Member, IEEE Stéphane Méric
email: stephane.meric@insa-rennes.fr

Franck Fayard

Fellow, IEEE Éric Pottier
email: eric.pottier@univ-rennes1.fr

A Multiwindow Approach for Radargrammetric Improvements

Keywords: Digital elevation model (DEM), matching correlation, radar, radargrammetry, stereoscopy, synthetic aperture radar (SAR). I

The most intuitive way to extract depth information from remote sensing images is stereogrammetry, in which a digital elevation model (DEM) is achieved by computing stereoscopic radar images. When only the amplitude of the radar images is considered, this computation is called radargrammetry. The main idea of which is to match stereopair radar images in order to create a disparity map from one image to the other and, finally, to compute the elevation. Therein, we present our studies on the extraction of 3-D information from radar images. We examine a way to produce a DEM of a challenging area of the French Alps. The central issue of this paper concerns improvements for radargrammetric synthetic aperture radar image processing for high-relief reconstruction, and we focus on the matching step, which is one of the most important points of the radargrammetric processing. Thus, we propose original methods using different correlation windows. On the one hand, we take the advantages of a multiwindow approach to combine relevant information by multiplying the correlation surfaces obtained for each correlation window size during the matching operation. On the other hand, the second improvement is based on the expansion of windows on foreshortened areas, particularly because of the side-looking radar view. These methods allow us to achieve reliable image matching and to improve the accuracy of the DEM.

from pairs of stereoscopic SAR images. This process is called radargrammetry [START_REF] Leberl | Radargrammetric Image Processing[END_REF], and even though the process is well known, given the recent studies on radargrammetric applications [START_REF] Gonzales De Oliviera | An assessment of the altimetric information derived from spaceborne SAR (RADARSAT-1, SRTM3) and optical (ASTER) data for cartographic application in the Amazon region[END_REF]- [START_REF] Toutin | Impact of RADARSAT-2 SAR ultrafine-mode parameters on stereo-radargrammetric DEMs[END_REF], we can regard the topic as still being important.

Radargrammetric processing requires a mastery of several steps to solve 3-D stereo intersection equations: viewing geometry, image matching, and geometric reconstruction. First, viewing geometry, of which the most common radar configurations are same-and opposite-side configurations, allows us to decide how to obtain the required radar images. The next step is image matching, which is based on an area correlation between stereo radar images. This step gives the information parallax between stereoscopic images, which is the main information required to compute elevation. From each pair of radar images, we get a disparity map along both the azimuth axis and the range axis. Finally, the computation of this disparity map, obtained under known flight conditions, produces terrain elevation.

One of the most sensitive steps in radargrammetric processing is the matching step. The most commonly used imagematching technique is based on an area correlation between stereo radar images; however, image matching can dramatically fail in some high-relief areas due to radiometric and geometric differences between SAR stereopair images. Most efforts to improve the performance of radargrammetry have focused on this matching step [START_REF] Paillou | Relief reconstruction from SAR stereo pairs: The "optimal gradient" matching method[END_REF]- [START_REF] Brunner | Building height retrieval from VHR SAR imagery based on an iterative simulation and matching technique[END_REF]. Herein, we propose a new approach for the matching computation by combining two methods. On the one hand, we use results from different correlation window sizes in order to collect more information for better reliability by multiplying these results. It is worth noting that the use of the results for different window sizes has already been accomplished [START_REF] Hensley | Automatic DEM generation using Magellan stereo data[END_REF], [START_REF] Frankot | Noise resistant estimation techniques for SAR image registration and stereo matching[END_REF]. On the other hand, we apply an expanded correlation window in order to make the correlation patterns more similar. Thus, a resampling operation, which is applied to this expanded correlation window by different amounts in the range direction, is carried out in order to account for unknown foreshortening effects, resulting in improved match correlations for high-relief terrain. Moreover, we apply our improvements at different steps of the pyramidal scheme that we established for our radargrammetric processing.

We will set out the discussion in three parts. First, we will present the basic extraction operations from radar data, as precisely described in [START_REF] Méric | Radargrammetric SAR image processing[END_REF] and [START_REF] Fayard | Generation of DEM by radargrammetric techniques[END_REF]. Second, we will develop the different suggested improvements in order to cancel reconstruction errors. Thus, we present the results that we obtained by considering one test pixel. Finally, we evaluate the performance of our correlation process improvements when applied to SIR-C mission data in order to produce a DEM of an area of the French Alps.

II. BASICS OF RADARGRAMMETRY

A. Principle

Leberl [START_REF] Leberl | Radargrammetric Image Processing[END_REF] stated that "radargrammetry is the technology of extracting geometric information from radar images." The main parameters used in the stereoscopic method are absolute parallax p (or disparity) and convergence angle ∆θ v . The baseline B S also has an important function as regards the quality and accuracy of terrain reconstruction [START_REF] Toutin | State-of-the-art of elevation extraction from satellite SAR data[END_REF]. Assuming a sameside stereoscopic configuration (the radar scene is located on the same side with respect to the position of the two radars), these parameters are described in Fig. 1. The parallax p of an observed point is directly connected to its elevation and increases according to its altitude h. The convergence angle ∆θ v = θ v1θ v2 is defined by the intersection of the two lines of sight of the radar; this angle increases as the baseline B S rises. For satellites, the altitude h can be defined as

h = p cot θ v1 -cot θ v2 . (1)
For same-side configurations, a large baseline makes it possible to achieve good geometry for stereo plotting because of the increase in parallax values. The higher the parallax value is, the more accurate the elevation reconstruction will be. In oppositeside configurations (the radar scene is located between the two radars), the large baseline results in precise stereo plotting. However, the radiometric and geometric differences between the two radar images are so great that matching is almost impossible without image preprocessing [START_REF] Toutin | State-of-the-art of elevation extraction from satellite SAR data[END_REF].

B. Matching Step

The objective of radargrammetry is to match two radar images using "registration" processing. The registration step aligns two images viewed from different positions, containing the same radar scene. The aim of the matching step applied to the stereopair radar images (primary image and secondary image) is to obtain a dense description in order to achieve the required image registration accuracy. The most common imagematching method is area correlation. For a given area in the primary image, the matching computation has to detect the closest corresponding area in the secondary image by searching for its best match. The standard method of finding matching areas is to use analytical metric comparison, while the zeromean normalized cross correlation (ZNCC) can be applied to radar image searching windows of radar images. The result of the ZNCC computation is given by the cross-correlation coefficient ρ and can be stated as follows:

ρ = E[I 1 I 2 ] -E[I 1 ]E[I 2 ] V (I 1 )V (I 2 ) (2)
where I 1 and I 2 represent the amplitude values of the pixels of the primary and the secondary image windows, respectively. These windows are defined by an n-by-m pixel window which are the sizes along the range and azimuth axes, respectively. The expression of E[•] gives the mean expectation, whereas V [•] is the variance expression. The value of ρ is bounded by (-1) and (+1), and the windows are considered to be matched for the maximum value of ρ. The coefficient ρ is calculated using (2) for each position (az s and rg s ) of the radar image searching window in the searched-for area. We also compute a correlation surface, obtained with the values of the coefficient ρ. The maximum value of this surface gives the disparity (disp az ) along the azimuth axis (disp az = |az s (max)az r |) and the disparity (disp rg ) along the range axis (disp rg = |rg s (max)rg r |). This ρ calculation step is carried out for each pixel in the primary image in order to obtain the disparity map. Fig. 2 shows the correlation computation applied to one pixel inside the primary image. Once the matching operation has been completed, we obtain the disparity map. However, the disparity values should be considered according to confidence in the correlation coefficient. When the highest value inside a correlation surface can be precisely detected and the corresponding position is obvious, we achieve a high degree of confidence correlation. However, when the maximum position cannot be clearly obtained, the confidence correlation is considered as low, and large main lobes or high sidelobes occur for the correlation surface. In this case, additional noise can modify the results of the disparity map, and refinements such as speckle reduction and pyramidal procedure must be applied to strengthen the correlation results. Several refinements can be applied to improve the matching operation. One way to reduce the false matching result is to limit the search area for the correlation windows. Thus, we apply an epipolar constraint [START_REF] Zhang | A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry[END_REF] between radar images and also reduce the search for the matched window along the azimuth axis. Epipolar geometry considerably reduces the size of the search area, so when matching one pixel, there are fewer candidates on the secondary image than with a larger window. In our case, the disparity value along the azimuth axis is almost null, and for a given pixel, its homologue is located on an epipolar line along the range axis (see Fig. 3). If SAR data are collected at nonzero Doppler, the Doppler sensitivity regarding height and azimuth displacements between the SAR images must be taken into consideration. However, for the SIR-C data that we used, this displacement is sufficiently small (less than one pixel) that we only take into account a fine strip (three pixels) along the azimuth axis in the search for the matched window. Thus, we can ignore the along-track disparity and consider that the position of the homologous pixel is only significant along the range axis. The correlation surface, obtained by sorting the values of ρ, can be consequently represented by a correlation profile along the range axis. It is well known that the speckle phenomenon affects the interpretation of a radar image, and this phenomenon is undesirable for radargrammetric applications. Thus, speckle reduction is required prior to image analysis in order to improve the use of radar images in radargrammetry. This can be achieved in two ways: multilook processing and filtering techniques applied to the SAR image. Finally, a hierarchical strategy can be considered to enhance the accuracy of the DEM [START_REF] Denos | A pyramidal scheme for stereo matching SIR-B imagery[END_REF]. From the original image, we build an image pyramid. At each level, the image size is reduced by a factor of two. Radargrammetry is applied to each step, and for each iteration, the matching process makes it possible to establish an approximate disparity map. Thus, we are able to predict the disparity offsets at the next level of the hierarchical process. In the final step, the last disparity map is used to produce a DEM. In our case, the original image studied is reduced from 352-by-304 pixels to 88-by-76 pixels, which means that the radargrammetric processing is achieved through three steps.

C. Computation of the Radar Stereo Model

The objective of this step is to extract 3-D geometric data from stereopair radar images by using the coordinates (position and velocity) of the satellite along its flight path. From this computation, we can calculate the coordinates (x, y, z) in the chosen reference. In our case, the reference system is described by the WGS84 system. Owing to the parameters describing the satellite path, it is possible to give geographic information for each pixel of the radar image. In each image, a pixel is referenced by its range and azimuth indexes [START_REF] Polidori | Cartographie Radar[END_REF]. For each pixel in the primary image, the disparity value gives the relation between the values r 1 and r 2 (see Fig. 1). On the one hand, the range distance locates the point on a range sphere whose center is the radar position. On the other hand, the azimuth position of a pixel gives the Doppler cone, which is replaced by a plane in our case because of the null Doppler frequency at the perpendicular direction of the radar beam [START_REF] Chen | A weighted least squares solution for space intersection of spaceborne stereo SAR data[END_REF]. The intersection of the range sphere and the Doppler plane provides two solutions, but only one can be right according to the direction of the radar beam. Deriving from the exact solution to the stereo equations given in [START_REF] Hensley | A combined methodology for SAR interferometric and stereometric error modeling[END_REF] and considering the small Doppler centroid for the SIR-C data, the solution (x, y, z) of the search point satisfies the following equation:

       (x -X 1 ) 2 + (y -Y 1 ) 2 + (z -Z 1 ) 2 = r 2 1 (x -X 1 ) Ẋ1 + (y -Y 1 ) Ẏ1 + (z -Z 1 ) Ż1 = 0 (x -X 2 ) 2 + (y -Y 2 ) 2 + (z -Z 2 ) 2 = r 2 2 (x -X 2 ) Ẋ2 + (y -Y 2 ) Ẏ2 + (z -Z 2 ) Ż2 = 0 (3)
where the position

(X (1,2) , Y (1,2) , Z (1,2)
) and the velocity

( Ẋ(1,2) , Ẏ(1,2) , Ż(1, 2
) ) of the radar must be known. Also, the raw DEM is directly obtained by resolving the system (3) for all the pixels of the radar image. To quantify the accuracy of our elevation reconstruction, we compared it to the Shuttle Radar Topography Mission (SRTM) DEM [START_REF] Rodriguez | An assessment of the SRTM topographic products[END_REF]. We also applied a geocoding operation in order to be able to process the comparison. Fig. 4 shows an overview of our entire radargrammetric process. As mentioned previously, we notice that some ground control points (GCPs) may be required in order to refine the stereo model parameters [START_REF] Méric | Radargrammetric SAR image processing[END_REF].

III. MULTIWINDOW APPROACH AS AN ORIGINAL IMAGE-MATCHING IMPROVEMENT

A. Available Data

The DEM reconstruction results that we exhibit were obtained by applying our radargrammetric operations to data on an area of the French Alps, recorded in April 1994 by the space shuttle Endeavour during the SIR-C mission (PR17310 and PR17429 satellite paths). The two radar images (1500by-3000 pixels) are recorded at incidence angles of 35.7 • and 50.1 • , respectively. Furthermore, the range resolution of these SAR images is 27.1 m. Because we apply multilook processing (four looks), we get a 24.8-m azimuth resolution. Moreover, a Lee speckle filtering operation using a 5-by-5 pixel window size is applied in order to reduce the speckle phenomenon. Finally, three GCPs are required in order to compensate for satellite position and velocity inaccuracies. Fig. 5 shows the study areas on which our radargrammetric processing was applied. These areas were chosen because specific radar image characteristics are included: foreshortening and shadowing effects on the one hand and homogeneous and heterogeneous areas on the other hand. As explained earlier, stereo configuration is critical on high-relief areas because the two images show many radiometric and geometric differences. Since the reliability of terrain reconstruction is very dependent upon the matching results, the generated DEM is not accurate enough. Our current studies focus on this point by applying original improvements at the matching step. First, we propose to show the results of our improvement methods by trying to match a test pixel inside the primary image with its homologous pixel inside the secondary image. Its relative position, i.e., 11 in the range direction (see Fig. 6), is given by operator-based matching. Second, we apply the proposed image-matching method to the whole study area, and we exhibit the comparison between our DEM and the SRTM one. This comparison is done at the first step and at the last step of the pyramidal scheme.

B. Combining Correlation Surfaces (Method #1)

For a homogeneous structure, we notice that a wide correlation window is required in order to collect useful information for the matching process, whereas a heterogeneous image only needs a small correlation window to be correctly matched. Rather than work with a unique size n-by-m for the correlation windows (n along the range axis and m along the azimuth axis), we use several correlation window sizes in order to by multiplying them to obtain a unique profile. One of the main objectives of this operation is the right location of the homologous pixel. This can be achieved by the cancellation of the correlation profile sidelobes, which induces a refined peakedness of the main lobe of the correlation profile as shown in Fig. 7. The correlation-coefficient values of this profile are used as confidence levels for the correlation result. Thus, the position of the maximum correlation coefficient defines the position of the matching pixel. Considering the test pixel, the correlation profiles that are shown in Fig. 7 are obtained for the 7-by-7 pixel and 23-by-23 pixel windows (we only show two profiles in order to have the clearest figure). Moreover, we exhibit the correlation profile of the product correlation profile along the range direction. Considering the position of the homologous pixel, these results mismatch because the range indexes (index 10 for the 7-by-7 pixel window and index 8 for the 23-by-23 pixel window) are obviously different. Furthermore, the range profiles of the correlation surface are quite different. On the one hand, the position of the maximum is obvious for the 7-by-7 pixel window, but some sidelobes appear along the range profile for this small correlation window. On the other hand, the confidence level of the 23-by-23 pixel window profile could not be sufficient because of the low value of the maximum. Finally, considering the profile of the product, the index value of the homologous pixel determined is equal to 10, which almost corresponds to the true value, which is 11. Moreover, no obvious sidelobe occurs for the correlation profile combination, an important contributing factor to the decision to choose the homologous pixel.

C. Expanded Correlation Windows (Method #2)

As mentioned previously, the matching operation tends to fail for pixels located in foreshortened areas particularly. Therefore, we notice bad DEM reconstruction around these areas. Thus, the main objective of the expanded correlation window improvement is to reduce the bad matches occurring for steep areas and resulting from the foreshortening effect between the two images. For such areas, the higher the difference of the angle of incidence between the primary and the secondary images, the more different the resulting images. As a consequence, the correlation windows in the primary and secondary images are not similar enough (see the black boxes in Fig. 8) to provide a reliable match. In order to avoid mismatching, the secondary correlation window is truncated along the range axis from n pixels to k pixels (k ≤ n). We only change the range size n of the window because this axis is particularly affected by the foreshortening effect of the radar image. Afterward, this extracted pattern is enlarged to retrieve the original window size and gives a secondary expanded window (see Fig. 8). The range resampling method used to extend the extracted pattern performs a bilinear interpolation as an extension of the linear interpolation for interpolating images. This secondary expanded window and the primary one are matched through the matching step. As we have no information about the range compression ratio, the minimum value of k, which corresponds to the maximum compression effect, is estimated with respect to the terrain slope of the studied site. Then, based on the 23by-23 pixel size for the primary window, we generate different truncated secondary window sizes (k-by-m) from 11-by-23 pixels to 23-by-23 pixels. The right value of k is obtained when the maximum coefficients of the cross-correlation operations raise the maximum. A more detailed study (see Section IV) establishes a basic relationship between the stretching factor k s = k/n and the slope value. For the test pixel, the value of k that maximizes the correlation coefficient is k = 15 (see Fig. 9). The maximum value of the corresponding correlation coefficient located at range index 11 is about 0.89, whereas it is 0.65 at range index 8 for the 23-by-23 pixel window size (see Fig. 7). Therefore, the index value of the homologous pixel is corrected, giving a better attached confidence value. Also, the method described makes it possible to compensate for the radar range foreshortening phenomenon.

D. Combining Both Improvement Methods (Method #3)

In order to further improve the DEM reconstruction accuracy, we take advantage of the two methods described in Sections III-B and C by combining them. While the method based on the expansion of the correlation window only works with a value of m equal to 23, the combination of improvements applies the expansion method to each m value (m ∈ {7, 13, 17, 23}) used by the multiplication profile procedure (method #1). For each value of m, the correlation profile that gives the maximum correlation coefficient is selected. Then, we multiply the four selected profiles to obtain the final unique profile. The test pixel results in a correlation profile using this procedure are sharper than the ones obtained with the other improvements (see Fig. 10).

E. Results

In order to generate a DEM, we apply both matching-step improvement methods (including ZNCC) to the study area described in Fig. 5. The quantitative accuracy results are performed over the entirety of the zone covered by the SRTM data. The elevation reconstruction is compared to the elevation data obtained during the SRTM. According to Rodriguez et al. [START_REF] Rodriguez | An assessment of the SRTM topographic products[END_REF], a C-band SAR-derived DEM has a global absolute vertical accuracy of less than 16 m. Moreover, we derive from the height expression (4) the relationship between the disparity error ∆p and the height error ∆h ∆p = ∆h(cot θ v1cot θ v2 ).

It should be noted that our extracted DEM has to be regridded in order to fit with the description of the SRTM DEM. Indeed, as it is shown in Fig. 4, the 3-D stereo intersection procedure results in a "cloud" of 3-D points. The results of the comparison of our extracted DEMs with the SRTM DEM are summarized both in the first step (Table I) and in the last step (Table II) of the pyramidal scheme. As expected, we note a significant improvement in reconstruction accuracy using our new image-matching methods instead of the one based only on the ZNCC operation. Also, for the first pyramidal step, we notice an improvement on the accuracy obtained with the ZNCC matching method. Therefore, in the first pyramidal step, the disparity map generated combining both methods (method #3) is more accurate and reliable than the disparity map generated by method #1 and method #2. However, contrary to the results obtained in the first pyramidal step, method #3 does not lead to improved results in the final step. Even if this method is efficient in the first step, applying it to all steps of the pyramidal scheme leads to worse results compared to method #2. Thus, for the first step, we decide to keep the method giving the best results, i.e., method #3. For the following steps, we apply the other methods in order to test the efficiency of each combination. The results are shown in Table III. Applying method #3 in the first step and method #2 in the following steps gives exactly the same results as applying method #2 in all the steps (see Table II). However, we recall that the disparity map generated using method #3 in the first pyramidal step is more accurate and reliable than the disparity map generated applying method #2. Thus, we recommend a combination of the two improvement methods (method #3 and then method #2) in order to ensure maximum accuracy and reliability throughout the radargrammetric process [START_REF] Fayard | Radargrammetric improvements: A multi-window approach[END_REF].

IV. DISCUSSION

Several methods are analyzed to increase DEM accuracy by obtaining greater match reliability. The results that we obtained for each method give rise to some issues related to the characteristics of the study area.

First, for method #1, we propose to use different correlation window sizes for the homogeneous or heterogeneous structure of the correlation window. The size and the number for the different correlation windows are arbitrarily chosen. Thus, further work could deal with an image-matching algorithm, taking into account an adaptive window with respect to the statistical behavior of the SAR image in order to improve the confidence of the matching computation.

Second, method #2 proposes to extend correlation windows in order to mitigate the range foreshortening effect. The stretching factor k s , defined in Section III-C, can be derived from the expression of the foreshortening equation, given the foreshortening factor k f , considering the incidence angle θ v and the slope θ of the terrain (see Fig. 11)

k f = 1 sin [θ v -arctan(θ)] (5)
where the foreshortening k f is also given with k f = d/d and the slope θ is determined with θ = h/x. Considering (5), k f 1 and k f 2 represent the foreshortening factors for the primary and the secondary images, regarding the incidence angles θ v1 and θ v2 , respectively. We can thus derive the stretching factor k s given for an observed slope

k s = k f 2 /k f 1 . (6)
Equation ( 6) is obtained under the assumption of a constant cross-track slope θ v . Thus, an rms slope variation relative to the mean slope within a correlation window will give an approximative value for the stretching factor k s . The significance of the correlation window size should once again be noted.

Moreover, in the case of our hierarchical scheme, the prediction of the stretching factor k f for each iteration allows us to reduce the number of possible values of k f at the next level of the radargrammetric hierarchical process. Thus, the pyramidal methodology applied to the stretching factor fixing obviously induces better accuracy of the DEM and gives computational advantages.

Finally, considering the different methods, we note a significant improvement in reconstruction accuracy (98.0% of pixels with an error less than 100 m and 85.5% of pixels with an error less than 50 m). From our studies, we can draw two major statements. First, the study area that we get is a very demanding one with respect to the high relief involved. Second, the intersection angle value accentuates the foreshortening effect occurring in the mountainous area. We can conclude that our improved matching methods are quite efficient for such steep terrain. In order to provide a quantitative indication of the slope amount, we can consider the histogram of the slopes (see Fig. 12) for the studied area.

V. CONCLUSION AND FURTHER DEVELOPMENT

In this paper, we have presented the relevance of using stereoscopic radar images in order to retrieve the DEM of terrain and the way to improve the accuracy of this DEM for a mountainous area. The accuracy of the reconstruction of terrain depends on the success of the matching operation. Moreover, the generated DEM is not accurate enough because this matching operation tends to fail for pixels located in foreshortened areas particularly. Thus, we have suggested improvements in order to cancel reconstruction errors. The first improvement takes advantage of a multiwindow approach which combines information by multiplying the correlation surfaces obtained for each correlation window size. The second improvement is based on the expansion of windows on foreshortened areas. Finally, we combine these two improvement methods. Considering that the high-relief area studied is a challenging one for matching operations, we can say that our methods are very appropriate for this kind of area. These encouraging results allow us to study further improvements.

In the first instance, it would be interesting to establish a confidence map in order to clearly indicate the area characterized by low-level confidence. Second, we have proposed to multiply the correlation profiles for different window sizes, allowing us to investigate some weighted functions (based on the integrated sidelobe ratio, for example) in order to improve the correlation profile sidelobe suppression. Third, the amount of foreshortening factor for a SAR image is calculated in the first step without knowledge of the local slope. This a priori knowledge of the slope would be essential to apply method #2 in the first step. Finally, further work could deal with an imagematching algorithm, taking into account an adaptive window with respect to the statistical behavior of the SAR image.

Fig. 1 .

 1 Fig. 1. One possible radar stereoscopic configuration.

Fig. 2 .

 2 Fig. 2. Matching operations between the primary image and the secondary image.

Fig. 3 .

 3 Fig. 3. Position of homologous pixels considering epipolar images.

Fig. 4 .

 4 Fig. 4. Radargrammetric processing overview.

Fig. 5 .

 5 Fig. 5. Study areas from the SIR-C stereopair SAR images.

Fig. 6 .

 6 Fig. 6. Relative position of the homologous pixel to the pixel inside the primary image.

Fig. 7 .

 7 Fig. 7. Range profiles considering two sizes of windows and the combination by multiplying profiles.

Fig. 8 .

 8 Fig. 8. Example of the procedure used when expanding correlation windows.

Fig. 9 .

 9 Fig. 9. Range profiles for several values of k for expanded correlation windows.

Fig. 10 .

 10 Fig. 10. Correlation profile comparison for different improvement methods in the matching step.

Fig. 11 .

 11 Fig. 11. Foreshortening geometry.

Fig. 12 .

 12 Fig. 12. Histogram of the slopes for the studied area.

TABLE I RECONSTRUCTION

 I ERRORS OF THE GENERATED DEMs IN THE FIRST PYRAMIDAL STEP

TABLE II RECONSTRUCTION

 II ERRORS OF THE GENERATED DEMS IN THE LAST PYRAMIDAL STEP TABLE III RECONSTRUCTION ERRORS OF THE GENERATED DEMS COMBINING BOTH IMPROVEMENT METHODS UNTIL THE LAST PYRAMIDAL STEP

ACKNOWLEDGMENT

The authors would like to thank the editor and the anonymous reviewers for their suggestions and time to improve the quality of this paper.

Since 1989, he has supervised more than 30 research students to graduation (Ph.D.) in radar polarimetry covering areas from theory to remote sensing applications. Since 1999, he has been a Full Professor with the University of Rennes 1, where he is currently the Deputy Director of the Institute of Electronics and Telecommunications of Rennes (CNRS UMR 6164) and also the Head of the Image and Remote Sensing Group, SAPHIR Team. He has published a book coauthored with Dr. J. S. Lee in 2009, nine publications in books, and more than 50 papers in refereed journals and has presented more than 330 papers during international conferences, symposia, and workshops. He has presented advanced courses and seminars on radar polarimetry to a wide range of organizations (DLR, NASDA, JRC, RESTEC, and IECAS) and events (ISAP2000, EUSAR'04, EUSAR'06, EUSAR'10, NATO'04, NATO'06, PolInSAR'05, PolInSAR'11, JAXA'06, IGARSS'03, IGARSS'05, IGARSS'07, IGARSS'08, IGARSS'09, and IGARSS '10). His current activities of research and education are centered in the topics of analog electronics, microwave theory, and radar imaging with emphasis on radar polarimetry. His research covers a wide spectrum of areas from radar image processing (synthetic aperture radar and inverse synthetic aperture radar), polarimetric scattering modeling, and supervised/unsupervised polarimetric segmentation and classification to fundamentals and basic theory of polarimetry.

Dr. Pottier was the recipient of the Best Paper Award at the Third European Conference on Synthetic Aperture Radar (EUSAR2000) and the 2007 IEEE GRS-S Letters Prize Paper Award. He was also a recipient of the 2007 IEEE GRS-S Education Award "in recognition of his significant educational contributions to geoscience and remote sensing." He has chaired and organized 35 sessions in international conferences and was a member of the technical and scientific committees of 32 international symposia or conferences. He has been invited to present 46 presentations in international conferences.


Benoît Combès

Charles Garraud

Xavier Morandi

Sylvain Prima

Pierre Hellier

MRI-free neuronavigation for transcranial magnetic stimulation in severe depression

This paper presents a MRI-free neuronavigation technique for repetitive transcranial magnetic stimulation (rTMS). This method is composed of three steps: 1) surface sampling of the subject's scalp and face thanks to a 3D tracker, followed by Poisson surface reconstruction, 2) non-linear surface registration of an atlas surface to the extracted surface using an efficient modified non-linear EM-ICP algorithm [2], and 3) extrapolation of the transformation to a cortical stimulation target. Results have been obtained on a database of 10 subjects and have shown an accuracy of 10.2 mm. Although clearly less accurate than neuronavigation on the subject's MRI, we advocate that this neuronavigation method is reproducible and acceptable for routine application of rTMS in severe depression.

Introduction

Repetitive transcranial magnetic stimulation (rTMS) is a cortical stimulation technique where a strong electromagnetic field is generated by a coil. The field modifies the neuronal activity beneath the coil and since the stimulation is focal, rTMS has a broad range of potential applications in psychiatry and neurology [START_REF] Ridding | Is there a future for therapeutic use of transcranial magnetic stimulation?[END_REF]. It has been recently shown that there is some correlation between the stimulation accuracy and the therapeutic efficacy [START_REF] Fitzgerald | A randomized trial of rTMS targeted with MRI based neuro-navigation in treatment-resistant depression[END_REF]. Therefore, the stimulation is preferably conducted using a neuronavigation system [START_REF] Nauczyciel | Assessment of standard coil positioning in transcranial magnetic stimulation in depression[END_REF] that allows one to visualize the actual stimulation locus on the subject's MRI; thus the clinician can move the coil so that the stimulation is at the planned anatomical target defined on the MRI prior to stimulation. In this paper, we propose a new method that allows neuronavigation without MRI in the context of rTMS for severe, drug-resistant depression. It is generally admitted that a good stimulation target for depression is the dorsolateral prefrontal cortex (DLPFC), defined as Brodmann areas 9-46 in [START_REF] Petrides | Lateral prefrontal cortex: architectonic and functional organization[END_REF]. There is a huge number of patients with severe depression that could benefit from rTMS but the cost of the MRI scan, together with the waiting time (approximately between 5 and 15 weeks depending on countries), is a bottleneck for widespread MRI-based neuronavigated rTMS. We argue that a system that would allow a fast, MRI-free navigation with a slightly degraded accuracy but an excellent reproducibility between sessions would be valuable in clinical routine. Hence, in this paper we propose a surface-based neuronavigation on atlas for rTMS. Firstly, the subject's skin surface (scalp and face) is sampled thanks to a pointer localized by a 3D tracker of the neuronavigation system and reconstructed using the Poisson method. Secondly, the atlas surface, on which the stimulation target has been localized beforehand, is registered to the subject's surface thanks to an EM-ICP non-linear registration technique. Thirdly, the non-linear transformation computed on the surface is extrapolated to the cortical stimulation target to predict the patient's stimulation target for treatment-resistant depression. Accuracy was evaluated on a dataset of 10 subjects and was found to be 10.2 mm on average. The closest work to our method was presented in [START_REF] Koikkalainen | Dynamic probabilistic atlas of functional brain regions for transcranial magnetic stimulation[END_REF], where the authors used a small number of surface points (22) to register a database of 56 subjects so as to create a functional probabilistic atlas. In our paper, the atlas is deformed toward the subject using a large number of points (generally, several thousands) and an anatomical target is transformed and used in the neuronavigation system to guide a rTMS coil.

Material and method

Method overview

An overview of the method is presented in Figure 1. For a given subject, a surface sampling is first performed, using a pointer tracked by a 3D localizer of the neuronavigation system. Then, the segmented surface of the atlas X is registered to the subject's surface Y and the resulting transformation T is used to map the coordinates of the target into the subject's space. The data are then used by the neuronavigation system to guide the rTMS coil. The next sections will describe the following steps: surface acquisition and reconstruction of Y in Section 2.2 and surface registration of X to Y in Section 2.3. Visual results are presented in Section 3.

Surface acquisition and reconstruction

Anatomical sampling of the subject's scalp and face is performed using an optical tracking system (Claron Technology Inc., Toronto) composed of the Micron-Tracker camera and recognized markers. Sampling of points is achieved by covering the subject's head with the calibrated pointer tooltip. A software module was developed to record 4 anatomical landmarks denoted as L Y on the subject's head (inion, nasion, left and right tragus) used for an initial landmark-based registration (coined the LDM method hereafter) and then at least 100 surface points. The average number of samples was 3500 points, and the maximal sampling time was 10 minutes.

Then, the set of unorganized points is processed and a closed surface is reconstructed: firstly, the point set is processed through functions dedicated to smoothing, outliers removal, normal estimation using the CGAL library [START_REF]Computational Geometry Algorithms Library[END_REF]. The output is an oriented, smoothed point set suitable for surface reconstruction. Secondly, a surface reconstruction algorithm is applied to generate an iso-surface from the oriented pre-processed point set. 3D surface reconstruction from points set is a well-studied issue. Commonly used surface reconstruction techniques are based on Delaunay triangulation, implicit functions or parametric models. Given that the output of the pre-processing stage is a non-uniform, outlier reduced and smoothed point set, the reconstruction method used in our study should (1) infer the topology of the unknown surface, (2) fit the data, and (3) fill holes. For these reasons, the Poisson reconstruction technique is used [START_REF] Kazhdan | Poisson surface reconstruction[END_REF]. This method allows reconstruction with greater details than other techniques. An implementation of the Poisson surface reconstruction algorithm based on the VTK framework [START_REF] Doria | Poisson surface reconstruction for VTK[END_REF] was used. This process produces the point set Y describing the subject's scalp and face, along with the landmark set L Y .

Surface registration: efficient EM-ICP algorithm for linear and non-linear registration

In this section, we show how to compute the transformation T that best superposes the surface of the atlas X on the surface of the subject Y (using additional landmarks L X = (l X k ) and L Y = (l Y k )) so as to compute the coordinates of the target in the subject's space.

General scheme

The EM-ICP algorithm [START_REF] Granger | Multi-scale EM-ICP: A Fast and Robust Approach for Surface Registration[END_REF] is an efficient and elegant solution for rigid registration of point sets. It relies on a probabilistic modeling of the point-to-point correspondences that allows i) a pragmatic definition of the superimposition of two point sets and ii) to deal with a relatively smooth cost function to minimize (in contrast to the classical ICP algorithm). Moreover, it is mathematically well-grounded (monotonic convergence), generic (no assumption on tessellation/topology/number of points) and can be specialized in many ways (e.g. to deal with non-linear deformations or to estimate shape models [START_REF] Chui | Unsupervised Learning of an Atlas from Unlabeled Point-Sets[END_REF]).

Most importantly, the EM-ICP algorithm [START_REF] Granger | Multi-scale EM-ICP: A Fast and Robust Approach for Surface Registration[END_REF] allows dealing very efficiently and robustly with large point sets. This algorithm can be shown to be equivalent to the alternated iterative minimization of a energetic criterion. In this work, we propose a slight modification of the underlying criterion that allows one i) to use pairs of landmarks to constrain the registration, ii) to symmetrize the estimation of point-to-point correspondences and iii) to add a regularization on T to deal with non-linear deformations:

E(T (X), Y, A, B) = j,k (A jk + B jk )ρ δ (||y j -T (x k )|| 2 ) + 2σ 2 β k ||l Y k -T (l X k )|| 2 +2σ 2 j,k A jk log(A jk ) + 2σ 2 j,k B jk log(B jk ) + 2σ 2 αL(T ), with ∀j, k A jk = 1 and ∀k, j B jk = 1 (1)
where if we drop matrix B for a moment, for the sake of clarity, A = (A jk ) is the unknown match matrix encoding the a posteriori probabilities of correspondence between points of X and Y . This probabilistic interpretation of A is made possible thanks to the barrier function jk A jk log(A jk ) [START_REF] Chui | Unsupervised Learning of an Atlas from Unlabeled Point-Sets[END_REF]. In essence, the greater A jk , the more likely the point x k ∈ X to be the correspondent of the point y j ∈ Y . σ 2 is the Gaussian noise variance of X. This fuzzy control on the correspondences allows one to handle problems due to differences of sampling/number of points between X and Y : we do not look for one-to-one correspondences between points of each surface but instead for "fuzzy" correspondences linking each point of Y to each point of X. This match matrix is a row stochastic matrix, which leads to many-to-one correspondences. This asymmetric formulation makes the algorithm unable to achieve a good matching in specific cases and can make the choice of the source and target sets critical. To tackle this problem, our criterion also contains a second match matrix B, that is column stochastic, in addition to the row stochastic matrix A. The a posteriori probabilities of correspondences between points of X and Y is encoded in both matrices A and B, making the point-to-point matching much more symmetrical compared to [START_REF] Granger | Multi-scale EM-ICP: A Fast and Robust Approach for Surface Registration[END_REF].

-T is a transformation (to be later defined) superposing X on Y . This transformation is subject to a regularizer L.

α and β are two positive parameters weighing respectively the regularization L(T ) term and the landmark-to-landmark discrepancy term k ||l Y k -T (l X k )|| 2 over the other terms.

the function (ρ δ : r -→ r if r < δ and δ else) is a robust function allowing points of X (resp. Y ) having no homologue in Y (resp. X) to be discarded from the estimation of T .

It can be shown that the criterion E can be minimized over the three unknown parameters T , A and B using the following two-step algorithm:

Algo NL-Sym-EM-ICP: Symmetric robust non-linear EM-ICP with landmarks

Step 1: initialise à and B to the null matrix ∀x k ∈ X; S = {y j ∈ Y such that ||y j -T (x k )|| 2 < δ} (using a kd-tree) ∀y j ∈ S; ∀y j ∈ S; Ãjk = exp(-(||y j -T (x k )|| 2 /(2σ 2 )) ∀y j / ∈ S; Ãjk is left equal to 0 B = à normalise à in rows and B in columns compute the vectors (p j ) : ∀j, pj = 0 if i Ãji = 0 and 1 else compute the vectors (q k ) : ∀k, qk = 0 if i Bik = 0 and 1 else

Step 2: solve the approximation problem: arg min T j,k (p j Ãjk + qk Bjk )||y j -

T (x k )|| 2 + 2σ 2 β k ||T (l X k ) -l Y k || 2 + 2σ 2 αL(T )
Specifying T /L In practice, we design a coarse-to-fine approach to estimate T by first computing the rigid transformation best superposing L X on L Y and then using the NL-Sym-EM-ICP algorithm by modeling T successively as a rigid R, an affine F and a non-linear transformation W . For rigid and affine transformations T , we take L(T ) = 0 and Step 2 has a closed-form solution. For the non-linear transformation, we parametrize W as a deformation field (i.e. W (x) = x + t(x)) and design L as a scalar Fourier-based regularizer over t:

L(t = (t 1 , t 2 , t 3 ) T ) = L(t 1 )+L(t 2 )+L(t 3 ), with L(t i ) = 1 (2π) 3 ∞ -∞ |t * i (ω)| 2 φ * (|ω|/b) dω,
where * is the Fourier transform operator, φ : R → R is an integrable function and b is a real strictly positive rescaling factor. We choose φ as a Wu compactly supported positive definite kernel. The advantage of such a regularization (over the TPS regularizer for example) is that it i) provides efficient solutions for Step 2 based on sparse linear algebra [START_REF] Wendland | Scattered Data Approximation[END_REF] and ii) introduces a scaling parameter b.

The larger the b value, the more drastic the penalization of the high frequencies, i.e. by choosing a large b value, we focus on capturing the global/high-scale deformation superposing X and Y .

Interpolating the target position Each estimated transformation R, F and W is defined over R 3 and has a closed-form expression. As a result, any point y of Y (thus those representing the DLPFC) can be mapped in the space of X as y = W (F (R(y))).

Material

Phantom To assess the accuracy of the point acquisition and reconstruction steps, a human-head phantom was used, shown in Figure 2-(a). The phantom was scanned with an isotropic 0.5 mm resolution CT (size 512×512×841). A set of 4099 points was acquired as described in Section 2.2. The surface of the phantom was extracted using heuristic thresholding and mathematical morphology operators.

Subjects

The experiments were performed using anatomical brain MRI of 10 healthy volunteers. Each subject had a brain MRI scan using a 3D T1-weighted sequence with 1 mm isotropic resolution, and the skin surface was extracted using thresholding and mathematical morphology operators. On the subjects, the surface representing the scalp and face was sampled using the process described in Section 2.2.

MRI Atlas

In the experiments, the MRI atlas described in [START_REF] Lalys | Construction and assessment of a 3-T MRI brain template[END_REF] was used. The skin surface was extracted using thresholding and mathematical morphology operators, and the four landmark points L X were manually localized. This atlas was used instead of the Colin27 atlas since on the latter, the surface extraction process is difficult due to an antenna visible on the top of the atlas.

DLPFC localization Manual positioning of the DPLFC on the subjects' MRI and on the atlas was performed by an expert in neuroanatomy. The DLPFC was defined as the second third, i.e. middle part, of the middle frontal gyrus along the antero-posterior axis, corresponding to Brodmann areas 9/46 as described in [START_REF] Petrides | Lateral prefrontal cortex: architectonic and functional organization[END_REF], and as shown in Figure 1-(b). We have chosen to characterize the position of the DLPFC by its centroid, shown by the red dot. Therefore, hereafter the DLPFC is considered as a point, what enables to compute Euclidean distances between estimated targets and reference targets.

3 Validation and results

Poisson reconstruction accuracy

The point set acquired on the physical phantom was registered to the phantom's skin surface extracted from the CT using a rigid EM-ICP. The computed transformation was then applied to the reconstructed Poisson surface. The mean point-to-point error between the Poisson surface and the surface extracted from the CT scan was 1.6 mm (standard deviation 1.08 mm). Results are presented in Figure 2. These results demonstrate the accuracy of the point sampling and show that the reconstructed surface is valid to represent the subject's scalp and face.

Distance between predicted and reference DLPFC

The skin surface extracted on the MRI was registered toward the Poisson reconstructed surface using rigid EM-ICP. On the other side, the Poisson reconstructed surface was registered toward the atlas skin surface using the nonlinear EM-ICP. Therefore, the predicted DLPFC can be compared to the reference DLPFC. Various degrees of freedom of the transformation were tested: landmark-based registration that corresponds to a Procrustes alignment using the 4 anatomical landmarks (LDM), LDM followed by a rigid registration (R), R followed by an affine registration (RA) and RA followed by a non-linear registration (NL). Table 1 shows the obtained errors for the 10 subjects for all transformations. Firstly, it can be observed that the mean error decreases when the degrees of freedom of the transformation increase. Secondly, the error obtained with the fully non-linear method is 10.2 mm on average. These results are discussed hereafter.

Conclusion

In this paper, a new method was proposed to perform neuronavigation without MRI for transcranial magnetic stimulation. The method is based on a subject's surface sampling and reconstruction, followed by a non-linear registration of an atlas surface to the obtained surface. The transformation is then used to map the coordinates of the DLPFC in the atlas to the subject's space. Firstly, we found the surface sampling and reconstruction on the phantom to be accurate (mean error 1.6 mm, standard deviation 1.08 mm). Secondly, we compared the surface-based DLPFC localization to a ground truth localization performed by an expert in neuroanatomy. Results have shown on 10 subjects that the mean error was 10.2 mm. In a previous study [START_REF] Nauczyciel | Localization of the dorsolateral prefrontal cortex in MRI images for neuronavigated TMS[END_REF], we have assessed the performance of 3 clinicians on 25 subjects to localize the DLPFC on MRI and found a large discrepancy between raters: accuracy compared to reference localization varied between 8 mm and 14 mm (standard deviation 5.7 mm). In comparison, the mean error of 10.2 mm can be considered acceptable. In addition, we focus on rTMS application where the electromagnetic field has some dispersion. Therefore, we argue that, although less accurate than neuronavigation using the subject's MRI, this MRI-free neuronavigation technique is reproducible between sessions and is valuable for a routine clinical use of rTMS. Further work should 1) enlarge the database of subjects and extend this technique to other stimulation targets, such as the temporoparietal cortex to treat auditory hallucination in schizophrenia for instance and 2) evaluate the therapeutic efficiency on patients.

Fig. 1 .

 1 Fig. 1. (a): overview of the surface-based neuronavigation on atlas. (b): a surface rendering of the cortex with the Brodmann area 9/46, or DLPFC, dashed on the surface. To compute Euclidean errors, the area is identified as the centroid, represented here as the red point.

Fig. 2 .

 2 Fig. 2. This figure shows the validation of the acquisition and reconstruction of a point set on a physical-head phantom. (a) shows a picture of the physical phantom used to assess the surface acquisition and reconstruction method. (b) shows the acquired point set and the reconstructed Poisson surface. (c) shows the skin surface extracted from CT. (d) shows the Poisson surface registered to the CT surface. The color represents the spatial distribution of errors after reconstruction and registration. The mean pointto-point error was 1.6 mm with standard deviation was 1.08 mm.

Table 1 .

 1 Results of the surface-based localization of the DLPFC when compared to the reference DLPFC. Various parametrization of the surface-based method were tested. The fully non-linear registration provided a mean error of 10.2 mm.

		Landmark-based Rigid	Affine	Non-linear
	Subject 1	11.3	5.7	3.5	3.3
	Subject 2	13.1	13.5	12.1	11.9
	Subject 3	23.8	15.1	13.6	12.3
	Subject 4	27.7	10.5	8.8	9.2
	Subject 5	16.8	4.7	3.2	3.1
	Subject 6	22.5	9.1	7.6	6.8
	Subject 7	32.9	21	20.3	19.5
	Subject 8	22.7	18.7	14.2	13.6
	Subject 9	21.3	19.2	15.6	15.4
	Subject 10	23.3	7.7	6.4	6.7
	Mean (mm)	21.54	12.52	10.53	10.18
	Std.dev. (mm) 6.46	5.86	5.56	5.33


Civil Engineer, PhD student, Conrad Boton
email: conrad.boton@tudor.lu

Henri Tudor

Dr Sylvain Kubicki
email: sylvain.kubicki@tudor.lu

Architect

Dr Gilles Halin
email: gilles.halin@crai.archi.fr

COLLABORATIVE CONSTRUCTION PLANNING: TOWARDS 4D VISUALIZATIONS ADAPTED TO PRACTITIONERS REQUIREMENTS

Keywords: Construction process, Collaboration, 4D CAD, Human-Computer Interface, Information visualization, Business view, Model driven engineering

Managing the intervention of various actors during the construction phase is a recurrent issue in the construction sector. This is partly due to the multiplicity of stakeholders and the need to manage interfaces necessary for efficient planning and coordination of construction tasks. 4D CAD technology appears to be an innovative approach to answer such issues. It consists in combining a 3D model with the time dimension, in order to simulate the progress of works construction along the time.

Our main hypothesis is that the use of 4D to support the actors' collaborative work is not adapted enough to the need of the sector because the classical view (Gantt + 3D model) does not take into account the specific requirements related to particular usages (planning of interventions and reservations request for a contractor; simulation and integration of works' interfaces for an engineer, etc..). It is therefore challenging to adapt the visualization to business needs of users.

Developments in Human-Machine Interface and Information Visualization fields could allow us selecting user views properties (I.e. Structure, Quantity of information displayable, Graphical attributes, Content description, Interaction principles, Business view) and compose "business views". Therefore, the article propose taxonomy to describe user views in order to setup a method for business visualization design, enabling to: 1) Identify business tasks (usages) related to the roles of different users, 2) Offer services tailored to different usages, and 3) Suggest visualization modes fitting each usage on the basis of our visualization model.

In a case study we formalize a collaborative process to identify the usages of each practitioners involved in the collaboration construction process planning. It especially targets collaborative management of works' interfaces. Then, after defining the required services, we suggest combining visualization methods suitable for each use in order to achieve views composition for each stakeholder.

INTRODUCTION

Managing the intervention of stakeholders in collaborative works such as in construction sector is an important issue. The main reasons are the multiplicity of stakeholders coming from different trades and also the need of managing work's interfaces between them. This issue has been previously explored [START_REF] Hanrot | Enjeux pour l'ingénierie de maîtrise d'oeuvre[END_REF][START_REF] Tahon | Le pilotage simultané d'un projet de construction[END_REF] but the question remains recurring. It is therefore necessary to explore new solutions both on human side of collaboration (i.e. processes and working practices) and on the technological side. Thus, 4D CAD appears to be an innovative approach to support the simulation of the construction activity. Several uses of the 4D CAD have been proposed and tested since its emergence (Chau & al. 2005). From the simple simulation of the construction to interventions and reservations management, the proposed developments provide solutions more or less relevant to the problem.

An important aspect of the construction industry is the flexibility that characterizes projects' management. Indeed, each stakeholder of a cooperative project's context has his own interests, his methods and specific tasks. In this context generic solutions are difficult to adopt successfully. It is then important to adapt solutions to the needs of users. One of the key points in adapting CSCW tools (groupware) is to design visualizations matching the business requirements of users. Considering previous 4D developments, the standard view (i.e. Gantt planning associated with 3D model) currently proposed to different actors in 4D CAD tools does not take into account this adaptation. Specific requirements related to tasks performed by particular roles (planning of interventions and reservations request for a contractor; simulation and integration of works' interfaces for an engineer, etc…) are not considered.

This work relies on previous works [START_REF] Kubicki | Usage-centered design of adaptable visualization services -Application to cooperation support services system in the AEC sector[END_REF]) that mainly aim to model the collaborative context of construction projects and to propose IT services and business views based on business tasks requirements. In this paper we will first make a brief state of the art of 4D CAD developments in the construction field in order to identify activities and services used to support the collaborative work. Then, an overview of research works in the fields of Human-Computer Interface and Information Visualization will allow us to define taxonomic attributes, in order to propose a metamodel that can describe "business views". As an application, we suggest a scenario of collaborative use of 4D model helping us to identify the tasks of different stakeholders, to define services and possible user views for these tasks. The developed metamodel allows us to describe and compare the user views in order to choose the most adapted one for each task and to compose coordinated multiple views for each actor involved in the process.

4D USE IN AEC AND IMPORTANCE OF ADAPTED VISUALIZATION

4D CAD technology consists in linking a three-dimensional (3D) model of a construction project with the works' planning. It leads to obtain an "augmented planning" that can represent the construction progress over time [START_REF] Kubicki | Assister la coordination flexible de l'activité de construction de bâtiments, Une approche par les modèles pour la proposition d'outils de visualisation du contexte de coopération[END_REF], Chau & al. 2005). The use of 4D helps to resolve recurrent problems in the AEC projects. To this end, several applications have been proposed and tested. [START_REF] Sriprasert | Multi-constraint information management and visualisation for collaborative planning and control in construction[END_REF]) made the assumption that in complex and simultaneous construction projects, reliable planning is central to effective collaboration. But they observed that the thousands of articles published during the previous 50 years on construction planning are very fragmentary and have not yet provided a universal system that addresses a typical problem in the construction sector. They proposed a method called "Planning multi-constraint" and developed a 4D prototype embedded in the environment of Autodesk Architectural Desktop. [START_REF] Chau | Four-Dimensional Visualization of Construction Scheduling and Site Utilization[END_REF]) estimated that the visual link between the timing and conditions of construction site could facilitate decision-making during both phases of planning and construction. The focus of 4D CAD developments has often been placed at the building components, always missing useful features that can help manage the site in the following areas: generation of on-site usage patterns, estimation of quantities of building materials help and costs estimate. To repair these deficiencies, they designed a 4D visualization model for both construction managers to plan daily activities more effectively, and also add to knowledge and understanding the relevance of modern computer graphics to the responsibilities of manager of the construction site. [START_REF] Kubicki | Assister la coordination flexible de l'activité de construction de bâtiments, Une approche par les modèles pour la proposition d'outils de visualisation du contexte de coopération[END_REF] has particularly mentioned the use of 4D as an attractive solution since, by integrating 3D model and Gantt chart, it can assist the preparation phase of construction by the 3D analysis sequence of implementation, and shows the progress during construction. Going further, he imagined to generalize the 4D visualization (planning + 3D model) by linking it to a third "view" specific to the coordination, i.e. the construction meeting report. There would thus be the trio: meeting reporting, 3D model and schedule to navigate through coordination information and improve understanding of the state of activity by each actor. To show the feasibility, he proposed a prototype (Bat'iViews). [START_REF] Lu | Construction planning methodology integrating operations simulation and four dimensional computer aided design (4D-CAD)[END_REF]) proposed a construction planning method that integrates operations simulation with critical path method (CPM)-based 4D-CAD in order to provide a more useful tool that overcomes the shortcomings of the current ones, and presented a trial application of the method on a precast viaduct construction project in Hong Kong. [START_REF] Seok | Improvement of Link Process in 4D CAD Viewer by Using Interface Board for Construction Project Management[END_REF] established that "the link methodologies in current 4D CAD viewer should be improved with understanding of characteristic by each project type and suggested a link method in 4D CAD system for plant project management.

Furthermore, studies have been conducted to assess the real value of the use of 4D CAD models in construction projects. [START_REF] Staub-French | 3D and 4D modeling for design and construction coordination: issues and lessons learned[END_REF] worked on two different building construction projects in California that have implemented 3D and 4D modeling in varying degrees throughout the design and construction process. They concluded that 3D and 4D modeling may have a significant impact on project implementation, including increased productivity, elimination of interference on the ground, pre-production increased, fewer times, fewer requests for information, unless change orders, unless increased costs and decreased time. They proposed a guideline to help teams to implement 3D and 4D models in construction projects, particularly to address technical problems, procedural and organizational issues that are often barriers to adopting these technologies. [START_REF] Dawood | Measuring the effectiveness of 4D planning as a valuable communication tool[END_REF]) conducted an experiment among participants of different age groups (11-22 years). The aim of the experiment is to assess how much information participants are able to extract and retain in their minds by the analysis of two different formats of graphical representation (4D model and 2D). The research results have provided quantitative data showing that the 4D group outperformed the 2D group by constructing 7% faster the physical model, spending 22% less time to extract intelligence information from the construction and reconstructing 77% less compared to the 2D Group. The 4D group participants were able to communicate and coordinate better compared to participants in the group 2D. [START_REF] Mahalingam | An evaluation of the applicability of 4D CAD on construction projects[END_REF]) made an assessment, through the study of four construction projects underway in India and the applicability of 4D CAD in construction projects. They established that it could offer advantages at the stage of development and project planning, and in the construction phase. According to them, it seems particularly useful during the construction phase for comparing the constructability of the working methods, to visually identify conflicts or clashes (overlaps), and as a visual tool for contractors, customers, subcontractors and suppliers to discuss and plan the project progress.

As we can see, the 4D models are of obvious interest to the AEC. In addition, efforts have been made to improve the collaborative 4D planning [START_REF] Sriprasert | Multi-constraint information management and visualisation for collaborative planning and control in construction[END_REF][START_REF] Zhou | An interactive approach to collaborative 4D construction planning[END_REF]. But adapting visualization to the business requirements of different actors still remains a challenging issue. It should be noted that some characteristics of AEC have to be taken into account. Indeed, "an AEC operation is characterized on the one hand by the particularities of the architectural object (situated object, prototype object) and on the other the specificities of the cooperative tasks (variable teams, decentralization of decision)" [START_REF] Kubicki | Assister la coordination flexible de l'activité de construction de bâtiments, Une approche par les modèles pour la proposition d'outils de visualisation du contexte de coopération[END_REF]. Then actors tend to use different visualization modes, depending on their role. It is therefore necessary to consider adapting the display to business needs of users. "Therefore visualization techniques of project context's information could be designed according to the tasks, and be identified as an adaptable visualization service which could be chosen, integrated and used by the actors to perform their activity inside a project" [START_REF] Kubicki | Usage-centered design of adaptable visualization services -Application to cooperation support services system in the AEC sector[END_REF]. Moreover many works showed the value of adapted visualization [START_REF] Davidson | What your database hides away[END_REF][START_REF] Norman | Things That Make Us Smart[END_REF]. So, visualization must be designed not only in terms of aesthetics and ergonomics, but also as meeting real needs related of each user and the actions they will have to operate within their design and construction process.

TOWARD ADAPTED BUSINESS VIEWS IN 4D CAD -SUPPORTED COLLABORATIVE WORK IN AEC

METHOD

Above we have shown the benefits of the use of 4D CAD as a medium for collaborative planning activity in AEC.

In most of the scenarios encountered in the literature, the same 4D view (3D + Gantt) is proposed to all players. Of course, as said, this view does not take into account the specific needs associated with certain tasks. In addition, an important principle of information visualization recommends not displaying more information than necessary to avoid cognitive overload. We propose to match business views to the tasks of actors. In order to design views adapted to actors' tasks in a 4D CAD use context, we followed a multi-step approach as shown in Figure 1. Initially, it's important to work on formalizing a process scenario. This process will allow to clearly identifying the tasks of each actor. Identifying such tasks helped us to understand the related information needed to achieve them and the visualization techniques that could be used (Step 1). After that, the visualization needs could be identified, i.e. the interaction principles and specific visualization tasks related to business tasks we previously identified (Step 2). Then, it would be possible to describe and compare possible visualization techniques in order to choose the most adapted one, according to the visualization needs. That will finally enable to design the most adapted business view (Step 3).

Process model

Identification of business tasks

Business tasks

Needed information

Identifying visualization needs

Needed interaction principles

Needed visualisation tasks Comparison of techniques

Choose business view

Choose adapted technique

Business view Possibles visualization techniques

+ Visualization needs

Step 1

Step 2

Step 3

Figure 1: Multi-step approach to compose business view To compare possible views, we propose to model them. Model Driven Engineering approach recommends the use of metamodels to define domain languages. The approach enables the design of models which have to be conformed to their metamodel. Applied to business views, the first step in the modeling is to define a business view metamodel.

BUSINESS VIEW METAMODEL

According to our specific context and to the literature, a user view displays content, using a technique. [START_REF] Lohse | A classification of visual representations[END_REF]) presented a classification and properties for visual representations. They identified ten properties for visual representation that are: spatiality (spatial or non spatial), temporality (temporal or non temporal), comprehensibility (easy to understand or hard to understand), continuity (continuous or discrete), concrete or abstract, numericity (numeric or non numeric), dynamism (static or dynamic), attractivity (attractive or unattractive), focus (emphasizes whole or emphasizes parts) and quantity of information (conveys a lot of information or conveys a little information). They also proposed eleven categories of representations: structure diagrams, cartograms, maps, graphic tables, process diagrams, icons, time charts, network charts, pictures, tables, graphs. [START_REF] Keim | Information Visualization and Visual Data Mining[END_REF] classified data in 7 display formats: one-dimensional, two-dimensional, multidimensional, text and hypertext, hierarchies and graphs, algorithms and software. This is close to the work of [START_REF] Shneiderman | The Eyes Have It: A Task by Data Type Taxonomy for Information Visualizations[END_REF] who described visualization contents into seven classes (one-dimensional or linear, twodimensional, three-dimensional, temporal, multidimensional, trees, networks). By their nature [START_REF] Mazza | Introduction to Information Visualization[END_REF] classified the data into 3 main categories (quantitative, ordinal and categorical) and proposed a graphical elements typology.

A business view also involves interaction techniques. These techniques are characterized by their type, their mode and their interactivity level. Following [START_REF] Keim | Information Visualization and Visual Data Mining[END_REF] there are 5 types of interaction: dynamic projection, interactive filtering (browsing and querying), interactive zoom, interactive deformation and "Link&Brush" [START_REF] Keim | Information Visualization and Visual Data Mining[END_REF]. Tweedie identified five interactivity levels: manual, mechanized, instructable, steerable and automatic [START_REF] Tweedie | Characterizing interactive externalizations[END_REF]. [START_REF] Spence | Information Visualization: Design for Interaction (2nd Edition)[END_REF] considered four interaction modes: continuous, stepped, passive and composite.

These various taxonomies from the HCI and information visualization fields allow us to consolidating business views concepts within the metamodel depicted on Figure 2.

CASE STUDY

According to the first step of the proposed method, Figure 3 depicts the process model that we formalized from our observation and which is related to the management of the interventions sequencing and reservations of the actors involved in a building project. To understand the concept of reservation, [START_REF] Kubicki | Assister la coordination flexible de l'activité de construction de bâtiments, Une approche par les modèles pour la proposition d'outils de visualisation du contexte de coopération[END_REF] gave the example of a reservation for the passage of plumbing in a slab. The mason makes the reservation in the slab on the request of the plumber who specifies to him the size and location of the ducts.

The scenario shows three kinds of actors involved: supervisor, engineer and contractors. This scenario brings up the tasks of these different actors. Note that this process is simply an example of scenario that shows a possible use of 4D for construction planning, integrating the reservations management. This example is based on our experience and knowledge as well as literature review. Our future works will focus on inventorying and validating all types of tasks in construction planning. In table 1, we summarized actors' tasks, information needed to perform them and possible views. In the table {a(b,c),d(e)} represents a composition of views a and d. b and c are the two parameters of the view a and e is the only one parameter of view d. The building elements are the different elements that compose the building. These elements correspond to some business tasks, according to the actor who is responsible of their realization. The realization of a task begins at a certain date and finishes at another date (execution date). That determines the duration of the task. One important information need is the location of the reservations. In the example of the reservation for the passage of plumbing in a slab, the plumber has to specify to the mason the reservation location according to size and specificity of the ducts that will be used. After working in situ, the contractor can send some feedbacks. Feedbacks are some notes about important changes that could impact the following of the building process.

The listed possible views are based on a previous experience [START_REF] Kubicki | Multi-visualization of the Cooperative Context in Building Construction Activity A Model-Based Approach to design AEC-specific Visualization Interfaces[END_REF]) that aimed to propose a model driven architecture for multi-view representation of the cooperation context. Of course, these views are not exhaustive and deserve to be supplemented. So, one aspect of our ongoing work is to identify other existing visualization techniques and to describe them from the metamodel presented.

After reading table 1, we see quite clearly that the tasks and the needed information are different from one actor to another according to their viewpoint in collaborative project. At this point, we can notice that according to their tasks, the contractors don't need to edit the 3D building representation. They often require working with lists and/or forms and a 2D representation to work in situ. At the contrary, supervisor (task 1) and Engineer (task 2 and task 6) need to work directly on an editable representation of the building. As possible visualization techniques, 2D plan and 3D view can be chosen to achieve the tasks Figure 4). Using the taxonomy of visualization tasks proposed by [START_REF] Valiati | A taxonomy of tasks for guiding the evaluation of multidimensional visualizations[END_REF], we can, in instance, describe the visualization needs for the engineer's task 6. So, in terms of visualization for this task, engineer will have to:

-Visualize the data (i.e. building representation) -Locate the position (i.e. of reservations) -Identify the dependencies (i.e. of tasks and reservations) -Compare the values (i.e. of simulation sequences with dates list) -Determine any variance (i.e. between simulation sequences and dates list) -Infer trends (i.e. validity or no) We see that this business task requires some specific visualization tasks and a visualization technique that enables adapted interaction principles supporting them. In order to do it, we suggest modeling the two proposed techniques (2D plan and 3D views) in order to compare them.

Visualizing the building representation corresponds to a passive mode of interaction and don't call at a particular interaction style. Both 2D plan view and 3D model view can enable to achieve it. To locate the position of reservations, engineer need to clearly see them among other kinds of information in the space. Thus, he needs a visualization technique that emphasis parts. To identify the dependencies of tasks and reservations, the engineer needs particular interactions that could be navigation or direct manipulations. Those kinds of interaction are possible with the 3D model view but not with the 2D plan view. Instances to describe the two proposed views are shown in table 2. Differences in attributes values are presented with red color. We can see that the 2D plan view is less adapted for those identified views tasks. For that reason, it is probably better in this case to choose the 3D view that appears more adapted.

In a view design process, our hypothesis is that one can apply the same operation to the other tasks in order to identify the best visualization techniques and propose adapted business views composition for each actor.

CONCLUSION

The use of 4D CAD in the AEC projects appears as being very helpful in resolving recurring problems in the sector such as the sequencing of the actors' intervention and the reservations' management. However, the existing visualization modes are not always sufficiently adapted to the needs of users. We proposed in this paper a first version of a "business view" metamodel, incorporating the key concepts found in the literature of HCI and Visualization fields. We suggested a method to adapted business views to the business tasks. In the case study, we showed that it is possible to propose different views to actors according to their tasks. With our metamodel we can model several possible views for a given task and compare them. The interest is to be able to choose the most appropriated according to the visualization needs related to the task.

In the future, we will work to define an experimental protocol, in order to consolidate, improve and validate the construction management process model according to a cooperative context. We will also work on the consolidation of the metamodel. Moreover, we have to describe better our three steps (business tasks, visualization needs and business views). In particular, it is important to deepen the second one (visualization needs) in order to create relationship with the two others. The corresponding model transformations should make our approach operational, and enable to develop a tool that could help to design business views.

Figure 3 :

 3 Figure 3: Collaborative process to manage actors' interventions sequencing

Figure 4 :

 4 Figure 4: Two possible views to support engineer task 6

Table 1 :

 1 Tasks and needs of information for each actor

		SUPERVISOR
	BUSINESS TASKS	INFORMATION NEEDS	POSSIBLE VIEWS
	Task 1: Create the building	Building elements,	-{List view(building_element), 2D plan view},
	représentation	Building representation	-{List view(building_element), 3D model view}
	Task 2: Link tasks to building	Tasks, building elements -{List view(building_element), List view(tasks)}
	elements		-{Table view(building_element, tasks)}
	Task 3: Link dates with tasks	Execution dates,	-{Table view(task, duration, date)}
		duration, tasks	-{List view(task), Table view(task, date, duration)}
			-{List view(task), Pert view(task, earlier date, late date)}
			-{Gantt view(task, beginind date, end date)}
	Task 4: Include reservations	Tasks, reservations	-{Table view(task, reservation location)}
		locations	-{(Table view(tasks, reservation), reservation sketch}
		ENGINEER
	BUSINESS TASKS	INFORMATION NEEDS	POSSIBLE VIEWS
	Task 1: Create tasks list	Tasks	-{List view(task)}
	Task 2: Examine the	Tasks, building	-{List view(task), 2D plan view(building_element)},
	representation conformity	representation	-{List view(task), 3D model view(building_element)}
	Task 3: Collect contractors'	Dates, tasks, reservations -{Table view(task, date, reservation)}
	proposals		-{Table view(task, date), Table view(task, reservation)}
			-{List view(reservation), Gantt view(task, beginind_date, end_date)}
			-{List view(reservation), Pert view(task, earlier_date, late_date)}
	Task 4: Check for conflicts	Tasks, durations,	-{Table view(task, duration, reservation)}
		reservations	-{Table view(task, duration), Table view (task, reservation)}
	Task 5: Define simulation	Dates, tasks, reservations -{Table view(task, date, reservation)}
	sequences		-{Table view(task, date), Table view (task, reservation)}
			-{List view(reservation), Gantt view(task, beginind_date, end_date)}
			-{List view(reservation), Pert view(task, earlier_date, late_date)}
	Task 6: Verify reservation	Building representation,	-{List view(reservation), 2D plan view(building_element)},
	validity	reservations	-{List view(reservation), 3D model view(building_element)}
	Task 7: Send reminders	Dates	-{List view(date)}
			-{Calendar view(date, event)}
	Task 8: Analyze feedbacks	Feedbacks, Dates	-{Table view(feedback, date)}
			-{List view(feedback), Calendar view(date, event)}
			-{Text view(feedback), Calendar view(date, event)}
		CONTRACTOR
	BUSINESS TASKS	INFORMATION NEEDS	POSSIBLE VIEWS
	Task 1: Plan execution dates	Dates, tasks	-{Table view(task, date)}
			-{List view(task), Calendar view(date, event)}
			-{Form view(task, date), Calendar view(date, event)}
	Task 2: Ask for reservation(s)	Tasks, reservation	-{Table view(task, reservation, location)}
		request	-{Form view(task, reservation, location)}
	Task 3: Work in situ	Reservation locations -{Table view(reservation, location), 2D plan view(building_element)}
			-{2D plan(building_element), reservation sketch(position, size)}
	Task 4: Send feedback	Feedback	-{List view(feedback)}
			-{Form view(feedback)}

Table 2 :

 2 instances for modeling and comparison of 3D view and 2D plan view

	3D view	2D plan view

ACKNOWLEDGMENT

This paper was supported by the AFR PhD Grants funded by the National Research Fund (FNR), Luxembourg.