ministry -France (from now on FAM), Archives of the French Occupation of Germany, Collections of Displaced Persons and Refugees, DPR 285, "Recensement des enfants dont l'un des parents est ressortissant des nations unies", s.d. ; DPR 396, letter from a non-commissioned officer, 31 August 1946.

To know more: Yves Denéchère, note 12.

Christopher Bagley (ed.), International and Transracial Adoptions, Newcastle 1993, p.160-163.

Jean-Claude Nicolle, Le service social d'aide aux émigrants et l'adoption, in L'adoption internationale, colloque Louis Chatin, 1994, ronéotypé, p.41-44.

CAAC, AC 1, No.3, "L'adoption des enfants entre pays", report of the Division des Questions sociales, CE/Soc (60) 24, 3 November 1960, p.2

CAAC AC 1, No. 3, "Rapport de mission rédigé par l'observateur du Conseil de l'Europe au Cycle d'études européen de Leysin sur l'adoption entre pays ", CE/Soc (60) 12, 25 July 1960, p.1-2.

Marie-Pierre Marmier, L'adoption, Paris 1972, p.100-102.


Caifang Cai
email: caifang.cai@lss.supelec.fr

Thomas Rodet
email: thomas.rodet@satie.ens-cachan.fr

Marc Lambert
email: marc.lambert@lss.supelec.fr

Influence of partially known parameter on flaw characterization in Eddy Current Testing by using a random walk MCMC method based on metamodeling

Keywords: flaw characterization, Eddy Current Testing, random walk, Markov Chain Monte Carlo (MCMC), metamodeling

First, we present the implementation of a random walk Metropolis-within-Gibbs (MWG) sampling method in flaw characterization based on a metamodeling method. The role of metamodeling is to reduce the computational time cost in Eddy Current Testing (ECT) forward model calculation. In such a way, the use of Markov Chain Monte Carlo (MCMC) methods becomes possible. Secondly, we analyze the influence of partially known parameters in Bayesian estimation. The objective is to evaluate the importance of providing more specific prior information. Simulation results show that even partially known information has great interest in providing more accurate flaw parameter estimations. The improvement ratio depends on the parameter dependence and the interest shows only when the provided information is specific enough.

Introduction

In Eddy Current Testing (ECT), the objective is to estimate the parameters of the flaws present in the specimen examined, like their positions, dimensions and parameters related to their shapes, etc. In our situation, the processed data is the variation of impedance caused by the presence of a flaw.

So, if we denote y ∈ C M as the impedance variation where M is the measurment dimension, x ∈ R N as flaw parameters where N is the unknown parameter dimension, without considering the measurement noise, they can be related to each other by y = f (x).

(1)

Here, f (x) represents the physical phenomenon from x to y. Obviously, it is not linear. The objective of flaw characterization is to estimate x from measurements of y, of course noisy. One of the major difficulties in ECT is the numerical realization of the mathematical description of the physical phenomenon represented by f (x). The method of moments [1,2,3] allows to get an accurate modeling of this phenomenon. However, it is computationally costly. This, in the inverse problem, limits the use of more sophisticated stochastic methods, like Maximum Likelihood (ML), Maximum A Posteriori (MAP) and Expected A Posteriori (EAP), since these methods are often solved by iterative numerical algorithms [4,5] or Markov Chain Monte Carlo (MCMC) sampling methods [6,7,8]. Those require to calculate f (x) many times.

A metamodeling method [START_REF] Sykulski | IET 7th International Conference on Computation in Electromagnetics[END_REF][START_REF] Pronzato | [END_REF]11] provides surrogate options to get f (x) with lower time cost. In metamodeling, this includes • a well-trained database containing samples of x and the corresponding f (x);

• an interpolator which allows to predict f (x) for any input x.

Bilicz et al. [12] present an optimal database training process by using the kriging interpolation. The kriging interpolation method [11,13,14] considers the interpolated samples as a Gaussian process guided by a covariance matrix. Interpolations minimizing the error distance have analytical expressions. Applying metamodeling in flaw characterization problem, the database only needs to be trained once at the beginning. When a forward calculation is required, it only needs to perform the kriging interpolation, which is much less costly computationally. For this reason, it makes the use of MCMC methods possible in ECT flaw characterization problem.

The interest of using MCMC sampling method here is first to get EAP estimations of flaw parameters, second, to calculate the variance of posterior distribution, third, to analyze the influence of a given parameter on other parameter estimations. Similar works [15,16] have been conducted in view of parameter estimation. We are going to focus on the influence of partially known information. This is managed by the means of the MCMC sampling method.

2. Parameter estimation using random walk MCMC method 2.1. Likelihood with Gaussian noise model Considering Gaussian noise present in the measurements, the forward model can be represented by y = f (x) + ǫ, with ǫ ∼ N (0, Σ).

(2)

f (x) is the non-linear model describing the relation between x and y. In our situation, it is replaced by the metamodel database and the kriging interpolator. Σ = ||σ y || 2 I M is the covariance matrix of the complex Gaussian noise. I M is an identity matrix of size M × M . The real and imaginary parts of ǫ both follow Gaussian distributions. Their variances are σ 2 R = σ 2 I . The standard deviation σ y = σ R + jσ I .

The likelihood of such a complex multivariate Gaussian model can then be given by

p(y|x) = 1 (πσ 2 ) M exp - 1 σ 2 ||y -f (x)|| 2 , (3)
where

σ 2 = ||σ y || 2 .
In our situation, it is calculated based on the data Signal-to-Noise Ratio (SNR).

Uniform prior model

As for the parameters of the flaw, we choose to use the following uniform distribution

x ∼ U (a, b) : p(x) = N i=1 p i (x i ), p i (x i ) = 1 b i -a i a i ≤ x i ≤ b i 0 else , i = 1, 2, • • • , N. (4)
a = [a 1 , a 2 , • • • , a N ] T and b = [b 1 , b 2 , • • • , b N ]
T denote the inferior and the superior borders for each parameter in the metamodel database. Denote U • as the support for x, it is bounded by the inferior and superior borders a and b.

EAP estimation

Bayesian methods impose prior distributions about flaw parameters to estimate their values from noisy measurements. The EAP estimation calculates the expectation of the posterior distribution which can be described by

x = (x∈U • ) x p(x|y) dx = (x∈U • ) x p(y|x)p(x) p(y) dx. ( 5
)
where p(y|x) is the likelihood given in Eq. (3). p(x) is the prior distribution given in Eq. ( 4). p(y) is the residual which is independent of x.

Random walk MCMC

In order to get the estimations of the posterior distribution p(x|y), we choose to use the following random walk Metropolis-Within-Gibbs (MWG) method as described in Tab. 1. It is combination of the random walk Hasting-Metropolis method [6,17,18] and the Gibbs alternating sampling strategy [7,19].

Table 1: scheme of random walk Metropolis-within-Gibbs method. K is the sampling number.

1). Initiation:

x(k) , k = 0, i = 1.
2). Alternating candidature proposition:

x(p) = x(k) , 2.1, alternating parameter x(p) i : generate randomly s i ∼ U (-0.5t i , 0.5t i ), x (p) i = x(k)
i

+ s i . if (i = N ) i = 1, else i + +; 2.2, verification: if (x (p) i ∈ [a i , b i ]) go to 3 , else repeat 2.1 . 3). Decision: if r = p( x(p) |y) p( x(k) |y) > 1 accept x(p) , x(k+1) = x(p) , else 3.1, generate u ∼ U (0, 1); 3.2, sub-decision: if (u < r) accept x(p) , x(k+1) = x(p) , else reject x(p) , x(k+1) = x(k) . k + +. 4). Repeat 2, 3 until k = K.
Once applied the sampling method, we get a set of samples {x k } K for k = 1, 2, • • • , K following the posterior distribution p(x|y) after a period of warm-up (or burn-in) time. Then the EAP estimation given in Eq. ( 5) can be approximated by averaging over all the samples:

x = (x∈U • ) x p(x|y) dx ≈ 1 K K k=1 x(k) . (6)
To appraise the corresponding estimation uncertainty, the variance of the generated samples can be used. It is defined by

σ 2 p = D x = E x -E[x] 2 (7)
It corresponds to the variances of the posterior distribution along different parameters. E(x) can be replaced by its EAP estimation given in Eq. ( 6), then σ p can be approximated by

σ p ≈ 1 K -1 K k=1 x(k) -x 2 .
(8)

Parameter estimation with partially known information

In certain situations, more specific prior information can be obtained. For example, the lift-off of the coil is often considered to be known while the width of a surface crack is often known to be small. The interest of studying the influence of a partially known parameter is to evaluate the importance of such kind of partial prior information, more importantly, the influence on other parameter estimations. Here, we define:

Partially known: if the parameter support x ∈ U is smaller than the metamodel database support U • , which means U ⊂ U • , then the parameter x is said to be partially known.

According to this definition, two situations might happen. One is that certain elements of x are totally known, the other is that the support for certain parameters are subsets of U • . In situations with partially known parameters, the same MWG method can be used to solve the estimation problem. It is only necessary to eliminate the known parameters from x or reset the inferior and superior borders to the corresponding borders in U.

ECT example 4.1. Ferromagnetic configuration and data simulation

In order to analyze the influence of partially known parameters, we use a simple example as sketched in Fig. 1. An opening crack affects the surface of a conductive plate. The crack center is located at the origin O. We wish to characterize the dimension of the crack. There are three unknown parameters in our problem: flaw depth d, length l and width w. For the following analysis, the noise-free data is simulated by using the metamodel trained from simulated data using the method of moments implemented in CIVA [20]. Gaussian noise with SNR equal to 20 dB is then added numerically as described in Eq. ( 2). The testing sample is taken arbitrarily by using Latin Hypercube Sampling (LHS) method. Its parameter values are d = 0.5428 mm, l = 8.7348 mm and w = 0.1523 mm.

All unknown

First, we apply the Bayesian inverse method based on random walk MWG as described in Sec. 2 on the simulated data to estimate the three unknown parameters. Fig. 2 shows the MCMC samplings according to different profile views and the estimated results after eliminating warmup samplings (around 700 out of 10 5 in total). In terms of CPU time, it takes around 4 minutes on a 3.4 GHz PC. We observe that the relative estimation error is less than 1.3% for flaw depth and length and around 4.9% for flaw width. From the w-d profile view, the EAP estimation is located in a narrow valley. This indicates that there is a determination difficulty between flaw width and depth. In other words, the flaw depth and width are highly dependent. In contrast, flaw length is less dependent on the other two parameters.

Partially known flaw width

In the above situation, we consider that all parameters are totally unknown. Strictly speaking, this is not correct, since we have benefited from prior information to get parameter inferior and superior borders in training the metamodeling database. But considering that the database support U • often covers a much larger range than the one of our interest, so it can still be seen as all unknown situation. To study the influence of partially known parameters, we choose to give more prior information to the flaw width. As we observe from Fig. 2, the flaw width is highly dependent on the flaw depth but lightly on the flaw length. This makes it becomes a very good object to study influence of partial information. We define r c as the radius of the confidence region for flaw width. It is the half distance from the inferior border to the superior border of U but given in ratio to the posterior standard deviation estimated in all-unknown situations. To simplify the simulation, U defined by r c is always centered at the true value. So when r c = 3, it means that more than 90% samples obtained in the all-unknown situation are located within the new support U. Tab. 2 shows the estimation errors and standard deviations with partially known information.

We see that the estimation relative error and standard deviation start to decrease when r c becomes less than 3. For flaw depth, an improvement of 85% on relative distance and 31% on standard deviation is achieved continuously while narrowing the confidence region. As for the flaw length, the improvement ratio is not as significant as for the depth. The improvement ratio is 40% for relative distance and 7% for standard deviation. This is because the flaw width is highly dependent on the flaw depth but less dependent on the flaw length, as seen from Fig. 2.

Conclusion and perspectives

This work analyzes the influence of partially known parameters on estimation of other unknown parameters. It is carried out by using a random walk MCMC sampling method based on a fast surrogate forward model. From the simulation results, we conclude that providing partially known information can help us to improve estimation accuracy. But this shows only when the confidence region for the parameter becomes smaller than 3 times of the range defined by the posterior standard deviation. In terms of improvement ratio, it depends on the dependence between parameters. The more they depend from each other the higher the improvement ratio becomes. For future work, it will be interesting to analyze the influence of nuisance parameters on flaw parameter estimation, for example, the lift-off of the coil which is often known roughly from manual measurement.

Figure 1 :

 1 Figure 1: a 3D testing example: a flaw (in gray) at the surface of a conductive plate.

Figure 2 :

 2 Figure 2: MCMC samples (K = 10 5 , walk step t = [0.01, 0.01, 0.04]) of random walk MWG method for tested sample d = 0.5428 mm, l = 8.7348 mm, w = 0.1523 mm. The estimated results are d = 0.5385 ± 0.0122 mm, l = 8.7310 ± 0.1739 mm and ŵ = 0.1597 ± 0.0110 mm.

Table 2 :

 2 influence of partially known flaw width on estimations of the flaw depth and length.

	Information level all unknown		flaw depth | x-x x | (%) σ p (mm) | x-x flaw length x | (%) σ p (mm) 0.7834 0.0122 0.0436 0.1739
	partially known width	5	0.7864	0.0120	0.0426	0.1742
	confidence radius r c	2.5	0.6777	0.0114	0.0434	0.1714
	(in times of σp = 0.011 for flaw width	1.5	0.2289	0.0111	0.0368	0.1685
	in all-unknown situation)	1	0.1438	0.0099	0.0287	0.1644
	known width w = 0.1523		0.1114	0.0084	0.0261	0.1611

Acknowledgments

The French National Research Agency (ANR) has been providing financial support for this research work in the framework of ByPASS project. CEA-LIST is to be thanked for providing metamodeling databases.