Khizar Hayat
email: khizar.hayat@lirmm.fr

William Puech
email: william.puech@lirmm.fr

Gilles Gesquière
email: gilles.gesquiere@lsis.org

Dr Xiaolin K Wu

W Hayat

Puech

Scalable 3D Terrain Visualization through Reversible JPEG2000-Based Blind Data Hiding

Keywords: 3-D visualization, data hiding, data synchronization, Digital Elevation Model (DEM), Discrete Wavelet Transform (DWT), Geographic Information System (GIS), JPEG2000

In this paper a new method is presented for 3-D terrain visualization via reversible JPEG2000-based blind data hiding with special focus on data synchronization and scalability. Online real-time 3-D terrain visualization involves considerable amount of data. The process is essentially the mapping of the aerial photograph, called texture, onto its corresponding digital elevation model (DEM) implying at least two distinct data inputs. The presence of large disparate data necessitates a compression strategy on one hand and the integration of the DEM and texture into one unit on the other. Whilst the compression must accommodate the scalability requirement originated by the diversity of clients, the unification of data ought to be synchronous. For scalability this paper relies on the multiresolution nature of the DWT-based JPEG2000 standard whereas the synchronized unification of DEM with the texture is realized by the application of a perceptually transparent data hiding strategy in the DWT domain.

The proposed method is blind in the sense that only a secret key, if any, and the size of the original DEM are needed to extract the data from the texture image. We believe that this is one of the pioneering methods to propose scalable embedding of DEM in the texture image. The method is cost effective, in terms of memory and bandwidths, which is an advantage, especially, in real-time environments when quicker transfer of data is required. The results of a 3-D visualization simulation effected with our method were encouraging and gave a useful insight to the effectiveness of our method in various bandwidth scenarios.

aerial photographs and satellite imagery which is being made available to these browsers ameliorates. All this comes at a cost as far as memory requirements are concerned. For example, a 5 meters/pixel resolution aerial photograph of a small district requires well over ten gigabytes of storage, even in the JPEG2000 compressed form. Alongside the storage is the network factor, when it comes to online real-time 3-D visualization, since the data must be transferred from the server towards a client application in a timely way. In such a client/server environment the visualization quality becomes dependent on the payload, bandwidth, distant server and data transfer rate. To cope with the aforementioned challenges, any strategy that would not focus on data compression is unthinkable. But there is more to compression strategy than meets the eye since the clients are diverse in terms of resource capacity and requirements. Thus one client may have a powerful workstation while others may have just a smart-phone. Similarly one client may have a 100 Mbps connection whereas the other may be using a 56 kbps dial up modem. Still one client may want to view a precise location at high accuracy but others may just want to quickly browse through the globe. There is also a possibility that the network path of a client may involve at least one weak link or node. In between these extremes, there may be thousands of clients with varying capabilities and needs. Moreover, the preferences of a client may adapt to his capacity, e.g. a client handicapped by bandwidth may be more interested in real-time visualization without interruption than in high resolution. A synchronized mechanism is needed so that the server is in a better position to cater for each of its client. The wide spectrum of clients thus necessitates the data compression to be ideally scalable for each hierarchy of clients. The JPEG2000 standard [START_REF]Information Technology, JPEG2000 Image Coding System, Part 1: Core Coding System ISO Central Secretariat: CH-1211[END_REF] serves this purpose since it is wavelet-oriented and wavelets have the property of multiresolution. The diversity of resolutions, that are resulting from a wavelet decomposition at various levels, is capable of offering the scalability needed in the situations discussed.

The 3-D visualization information is in general stored in three different files: digital elevation model (DEM), an orthorectified photo and projection system and geo-referencing employed. The process of visualization in three dimensions is, essentially, the linking of the aerial photograph of the terrain, called texture, with the geometry of the terrain, called DEM. Each of the DEM coefficient represents the altitude of a particular square block of texture pixels and the process of visualization is the overlaying of texture over a regular triangle network [START_REF] Losasso | Geometry clipmaps: Terrain rendering using nested regular grids[END_REF], [START_REF] Pajarola | Survey on semi-regular multiresolution models for interactive terrain rendering[END_REF] obtained from the DEM. This linking is possible by geo-referencing the coordinates (longitude/latitude) of these elements depending on the scale and system of projection used. Rather than using two disparate DEM and texture files it is advisable to interleave them into a single file. For this purpose one can take a cue from the technique of data hiding and embed the smaller DEM data inside the larger texture image. The underlying assumption of our method is that the texture image must have at least 16 times more pixels than the total number of coefficients in the corresponding DEM.

It is to be noted that the context of this data hiding would be unconventional unlike steganography or watermarking as neither we are exchanging secret messages nor is copyrighting our goal. The embedding scheme must address the issue of correspondence between the texture and its DEM. In other words the integration of texture and its DEM into a single file must be synchronous. As far as JPEG2000 is concerned there are solutions like GeoJP2 [START_REF] Gerlek | The "GeoTIFF Box" Specification for JPEG 2000 Metadata-DRAFT Version[END_REF] and GMLJP2 [START_REF] Lake | GML in JPEG 2000 for Geographic Imagery (GMLJP2) Implementation Specification Open Geospatial Consortium (OGC)[END_REF] but these serve the purpose partially since the data is not synchronized and there is an increase in the original size of the JPEG2000 file. It would be expedient to follow a different course, to have the advantage of synchronization without any change in the JPEG2000 file size and form, by applying a scalable data hiding algorithm. This approach would neither be XML-based, like GMLJP2, nor would it introduce some kind of Universally Unique IDentifier (UUID) boxes, like GeoJP2.

This work is a continuation of our previous efforts [START_REF] Hayat | An efficient data-hiding method based on lossless JPEG2000 for a scalable and synchronized visualization of 3D terrains[END_REF], [START_REF] Hayat | Wavelet based data-hiding of DEM in the context of real time 3D visualization[END_REF] for the synchronized unification of the DEM and texture wherein lossless DWT decomposition level of both the message (transformed DEM) and the carrier (transformed Y plane of the texture) are the same before embedding. Moreover, in the current paper, the method is more detailed and the results have been improved. The crux of our argument is to realize a 3-D visualization system that will cater for the two desirable requirements, i.e., scalability and synchronized unification of 3-D data, without developing any new proprietary file format and maintaining compression performances. For scalability the DWTbased JPEG2000 standard can be relied upon for its multiresolution characteristic due to wavelets. In addition JPEG2000 is the standard that is fast establishing itself. The synchronized integration of the disparate 3-D data into one whole is achievable through the application of a perceptually transparent data hiding technique in the transform domain. All this crystallizes to the proposal of an LSB-based strategy that would embed the lossless transformed DEM in the corresponding transformed luminance component of texture of the lossless JPEG2000 coding pipeline. For the extraction step, the proposed method is blind and only the size of the original DEM is needed for extraction.

The rest of the paper is arranged as follows. Section II presents the essential concepts and previous work relevant to our approach. Our method is explained in Section III while the results which we obtained are elaborated in Section IV. Section V concludes the paper.

II. 3-D TERRAIN VISUALIZATION, JPEG2000, AND DATA HIDING

This work relies on a JPEG2000-based data hiding technique in order to achieve synchronous and scalable 3-D terrain visualization. In this context it would be worthwhile to present the notions of 3-D terrain visualization (Section II-A) and JPEG2000 (Section II-B). Alongside, related work on data hiding in the wavelet domain is highlighted in Section II-C whereas Section II-D is dedicated to a description on the integration of geographical data into a JPEG2000 format file.

A. 3-D Terrain Visualization

For years the geospatial professionals thought of mapmaking as inventing ways to flatten Earth's 3-D surface onto a 2-D map. The various methods and projection systems which were developed are still far from reality. With the advent of 3-D computer graphics it became easier to create 3-D computer models to view different 3-D objects from various angles as well as rotate, zoom in and out, fly through and manipulate them. However, the chronic challenge persisted because the viewer just observed a snapshot of the 3-D models projected to a 2-D computer screen. The recent years' technological developments have now made it possible to create realistic 3-D terrain models from scanned contour maps and other data sources. 4 The popularity and importance of 3-D terrain visualization is increasing day by day in many areas, for example decision making, 3-D urban models, flight and driving simulations, and more generally, multiplayer applications.

Geographic data can be broadly classified into four fundamental classes: raster images, vector data, elevations and spatial databases. Images include aerial photos, scanned maps, satellite imagery and the like. Aerial photographs are the starting point for many mapping projects. By vector data is meant the traditional geometric structures like polylines, points, and polygons that have been used to represent roads, streams, power lines, lakes, county boundaries and topographic lines, on a particular scale. In digital form (e.g. digital line graphs) this representation has the advantage of having files much less heavier than images. Moreover such a data can be resized without any loss of clarity. Elevations are usually in the form of grid of terrain heights recorded at regularly spaced horizontal intervals: the result being a DEM. DEMs are used to create 3-D images of a landscape when overlaid by the corresponding 2-D aerial photos or satellite images thus producing, for example, lighting effects to reveal hills and valleys. The repositories of information like census data, resource inventory data and spatial event data constitute spatial databases that are helpful to a mapmaker in special cases, e.g. highlighting regions in the map or forecasting changes in the terrain.

Essentially, 3-D terrain representation implies to use two kinds of data combined for the visualization [START_REF] Martin | Real time 3D visualisation of DEM combined with a robust DCT based data-hiding method[END_REF].

• Height field data which corresponds to the elevation of terrain [Fig. 1 In order to get the DEM, the simplest solution consists of using a uniform discretization of the terrain. This gives a good accuracy but leads to a quite large number of triangles, thus implying a considerable memory cost for the 3-D visualization of a large area. Many methods have been proposed to reduce the number of triangles provided by the uniform discretization, while preserving a good approximation of the original surface. One of the main approaches consists of obtaining an irregular set of triangles: Triangulated Irregular Network (TIN). A great deal of work has been done in order to create the TIN starting from a height field by using, for example, a Delaunay triangulation [START_REF] Fowler | Automatic extraction of irregular network digital terrain models[END_REF] or a progressive mesh representation [START_REF] Hoppe | Progressive meshes[END_REF]. Hierarchical representations of these triangulations have been proposed, thus making it possible to introduce the concept of level of detail [START_REF] Floriani | Hierarchical triangulation for multiresolution surface description[END_REF]. Consequently one can obtain various levels of surfaces with an accuracy which is similar to a uniform grid but with a lower number of triangles.

To obtain a three dimensional visualization, one has to bind the texture to the terrain DEM. This bond is allowed by georeferencing coordinates (longitude and latitude) depending on the projection system used. The information is usually stored in three different files; one for the DEM, one for the texture and one for the geo-referenced coordinates. By mapping the satellite or aerial image on the corresponding 3-D terrain model. Thus, a realistic 3-D model can be created with the elevations and the surface texture.

In our work we have relied on the data provided by IGN5 France which consists of vectorial data in the form carto, raster images in the form BD Ortho or BD Scan and DEM usually at 50 m resolution. We seek to put in place the correspondence between the texture and its DEM. Using a uniform grid would allow this mapping since one would be able to do the similar thing for the ground and the images. The proposed method is about the interleaving of the above data to get a single file.

B. Discrete Wavelet Transform and JPEG2000

In standard image compression techniques, one of the essential steps is the domain transformation. The transform results in the decorrelation of the pixels. Pixel energy is thus compacted into a small number of coefficients. The idea is to enable the quantization step to trim the samples selectively, i.e., irrelevant samples must be quantized more heavily than the relevant ones [START_REF] Taubman | JPEG2000: Image Compression Fundamentals; Standards and Practice[END_REF]. One aspect of the success of JPEG [START_REF] Pennebaker | JPEG: Still Image Data Compression Standard[END_REF] is in the efficiency of its transform, i.e., discrete cosine transformation (DCT) applied to each image block of 8 8. But the use of block-based transforms rests on the unrealistic assumption of the independence of blocks.

Of the alternatives available to the block-based transforms the one that got the approval of JPEG2000 [START_REF]Information Technology, JPEG2000 Image Coding System, Part 1: Core Coding System ISO Central Secretariat: CH-1211[END_REF] proponents is the discrete wavelet transform (DWT). The key being its multiresolution nature resulting in subbands containing some level of detail derived from the whole image or at least a considerably large tile, if the image is of very large size. The quality in such a situation is incremental as the lowest subband has the most important and relevant information and the higher subbands have finer details. Most of the energy is thus compacted into a few large transform coefficients-an entropy coder easily locates these coefficients and encodes them. DWT offers better energy compaction than the DCT without any blocking artifact after coding. In addition the DWT decomposes the image into an L-level dyadic wavelet pyramid. The resultant wavelet coefficient can be easily scaled in resolution as one can discard the wavelet coefficients at levels finer to a given threshold and thus reconstruct an image with less detail.

The multiresolution nature of DWT, therefore, makes it ideal for scalable image coding. After the color transformation, the DWT decomposes each component (luminance Y and chrominance Cr and Cb) into numerous frequency bands called subbands. For each level, DWT is applied twice, once row-wise and once column-wise and hence four subbands result: 1) horizontally and vertically lowpass , 2) horizontally lowpass and vertically highpass , 3) horizontally highpass and vertically lowpass and 4) horizontally and vertically highpass . Let us consider the input image signal (or tile-component signal if image is large) as the band. A -level wavelet decomposition is associated with resolution levels. Each subband of the decomposition is identified by its orientation (i.e., , , , and ) and its corresponding decomposition level

. At each resolution level (except the lowest) the band is further decomposed. Thus the band is decomposed to yield the , , and bands. Then, at the next level, as illustrated in Fig. 2(a), the band is decomposed. This process is repeated until the band is obtained. If no transform is applied then there is only one subband: the subband. A level-2 wavelet decomposition of the image Lena, given in Fig. 2(b), is illustrated in Fig. 2(c).

Right from the beginning, JPEG2000 has been supporting two kinds of transforms: the reversible integer-to-integer Daubechies (5/3) and the irreversible real-to-real Daubechies (9/7) [START_REF] Daubechies | Factoring wavelet transforms into lifting steps[END_REF], [START_REF] Sweldens | The lifting scheme: A new philosophy in biorthogonal wavelet constructions[END_REF] with the former being lossless and the latter being lossy. The transformation can then be carried out by separately applying the version horizontally and vertically one after the other. Let the (pixel row or pixel column) input signal be then for the reversible 5/3 wavelet transform the lowpass subband signal and highpass subband signal are given by [START_REF] Bender | Techniques for data hiding[END_REF] In a simplified way, a typical JPEG2000 encoder6 consists of the following steps [START_REF] Taubman | JPEG2000: Image Compression Fundamentals; Standards and Practice[END_REF] which are illustrated in Fig. 3.

1) Preprocessing such as tiling and shifting the origin of the pixel values to 0 by subtracting 128. 2) Intercomponent transform in the form of irreversible or reversible color transform to pass from RGB space to YCrCb space. 3) Intracomponent transform that may be lossy or lossless DWT. 4) Quantization which decreases the size of the large coefficients and nullifies the small ones. 5) Tier 1 coding when the quantized coefficients are partitioned into rectangular code blocks and each is subjected independently to three coding passes. This step involves entropy coding too.

6) Tier 2 coding which is the packetization step whereby the code pass data is converted to packets-these packets are combined to get the final image in the JPEG2000 format.

It must be noted that in a JPEG2000 coding pipeline there are two primary sources of data loss. One is obviously quantization and the other is the stage in tier-1 coding when a decision is made about the exclusion of certain coding passes from the final JPEG2000 file. For the method proposed in this paper, the scalability prospects offered by JPEG2000 in the form of multiresolution is to our advantage, especially in the client/server environment.

C. Data Hiding in the Wavelet Domain

Data hiding is an established field and that is why a lot has been written about it [START_REF] Cox | Digital Watermarking[END_REF], especially for the last two decades. We, therefore, focus on the literature about wavelet-based data hiding which is again very extensive and one is compelled to be brief. Data hiding deals with embedding an information, called message, inside some host signal, like image, sound or video, called cover. The message may be small and robust as in the case of copyright protection in the form of watermarking or it may be large, critical and statistically invisible as in steganography. Four factors [START_REF] Bender | Techniques for data hiding[END_REF] characterize the effectiveness of a data hiding method, namely hiding capacity, perceptual transparency, robustness and tamper resistance. Hiding capacity refers to the maximum payload that can be held by the cover. Perceptual transparency ensures the retention of visual quality of the cover after data embedding. Robustness is the ability of the cover to withstand various signal operations, transformations and noise whereas tamper resistance means to remain intact in the face of malicious attacks. The relative importance of these four factors depends on the particular data hiding application. For example, for visually sensitive applications perceptual transparency becomes very important. Domain-wise, embedding can be carried out in the spatial domain or the transform domain. Pixel or coefficient allocation for data embedding may be regular (e.g. every pixel) or irregularly distributed (e.g. pseudo-random). Probably the most preferred pixel allocation is by running a pseudo-random number generator (PRNG) using some secret key as a seed. Finally, an embedding method is blind if data extraction by the recipient does not require the original cover.

Many methods have been proposed in the literature for wavelet-based data hiding but few of these are compatible with the JPEG2000 scheme. According to [START_REF] Meerwald | A survey of wavelet-domain watermarking algorithms[END_REF], data hiding methods for JPEG2000 images must process the code blocks independently and that is why methods like inter-subband embedding [START_REF] Kundur | Improved digital watermarking through diversity and attack characterization[END_REF] and those based on hierarchical multiresolution relationship [START_REF] Kundur | Digital watermarking using multiresolution wavelet decomposition[END_REF] have not been recommended. In the same breath the authors of [START_REF] Meerwald | A survey of wavelet-domain watermarking algorithms[END_REF] rejects the correlation-based method [START_REF] Wang | An integrated approach to embedded image coding and watermarking[END_REF] as well as non-blind methods. The reason for this is the limited number of coefficients in a JPEG2000 code-block that are likely to fail in reliably detecting the hidden information in a single independent block. There are methods [START_REF] Kundur | A robust digital image watermarking scheme using the wavelet-based fusion[END_REF], [START_REF] Xia | A multiresolution watermark for digital images[END_REF] for embedding invisible watermarks by adding pseudo-random codes to large coefficients of the high and middle frequency bands of DWT but the methods have the disadvantage of being non-blind. The blind scheme proposed in [START_REF] Su | An integrated approach to image watermarking and JPEG-2000 compression[END_REF] is to integrate data hiding with the Embedded Block Coding with Optimized Truncation (EBCOT) and embed data during the formation of compressed bit stream. The scheme is claimed to have robustness and good perceptual transparency. One particular technique [START_REF] Meerwald | Quantization watermarking in the JPEG2000 coding pipeline[END_REF] embeds the watermark in the JPEG2000 pipeline after the stages of quantization and region of interest (ROI) scaling but before the entropy coding. For reliability purposes the finest resolution subbands are avoided. A window sliding approach is adopted for embedding with the lowest frequencies having higher payload. Piva et al. have proposed an authentication scheme that embeds an image digest in a subset of the subbands from the DWT domain [START_REF] Piva | Self recovery authentication of images in the dwt domain[END_REF]. The image digest is derived from the DCT of the level 1 DWT subband of the image. The resultant DCT coefficients are scaled down by quantization and ordered from most to least significant through a zig-zag scan. A most significant subset, after discarding the DC coefficient, is quadruplicated for redundancy and then rescaled and scrambled by using two different keys. This gives the message which is substituted to the subbands selected from a set obtained by the further wavelet decomposition of the level 1 and subbands of the original image. One blind method [START_REF] Liu | A robust watermarking scheme using self-reference image[END_REF] transforms the original image by one-level wavelet transform and sets the three higher subbands to zero before inverse transforming it to get the modified image. The difference values between the original image and the modified image are used to ascertain the potential embedding locations of which a subset is selected pseudo-randomly for embedding. The method of Kong et al. embeds watermark in the weighted mean of the wavelets blocks, rather than in the individual coefficient, to make it robust and perceptually transparent [START_REF] Kong | Object watermarks for digital images and video[END_REF]. While explaining their method of embedding biometric data in fingerprint images, Noore et al. argue against the modification of the lowest subband to avoid degradation of the reconstructed image as most of the energy is concentrated in this band [START_REF] Noore | Enhancing security of fingerprints through contextual biometric watermarking[END_REF]. Instead they propose to redundantly embed information in all the higher frequency subbands.

D. Geographical Metadata Integration into the JPEG2000 Codestream

As far as the insertion of GIS information, as metadata, into a JPEG2000 coding pipeline is concerned there have been limited efforts to date. There are already efforts like GeoJP2 [START_REF] Gerlek | The "GeoTIFF Box" Specification for JPEG 2000 Metadata-DRAFT Version[END_REF] and GMLJP2 [START_REF] Lake | GML in JPEG 2000 for Geographic Imagery (GMLJP2) Implementation Specification Open Geospatial Consortium (OGC)[END_REF] for the integration of geographical data with the related aerial photographs. The GeoJP2 is a GeoTIFF-inspired method for adding geospatial metadata to a JPEG2000 file. The GeoTIFF specification7 defines a set of TIFF tags provided to describe all cartographic information associated with TIFF imagery that originates from satellite imaging systems, scanned aerial photography, scanned maps and DEM. Its aim is to allow means for tying a raster image to a known model space or map projection, and to describe those projections. GeoTIFF does not intend to become a replacement for existing geographic data interchange standards. GeoTIFF uses a small set of reserved TIFF tags to store a broad range of georeferencing information, catering to geographic as well as projected coordinate systems needs. It uses numerical codes to describe projection types, coordinate systems, datums and ellipsoids.

The additions made to the box-based JPEG2000 format are two UUID boxes, namely, the GeoTIFF box and the optional world file box. The former contains a degenerate GeoTIFF file and the resultant JPEG2000 file have the same level of geospatial metadata as is provided by the GeoTIFF standard. The mechanism is simple using the widely supported GeoTIFF implementations but the introduction of new UUID boxes have the disadvantage that there is an increase in the original JPEG2000 file size. The GMLJP2 envisages the use of the Geography Markup Language (GML) within the XML boxes of the JPEG 2000 data format in the context of geographic imagery. A minimally required GML definition is specified for geo-referencing images while also giving guidelines for encoding of meta-data, features, annotations, styles, coordinate reference systems, and units of measure as well as packaging mechanisms for both single and multiple geographic images. DEMs are treated the same way as other image use cases whereas coordinate reference system definitions are employed using a dictionary file. Thus DEM is either provided as TIFF file and its name is inserted between proper GML tags or its points are directly inserted into the GMLJP2 file. In the former case, there is no reduction in the number of files whereas in the latter case the amount of data is increased.

III. THE PROPOSED METHOD

As described in Section II-A, the 3-D visualization needs more than one file: the DEM and the image of texture being the essential. To coalesce this disparate data to a single JPEG2000

A. Overview

In this work the thrust is on the performance of the proposed method by the inclusion/exclusion of high frequency subbands in the DWT resolution hierarchy rather than modifying the data by quantization or tier-1 coding. That is why the JPEG2000 encoder has been set at the lossless mode and the wavelet transform is integer-to-integer. As already stated, the scalability prospects offered by JPEG2000 in the form of multiresolution is to our advantage, especially in the client/server environment. In a nutshell, our method is the LSB-based embedding of lossless wavelet transformed DEM into wavelet transformed luminance (Y) plane of texture extracted from a reversible JPEG2000 coding pipeline after the DWT step. Because of the small embedding factor needed for our application, we have chosen to embed the data only in the Y component in order to have a fast extraction and to preserve a better bitrate. The marked Y plane of texture is then reinserted to the JPEG2000 coding pipeline. Two factors have been taken into account in the course of embedding. First, the level of transform in both the cases, i.e., DEM and texture, is the same. Second, there is a synchronization in embedding: low subband DEM coefficients are to be embedded into those of low subband of texture while higher ones in the higher. The method is blind since there is no need of original texture image at the decoding side. The final image format is thus JPEG2000 compliant implying that there is no need of additional technology for the proposed method. A generalized scheme of the method is given in Fig. 4.

B. Transformation to Get the Cover and the Message

The two files of DEM and texture are the inputs whereby the former would process into the message and the latter would give the cover in the data embedding step. The DEM consists of 16 bit coefficients that represent the elevations in the form of altitudes. Each of these coefficients corresponds to a particular square block of pixels in the texture. Texture is already a color image in some standard format with RGB components. From the size of the DEM we can calculate the ratio between a DEM coefficient and its associated block of texture. Lossless DWT is applied, in isolation, to the DEM at a particular level, say that corresponds to resolutions. The resultant coefficients constitute the bits of our message in the traditional sense of data hiding. In fact, to represent the DEM in the spatial domain, only 14 bits per coefficient are necessary (altitude between 8192 m and 8191 m), but after the DWT 16 bits are necessary to represent each coefficient. Simultaneously, the RGB space texture image is introduced to a standard JPEG2000 encoder. The encoder, after necessary preprocessing, passes it from RGB space to the luminance-chrominance (YCrCb) space. In the next step, i.e., DWT step, the three YCrCb components are reversibly transformed at level . As can be seen in Fig. 4, the encoding path is diverted, after the DWT step, as far as the luminance (Y) image is concerned. The transformed Y component is our cover . Note that whether it is the transformation of the DEM or it is the JPEG2000 encoder for texture, the implementation of DWT is based on the lifting method [START_REF] Mallat | A Wavelet Tour of Signal Processing[END_REF] that employs the JPEG2000 supported reversible Daubechies (5/3) filter [START_REF] Daubechies | Factoring wavelet transforms into lifting steps[END_REF].

C. Embedding of the Data

This section explains the embedding of the message into the cover to get the marked cover . It has been ensured that both and are at the same level of transformation and embedding is according to the synchronization of subbands as illustrated in Fig. 4. One important point to mention is that in this work neither any copyright problem is solved nor is there any threat to the security of message. What we want is to carry out embedding without significant loss in the visual quality of the 3-D rendering. At the same time, the hiding capacity is also important since day by day the resolution quality is improving at the expense of data size. Hence, of the traditional requirements of data hiding, we are more particular about perceptual transparency and payload which implies that robustness and tamper resistance are secondary in importance.

From a pixel texture image and the corresponding map of altitudes, we deduce the embedding factor altitude coefficients per pixel. To ensure a spatial coherence between the altitudes and the texture, the cover is partitioned into square blocks of coefficients for data embedding and every such block would hide one transformed altitude coefficient of the message . We thus achieve a synchronization in the embedding as far as the incremental levels of the wavelets are concerned, i.e., low resolution coefficients of the altitude map are embedded in the low resolution subbands of texture whereas high resolution coefficients of the altitude map are embedded in the high resolution subbands. In this way the transmission of the part concerned with the low resolution of the texture map enables us to directly access the corresponding low resolution part of the altitude map.

For perceptual transparency, an embedding strategy based on least significant bit (LSB) substitution is proposed. The data embedding is carried out by modifying the LSBs of a certain number of coefficients of the luminance plane of the texture. An allocation policy is needed to determine which coefficients are to carry the message. These coefficients are chosen by using a PRNG with a key, , as a seed. The use of a secret key allows us to restrict access to DEM data. Since the chosen JPEG2000 coding is reversible the hidden message can be extracted losslessly. A high level description of the embedding strategy is outlined in Algorithm 1. , respectively. Embedding involves the hiding of each of the 16 bits in as many different coefficients of the given block. These coefficients are selected by running a PRNG using the key for one time initialization. The PRNG that will generate 16 numbers per which correspond to the allocated coefficients. Care must be taken to avoid collisions so that the same subscript is not generated twice. One of the bits would substitute the LSB of the allocated coefficient that would yield after embedding. Hence 16 of the coefficients of each of the embedded block would be changed from to . The procedure mentioned in the previous lines is followed for each block of the transformed Y texture and for each subband of , as described in Algorithm 1.

The resultant embedded image, , i.e., marked Y plane of the texture in the wavelet domain, is then reinserted into the JPEG2000 pipeline at the same point from where it was extracted. The final encoded image thus carries the DEM coefficients hidden in some DWT coefficients.

D. Extraction and Scalable 3-D Reconstruction and Visualization

The above coded image can be utilized like any other JPEG2000 image and sent across any communication channel. The decoding is the reverse of the above process. Since the method is blind, only the secret key is needed, along with the size of the original DEM, to recover the hidden DEM coefficients at the receiving end. Just before the inverse DWT stage of the JPEG2000 decoder, the DEM can be extracted using the above mentioned partitioning scheme and PRNG with as the seed. All the DEM bits are LSBs of the coefficients, indexed by the PRNG sequence, in the luminance plane of the carrier texture.

One advantage of the method is in the fact that the DEM and texture can be reconstructed at the original size, even if we have only a small subset of the coefficients of the cover. The resolution scalability of wavelets and the synchronized character of our method enable a 3-D visualization even with a number of layers smaller than the number of original resolution layers as a result of partial or delayed data transfer. The method thus enables to effect a visualization from a fraction of data in the form of the lowest subband, of a particular resolution level. The idea is to have a 3-D visualization utilizing lower frequency subbands out of the initial subbands , by padding a 0 for each of the coefficient of the rest of the high frequency parts. Indeed, it is always possible to stuff 0's for the higher bands. Hence a reconstruction with level lowest frequency subband is effected with just percent of the count of the original coefficients: the result would be what is called level approximation image. With this padding approach, irrespective of the number of subbands used for the reconstruction, the reconstructed DEM and texture have the same spatial sizes as the original ones. The reconstruction procedure from a JPEG2000 codestream of the marked texture is depicted in Fig. 6.

It is important to note that level wavelet decomposition corresponds to resolution levels in the range to 0 in ascending order of quality as well as quantity of data. This implies different visualizations of which the first one requires only the lowest subband. The second visualization would require four subbands which include the previous one, , and three others namely and . Seven subbands, , , , and constitute the data for third visualization. In general visualization is based on lowest subbands , , , and

. All the subbands are necessary for the highest quality visualization.

In a loose sense, any given resolution is a superset of all the preceding ones. The scalability has its origin in the fact that one can have different images of approximation. Choice can be dynamically made among these different options depending on the client's resources, constraints and requirements as well as network and distance considerations. A client with a powerful platform and high available bandwidth may be able to download all the data timely and decode the level 0 JPEG2000 image to get the highest quality visualization. On the other hand a client on a smart-phone and weak signal may have to be content with a small subset of subbands (Fig. 6) which it will stuff with 0's for higher frequency bands during the decoding process to get the approximation rather than the original image with the improvement of signal he may have the luxury to go for higher quality. All this becomes more critical in the real-time case since now the frame rate, for example, can become more important than the quality and one can compromise over latter to certain extent. In essence, even for a very small fraction of the number of initial coefficients, of the texture and its DEM, one can have a 3-D visualization that is considerably cost effective.

IV. RESULTS

This section has two parts. In Section IV-A we analyze the application of our method when applied to an example altitude map of 64 64 coefficients [Fig. 7(a)] associated with a 3200 3200 pixel texture [Fig. 7(b)]. For the purpose of comparison a 128 128 pixel detail of the above mentioned image of texture is presented in Fig. 7(c). Section IV-B is concerned with the 3-D visualization simulation with respect to another example that is to be demonstrated at high and low bitrates.

A. Analysis of the Method as Applied to a Real World Example

For the example illustrated in Fig. 7, each coefficient of the altitude is coded with 2 bytes implying the embedding factor of 1 coefficient per 50 50 pixels of texture. The application of a level 1 lossless wavelet transformation to the DEM results in Fig. 8(a). The corresponding transformed Y-plane of the texture [Fig. 8(b)] is extracted in situ from the JPEG2000 encoding process of the texture image. The same set of images for level 3 are illustrated in Fig. 8(c) and(d).

To analyze the quality of the embedded texture image, with respect to the original, the measure of PSNR (peak signal to noise ratio) has been employed: [START_REF] Cox | Digital Watermarking[END_REF] where mean square error (MSE) is a measure used to quantify the difference between the initial image and the distorted image . If the image has a size of then

In order to judge compression performance, a measure called bitrate, which is the amount of necessary bits per pixel (bpp), is utilized:

Strictly speaking, DEM is a set of altitude coefficients rather than pixels which requires some modifications in the definition of the above measures. Hence, instead of bitrate, a measure we call bits per coefficient (i.e., amount of information per altitude coefficient) has been used. Since altitudes are expressed in meters, it would be better to use MSE in square meter unit for error measurement. For a more comprehensive explanation one can rely on the one dimensional version of root mean . Embedding of the transformed DEM in the transformed texture takes place according to the policy explained in Section III. It is worthwhile to note that, in general, the data embedding at level decomposition takes place in partitions. Hence for the DWT at level 1 [Fig. 8(a)] the embedding has been done in four partitions ( , , and

) whereas for level 3 wavelet decomposition, the embedding of data has been realized in ten partitions. The marked luminance plane of texture is reintroduced to the JPEG2000 coding pipeline at the point where it was extracted and thus the output is JPEG2000 compliant. No matter what is the level of decomposition , degradation in the texture image, due to data embedding, amounts to a mean square error (MSE) of 0.01 corresponding to a PSNR of 68.5 dB. This is attributed to the meager embedding factor of altitude coefficients per pixel since only one 16 bit DEM coefficient is embedded per 50 50 block of coefficients of the Y component of texture. Fig. 9(a) shows an altitude map reconstructed from the coefficients extracted from a level 1 image of approximation of the embedded texture image. The reconstruction has been done by stuffing 0's in place of the three higher subbands and subsequently applying inverse DWT. Thus only 25% of the count of the initial coefficients have been used for reconstruction. The difference of this image with the original altitude is illustrated in Fig. 9(b). When the above process of reconstruction is applied to the level 1 lowest subband of the embedded texture image Fig. 9(c) is obtained. For comparison with the original example, the 128 128 pixel magnified part is shown in Fig. 9(d). The same sequence of four figures, i.e., to , is maintained in each of the Fig. 10-12 which corresponds to the reconstruction from levels 2 to 5 lowest subbands, respectively. For subjective analysis, one can visually compare the part of Fig. 7, with the same of each of Fig. 9-12. There is certainly degradation in the visual quality but it is far more less in the face of the quantity of data utilized for reconstruction, e.g. level 3 reconstruction has been carried out with only 1.56% of the total coefficients. The degradations in the quality of texture are presented in Fig. 13 in the form of difference images in terms of the magnified part corresponding to Fig. 7(c).

Objectivity demands a quantitative comparison which we have done in terms of the images of difference by observing the measures, like MSE or PSNR, as a function of bitrate. The results are summarized in Table I for the DEM and Table II for the texture. The effectiveness of our method is revealed by the fact that even for a bitrate as low as 0.26 bpp (corresponds to level 3 approximation image of texture, Table II) one observes a of 25.47 dB corresponding to a for DEM of 22.02 meters (Table I). Given the fact that being computed from a small fraction of initial data, this error is tolerable if the observation is made from a high altitude. To elaborate further, MSE has been plotted as a function of bitrate for the texture [Fig. 14(a)] and as a function of bits per coefficient for DEM [Fig. 14(b)]. In the latter case, we have plotted MSE against bits per coefficient due to the fact that rather than the whole JPEG2000 encoding only DWT has been applied to the DEM coefficients. As can be seen in Fig. 14 The reconstructed 3-D surfaces drawn from the various approximation DEMs are shown in Fig. 15. These surfaces when overlaid by their corresponding textures effect 3-D visualizations (Fig. 16). One can compare the final result between a 3-D visualization with all the data [Fig. 16(a)], after being subjected to our method, and a visualization with the level 1, 2, 3 and 4 [Fig. 16(b)-(e)], corresponding to 25%, 6.25%, 1.56%, and 0.39% of the transmitted coefficients, respectively.

B. Simulation Example

To present an application of our method it would be worthwhile to run a practical visualization simulation. The inputs used in the simulation example are given in Fig. 17. The DEM (64 64) from Fig. 17(a) and its corresponding 3200 3200 aerial image [Fig. 17(b)] are subjected to our method. Two series of simulations were effected with one based on full resolution, i.e., level 0 approximation images, and the other on level four images of approximation. Some snapshots of the simulations, at regular intervals, from a transmitted image sequence of more than 300 images are presented.

Five different snapshots from the 3-D visualization of our example are illustrated Fig. 18 for level 0 (corresponding to a bitrate of 240 Mbps) and Fig. 19 for level 4 (corresponding to a bitrate of 640 kbps). The snapshots are at regular intervals when the distant observer is coming closer and closer to the terrain and such they are taken as a function of the decreasing aerial distance of the viewer from his point of focus. The viewer's aerial position is the same for the two bitrates (240 Mbps in Fig. 18 and 640 kbps in Fig. 19) at a given interval. The difference is obvious but not glaring given the fact that the data of Fig. 19 For the level 4 approximation, a closer examination of Fig. 19 reveals that of the DEM/texture pair it is the DEM which is affected the most in terms of quality. This means that the DEM is more sensitive than the texture to a partial reconstruction. This sensitivity of DEM necessitates the fact that the level of wavelet decomposition could be lower for DEM than texture before embedding. Since the size of DEM file is much smaller than that of the texture, the lowest frequency subband at some level can be used for embedding. But this would undermine the perceptual transparency since the embedding density of the energy-richer part would be increased. Moreover, the synchronization management between DEM and texture would be more difficult and this could be be costlier in terms of time.

V. CONCLUSION

In this paper we presented a new method for a scalable 3-D terrain visualization through reversible JPEG2000-based blind data hiding. This paper is focused on the topic of data synchronization and scalability. The results reveal that the proposed method offers at least three advantages. First is the synchronized integration of disparate 3-D data into one whole by the application of data hiding. The second advantage is the scalability in 3-D visualization through the utilization of JPEG2000 supported DWT. Last, but not the least, is the integrability of the method with the JPEG2000 encoders to result in a monolithic standalone JPEG2000 format file that eliminates the need to develop any additional technology or data format, thus implying portability and conformance which is asked by our industrial constraints. In addition the approach is cost effective in terms of memory and bandwidths. The results shown in the case of our examples are witness to this fact since even with a tiny number of coefficients a comparatively better 3-D visualization was effected. The resolution scalability of wavelets enables this 3-D visualization to improve incrementally with the reception of higher frequencies/subbands. Besides, this property is helpful in real-time environment when quicker transfer of data is required. The results of 3-D visualization simulation give a useful insight to the effectiveness of our method in various network conditions.

In the continuation of this work it would be worthwhile to develop a method based on lossy wavelets to further decrease bitrate. This option will however eliminate, to a considerable extent, the possibility of very high quality visualization since the lossy case is not fully reversible. A situation may thus arise that losing details of texture becomes less important than that of DEM. Using a desynchronized algorithm would be a good way and should be taken into consideration in the near future. The LSB-based embedding strategy adopted in this work has to be reconsidered for the lossy case and it will be important to explore some other embedding strategies, like the spread spectrum embedding [START_REF] Cox | Digital Watermarking[END_REF], in order to keep DEM quality high for the reconstruction. As far as triangulation is concerned, there is also every likelihood of using a non-uniform grid on various levels of details, thus allowing a considerable reduction in the number of triangles necessary for a good representation of the terrain. In this paper links between tiles are not managed but our future focus is likely to be on the strategies to generate a soft transition between several tiles without cracks. In future, the streaming management between the server and its clients is also being mulled.

  (a)]. It is defined by a grid of points separated by a given step. These points are used to generate the geometry and are connected by triangles [Fig. 1(b)]. • Aerial photographs can be acquired in various spectral domains such as visible or infrared. Theses are used to map 3-D triangles previously computed [Fig. 1(c)].

Fig. 1 .

 1 Fig. 1. (a) Visualization of the uniform grid corresponding to the elevations of the terrain, (b) 3-D triangulated surface linking the elevations, and (c) Texture mapping the ortho-photograph onto the geometry.

Fig. 2 .

 2 Fig.2. DWT: (a) Subband structure, (b) Lena, and (c) Lena at level 2 DWT decomposition.

Fig. 3 .

 3 Fig. 3. Generalized scheme of the JPEG2000 encoder.

Fig. 4 .

 4 Fig. 4. Description of the method: embedding transformed DEM coefficients into the transformed coefficients of each Y texture subband.

  Authorized licensed use limited to: IEEE Xplore. Downloaded on November 18, 2008 at 09:46 from IEEE Xplore. Restrictions apply.

Algorithm 1 16 :

 116 The embedding strategy 1: begin 2: read which is level-transformed Y texture from the JPEG2000 coding pipeline 3: read the corresponding DEM file as an image 4: apply lossless DWT to DEM at level to get 5: for each subband of and its counterpart in do 6: partition the subband into square blocks in relation to the subband 7: initialize a PRNG with a seed 8: for each correspondence of subband block and label the block-wise marked as 17: endIn Fig.5, we illustrate the low level detail of the embedding procedure.

Fig. 5 .

 5 Fig. 5. Embedding a subband of the transformed DEM coefficient in a block from a subband of the transformed texture.

Fig. 6 .

 6 Fig. 6. Decoding, data extraction and scalable 3-D reconstruction and visualization.

Fig. 7 .

 7 Fig. 7. Example images: (a) Original altitude map, (b) Original texture map, and (c) a part of texture magnified.

Fig. 8 .

 8 Fig. 8. DWT at Level 1: (a) altitude, (b) Y Plane of texture. DWT at Level 3, (c) altitude, and (d) Y plane of texture.

Fig. 9 .

 9 Fig. 9. Reconstruction of the images from the approximation image at Level 1: (a) extracted altitude, (b) difference image between the original altitude and the extracted one, (c) texture, and (d) magnified part of texture corresponding to Fig. 7(c).

Fig. 10 .

 10 Fig. 10. Reconstruction of the images from the approximation image at Level 2: (a) extracted altitude, (b) difference image between the original altitude and the extracted one, (c) texture, and (d) magnified part of texture corresponding to Fig. 7(c).

Fig. 11 .Fig. 12 .

 1112 Fig. 11. Reconstruction of the images from the approximation image at Level 4: (a) extracted altitude, (b) difference image between the original altitude and the extracted one, (c) texture, and (d) magnified part of texture corresponding to Fig. 7(c).

Fig. 13 .

 13 Fig. 13. Difference between the original luminance and reconstructed texture [for the magnified part of texture corresponding to Fig. 7(c)] of (a) Level 1, (b) Level 3, and (c) Level 5.

  (a) the MSE decreases as further levels of information are added to the image of approximation, e.g. for 1.06 bpp (level 2) the MSE is 107.97 and for 4.14 bpp (level 1) the MSE is 42.01. A similar trend is observed in case of for the DEM [Fig. 14(b)]. For 3-D visualization, the acceptable quality of both DEM and texture is a function of the distance between the 3-D surface and the viewpoint. The more this viewpoint is near the 3-D surface, better must be the quality of both DEM and texture.

  corresponds to only 0.39% of the number of coefficients of the data of Fig. 18. This lower than expected degradation in quality motivate us to have an effective scalable visualization. For example a 3200 3200 aerial image requires 30 MB of storage employing a 240 Mbps bandwidth requirement if only one image is to be transferred per second. In other words a 100 Mbps connection would require 2.4 seconds for a single image to transfer and the same for wireless networks is arround 1200, 625, 133 and 48 seconds for EDGE (200 Kbps), 3G (384 Kbps), HSDPA (1.8 Mbps), and WIFI (5 Mbps), respectively. A level 4 approximation of the same embedded image in JPEG2000 format would have a size in the order of 80 KB implying the requirement of 640 kbps for transferring one image per second. With EDGE one can transfer one such image in about 3 s and WIFI can transmit eight such images/s. Level 5 approximation may further reduce the payload and now one can transfer one image per second over EDGE and 32 images over WIFI making the latter suitable for video based streaming.

Fig. 14 .

 14 Fig. 14. Graphical display of variation in quality as a function of bitrate: (a) texture and (b) DEM.

Fig. 15 .

 15 Fig. 15. The 3-D surface representation using the extracted DEMs and obtaining their approximations at various levels. (a) Level 0 (all the data), (b) Level 1, (c) Level 3, and (d) Level 4.

Fig. 16 .

 16 Fig. 16. The 3-D visualization with the approximation images at various levels. (a) Level 0 (all the data), (b) Level 1, (c) Level 3, and (d) Level 4.

Fig. 17 .

 17 Fig. 17. Example altitude/texture pair utilized in the visualization simulation: (a) original altitude map and (b) original texture map.

Fig. 18 .

 18 Fig. 18. Snapshots of the 3-D visualization simulation based on level 0 (for 240 Mbps) images of approximation extracted and reconstructed from the DEM embedded texture.

Fig. 19 .

 19 Fig. 19. Snapshots of the 3-D visualization simulation based on level 4 (for 640 kbps) images of approximation extracted and reconstructed from the DEM embedded texture.

TABLE I RESULTS

 I OBTAINED FOR DEM AFTER THE EXTRACTION AND RECONSTRUCTION AS A FUNCTION OF THE USED DATA (for level 0, all of the transmitted data is used for reconstruction)

TABLE II RESULTS

 II OBTAINED AFTER THE EXTRACTION AND RECONSTRUCTION OF THE TEXTURE AS A FUNCTION OF THE USED DATA IN THE FORM OF EMBEDDED TEXTURE

http://www.geoplace.com. Authorized licensed use limited to: IEEE Xplore. Downloaded on November 18, 2008 at 09:46 from IEEE Xplore. Restrictions apply.

http://www.ign.fr/.

http://www.ece.uvic.ca/~mdadams/jasper/.

Authorized licensed use limited to: IEEE Xplore. Downloaded on November 18, 2008 at 09:46 from IEEE Xplore. Restrictions apply.

http://www.remotesensing.org/geotiff/spec/contents.html. Authorized licensed use limited to: IEEE Xplore. Downloaded on November 18, 2008 at 09:46 from IEEE Xplore. Restrictions apply.

This work was supported in part by the Higher Education Commission (HEC) of Pakistan.

He is currently an Assistant Professor at the LSIS Laboratory, Aix-Marseille University, France. His research interests include geometric modeling, 3-D visualization and deformation. He is currently working on projects focused on 3-D geographical information systems.


Mariane Sentenac
email: mariane.sentenac@inserm.fr

Anna Chaimani

Sabrina Twilhaar

Valérie Benhammou

Samantha Johnson

Andrei Morgan

Jennifer Zeitlin

An umbrella review and meta-regression analysis

teaching and research institutions in France or abroad, or from public or private research centers.

The challenges of heterogeneity in gestational age and birthweight inclusion criteria for research synthesis on very preterm birth and childhood cognition

SOCIAL MEDIA QUOTE

These results suggest that meta-analyses on the consequences of very preterm birth would benefit from using gestational age and birthweight criteria to increase the number of studies and the generalizability of results

SYNOPSIS

Study question

Do gestational age (GA) and birthweight (BW) inclusion criteria in studies on very preterm birth and cognition affect the results of meta-analyses?

What's already known

Meta-analyses consistently show the negative consequences of very preterm birth on cognitive development in childhood but with large unexplained between-study heterogeneity.

What this study adds

This study showed that the use of gestational age vs birthweight criteria was more common in European and recent studies, with no substantial effect on meta-analysis results after adjustment for degree of prematurity. These results suggest that meta-analyses on the consequences of very preterm birth would benefit from broad inclusion criteria to increase the number of studies and the generalisability of results. combinations. BW-only criteria were more frequent in North America than Europe (63% vs 24%), and for cohorts before rather than after 1990 (67% vs 26%). Pooled SMD in IQ varied with the degree of prematurity (SMD EPT/ELBW =-0.94, 95%CI -1.07, -0.82; SMD VPT/VLBW =-0.78, 95%CI -0.85, -0.71; SMD MPT/MLBW =-0.68, 95%CI -0.79, -0.57), but there was no difference in SMD between cohorts using BW compared to GA criteria after adjustment on risk group.

Conclusions

Our results support the inclusion of studies using GA and/or BW criteria in meta-analyses on VPT birth and cognition to increase the geographical and temporal generalisability of the results and to allow investigation of the impact of the heterogeneous inclusion criteria in this literature on outcomes.

BACKGROUND

Since the 1990s, advances in obstetrical and neonatal care have led to major survival gains very preterm (VPT, <32 weeks of gestation) infants, [START_REF] Ancel | Survival and morbidity of preterm children born at 22 through 34 weeks' gestation in France in 2011: results of the EPIPAGE-2 cohort study[END_REF][START_REF] Costeloe | Short term outcomes after extreme preterm birth in England: comparison of two birth cohorts in 1995 and 2006 (the EPICure studies)[END_REF][START_REF] Fellman | One-year survival of extremely preterm infants after active perinatal care in Sweden[END_REF] but have also raised concerns about high levels of impairment among survivors. In this context, studies of the association between VPT birth and neurodevelopment, especially cognitive development, have increased in number over the past four decades. More recently, this voluminous literature has been combined in systematic reviews and summarized using meta-analysis. [START_REF] Allotey | Cognitive, motor, behavioural and academic performances of children born preterm: a meta-analysis and systematic review involving 64 061 children[END_REF][START_REF] Arpi | Worse global intellectual and worse neuropsychological functioning in preterm-born children at preschool age: a meta-analysis[END_REF][START_REF] Brydges | Cognitive outcomes in children and adolescents born very preterm: a meta-analysis[END_REF][START_REF] Kerr-Wilson | Meta-analysis of the association between preterm delivery and intelligence[END_REF][START_REF] Twilhaar | Cognitive outcomes of children born extremely or very preterm since the 1990s and associated risk factors: A meta-analysis and meta-regression[END_REF] One of the challenges for systematic reviews on VPT and cognition is establishing criteria for study selection given the heterogeneity in gestational age (GA) and birthweight (BW) inclusion criteria in primary studies. [START_REF] Allotey | Cognitive, motor, behavioural and academic performances of children born preterm: a meta-analysis and systematic review involving 64 061 children[END_REF][START_REF] Arpi | Worse global intellectual and worse neuropsychological functioning in preterm-born children at preschool age: a meta-analysis[END_REF][START_REF] Brydges | Cognitive outcomes in children and adolescents born very preterm: a meta-analysis[END_REF][START_REF] Kerr-Wilson | Meta-analysis of the association between preterm delivery and intelligence[END_REF][START_REF] Twilhaar | Cognitive outcomes of children born extremely or very preterm since the 1990s and associated risk factors: A meta-analysis and meta-regression[END_REF][START_REF] Sentenac | Defining Very Preterm Populations for Systematic Reviews With Meta-analyses[END_REF] There has been a longstanding debate about the best way to define populations for research on the sequelae of VPT birth. BW is considered a more reliable measure than GA, but leads to the inclusion of infants born at later GAs with growth pathologies. [START_REF] Brydges | Cognitive outcomes in children and adolescents born very preterm: a meta-analysis[END_REF] In contrast, GA is a direct measure of the degree of prematurity and allows investigation of the distinct effects of prematurity and growth restriction, but its measurement may be imprecise when ultrasounds are not routinely used to date pregnancies. [START_REF] Hall | Evaluation of gestational age estimate method on the calculation of preterm birth rates[END_REF] This leads to misclassification, which can be particularly acute among disadvantaged groups with sub-optimal antenatal care. [START_REF] Van Oppenraaij | Determinants of number-specific recall error of last menstrual period: a retrospective cohort study[END_REF] This is of concern because disadvantaged families face higher risks of VPT birth [START_REF] Van Oppenraaij | Determinants of number-specific recall error of last menstrual period: a retrospective cohort study[END_REF] and social disadvantage is associated with worse long-term cognitive outcomes. [START_REF] Sentenac | Maternal education and cognitive development in 15 European very preterm birth cohorts from the RECAP Preterm platform[END_REF] Systematic reviews have adopted different approaches, with some including all studies based on GA and/or BW, while others have aimed to reduce heterogeneity by selecting only studies that used GA inclusion criteria. In a review of five systematic reviews with metaanalyses on the topic of VPT birth and cognition, we previously showed that investigators' methodological choices with regard to inclusion and exclusion criteria for primary studies resulted in minimal overlap in the included studies across systematic reviews. [START_REF] Sentenac | Defining Very Preterm Populations for Systematic Reviews With Meta-analyses[END_REF] While these meta-analyses consistently showed the negative consequences of VPT birth on cognitive development in childhood, [START_REF] Sentenac | Defining Very Preterm Populations for Systematic Reviews With Meta-analyses[END_REF] they reported substantial unexplained between-study heterogeneity and some conflicting results regarding whether this effect varied with the degree of prematurity. [START_REF] Allotey | Cognitive, motor, behavioural and academic performances of children born preterm: a meta-analysis and systematic review involving 64 061 children[END_REF][START_REF] Arpi | Worse global intellectual and worse neuropsychological functioning in preterm-born children at preschool age: a meta-analysis[END_REF][START_REF] Brydges | Cognitive outcomes in children and adolescents born very preterm: a meta-analysis[END_REF][START_REF] Twilhaar | Cognitive outcomes of children born extremely or very preterm since the 1990s and associated risk factors: A meta-analysis and meta-regression[END_REF] This inconsistency causes confusion and may represent a missed opportunity to synthesize and analyse all available data. Therefore, using the primary studies included in these five systematic reviews, our aim is to describe the GA and BW inclusion criteria in studies investigating VPT birth and cognition and to determine whether between-study heterogeneity in meta-analyses can be explained by the GA and BW criteria used in the selected studies.

METHODS

This study is registered with PROSPERO, under the registration number CRD42020176193.

Eligibility criteria, information sources and search strategy

Our eligibility criteria were primary studies included in systematic reviews carrying out metaanalyses based on observational studies investigating general cognitive ability (IQ), regardless of the instrument used, in childhood (<18 years of age) for VPT infants in comparison with a term-born control group. Systematic reviews were considered eligible if other neurodevelopmental outcomes or populations were also investigated. Systematic reviews without meta-analysis were excluded, as well as studies focusing only on other neurodevelopmental outcomes such as executive function. Eligible systematic reviews were searched in PubMed, Web of Science, the Cochrane Database of Systematic Reviews, and the PROSPERO databases from January 2000 to February 2020 without any language restrictions, as previously described. 9

Data extraction and study selection

Data were extracted in two stages. First, two researchers (MS and JZ) independently extracted data from eligible systematic reviews, including the study objectives, selection criteria and statistical methods. In a second stage, each primary study included in the selected systematic reviews was independently reviewed by two of the co-authors (MS, ST, VB, JZ, AM) to extract information on country of origin, range of birth years, and study design features (whether the study was population-based, multi-centric or single-centre).

Additionally, we extracted selection criteria for VPT participants regarding GA and/or BW (cut-off and combination of criteria); IQ mean scores (unadjusted as well as adjusted for potential confounders, if available), standard deviations and sample sizes were extracted for cases and controls. The reviewers identified which primary studies came from the same cohort (i.e. follow-up studies giving rise to several publications either at the same age point or at multiple age points). They also identified situations where data from two cohorts were presented in the same primary study. Disagreements were resolved by consensus.

For this study, we selected one primary study per cohort. In cases of multiple studies from the same cohort, we selected the study with the longest follow-up but before 18 years of age. This convention was adopted because the stability of cognitive abilities increase with age. [START_REF] Deary | The impact of childhood intelligence on later life: following up the Scottish mental surveys of 1932 and 1947[END_REF] If two studies from the same cohort had the same follow-up year, we selected the study with the larger sample size (less selective).

Cohort classification

Cohorts were first classified according to their selection criteria used to define the study population (GA/BW criteria: GA-only, BW-only, GA/BW combined). Then, we derived three subgroups of cohorts reflecting the degree of prematurity using the GA and BW upper thresholds from the WHO definitions [START_REF] Blencowe | Born too soon: the global epidemiology of 15 million preterm births[END_REF][START_REF]Preterm birth fact sheet[END_REF][START_REF]ICD-11 for mortality and morbidity statistics (ICD-11 MMS)[END_REF] : EPT (GA<28 weeks' GA) or extremely low birthweight (ELBW, <1000 grams); VPT (<32 weeks) or very low birthweight (VLBW, <1500 grams); and as many of the included studies used 32 or 33 weeks as an upper threshold for inclusions, these studies were retained in a third group classified as moderate preterm (MPT, <34 weeks' GA) or moderate low birthweight (MLBW, <1800 grams). Within each of these three preterm/low birthweight subgroups, studies with higher perinatal risk infants were identified based on GA and BW thresholds (e.g. infants with BW<800 grams or GA<27 weeks were classified as higher risk EPT/ELBW).

Statistical analysis

We estimated the standardized mean difference (SMD) (Hedge's formula) in IQ between VPT and term-born controls for each study, and DerSimonian and Laird random effects models were performed to generate pooled SMDs and their 95% confidence interval (95%CI). [START_REF] Sterne | Statistical methods for assessing the influence of study characteristics on treatment effects in 'metaepidemiological' research[END_REF] Unadjusted scores were used, except for one study which provided scores adjusted for parental education. To investigate whether thresholds and combinations of BW and GA criteria explain heterogeneity in study results, we computed pooled SMDs in sub-group meta-analyses, and we performed meta-regressions based on random-effect models using as covariates GA/BW criteria, degree of prematurity, and level of perinatal risk. The percentage of the between-study variance explained by the meta-regression model (R 2 meta )

was calculated as a proportion of the between-study variance unexplained by the model (Tau 2 , DerSimonian-Laird estimator) related to the total between-study variance. [START_REF] Aloe | An alternative to R2 for assessing linear models of effect size[END_REF] We did not reevaluate the quality of the primary studies using a standardized instrument, as performed in four reviews. [START_REF] Allotey | Cognitive, motor, behavioural and academic performances of children born preterm: a meta-analysis and systematic review involving 64 061 children[END_REF][START_REF] Arpi | Worse global intellectual and worse neuropsychological functioning in preterm-born children at preschool age: a meta-analysis[END_REF][START_REF] Brydges | Cognitive outcomes in children and adolescents born very preterm: a meta-analysis[END_REF][START_REF] Twilhaar | Cognitive outcomes of children born extremely or very preterm since the 1990s and associated risk factors: A meta-analysis and meta-regression[END_REF] No studies were removed from the reviews based on quality assessments; two reviews [START_REF] Brydges | Cognitive outcomes in children and adolescents born very preterm: a meta-analysis[END_REF][START_REF] Twilhaar | Cognitive outcomes of children born extremely or very preterm since the 1990s and associated risk factors: A meta-analysis and meta-regression[END_REF] investigated whether the results were affected by study quality and found no impact on results. The potential for small study-effects was investigated graphically using funnel plot, with asymmetry suggesting a differentiated effect between large and small studies. Analyses were performed using R version 4.0.

RESULTS

The search yielded five eligible systematic reviews with meta-analyses of observational studies investigating the association between VPT birth and IQ in childhood. Table 1 summarizes criteria specified for the target population (i.e. VPT children) for the five reviews. Criteria differed regarding GA boundaries (<32 weeks of gestation or <34 weeks)

and consideration of studies using BW limits (<1000 or <1500 grams), which were either explicitly included, excluded or not mentioned.

After removing duplicates, 156 primary studies were identified from these reviews. Of these, 55 were considered as non-eligible and were excluded (eFigure 1). The reasons for exclusion were: age at assessment >17 years (8), no full text (1), no IQ scores provided (3), studies on the same cohort at the same age (23), or a different age (11), late preterm birth (GA<35;

GA<36 and BW<2500 grams) (3) and other (7). The analysis sample included 101 primary studies reporting results on 103 unique cohorts of children.

The GA/BW inclusion criteria in these studies were highly varied as shown in Table 2 with 27 different combinations. The most common were BW <1500 g (24 cohorts), GA <32 weeks (12), GA <33 weeks (12) and BW<1000 grams (12). Few cohorts (2) had GA <28 weeks as an inclusion criterion. Combinations of BW and GA criteria were frequent, but combinations differed. Some combinations were not considered to be consequential and they were combined with other criteria; for instance, BW<1000 grams and GA<34 weeks will not differ much from BW<1000 grams since having a BW<1000 grams and a gestational age of 34 weeks or more is rare. Out of the 103 unique cohorts, 25 were classified as reporting results on children born EPT or ELBW including 5 cohorts targeting a population at higher risk. A further 58 studies reported results on children born VPT or VLBW from which 20 were classified as at higher risk, and 20 studies reported results on children born MPT or MLBW, including 16 studies classified as at higher risk (see Table 2 for detailed criteria).

The characteristics of cohorts using BW versus GA criteria differed (Table 3). Cohorts from North America were more likely to use BW only (63%) to select the study population compared to European cohorts, which were more likely to include infants based on GA only (59%). Cohorts with birth years from 1977 to 1990 were more likely to be based on BW only (67%) compared to more recent cohorts which were more likely to include infants based on GA only. Table 4 provides the results from random-effect meta-regressions. No clear association was found between the type of GA/BW criteria and the effect size, before (model 1) and after adjustment (models 2 and 3). In contrast, the effect size increased with the degree of prematurity, as well as with the level of perinatal risk (models 2 and 3). The estimated amount of residual heterogeneity between studies (Tau 2 ) reduced from 0.0486 in model 1 to 0.0380 in model 3, corresponding to less than 3% of between-study variance explained (R 2 meta) in model 1 to 24% in the fully adjusted model 3.

No asymmetry was observed in the funnel plot, suggesting that the results were not distorted by smaller studies (eFigure 3).

COMMENT Principal findings

This study illustrated the wide range of different GA and BW criteria that are used to define longitudinal cohorts for research on the developmental consequences of VPT birth. There were geographical and temporal patterns in inclusion criteria, with BW criteria more commonly used in the North America versus Europe and in older versus more recent studies.

In synthesising the results from these studies, we found similar results within preterm/low birthweight subgroups, reflecting the degree of prematurity, regardless of whether GA or BW criteria were used. Taken together, these results provide support for a more inclusive approach to primary study selection for reviews on cognition and VPT birth, allowing for systematic and transparent reporting of primary study inclusion/exclusion criteria and making it possible to increase the number of studies and generalisability of results.

Strengths of the study

Strengths of our study are inclusion of all primary studies from 5 systematic reviews, with data extraction by 2 reviewers making it possible to reanalyse the data using standardised definitions.

Limitations of the data

Limitations of the study are small sample sizes in some GA/BW combinations which limited sub-group analysis. Because we used data from published meta-analyses, the last primary study included in this analysis is from 2017. Further, the large remaining unexplained between-study variance tends to reduce certainty in the evidence, suggesting the possible effect of other study design characteristics (e.g. type of IQ assessment, study period, analysis of children with severe conditions, follow-up rates) not considered in this study.

Interpretation

The variability in inclusion criteria for the target populations in primary studies of cognitive outcomes after VPT birth represents a methodological challenge for systematic reviews and meta-analyses. Heterogeneity is a problem for combining study results because pooled measures of effect are difficult to interpret in the presence of high between-study heterogeneity. [START_REF] Metelli | Challenges in meta-analyses with observational studies[END_REF][START_REF] Stroup | Metaanalysis of observational studies in epidemiology: a proposal for reporting. Metaanalysis Of Observational Studies in Epidemiology (MOOSE) group[END_REF][START_REF] Mueller | Methods to systematically review and meta-analyse observational studies: a systematic scoping review of recommendations[END_REF] The investigation of sources of heterogeneity is crucial, [START_REF] Mueller | Methods to systematically review and meta-analyse observational studies: a systematic scoping review of recommendations[END_REF][START_REF] Thompson | Why sources of heterogeneity in meta-analysis should be investigated[END_REF] but it is often not possible to disentangle effects due to sample characteristics (i.e. clinical heterogeneity)

and those attributable to study design and methods (i.e. methodological heterogeneity).

Therefore, attempts to include primary studies with similar inclusion criteria in systematic reviews in order to reduce methodological heterogeneity may be justified. However, in our study, applying more stringent inclusion criteria limited the number of included studies, their geographic and temporal generalizability and the precision of results, without reducing statistical heterogeneity.

Systematic reviews are increasingly undertaken to summarize research results before starting new studies or to underpin recommendations and guidelines and having several systematic reviews on the same topic is a common occurrence. Differences in authors' methodological choices can lead to situations where results diverge or even conflict. [START_REF] Ioannidis | The Mass Production of Redundant, Misleading, and Conflicted Systematic Reviews and Meta-analyses[END_REF] All five systematic reviews in our study produced consistent pooled effects showing lower IQ among children born VPT compared to term-born controls but there was variability in findings related to the impact of GA. [START_REF] Allotey | Cognitive, motor, behavioural and academic performances of children born preterm: a meta-analysis and systematic review involving 64 061 children[END_REF][START_REF] Arpi | Worse global intellectual and worse neuropsychological functioning in preterm-born children at preschool age: a meta-analysis[END_REF][START_REF] Brydges | Cognitive outcomes in children and adolescents born very preterm: a meta-analysis[END_REF][START_REF] Kerr-Wilson | Meta-analysis of the association between preterm delivery and intelligence[END_REF][START_REF] Twilhaar | Cognitive outcomes of children born extremely or very preterm since the 1990s and associated risk factors: A meta-analysis and meta-regression[END_REF] Several found no clear association between GA and IQ. [START_REF] Allotey | Cognitive, motor, behavioural and academic performances of children born preterm: a meta-analysis and systematic review involving 64 061 children[END_REF][START_REF] Arpi | Worse global intellectual and worse neuropsychological functioning in preterm-born children at preschool age: a meta-analysis[END_REF][START_REF] Brydges | Cognitive outcomes in children and adolescents born very preterm: a meta-analysis[END_REF] While the effect of GA on the cognitive development of children born VPT will be more limited if the included GA range is narrow, [START_REF] Linsell | Prognostic Factors for Poor Cognitive Development in Children Born Very Preterm or With Very Low Birth Weight: A Systematic Review[END_REF] this finding does not align with clinical knowledge or results from large population-based cohort studies. [START_REF] Pierrat | Neurodevelopmental outcomes at age 5 among children born preterm: EPIPAGE-2 cohort study[END_REF][START_REF] Draper | EPICE cohort: two-year neurodevelopmental outcomes after very preterm birth. Archives of disease in childhood[END_REF] By combining all available information from the five reviews, we showed a significant gradient related to degree of prematurity/low birthweight, when using grouped categories of GA/BW and when including an additional measure of perinatal risk within categories.

Our results did not reveal a significant impact on effect sizes of using either GA or BW to define the study population when the degree of prematurity/low birthweight was taken into account. While both GA and restricted growth have an impact on cognition, this finding should not be interpreted to mean that their effect on cognition is the same or that there are shared underlying causal mechanisms. Rather it illustrates that, at the study level, there is high overlap between GA and BW groups. [START_REF] Koller-Smith | Comparing very low birth weight versus very low gestation cohort methods for outcome analysis of high risk preterm infants[END_REF] This overlap has been the justification for using BW, considered more reliable, as a proxy for GA. Until the beginning of the 1980s these terms were used interchangeably, although as early as 1961 WHO recommended not using LBW to define prematurity. [START_REF] Blencowe | Born too soon: the global epidemiology of 15 million preterm births[END_REF][START_REF] Wilcox | On the importance--and the unimportance--of birthweight[END_REF][START_REF] Quinn | Preterm birth: Case definition & guidelines for data collection, analysis, and presentation of immunisation safety data[END_REF] However, babies with BW under 1500 grams are principally preterm, [START_REF] Quinn | Preterm birth: Case definition & guidelines for data collection, analysis, and presentation of immunisation safety data[END_REF][START_REF] Villar | International standards for newborn weight, length, and head circumference by gestational age and sex: the Newborn Cross-Sectional Study of the INTERGROWTH-21st Project[END_REF] although they can be moderate or late preterm. Use of BW may also overestimate prematurity in some countries, such as south Asia, where there are a high proportion of small for GA term births. [START_REF] Blencowe | Born too soon: the global epidemiology of 15 million preterm births[END_REF] Even though there are differences between the aetiology and consequences of low BW and low GA, a systematic review is not an appropriate study design for distinguishing between these effects, although the use of participant level meta-analyses would make it possible to create sub-groups defined at the individual level and allow investigation of this source of heterogeneity. [START_REF] Gagnier | Consensus-based recommendations for investigating clinical heterogeneity in systematic reviews[END_REF] Initiatives, such as the RECAP Preterm platform (https://recap-preterm.eu/) of European cohorts of children and adults born VPT, provide opportunities for research using similarly defined subpopulations.

The problems for systematic reviews posed by methodological heterogeneity in primary studies are the justification for initiatives such as COMET [START_REF] Williamson | The COMET Handbook: version 1.0[END_REF] to define common data sets for clinical trials, [START_REF] Williamson | Developing core outcome sets for clinical trials: issues to consider[END_REF][START_REF] Pavlek | Eligibility Criteria and Representativeness of Randomized Clinical Trials That Include Infants Born Extremely Premature: A Systematic Review[END_REF] and several of these have focused on pregnancy outcomes and neonates. 37- 39 Similar initiatives would be helpful for establishing guidelines for inclusion criteria for very preterm or very low birthweight longitudinal cohorts. The WHO terminology based on GA [START_REF]Preterm birth fact sheet[END_REF] may need to be expanded to include higher risk sub-groups used for some studies, such as births <27 weeks, or births close to the limits of viability at <24 weeks (sometimes termed periviable). [START_REF] Pavlek | Eligibility Criteria and Representativeness of Randomized Clinical Trials That Include Infants Born Extremely Premature: A Systematic Review[END_REF] Furthermore, while GA may be the preferred inclusion criteria, investigators in low-and middle-income countries may continue to opt for BW criteria because of availability and quality of GA measurement. [START_REF] Blencowe | Born too soon: the global epidemiology of 15 million preterm births[END_REF][START_REF] Lawn | Global report on preterm birth and stillbirth (1 of 7): definitions, description of the burden and opportunities to improve data[END_REF] Our results also suggest that specific guidelines for reviews with meta-analyses of VPT birth are needed. While the five systematic reviews reported on characteristics of primary studies, including mean GA and BW, none provided a comprehensive description of the GA and BW inclusion criteria. One easily applicable recommendation for improving systematic reviews would be to systematically report and analyse this information. This recommendation would have relevance for future reviews of cognition as well as those focusing on other outcomes after preterm birth. The consequences of preterm birth are diverse, affecting multiple facets of cognition, and also motor function, sensory capacities and behaviour and mental health.

Adults born preterm continue to experience challenges in the labour market and forming families, and may be more vulnerable to a wide range of non-communicable diseases, notably cardiovascular and psychiatric problems. [START_REF] Wolke | The Life Course Consequences of Very Preterm Birth[END_REF] Birth cohorts are constituted to respond to a range of different research questions and include measures of multiple outcomes.

Therefore, our results demonstrating heterogeneity in the inclusion criteria of primary studies likely apply to reviews of other outcomes which have grown in number over past years. [START_REF] Barre | Language abilities in children who were very preterm and/or very low birth weight: a meta-analysis[END_REF][START_REF] Aarnoudse-Moens | Metaanalysis of neurobehavioral outcomes in very preterm and/or very low birth weight children[END_REF][START_REF] Pascal | Neurodevelopmental outcome in very preterm and very-low-birthweight infants born over the past decade: a meta-analytic review. Developmental medicine and child neurology[END_REF][START_REF] Sømhovd | Anxiety in adolescents born preterm or with very low birthweight: a meta-analysis of case-control studies[END_REF] By transparently reporting and evaluating inclusion criteria in new reviews, it will be possible to assess if the results found for cognition can be transposed to other outcomes.

Conclusions

Reviews to synthesize the literature on VPT populations should consider using broad inclusion criteria based on both GA and BW to encompass studies from all countries, older studies and those from settings where GA data are not available or of poor quality. This approach will make it possible to maximize the number and representativeness of primary studies included in reviews. However, investigators should abstract and report GA and BW inclusion criteria as well as any other potential effect modifiers and use these in analyses for investigating heterogeneity. a Model 1 adjusted for the type of GA/BW criteria, model 2 adjusted for the type of GA/BW criteria and the degree of prematurity, and model 3 adjusted for the type of GA/BW criteria, the degree of prematurity and the level of perinatal risk.

TABLES

Figure 1 and eFigure 2

 2 Figure 1 and eFigure 2 provide results of meta-analyses in sub-groups of cohorts defined by

Figure 1 -

 1 Figure 1 -Forest plot of standardized mean differences (SMDs) by degree of prematurity and by inclusion criteria for GA and BW

Table 1 -

 1 Gestational age and birthweight inclusion criteria used to select primary studies in systematic reviews of very preterm (VPT) birth and IQ in childhood

	Systematic	Gestational age (GA) criteria Birthweight (BW)	Number of
	review (first		criteria	studies (VPT
	author, year)			children only)
	Kerr-Wilson et	Inclusion of studies on all	Birthweight not	27 (na) a
	al. 2012	preterm (with sub-group analyses: GA<28 weeks; 28-	mentioned as part of inclusion or exclusion
		31 weeks; ≥32 weeks);	criteria
	Allotey et al.	Inclusion of studies on all	Birthweight not	57 (50)
	2018	preterm (with sub-group analyses very: <28 weeks;	mentioned as part of inclusion or exclusion
		moderate: 28-33+6 weeks;	criteria
		late: 34-36+6 weeks);
	Brydges et al.	Inclusion of studies on	Exclusion of studies	44 (44)
	2018	children with GA <32 weeks;	examining exclusively low BW children
	Twilhaar et al.	Inclusion of studies on	Inclusion of studies	71 (71)
	2018	children with GA< 32 weeks	with BW<1000g or <1500g
	Arpi et al. 2019 Inclusion of studies on	Inclusion of studies	7 (7)
		children with GA< 32 weeks	with BW<1500g
	Abbreviations: na=not available; GA=gestational age; BW=birthweight

a Studies on VPT not identified in the systematic review

Table 2 -

 2 Classification of cohorts regarding the study criteria on gestational age (GA) and birthweight (BW)

		GA/BW criteria	Study criteria (27 different criteria, including 18 denoting higher perinatal risk)	Number of cohorts
	Extremely preterm birth (EPT, <28 weeks) or extremely	GA	GA <28 weeks GA <27 weeks a GA <26 weeks a	2 1 2
	low birthweight (ELBW, <1000 grams)	BW	BW<1000g [and (GA<34 wks)] BW <800g a	12 2
		GA or BW	GA<28 or BW<1000g	6
			GA<32 weeks	12
		GA	GA <31 weeks a GA <30 weeks a	5 1
			GA<29 weeks a	1
	Very preterm birth (VPT, <32 weeks) or very low birthweight	BW GA or BW	BW<1500g [and GA<36/37] BW < 1250g a GA<32 weeks or BW<1500g GA <30 weeks or BW<1000g a	24 4 2 1
	(VLBW, <1500 grams)		GA <30 weeks or BW<1250g a	1
			BW < 1500 g and GA<29 weeks a	1
			BW < 1500 g and GA<30 weeks a	1
		GA and BW	BW < 1500 g and GA<32 weeks a BW < 1500 g and GA<33 weeks a	1 2
			BW < 1500 g and GA<34 weeks a	1
			BW < 1500 g and GA<35 weeks a	1
	Moderate preterm birth (MPT, <34 weeks) or moderate low birthweight (MLBW, <2000 grams)	GA GA or BW GA and BW	GA <34 weeks GA <33 weeks a GA <34 weeks or BW<1800g GA <33 weeks or BW<1500g a GA <34 weeks and BW<1800g GA <37 weeks and BW<1600g a	2 12 1 3 1 1
	a criteria classified as targeting a population of children with higher perinatal risk

Table 3 -

 3 Characteristics of cohorts by their use of gestational age (GA) or birthweight (BW) inclusion criteria

	Cohort characteristics	Number of cohorts	Combination of the gestational age (GA) and birthweight (BW) criteria GA only BW only GA or BW GA and BW n=38 n=42 n=14 n=9
	Geographical area, n (%)

Table 4 -

 4 Results from random-effect meta-regressions of the association between GA/BW criteria and SMDs in IQ between EPT/VPT and full term children

			Model 1 a		Model 2 a		Model 3 a
	k	coef.	95%CI	coef.	95%CI	coef.	95%CI

b Total between-study variance estimated from model without covariate = 0.0498

eFigure 3 : Funnel plot of standardized mean differences (SMDs) in IQ (103 cohorts)

FUNDING

This study is part of research on the consequences of very preterm birth for use in developing a research agenda for the RECAP Preterm project, an EU Horizon 2020 (grant agreement No 733280) study to construct a platform combining data from very preterm cohort studies in Europe. The funders had no role in the design and conduct of the study.


EVIDENCE TO PRACTICE COMMENTARY

Health-Related Quality of Life among children with disabilities: is there a place for parent- term effect on HRQoL from the child's perspective, but not the parents'. This result raises several questions, but above all provides an opportunity to reaffirm the importance of considering quality of life as a key outcome when evaluating interventions, and more broadly in epidemiological studies among children with disabilities. HRQoL is a multidimensional construct that reflects the subjective perception of the patient's health status, including physical, emotional, and social components in line with the World Health Organization's (WHO) definition of health. An emphasis on the importance of understanding patients' views on their care including the effectiveness of interventions on children's or adolescents' HRQoL has led to its increasing use in pediatric clinical trials. Furthermore, there is now recognition of the need to capture the changes in health that matter most to patients; therefore, patients' views on their treatment/care are also increasingly sought in clinical practice.

A main question raised by the Alkan and colleagues (2021) study concerns the value of parentproxy reports, which did not capture the benefits of the intervention perceived by the children. HRQoL is by definition subjective and should be assessed from the individual's perspective whenever possible. However, when this is not possible, due to the child age or cognitive abilities, the parents' perspective is used as a proxy. In this case the parent's proxy report is intended to represent the child's perspective as closely as possible. However, consistency between self-report and proxy-report has been investigated over the past decades agreement has generally been shown to be low to moderate. In general, parents proxy-report lower scores than those of their children, and differences between raters tend to increase in areas covering subjective appraisals of life, such as social relationships and emotional feelings (Sentenac, Rapp, Ehlinger, Colver, Thyen, & Arnaud, 2021). While these findings may lead some to discredit parent reports, parent-proxy HRQoL can provide valuable information as long as their limits are understood. They do not suggest that parents are not suitable respondents, rather highlight the importance of considering the multidimensional nature of HRQoL. Of particular interest are studies that have looked at patterns of discrepancies and have investigated factors that might explain the magnitude of discrepancies. First, child-parent discrepancies in reporting HRQoL are strongly related to the nature, severity and pain associated with the child's health conditions [START_REF] Sentenac | Disparity of child/parent-reported quality of life in cerebral palsy persists into adolescence[END_REF]. Of even less magnitude, social desirability, a phenomenon well documented in the literature, especially in children, is often responsible for an underestimation of psychological symptoms when they are self-reported [START_REF] Logan | Social desirability response bias and selfreport of psychological distress in pediatric chronic pain patients[END_REF]. Interestingly, parental psychological distress has also been shown to be crucial in explaining part of the distorted perspective that parents have of their child's HRQoL [START_REF] Sentenac | Disparity of child/parent-reported quality of life in cerebral palsy persists into adolescence[END_REF][START_REF] Eiser | Health-related quality of life and symptom reporting: similarities and differences between children and their parents[END_REF]. Parental depression or highly emotionally invested situations are factors associated with larger discrepancies between parents' and children's views. Proxy-reported HRQoL by parents is also related to poor parenting experience, as measured by parental stress, and poor adjustment to the child's chronic condition, especially mothers who are more often involved in daily care [START_REF] Eiser | Health-related quality of life and symptom reporting: similarities and differences between children and their parents[END_REF].

Finally, we must consider what can be learned from assessing changes in HRQoL after an intervention, a treatment or over time. In their study, Alkan and colleagues (2021) examined the potential effect of participation in arts-oriented leisure activities on HRQoL. Participation in such activities has the potential to improve feelings of self-confidence, self-esteem, fairness, and socialisation with a potential impact on psychological, emotional and social well-being (Dahan-Oliel, Shikako-Thomas & Majnemer, 2012), with a lesser impact on the child's physical well-being and autonomy. We can therefore expect that the different dimensions of HRQoL are not impacted in the same way based on the intervention, which could be one of the possible reasons for the discrepancies between parent proxy-and self-reported HRQoL. In other words, the potential effect on HRQoL attributable to the educational program observed in the self-reports may only influence the more subjective domains which are less likely to be perceived and reported by parents compared to changes in observable behaviour. The results presented on median total HRQoL scores do not allow for interpretation of changes in specific domains; but, findings on secondary outcomes can confirm the positive effect of the intervention on self-esteem and life satisfaction. The choice of instrument is therefore crucial and must address pre-specified hypotheses about where the intervention might be most effective.

Overall, it is clear that the child's perspective should be privileged in all cases where an intervention is directed towards improving emotional or social well-being due to the numerous influences that may lead to discrepancies between self and proxy-report. Furthermore, careful consideration of the match between the expected domain changes in HRQoL following intervention and the instrument used to measure change is needed in both research and clinical practice.

  photography education program on Health-Related Quality of Life (HRQoL), among other outcomes,