Jean-Yves Didier
email: didier@iup.univ-evry.fr

Malik Mallem
email: mallem@iup.univ-evry.fr

Hybrid camera pose estimation combining square fiducials localisation technique and orthogonal iteration algorithm

Keywords: Augmented reality, pose estimation, fiducial localization, orthogonal iteration

Camera pose estimation from video images is a fundamental problem in machine vision and Augmented Reality (AR) systems. Most developed solutions are either linear for both n points and n lines, or iterative depending on nonlinear optimization of some geometric constraints. In this paper, we first survey several existing methods and compare their performances in an AR context. Then, we present a new linear algorithm which is based on square fiducials localisation technique to give a closed-form solution to the pose estimation problem, free of any initialization. We propose also an hybrid technique which combines an iterative method, in fact the orthogonal iteration (OI) algorithm, with our own closed form solution. An evaluation of the methods has shown that this hybrid pose estimation technique is accurate and robust. Numerical experiments from real data are given comparing the performances of our hybrid method with several iterative techniques, and demonstrating the efficiency of our approach.

Introduction

Camera pose estimation is the problem of determining the position and orientation of an internally calibrated camera from known 3D reference points and their images. It is essential to the so-called registration problem in an Augmented Reality context. Indeed, the objects in the real and virtual world must be properly aligned with respect to each other, which requires knowing the camera's pose. Accurate estimation of the 3D pose data will absolutely affect the accuracy and visual performance of virtual objects in the AR space.

In this paper we propose efficient real-time solutions to the camera pose estimation problem that can handle large camera displacements. While commercial products, are already available for offline camera pose estimation, efficient online registration remains an open issue because it must be fast and reliable. Many of the real-time algorithms described in the literature still lack robustness, tend to drift, and are prone to jitter that makes them unsuitable for applications such as Augmented Reality [START_REF] Azuma | Recent advances in augmented reality[END_REF] .

To efficiently solve the camera pose estimation problem, we have developed two approaches. The first one is an analytical solution from 4 points, it is based on square fiducials localization technique and returns a unique solution, free of any initialization. The second developed solution is an hybrid approach that combines the orthogonal iteration (OI) algorithm [START_REF] Lu | Fast and globally convergent pose estimation from video images[END_REF] with our analytical pose estimation technique. It is a real time extension of some of our previous works using OI for camera pose recovery using fiducials [START_REF] Ababsa | Robust camera pose estimation using 2d fiducials tracking for real-time augmented reality systems[END_REF] . As we will see, the performances of the OI algorithm are heavily affected by the initialization process, so it is very important that the initialization is close to the optimum. The original OI algorithm uses a weekperspective approximation to initialize the rotation matrix, so we propose to use our analytical solution to initialize the OI algorithm. This combination results in a system that does not suffer from any of the above difficulties and can deal with real-time aspect. Experimental results demonstrate that our hybrid algorithm is extremely efficient and converges in few iterations. It outperforms the original OI algorithm in terms of convergence and accuracy.

The remainder of this paper is organized as follows. First, we will study related works in camera pose estimation algorithms as well as augmented reality systems using fiducial detection. Then, section 3 is devoted to the formulation of the camera pose estimation problem and to the original OI algorithm review. Section 4 describes the developed square fiducials localization technique whereas section 5 will introduce an hybrid method composed of OI initialized using the algorithm detailed in the previous section. Experimental results are then presented in section 6, detailed performance analysis are given to compare our method to existing methods. Finally, section 7 provides conclusions and suggests some directions of our future works.

Related work

The camera pose computation is based on the extraction of geometric primitives which allow to match the 2D points (extracted from images) and the 3D points (known on the object). To deal with this problem, many approaches have been developed these last years, they can be subdivided into two main categories: 1) analytical methods based on a low number of points and/or lines, and 2) optimization methods based on minimizing an error criteria. Finally, we will survey some augmented reality localization tools based on fiducials tracking. ijig Hybrid camera pose estimation combining square fiducials localisation and orthogonal iteration 3

Analytical methods

The analytical methods use a low number of points and have a finite set of solutions. Their complexity is generally low, and when implemented their computing time is short. The pose estimated by these methods is generally accurate. However, the pose computation is dependent on the extraction process of the image points to be matched with points of the 3D object. According to the quality of the acquired image and the processing carried out, these methods can produce less accurate results. Many analytical methods were proposed these twenty last years. Using 3 points, the problem generically has four possible solutions. Haralick et al. [START_REF] Haralick | Analysis and solutions of the three point perspective pose estimation problem[END_REF] review many old and new variants of the basic 3-points method and carefully examine their numerical stabilities due to different orders of substitution and elimination. Lastly, in 1992, Dementhon and Davis also proposed 5 a three points based pose estimation technique. They have shown that by using two perspective approximations: paraperspective and orthoperspective, 2D lookup tables can be built and can be used to reduce the number of runtime floating-point operations needed to compute pose estimates. If a unique solution is required, additional information must be given, a fourth point generally suffices. But there are certain degenerate cases for which no unique solution is possible. All these critical configurations for which multiple distinct or coinciding (unstable) solutions occur are known. In 1981, Fischler and Bolles propose several methods to resolve the pose estimation problem. In their paper on the RANSAC method 9 (RAndom SAmple Consensus), they have shown that, knowing the coordinates of a number of 3D points and their corresponding image points, it is possible to compute the pose of the camera using a geometric closed-form technique. They also described results on the conditions under which multiple solutions exist for various numbers of correspondences between image and target, particularly for the Perspective-4-Points (P4P) problem. They extended their solution to 4 points by taking subsets and using consistency checks to eliminate the multiplicity for most point configurations. Horaud et al. [START_REF] Horaud | Object pose: The link between weak perspective, paraperspective, and full perspective[END_REF] developed a closed form solution on 4 points which avoids this reduction to a 3 points solution. These closed form methods can be applied to more points by taking subsets and finding common solutions to several polynomial systems, but the results are susceptible to noise and the solutions ignore much of the redundancy in the data. Hung et al. [START_REF] Hung | Passive ranging to known planar point sets[END_REF] have proposed in 1985 a method for fiducial pose estimation using 4 non-aligned and coplanar points. Quan and Lan [START_REF] Quan | Linear n-point camera pose determination[END_REF] propose a family of linear methods that yield a unique solution to 4-and 5-points pose determination for generic reference points. They also extended their 5-points method to handle more than five points. Their method does not degenerate for coplanar configurations and even outperform the special linear algorithm for coplanar configurations in practice. Furthermore, methods for pose estimation using line segments instead of points as image features have also been developed. Dhome et al. [START_REF] Dhome | Determination of the attitude of 3d objects from a single perspective view[END_REF] developed algebraic solutions for 3-lines algorithms. Only three edges of the object are used to estimate the pose. A polynomial of degree 8 is then resolved and the obtained solutions sorted according to the validity of the edge's configuration. Liu, et al. [START_REF] Liu | Determination of camera location from 2d to 3d line and point[END_REF] combined points and line segments into the same pose estimation procedure.

Optimization methods

As the analytical methods are quite dependent on the quality of the acquired image. The solution thus is to carry out the pose computation on a larger set of points. However, For more than four points, closed form solutions do not exist. So, it is necessary to formulate pose estimation as a nonlinear least-squares problem of a polynomial equation in the image observables and the pose parameters and to solve it by nonlinear optimization algorithms, most typically, the Gauss-Newton method. Iterative solutions are a subset of optimization methods and are based on minimizing the error in some nonlinear geometric constraints. The pose is computed first once, then an iterative algorithm progressively refines the estimate. These methods allow to obtain a high accuracy of the camera localization within its environment. However, each iteration carried out involves an additional cost in computing execution time of the pose estimation. So, it is necessary to take into account this constraint in order to optimize the iteration number and the operations carried out during each iteration. Kumar and Hanson [START_REF] Kumar | Robust methods for estimaging pose and a sensitivity analysis[END_REF] have developed an iterative algorithm based on constraints on image lines using an update step adapted from Horn's solution [START_REF] Horn | Closed-form solution of absolute orientation using orthonomal matrices[END_REF] of the relative orientation problem. Dementhon and Davis 6 initialize their iterative scheme (named POSIT) by relaxing the camera model to scaled orthographic. It uses at least four non coplanar points. Haralick et al. [START_REF] Haralick | Pose estimation from corresponding point data[END_REF] introduced also an iterative pose estimation algorithm which simultaneously computes both object pose and the depths of the observed points. Lu et al. [START_REF] Lu | Fast and globally convergent pose estimation from video images[END_REF] reformulate the pose estimation problem as that of minimizing an object-space collinearity error. They combine a constraint on the world points, effectively incorporating depth, with an optimal update step in the iteration. These iterative approaches typically suffer from slow convergence for bad initialization, convergence to local minima and the requirement of a large number of points for stability.

Table 2.2 summarizes the properties of the various pose estimation techniques surveyed above, it gives some practical advice allowing to choose the appropriate approach in a given situation.

The use of fiducials in Augmented Reality

At the same time, in augmented reality projects, coded fiducials techniques were applied to determine feature points and estimate camera pose in real-time in a video sequence. Amongst those projects some are using circular coded fiducials like Cho et al. [START_REF] Cho | Multi-ring color fiducial systems for scalable fiducial tracking augmented reality[END_REF] or later the Intersense system 20 . Such fiducial shape implies that there are several of them stuck on an object to recover the camera pose. That's why the most current systems in augmented reality are using square fiducials. This shape gives 4 points per fiducials, which is enough to compute the camera pose relative to the fiducial even if there is only one of them. The number of ijig Hybrid camera pose estimation combining square fiducials localisation and orthogonal iteration 5 [START_REF] Lu | Fast and globally convergent pose estimation from video images[END_REF] robust to noise systems using such fiducials have increased in the past ten years as well as interest is growing in using them. We can cite the Matrix system [START_REF] Rekimoto | Matrix: A realtime object identification and registration method for augmented reality[END_REF] which became later the Cybercode system [START_REF] Rekimoto | Cybercode: designing augmented reality environments with visual tags[END_REF] . More and more augmented reality projects are using the ARToolkit library 16 10 , which is working with the same kind of principle and which is available freely to public. To these systems, we must add some that were developed by several laboratories as we can conclude from reading Zhang [START_REF] Zhang | Visual marker detection and decoding in ar systems: A comparative study[END_REF] comparative study of 4 different systems. Recently some work has been performed to increase the robustness of fiducial recognition and code extraction 21 8 . Some of these fiducials are shown in figure 1. This illustrates the potential interest of fiducials in augmented reality applications. We will now study in detail the pose estimation problem related to the extraction of feature points from ARToolkit-like markers. First, we will study a generic iterative algorithm which the OI. We will then expose an analytic pose estimation method based on particular geometrical constraints of the square fiducials and then study a variation combining the two previous methods.

Formulation of the pose estimation problem

Given a calibrated camera and correspondences between 3D reference points and 2D points found in the image, the goal in pose determination is to find the rotation and translation matrices which map the world coordinate system to the camera coordinate system. In this paper we assume a perspective projection model. Let p i = (x i , y i , z i ) t , i = 1, ..., n, n ≥ 3 a set of 3D non-collinear reference points defined in an object-centered reference frame, the corresponding camera-space coordinates q i = (x , i , y , i , z , i ) are given by :

q i = Rp i + t (1)
where R = (r t 1 , r t 2 , r t 3 ) t and t = (t x , t y , t z ) t are a rotation matrix and a translation vector, respectively.

Let the image point v i = (u i , v i , 1) t be the projection of p i on the normalized plane. Using the camera pinhole model, the relationship between v i and p i is given by :

u i = r t 1 p i + t x r t 3 p i + t z v i = r t 2 p i + t y r t 3 p i + t z (2)
or

v i = 1 r t 3 p i + t z (Rp i + t) (3)
which is known as the collinearity equation. This equation is used in a different manner according to the desired approach to be implemented.

For linear solutions

Each pair of correspondences p i → v i and p j → v j gives a constraint on the unknown camera-point distances d i = p ic (cf. Fig. 1) :

d ij 2 = d i 2 + d j 2 -2d i d j cosθ ij (4)
where d ij = p ip j is the known inter-point distance between the i-th and j-th reference points and θ ij is the 3D viewing angle subtended at the camera center by the i-th and j-th points. The cosines of this angle is directly computed from the image points and the calibration matrix of the internal parameters of the camera [START_REF] Quan | Linear n-point camera pose determination[END_REF] . Using the points geometric constraints for 3 or 4 points allows to obtain a polynomial system for the unknown distances d i . Linear algebra is often used to resolve this system in closed form [START_REF] Ansar | Linear pose estimation from points or lines[END_REF][START_REF] Quan | Linear n-point camera pose determination[END_REF] . The recovered camera-point distances d i are used to estimate the coordinates of the 3D reference points in a camera-centered 3D frame. To find the camera pose, the rigid 3D motion that best aligns these points with their known world-frame coordinates is then estimated.

For solutions using optimization techniques

The pose estimation problem is to develop an algorithm for finding the rigid transform (R, t) that minimizes some form of accumulation of the errors, generally the summation of squared errors of the collinearity equations (see Fig. 2). It is formulated as the problem of optimizing the following objective function :

n i=1 ûi - r t 1 p i + t x r t 3 p i + t z 2 + vi - r t 2 p i + t y r t 3 p i + t z 2 (5)
Given observed image points vi (û i , vi , 1) t . The minimization is over image-space collinearity. To resolve this problem, two commonly optimization algorithms are used: the Gauss-Newton method and the Levenberg-Marquardt method.

Analytical square fiducials pose estimation

The aim is to recover the camera pose relative to a square fiducial. We will use the geometry constraints of this marker to compute its localization.

In this section, we will assume that the camera is calibrated (its intrinsic parameters are known). At the same time, we assume that the fiducial is already detected and the matching of 2D/3D points is already done.

First we will introduce some notations, then detail our algorithm and describe how we will be able to use it with orthogonal iteration.

Notations

We will use three different frame coordinates. The first one is the world space coordinates. They're computed relative to the fiducial. The center of the fiducial is the origin of world space coordinates. The second one is the camera space coordinates. The last one is the image space coordinates. The coordinates of a 3D point M are written (X, Y, Z) in world coordinates, (x, y, z) in camera space and (u, v) are the coordinates of the corresponding point in the image plane. The four corners of the fiducials are called A, B, C and D as shown in Fig. 3.

Pin-hole camera model

The pin-hole camera model is a widely spread model for camera calibration. In our case, we will assume that the optical distortion are already corrected. In its simplest formulation, the pin-hole model, when we're writing the relations in camera space are linking an image point m with image coordinates (u, v) to a 3D point M of coordinates (X, Y, Z) in world space by the following relations :

X = Z f k u (u -u 0 ) Y = Z f k v (v -v 0 ) (6)
In our method, we will first apply an arbitrary depth estimation of our points A, B, C and D in camera space using geometrical constraints of our fiducial. Then we will compute the real depth using metric constraints.

Applying geometrical constraints

Since our fiducial has a square geometry, we can write the following property : We can multiply the two first lines of the equation by f (the camera focal length parameter) and apply 6 :

--→ AB = --→ DC ⇔   X B -X A Y B -Y A Z B -Z A   =   X C -X D Y C -Y D Z C -Z D
   Z B ku (u B -u 0 ) -Z A ku (u A -u 0 ) Z B kv (v B -v 0 ) -Z A kv (v A -v 0 ) Z B -Z A    =    Z C ku (u C -u 0 ) -Z D ku (u D -u 0 ) Z C kv (v C -v 0 ) -Z D kv (v D -v 0 ) Z C -Z D    (7)
If we look at the first line, we notice we can simplify it and rewrite it like this :

u B Z B -u A Z A -u 0 (Z B -Z A ) = u C Z C -u D Z D -u 0 (Z C -Z D ) (8)
Since Z B -Z A = Z C -Z D , we can simplify again this line. We can do the same for the second line and then we obtain :

  u B Z B -u A Z A v B Z B -v A Z A Z B -Z A   =   u C Z C -u D Z D v C Z C -vDZ D Z C -Z D   (9)

Arbitrary relative depth estimation

To differentiate the arbitrary depth to the real ones, we will call them

Z ′ A , Z ′ B , Z ′ C and Z ′ D .
In the first move, we will arbitrarily set Z ′ A to 1, so that we will be able to compute Z ′ B , Z ′ C et Z ′ D , we will then have to solve the following system :

  u B -u C u D v B -v C v D -1 1 -1     Z ′ B Z ′ C Z ′ D   =   v A u A -1   (10)
We will then obtain :

Z ′ B = 1 δ [u A (v C -v D )+v A (u D -u C )-(u C v D -u D v C )] Z ′ C = 1 δ [u A (v B -v D )+v A (u D -u B )+(u D v B -u B v D )] Z ′ D = 1 δ [u A (v B -v C )+v A (u C -u B )-(u B v C -u C v B )] δ = (u C v D -v C u D ) + (u D v B -u B v D ) + (u B v C -u C v B )

Real depth estimation

The arbitrary depths we obtained are related to the real depth by a scale factor, therefore we note r 1 as the ratio

Z A /Z C = Z ′ A /Z ′ C and r 2 the ratio Z B /Z D = Z ′ B /Z ′ D .
Since we can recover the arbitrary depth, we know the values of the ratios.

We will now express some equations related to r 1 . The same principle could be applied to r 2 . Using equations 6 we can write :

X A = Z A αu (u A -u 0 ) Y A = Z A αv (v A -v 0 ) X C = Z C αu (u C -u 0 ) Y C = Z C αv (v C -v 0 ) (11)
Where

α u = f k u and α v = f k v .
We know the value of -→ AC since the metric constraints of our fiducial is known. Using this constraint and the value of r 1 , we can express the value of Z A :

Z A = - -→ AC (r 1 -1) 2 + (f (r 1 )) 2 + (g(r 1 )) 2 (12)
with

f (r 1 ) = r 1 (u C -u 0 ) -(u A -u 0 ) α u (13) g(r 1 ) = r 1 (v C -v 0 ) -(v A -v 0 ) α v (14)
Once Z A is computed, we can obtain Z C using r 1 . We can perform the same process to obtain Z B and Z D values. By using 11, we can determine the missing coordinates of points A, B, C and D.

Pose estimation

When the real depth are known, we can determine the translation and the rotation associated to our fiducial in camera space. The fiducial origin is placed in its center which coordinates are computed using those of A, B, C and D. The fiducial's center coordinates are also the translation between the camera and the fiducial.

We can then compute a rotation matrix (we will note it R 3×3 ) its lines will be noted r 1 * , r 2 * , r 3 * and will be equal to the following :

r 1 * = --→ AB --→ AB r 2 * = -→ AC -→ AC r 3 * = r 1 * ∧ r 2 * ( 15
)
The camera pose is obtained by inverting the found transformation. Once the pose is known, we can combine this algorithm with OI by feeding the initialization step using the newly computed pose. We will now see how it benefits to the OI algorithm.

Hybrid Solution for pose estimation

In this section we propose an hybrid approach for camera pose estimation that combines the orthogonal iteration (OI) algorithm [START_REF] Lu | Fast and globally convergent pose estimation from video images[END_REF] with our analytical pose estimation technique described above. We propose to use the (OI) for its accuracy, global convergence and rapidity. Another strong point is it is taking into account the structure of the rotation parameter which is not achieved when using standard optimization method such as Levenberg-Marquart or Gauss-Newton.

The OI algorithm overview

The starting point for the algorithm is to state the pose estimation problem using the following object-space collinearity error vector (cf. Fig. 4) :

e i = I -Vi (Rp i + t) ( 16
)
where Vi is the observed line-of-sight projection matrix defined as :

Vi = vi vt i vt i vi (17)
The algorithm minimize the sum of the squared error

E(R, t) = n i=1 e i 2 = n i=1 I -Vi (Rp i + t) 2 (18)
over R and t. Given a fixed rotation R, the optimal value of t can be computed in closed form as :

t(R) = 1 n   I - 1 n j Vj   -1 j Vj -I Rp j (19)
Thus, equation ( 18) can be written :

E(R) = n i=1 Rp i + t(R) -q i (R) 2 (20)
The matrix R can be computed iteratively as follows : First, assume that the kth k) , and q k+1) , is determined by solving the following classical absolute orientation problem [START_REF] Horn | Closed-form solution of absolute orientation using orthonomal matrices[END_REF] :

estimate of R is R (k) , t (k) = t R (
(k) i = R (k) p i + t (k) . The next estimate, R (
R (k+1) = arg min R n i=1 Rp i + t -Vi q (k) i 2 (21)
The next estimate of translation is then computed using (19).

t (k+1) = t R (k+1) (22)
The process is repeated. A solution R * to the pose estimation problem using the (OI) algorithm is defined to be a fixed point to (21), that is, R * satisfies :

R * = arg min R n i=1 Rp i + t -Vi (R * p i + t(R * )) 2 (23)

Initialization of the OI algorithm

The OI algorithm is initiated using a weak perspective approximation. Weak perspective assumes that the object points lie in a plane parallel to the image plane passing through the origin of the object frame [START_REF] Horaud | Object pose: The link between weak perspective, paraperspective, and full perspective[END_REF] . In this case, the image points v i are treated as the first hypothesized scene points. This leads to an absolute orientation problem between the set of 3D reference points p i and the set of image points v i considered as coplanar 3D points. This initial absolute orientation problem allows to compute the initial rotation matrix R (0) and thus to start the (OI) algorithm.

The performances of the OI algorithm are heavily affected by the initialization process, so it is very important that the initialization is close to the optimum. We propose to use our square fiducials localization method to compute a good initial guess better than given by the weak perspective approximation. This will considerably improve the pose solution accuracy and computing time as demonstrated in section 6.

Experimental results

In this section, we will compare the results given by OI method, our pose estimation method for square fiducials, the hybrid method using OI (we will call it later Customized OI or C-OI) and initialized using our analytical method and a ground truth : the least mean squares (LMS) algorithm for pose estimation. The three first methods are using the four corners of a detected fiducial (Fig. 5) whereas the LMS needs more points. To use this last one, we had to detect internal corners of the fiducial.

We will compare the results given by the three methods according several criteria : • Reconstruction error, i.e. the error in pixels between reprojection on the image of the fiducial model, • Generalization error, i.e. the error in pixels when we reproject other objects on the images according to the pose computed using only one fiducial, • Distance estimation error, i.e. the metric error we measure between the estimated pose and the actual one.

• Computation time,
Each study is performed by computing the pose of only one fiducial, placing us in the worst case scenario of fiducials detection.

The test-bench we're using for experiments is composed of one computer PIII 1.1 GHz, a camera Sony XC-555P, a Matrox Meteor II framegrabber. The whole is orchestrated by a linux operating system. The camera is calibrated using Zhang method [START_REF] Zhang | Flexible camera calibration by viewing a plane from unknown orientations[END_REF] . Intrinsic parameters are displayed in table 2.

First series of results

For the first series of experiments, we hold the camera by hand and we're freely moving around a set of two square fiducials of 6cm side-length. One is needed to compute the camera pose and the reconstruction error. During the pose estimation, the computation time is also determined. The projection of the second fiducial on the image is performed to determine the generalization error. It leads to the figures given in table 3. The best values for each criterion of comparison is highlighted in green whereas the worst are the red ones. The angular error given is extrapolated from the results given by generalization error study.

If we have a first look on these values, one can notice that our direct pose estimation algorithm is the fastest as expected since it is a specific method developed for square fiducials. At the same time, the LMS is quite slow. This is partly due to the additional corners detection. The reconstruction errors are roughly the same for each algorithm and looks like in figure 5 whereas it drastically changes for generalization error. The customized-OI method seems to have the best performances on generalization error contrary to the OI algorithm with its standard initialization which has one of the worst performances. This is mainly due to the fact that OI is not designed for solving the camera pose problem using coplanar points as it is the case in our application. It is a degenerate case where OI can converge to two different solutions. If the initialization of the pose estimation is not close enough to the real solution then OI will be able to converge to the wrong solution, hence having poor results for generalization error.

If we plot the generalization error according to distance separating two fiducials, Hybrid camera pose estimation combining square fiducials localisation and orthogonal iteration 15

we will have the curve shown in figure 6. It shows that, for some series, OI has performed a wrong pose estimation, resulting in a jittering curve. Mean performances of our analytical algorithm and customized-OI are basically not very different unless we separate the two fiducials by a distance of seven times the square side size of each fiducial. This is mainly due to the fact that our direct algorithm doesn't return a real rotation matrix but an approximation of it, whereas OI is intended to optimize such a matrix. Generalisation error (pixel)

Ratio square fiducial size / distance between fiducial centers

Analytical method Orthogonal Iteration (OI)

Customized OI Least Mean Square Fig. 6. Generalization error according to distance separating fiducials

Distance estimation error

For this experiment, we changed the square fiducial size (20cm side-length). The camera was mounted on a XY-axes robot realizing the setup from Fig. 7. The robot coordinate frame and the camera frame were calibrated. The robot positions taken from a given trajectory (Fig. 8 are then giving the actual camera pose we can compare with our pose estimation algorithms. Fig. 9 is a scatter plot of the pose estimations we obtained using the different methods. One can notice that the Direct and OI methods are having an error of distance estimation around two percents whereas the LMS method has a rapidly increasing distance error estimation.

Since the scatter plot is not easily readable, we separated data into ten classes (Fig. 9(c)) to elaborate a simplified graph (Fig. 9(b)). The middle of each bar is the mean value for the distance evaluation in a given class and the two extremities are showing the standard deviation around the computed mean. It particularly shows that the pose estimations coming from our analytical method is more sensible to noise than customized-OI or OI itself.

Effects of OI customization

By studying the provided results, the customized OI has several strong points genuine OI and our direct analytical method do not have. First of all, C-OI is more stable than the two other algorithms, providing a more accurate pose estimation with an increase of the accuracy for objects far from the vertices of the fiducials used to estimate the camera pose.

The second one is that the C-OI is compensating some of the side effects of OI, that is to say the initialization problem as well as the computation time. The provided initialization is close enough to the pose estimation we want to reach so that the OI converge about 30 percents faster to the right solution.

However, even if the C-OI has some interesting features, the computation time cost to increase accuracy is five times bigger than the basic analytical method.

Conclusion

In this paper, we proposed the use of a square fiducials pose estimation to compute a good initial guess for the OI method. According to evaluations performed on 4 different algorithms, this customized-OI is presenting the following strong points :

• the distance evaluation accuracy has less than two percents of relative error, • the rotation estimation is accurate and optimized using the OI algorithm, • its computation speed is quite a good compromise between speed and accuracy, the pose being computed in about 100 µs, • this method is more stable than all compared method. This study will help us to establish guidelines in using fiducials in augmented reality projects according to the requirements of applications in terms of tracking, robustness and accuracy in overlaying virtual images on real images as well as accuracy of localization. Some of them would answer to questions such as how many markers should we place, where and what size should they have ?

Further area of investigation will be towards the improvement of the robustness of our square fiducial localization algorithm, especially in case of occlusions of a part of the fiducial. We will also try to combine this method with markerless algorithms to bypass the drawbacks of both family of methods.

Fig. 1 .

 1 Fig. 1. Some examples of fiducials frequently used in augmented reality systems

Hybrid camera pose estimation combining square fiducials localisation and orthogonal iteration 7 Fig. 2 .

 72 Fig. 2. Geometry of camera pose from points correspondences

  Fig. 3. Notations

  estimation combining square fiducials localisation and orthogonal iteration 9

Fig. 4 .

 4 Fig. 4. The reference frames

Fig. 5 .

 5 Fig. 5. Registration sample on a coded fiducial

Fig. 7 .

 7 Fig. 7. Robot test-bench for distance estimation error

October 12 ,

 12 2007 9:53 WSPC/INSTRUCTION FILE ijig Hybrid camera pose estimation combining square fiducials localisation and orthogonal iteration 17

Fig. 8 .

 8 Fig. 8. Camera trajectory in the XY robot plane

  Scatter plot of the measured distance error for each computed pose Classes and their population.

Fig. 9 .

 9 Fig. 9. Distance estimation error, 1957 pose estimations

Table 1 .

 1 Summary of camera pose estimation techniques.

	Techniques	Rely on	Failure mode	Initialization Accuracy
	Haralick et al. 12	Linear -3 points	Noisy data +	No	Can jitter
	DeMenthon and Davis 5		occlusion
	Horaud et al. 13	Linear -4 and 5	Noisy data +	No	Can jitter
	Quan and Lan 22	points	occlusion
	Fischler and Bolles 9	Linear -4 points	Robust to noise No	Accurate
		and more	and occlusion
	Dhome et al. 7	Linear -3 edges	Noisy data +	No	Can jitter
			occlusion
	Kumar and Hanson 17	Iterative -3 lines	Robust to noise Yes	Highly accurate
			and occlusion
	Dementhon and Davis 6 Iterative -4 non	Fast motion +	No	Accurate
		coplanar points	noisy data
	Haralick et al. 11	Iterative -3 points Fast motion +	Yes	Highly accurate
	Lu et al.

Table 2 .

 2 Hybrid camera pose estimation combining square fiducials localisation and orthogonal iteration 13 Intrinsic parameters of the Sony XC-555P used in experiments.

	Image size		736×571
	Projection parameters	Distortion parameters
	Scale factors	Radial distortion coefficients
	α u	706.1 k 1	-0.2279
	α v	731.1 k 2	0.1479
	Optical center projection Tangential distortion coefficients
	u 0	388.0 p 1	-0.0007985
	v 0	269.6 p 2	0.0006245

Table 3 .

 3 Raw results on the different experiments performed.

J.-Y. Didier, F. Ababsa, M. Mallem

J.-Y. Didier, F. Ababsa, M. Mallem

J.-Y. Didier, F. Ababsa, M. Mallem

J.-Y. Didier, F. Ababsa, M. Mallem

J.-Y. Didier, F. Ababsa, M. Mallem

J.-Y. Didier, F. Ababsa, M. Mallem

J.-Y. Didier, F. Ababsa, M. Mallem

J.-Y. Didier, F. Ababsa, M. Mallem

J.-Y. Didier, F. Ababsa, M. Mallem

J.-Y. Didier, F. Ababsa, M. Mallem


Maxime Guye
email: maxime.guye@ap-hm.fr

Fabrice Bartolomei

Jean-Philippe Ranjeva

Malformations of cortical development: the role of 7 Tesla magnetic resonance imaging in diagnosis

Keywords: 7 Tesla MRI, Ultra-high field MRI, Malformation of cortical development, Focal cortical dysplasia, Polymicrogyria, Periventricular nodular heterotopia

Comparison studies between 7T and 1.5 or 3T magnetic resonance imaging (MRI) have demonstrated the added value of ultra-high field (UHF) MRI to better identify, delineate and characterize malformations of cortical development (MCD), and to disambiguate doubtful findings observed at lower field strengths. High-resolution structural sequences such as magnetization-prepared two rapid acquisition gradient echoes (MP2RAGE), fluid and white matter suppression MP2RAGE (FLAWS), and susceptibility-weighted imaging (SWI) appear to be key to the improvement of MCD diagnosis in clinical practice.

7T MRI offers not only images of high resolution and contrast but also provides many quantitative approaches capable of acting as more efficient probes of microstructure and ameliorating the categorization of MCDs. Postprocessing of multiparametric ultra-high resolution and quantitative data may also be used to improve automated detection of MCD via machine learning.

Therefore, 7T MRI can be considered as a useful tool in the presurgical evaluation of drug-resistant partial epilepsies, particularly, but not exclusively, in cases of normal appearing conventional MRI. It also opens many perspectives in the fields of in vivo histology and computational anatomy.

Introduction

Magnetic resonance imaging (MRI) is tightly linked to the history and classification of malformations of cortical development (MCD). Depicting, characterizing, and accurately delineating MCDs is particularly crucial in drug-resistant partial epilepsies (DRPE) in which MCD are common causes of epileptogenic lesions, particularly in children. Currently, using optimal protocols, conventional MRI at 1.5 or 3T allows for identification and classification of most MCDs [START_REF] Guerrini | Malformations of cortical development: clinical features and genetic causes[END_REF].

However, in those patients presenting with refractory epilepsy, from 15 to 40% are still MRI-negative even with adapted protocols, and a normal appearing MRI has been identified as a negative predictive factor for surgery in several studies [START_REF] Guerrini | Malformations of cortical development: clinical features and genetic causes[END_REF][2][3] [START_REF] Mcgonigal | Stereoelectroencephalography in presurgical assessment of MRI-negative epilepsy[END_REF]. Conversely, identification of focal cortical dysplasia, particularly type II, has been demonstrated to be a positive factor for surgical outcome [START_REF] Téllez-Zenteno | Surgical outcomes in lesional and non-lesional epilepsy: A systematic review and meta-analysis[END_REF] [START_REF] Edelvik | Long-term outcomes of epilepsy surgery in Sweden: A national prospective and longitudinal study[END_REF]. In addition, complete resection of malformations has been consistently associated with better outcomes [START_REF] Oluigbo | The influence of lesion volume, perilesion resection volume, and completeness of resection on seizure outcome after resective epilepsy surgery for cortical dysplasia in children[END_REF] [START_REF] Jalloh | The role of surgery in refractory epilepsy secondary to polymicrogyria in the pediatric population[END_REF]. In a retrospective study, Fois et al. analyzed 612 patients admitted for presurgical assessment in a tertiary center [START_REF] Fois | Predictors for being offered epilepsy surgery: 5-year experience of a tertiary referral centre: Table 1[END_REF]. Using a multivariate regression model, non-lesional MRI was one the three factors (with bilateral lesions and extra-temporal epilepsy) that significantly decreased the probability of being operated on. It is actually very likely that many patients are referred to surgery or to specialized centers only when a visible lesion is present on MRI, even if effective surgery is possible in patients with a normal appearing MRI [START_REF] Mcgonigal | Stereoelectroencephalography in presurgical assessment of MRI-negative epilepsy[END_REF].

As such, although the surgical management of patients with negative MRI has been improved over in recent years [START_REF] Baud | European trends in epilepsy surgery[END_REF], the yield of MRI in the definition and delimitation of MCD responsible for DRPE is still a key factor in presurgical assessment. In this context, ultra-high field (UHF) MRI -particularly at 7T -can play a major role. In this paper we will review the literature and show an illustrative case, demonstrating the added value of UHF as well as the perspectives it offers in the diagnosis of MCD.

Principal MCD responsible for DRPE and usual radiological features

Focal cortical dysplasia

Within the broad spectrum of MCDs, focal cortical dysplasias (FCDs) represent the vast majority of malformations responsible for DRPE considered for surgery. FCDs are localized cortical malformations encompassing a large spectrum of histopathological types [START_REF] Blümcke | The clinicopathologic spectrum of focal cortical dysplasias: a consensus classification proposed by an ad hoc Task Force of the ILAE Diagnostic Methods Commission[END_REF]. Type I FCDs are characterized by localized radial (type Ia) or tangential (type Ib) cortical lamination abnormalities (type Ic referring to lesions with both lamination anomalies). Type II are characterized by disrupted cortical lamination and cytological abnormalities which differentiate type IIa (presenting with dysmorphic neurons) from type IIb (presenting with dysmorphic neurons associated with balloon cells). Type III are characterized by cortical lamination abnormalities associated with another principal lesion generally located in the same cortical region or lobe. Depending on the associated lesion, four subtypes are identified: type IIIa is associated with hippocampal sclerosis, type IIIb is associated with tumors, type IIIc is associated with vascular malformations and type IIId is associated with another type of lesion. MRI has contributed greatly to the definition of FCDs, particularly in type II FCDs which exhibit a typical radiological semiology including: cortical thickness alterations, signal intensity changes (mainly hypersignal on T 2 -weighted images and usually better depicted in fluid-attenuated inversion recovery (FLAIR) sequences), grey/white matter interface blurring (better seen on T 1 -weighted images), gyration and sulcation (sulcal depth and shape) anomalies [START_REF] Mellerio | Optimizing MR Imaging Detection of Type 2 Focal Cortical Dysplasia: Best Criteria for Clinical Practice[END_REF]. Signal hyperintensity can involve both cortical and subcortical regions, the hypersignal traversing white matter from the periventricular region to the abnormal cortex ("transmantle sign") being prototypical of FCD type IIb.

Type I FCDs are more often MRI-negative and present with more subtle abnormalities compared to type II. Type III presentation depends on the associated lesion. Type IIIa is more often identified by a blurred grey-white matter interface than signal intensity or gyration abnormalities [START_REF] Fauser | Long-term seizure outcome in 211 patients with focal cortical dysplasia[END_REF].

Polymicrogyria with or without schizencephaly

Polymicrogyria (PMG) is a malformation characterized by excessive folding of small convolutions.

These microgyri surround the cleft when associated with schizencephaly.

With a sufficiently high resolution, MRI may provide evidence of cortical overfolding (better seen on T 1 -weighted images). Signal in the cortex is usually not modified on T 2 -weighted images [START_REF] Guerrini | Malformations of cortical development: clinical features and genetic causes[END_REF].

However, PMG often appears as a slight cortical thickening and is sometimes misdiagnosed as pachygyria. The classical location of PMG in the perisylvian region(s) can extend to other regions, and is often bilateral (either symmetrical or asymmetrical), but can be unilateral. Other forms, generally symmetrical and bilateral, involve the frontal lobes, posterior regions, parasagittal regions or are generalized. This MCD, often broader than FCD and often involving eloquent cortex, can be considered for surgery with a careful presurgical evaluation [START_REF] Maillard | Stereoelectroencephalography and surgical outcome in polymicrogyria-related epilepsy: A multicentric study: SEEG and Epilepsy Surgery in PMG[END_REF]. A fine delineation of the entire abnormal cortex for potential complete resection is useful [START_REF] Jalloh | The role of surgery in refractory epilepsy secondary to polymicrogyria in the pediatric population[END_REF] even if good results may be obtained with partial resection when guided by stereo-electroencephalography (SEEG) [START_REF] Maillard | Stereoelectroencephalography and surgical outcome in polymicrogyria-related epilepsy: A multicentric study: SEEG and Epilepsy Surgery in PMG[END_REF].

Periventricular nodular heterotopia

Periventricular nodular heterotopias (PNHs) are characterized by single or multiple agglomerates of normal neurons in ectopic position lining the ventricular wall and protruding into the ventricle. MRI can identify grey matter nodules located bilaterally in its typical form or in posterior regions.

Association with other malformations including PMGs has also been reported [START_REF] Guerrini | Malformations of cortical development: clinical features and genetic causes[END_REF].

PHNs are difficult cases for surgery and require invasive recordings with sampling of both relevant nodules and adjacent cortex [START_REF] Pizzo | Epileptogenic networks in nodular heterotopia: A stereoelectroencephalography study[END_REF]. Recent conservative approaches such as radio-frequency thermocoagulation of selected nodules during SEEG procedures have been proposed as potential efficient alternatives [START_REF] Mirandola | Stereo-EEG: Diagnostic and therapeutic tool for periventricular nodular heterotopia epilepsies[END_REF]. Therefore, depiction of nodules is a prerequisite for optimal presurgical assessment.

Key sequences of structural 7T MRI for MCD diagnosis

Given higher signal-to-noise ratio (SNR) -with a 2 to 6-fold increase in the brain -and higher contrast-to-noise ratio (CNR), UHF significantly improves image resolution and sensitivity compared to 1.5 and 3T [START_REF] Trattnig | Key clinical benefits of neuroimaging at 7 T[END_REF]. However, UHF also suffers from drawbacks, particularly transmit field (B 1 ) inhomogeneities in structural MRI. In order to both overcome the drawbacks of UHF and to take advantage of signal and contrast increases, several sequences have been developed and implemented at 7T. Of particular interest for structural imaging, T 1 -weighted double-inversion recovery sequences such as Magnetization Prepared with 2 RApidely Acquired Gradient Echos (MP2RAGE) [START_REF] Marques | MP2RAGE, a self bias-field corrected sequence for improved segmentation and T1-mapping at high field[END_REF] and fluid and white matter suppression MP2RAGE (FLAWS) [START_REF] Tanner | Fluid and white matter suppression with the MP2RAGE sequence[END_REF] allow for high-resolution images while mitigating transmit field inhomogeneities responsible for signal loss in some regions of the brain. The MP2RAGE sequence offers T 1 -weighted images, quantitative T 1 mapping, and a set of images obtained with a specific inversion time for which grey and white matter have the same longitudinal magnetization magnitude but with opposite signs (Fig. 1). This results in a null signal in the voxels where the same amount of grey and white matter is present. Thus, grey/white matter interfaces appear as hyposignal, clearly delineating grey/white matter transitions. The use of this kind of inversion time as also been called tissue-border-enhancement (TBE) and may be used in other types of sequences [START_REF] De Ciantis | Ultra-High-Field MR Imaging in Polymicrogyria and Epilepsy[END_REF]. Both FCD depiction (Fig. 1) as well as PMG delineation [START_REF] De Ciantis | Ultra-High-Field MR Imaging in Polymicrogyria and Epilepsy[END_REF] can be aided/improved by this kind of protocol.

The FLAWS sequence uses two inversion times selected for the suppression of both cerebrospinal fluid (CSF) and white matter, resulting in 'pure' grey matter images. The use of this sequence in MCD

diagnosis has yet to be published. We propose to use FLAWS in case(s) of suspected FCD, as it can identify the "transmantle sign" more accurately (Fig. 1). FLAWS is also likely to detect heterotopic neurons outside the cortex. Susceptibility-weighted imaging (SWI) is a technique using susceptibility differences between tissues to enhance contrasts between brain structures such as grey/white matter or between different subcortical or cortical structures. SWI images are T2*-weighted images created from both magnitude and phase in gradient echo data and are sensitive to both paramagnetic and diamagnetic compounds.

These images can also be reconstructed as a minimum intensity projection (MIP) to provide highresolution angiograms. Both SWI and angiograms have been found to be useful in FCD and PMG diagnosis [START_REF] De Ciantis | 7T MRI in focal epilepsy with unrevealing conventional field strength imaging[END_REF] [START_REF] De Ciantis | Ultra-High-Field MR Imaging in Polymicrogyria and Epilepsy[END_REF].

The high-resolution of these sequences (0.6mm isotropic voxels for ≈10min acquisition in our protocol) is also an asset for MCD diagnosis.

Demonstrated added value of structural 7T MRI in MCD diagnosis

Since the earliest experience, 7T MRI seems to provide gains for better characterizing the localized forms of MCDs such as FCD or PMG [START_REF] Guerrini | Malformations of cortical development: clinical features and genetic causes[END_REF]. More recent studies have now demonstrated the added value of UHF by comparing images obtained at 7T to those obtained at 1.5 and 3T MRI in several neurological diseases (n=40 and n=104 respectively) [START_REF] Springer | Comparison of Routine Brain Imaging at 3 T and 7 T[END_REF] [START_REF] Obusez | 7T MR of intracranial pathology: Preliminary observations and comparisons to 3T and 1.5T[END_REF]. These studies found both better conspicuity and unambiguity on images obtained at 7T. In the first study, among the 55 epileptic patients included, 22 presented with MCD (13 FCD, 6 FCD type IIIa, 2 PNH and 1 PMG) [START_REF] Springer | Comparison of Routine Brain Imaging at 3 T and 7 T[END_REF]. In all of those, 7T exhibited better conspicuity and delineation based on inter-rater agreement among 10 experienced radiologists. Interestingly, 25 patients with ambiguous images at lower field had no abnormality at 7T. The second study included nine patients with epilepsy (5 MRI-negative) [START_REF] Obusez | 7T MR of intracranial pathology: Preliminary observations and comparisons to 3T and 1.5T[END_REF].

Using a semi-quantitative diagnostic confidence score between two experienced neuroradiologists, MCDs were found to be better defined or excluded but differences between 3T and 7T did not reach statistical significance.

The yield of 7T MRI in the diagnosis of subtle lesions in patients presenting with DRPE and negative-MRI at lower field has been specifically addressed in two other recent studies [START_REF] De Ciantis | 7T MRI in focal epilepsy with unrevealing conventional field strength imaging[END_REF] [START_REF] Veersema | Seven tesla MRI improves detection of focal cortical dysplasia in patients with refractory focal epilepsy[END_REF]. De Ciantis et al. studied 21 patients with normal appearing MRI at 1.5 or 3T [START_REF] De Ciantis | 7T MRI in focal epilepsy with unrevealing conventional field strength imaging[END_REF]. They found structural lesions compatible with FCD in 6 (28%) on T2*-weighted and FLAIR images at 7T. Among those six6 lesional patients, four had resective surgery and histopathology revealed FCD type II in three and type IIIa in one, demonstrating higher sensitivity than at lower field strength. In the 15 patients remaining apparently non-lesional at 7T, four were operated-on and histopathology showed only gliosis, suggesting UHF also has higher specificity than examinations at lower field strengths.

Veersema et al. studied a series of 38 patients presenting with DRPE and normal appearing MRI at 3T

(88%), 1.5 (10%) or 1T (one patient only) [START_REF] Veersema | Seven tesla MRI improves detection of focal cortical dysplasia in patients with refractory focal epilepsy[END_REF]. They found structural lesions compatible with FCD in eight patients at 7T. Among those eight lesional patients, six had resective surgery, with histopathology revealing FCD type II in five and proliferative oligodendroglial hyperplasia with mild MCD in one. In the 30 patients remaining non-lesional at 7T, six were operated on and histopathology showed gliosis in three and FCD type II in three. Two other patients had suspicion of dual pathology at 3T. 7-Tesla showed an additional lesion in one patient with confirmed FCD type II and no hippocampal sclerosis, but no additional lesion in the second patient despite the presence of FCD type IIIa in the pathological specimen.

7-Tesla MRI has demonstrated the ability to depict finer anatomic detail compared to 3T in 10 patients presenting with PMG [START_REF] De Ciantis | Ultra-High-Field MR Imaging in Polymicrogyria and Epilepsy[END_REF]. Interestingly, the additional details revealed at 7T could have implications for diagnosis and surgical management. Among the six patients diagnosed as bilateral at 7T, four were considered as unilateral at 3T. Susceptibility-weighted angiography also depicted dilated superficial veins suggesting a potential role of vascular dysgenesis.

Several case series have also illustrated the added value of UHF in the diagnosis of other types of localized epileptogenic lesions such as ganglioglioma, dysembryoplastic neuroepithelial tumor (DNET), cavernomas or subtle lesions associated with tuberous sclerosis complex [START_REF] Pittau | MP2RAGE and Susceptibility-Weighted Imaging in Lesional Epilepsy at 7T: Epilepsy and 7TMR[END_REF][25] [START_REF] Sun | Magnetic resonance imaging of tuberous sclerosis complex with or without epilepsy at 7 T[END_REF].

Perspectives for quantitative and functional 7T MRI in MCD

Quantitative MRI -towards in vivo histology

Quantitative MRI provides measures of biophysical properties acting on signal intensity. With high SNR and CNR, 7T enables wider application of qMRI and broader use of quantitative images to probe the microstructure of MCDs. This could help in the identification of subtypes depending on histopathology [START_REF] Adler | Towards in vivo focal cortical dysplasia phenotyping using quantitative MRI[END_REF].

Zucca et al. explored 13 surgical specimens with FCD type II at 7T [START_REF] Zucca | Type II focal cortical dysplasia: Ex vivo 7T magnetic resonance imaging abnormalities and histopathological comparisons: 7T Imaging in FCD II[END_REF]. They quantified T 2 signal intensities in regions of interest (ROI) within the lesion and in the perilesional grey and white matter.

Different patterns could help to differentiate type IIa and IIb even in MRI-negative patients. In FCD type IIb, T 2 hyperintensity of the white matter was related to dysmyelination, severe fiber loss and abnormal cells. The mild alteration in MRI was in line with less severe histopathological findings in Type IIa.

Reeves et al. combined 9.4T MRI and immunohistochemistry in 13 surgical resections with confirmed FCD (in five cases) and in normal cortex [START_REF] Reeves | Combined Ex Vivo 9.4T MRI and Quantitative Histopathological Study in Normal and Pathological Neocortical Resections in Focal Epilepsy: Cortical 9.4T MRI and neuropathology in epilepsy[END_REF]. T 1 , T 2 , T 2 * and magnetization transfer ratio (MTR) signal intensities were quantified in 43 ROI and compared to quantitative immunohistochemistry for myelination, neuronal populations, glia and blood-brain-barrier. Significant correlations were found between quantitative signal measures and myelin and neuronal contents in all ROI, additionally demonstrating the ability of UFH MRI to quantify pathological changes in FCD with altered cortical lamination and myelination. As in Zucca et al., significant MRI alterations were observed even in normal appearing cortex on in vivo preoperative MRI at lower field. This semi-quantitative approach compared to histological findings in FCD opened a perspective towards a better phenotyping of MCD using qMRI in vivo.

By quantifying the sources of magnetic field distortions that generate different phase shifts in SWI, the quantitative susceptibility mapping (QSM) technique can theoretically differentiate paramagnetic (iron) from diamagnetic (calcified) substances and interrogate microstructure and molecular content [START_REF] De Rochefort | Quantitative MR susceptibility mapping using piece-wise constant regularized inversion of the magnetic field[END_REF]. Although QSM at 7T has been demonstrated to be useful for lesion characterization in several brain diseases, the method has not yet been applied in the diagnosis of MCD [START_REF] Bian | In Vivo 7T MR Quantitative Susceptibility Mapping Reveals Opposite Susceptibility Contrast between Cortical and White Matter Lesions in Multiple Sclerosis[END_REF] [START_REF] Tiepolt | Quantitative Susceptibility Mapping of Amyloid-β Aggregates in Alzheimer's Disease with 7T MR[END_REF].

Diffusion MRI (dMRI) can probe microstructural changes by quantifying the self-diffusion of water molecules constrained by cell membranes in intra and extracellular spaces. Using specific sequence schemes and models, dMRI provides several parameters capable of quantifying histological changes. So far, even though diffusion parameter changes have been observed in MCD, dMRI has not been demonstrated to be specific of malformations [START_REF] Adler | Towards in vivo focal cortical dysplasia phenotyping using quantitative MRI[END_REF]. At 7T, dMRI suffers from many technical challenges. However, it is also very promising since it can be performed at high-spatial and highangular resolution not only for microstructure analyses but also for reconstruction of whole-brain high-resolution structural connectivity using tractography [START_REF] Vu | High resolution whole brain diffusion imaging at 7 T for the Human Connectome Project[END_REF].

Ultra-high resolution and quantitative data for computational neuroanatomy

MR image postprocessing is a very active and fruitful domain in constant evolution that is entering a new era thanks to artificial intelligence (AI) methods [START_REF] Kini | Computational analysis in epilepsy neuroimaging: A survey of features and methods[END_REF]. At 7T, higher contrast and resolution will also improve this field of computational anatomy by increasing the range of image features that can be used as inputs. Automated methods for detecting FCD, using machine learning and deep learning mainly applied to T 1 -weighted or/and FLAIR volumetric sequences, have been proposed and proven to be effective in MRI-negative patients with histologically confirmed FCD [START_REF] Jin | Automated detection of focal cortical dysplasia type II with surface-based magnetic resonance imaging postprocessing and machine learning[END_REF]. Many features have been analyzed, including cortical thickness, gray-white matter intensity contrast (gradient), curvature, sulcal depth, local cortical deformation, and found to be efficient in detecting FCD [START_REF] Adler | Towards in vivo focal cortical dysplasia phenotyping using quantitative MRI[END_REF]. Thus, highresolution morphological images offered by 7T MRI are of particular interest for these approaches, most especially using multiparametric approaches as have been successfully applied at lower field [START_REF] Adler | Towards in vivo focal cortical dysplasia phenotyping using quantitative MRI[END_REF].

Functional MRI

At 7T, task-related functional MRI (fMRI) used for presurgical mapping has higher specificity, sensitivity, and reliability of localization in addition to decreased scan time compared to 3T [START_REF] Trattnig | Key clinical benefits of neuroimaging at 7 T[END_REF].

However, fMRI at 7T also suffers more from artifacts, particularly movements and static magnetic field inhomogeneities, as is the case for dMRI. Nevertheless, many solutions are now available to overcome these pitfalls.

High-resolution resting-state fMRI may also be used for whole-brain high-resolution functional connectivity in order to better understand the interrelation between MCD and the rest of the brain [START_REF] Hong | The spectrum of structural and functional network alterations in malformations of cortical development[END_REF].

Limitations of 7T MRI

The dramatic increased SNR and gain in resolution is accompanied by several limitations. The first is the increase number of contraindications principally due to implants or implanted medical devices not tested yet at UHF. The second is the highest sensitivity to patients' movements as a side effect of increased resolution. The advantages of increased magnetic field strength come also with drawbacks such as principal magnetic field (B 0 ) and B 1 field inhomogeneities leading to potential artifacts and signal inhomogeneities that need to be corrected or mitigated. In addition, considering the higher energy of the radio-frequency (RF) at UHF the regulatory limitation of energy absorption imposed in MRI -that is the same for every field strength -obliges to use specific and often complex RF pulse design and a difficult adaptation of several sequences usually used at lower field strengths.

Nevertheless, improvement of acquisition schemes and optimization of RF pulses allow today clinically compatible protocols able to explore FCDs efficiently.

Conclusion

7T MRI is of major interest in patients presenting with DRPE and normal appearing MRI at lower field. UHF MRI is also very useful for better delineating lesions in patients with visible MCDs in the perspective of surgery. It is also likely that in the near future, 7T MRI will provide valuable quantitative multiparametric measures capable of probing histopathological features, as well as highresolution images for application with AI approaches for automated detection of MCDs. Thus, despite the technical challenges and the higher number of contraindications, 7T MRI is clearly emerging as a key tool in the presurgical evaluation of difficult cases. The FDA and CE approval of 7T systems for clinical use will likely further open up access to UHF MRI, a prerequisite for large cohort studies and formal validation.

Figure legend

Fig. 1. Structural 7T MRI in a patient presenting with a focal cortical dysplasia (FCD) type IIb confirmed by histopathology, not diagnosed on 3T MRI. The malformation located in the anterior part of the left cingulate gyrus is visible on the three contiguous images of all the 3D high-resolution sequences (i.e. FLAIR, T 2 SPACE, MP2RAGE and FLAWS). Note the clear modification of the grey/white matter interface particularly well depicted using a specific inversion time providing "tissue border enhancement" (white arrow). Note also the "transmantle sign", typical of FCD type II, identified by the FLAWS sequence only (dashed white arrow).

MP2RAGE (0.6mm) 3 FLAWS

 3

Acknowledgements

This work was supported by the Excellence Initiative of Aix-Marseille University -A*MIDEX (grant A*MIDEX-EI-13-07-130115-08.38-7T-AMISTART and A*MIDEX-EI-17-29-170228-09.43-Imetionic-7); the 7T-AMI EQUIPEX project (grant ANR-11-EQPX-0001); and France Life Imaging network (grant ANR-11-INBS-0006).

We would like to thank Dr Ben Ridley for his input on the language of the final version of the manuscript.

Declarations of interest

The author declare that they no conflict of interest concerning this article.


Louis Maillard

Hélène Brissart
email: h.brissart@chru-nancy.fr

Attention disorders in adults with epilepsy. Determinants and Therapeutic strategies

Keywords:

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Epilepsy is a "disorder of the brain characterized by an enduring predisposition to generate epileptic seizures and by the neurobiologic, cognitive, psychological and social consequences of this condition" [START_REF] Fisher | Epileptic seizures and epilepsy: definitions proposed by the International League Against Epilepsy (ILAE) and the International Bureau for Epilepsy (IBE)[END_REF] Cognitive consequences in epilepsy are often described in verbal memory, language, and/or executive functions [START_REF] Wilson | Indications and expectations for neuropsychological assessment in routine epilepsy care: report of the ILAE Neuropsychology Task Force, Diagnostic Methods Commission, 2013-2017[END_REF], but attention is rarely exhaustively studied. Attention is involved in all cognitive activities, and attention disorders (AD) are reported in patients with various neurological diseases [START_REF] Belanger | Factors moderating neuropsychological outcomes following mild traumatic brain injury: A meta-analysis[END_REF][START_REF] Sachdev | The neuropsychological profile of vascular cognitive impairment in stroke and TIA patients[END_REF][START_REF] Mccarthy | Modality-specific aspects of sustained and divided attentional performance in multiple sclerosis[END_REF]. A systemic review and a consensus from the ILAE have been recently published on diagnosis, screening and management of ADHD in children with epilepsy [START_REF] Auvin | Systematic review of the screening, diagnosis, and management of ADHD in children with epilepsy. Consensus paper of the Task Force on Comorbidities of the ILAE Pediatric Commission[END_REF]. So, this opinion paper proposes to define the concept of AD and its assessment in adults with epilepsy, to consider their determinants and therapies (drug or not).

Attention: definition and assessment

Attention is a complex process, with cognitive and behavioral features. In the literature, many definitions are available. ADs are linked with attention deficit /hyperactivity disorder (ADHD). Criteria for ADHD according to the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5) [START_REF]Diagnostic and statistical manual of mental disorders (DSM-5®)[END_REF] include six or more inattention and/or six or more hyperactivity-impulsivity symptoms in more than one situational context. In this review, we consider cognitive features of AD, not ADHD.

The first definition of attention was proposed by William James in 1890: "Everyone knows what attention is. It is the taking possession by the mind in clear and vivid form, of one out of what seem several simultaneously possible objects or trains of thoughts…It implies

withdrawal from some things in order to deal effectively with others". This definition is still topical. The current concept of attention comprises four dimensions: sustained attention, selective attention, divided attention, alertness [START_REF] Cohen | The neuropsychology of attention[END_REF]. More precisely, sustained attention refers to the ability to maintain vigilance over time; selective attention refers to goal-directed focus on task-relevant information while ignoring other irrelevant information; divided attention requires participants to perform two or more task simultaneously; alertness refers to reaction time. For example, when you drive, sustained attention is required throughout the way, selective attention is directed by events in the environment (car's flashing lights, child crossing the street, …), divided attention is required in dual tasks when you drive and listen to the radio simultaneously; and alertness is required when you wait at traffic lights. In daily life, these mechanisms are simultaneously involved all the time.

Several clinical tools are available to assess these different facets of attention. Attention depends on information processing speed, which must be controlled (TAP, subtest alert [START_REF] Zimmermann | Test batterie zur Aufmerksamkeitsprüfung : (TAP)[END_REF], WAIS 4, subtest Code [START_REF] Wechsler | Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV)[END_REF], TMT A [START_REF] Roussel | La batterie GREFEX: données normatives[END_REF]). Attention assessment should not be restricted to information processing speed. Cancelation tasks are often used to briefly evaluate selective attention (i.e d2 task [START_REF] Brickenkamp | Aufmerksamkeits-Belastungstest (Test d2-R). 9[END_REF]; Ruff 2&7 task [START_REF] Ruff | The Ruff 2 and 7 selective attention test: A neuropsychological application[END_REF]), however only the visual modality is explored. Specific cognitive batteries have been designed to evaluate more precisely AD: TAP [START_REF] Zimmermann | Test batterie zur Aufmerksamkeitsprüfung : (TAP)[END_REF]; Vienna test System [START_REF] Schuhfried | Vienna Test System: Psychological assessment[END_REF]; CANTAB [START_REF] Robbins | Cambridge Neuropsychological Test Automated Battery (CANTAB): a factor analytic study of a large sample of normal elderly volunteers[END_REF]. The benefit of these specific batteries is to propose an exhaustive assessment of attention, with several subtests (sustained attention, selective attention, divided attention, alertness). The inconveniences of these tools are their duration (15 to 60 minutes) and their cost. Finally, attention is often confused with working memory and executive functions, because they require one or more of these attentional mechanisms.

For example, Stroop Test [START_REF] Roussel | La batterie GREFEX: données normatives[END_REF], a verbal inhibition task requiring selective attention, is sometimes used by some authors as a marker of attention. Such interpretations must be considered with caution and we recommend to use at least one specific attentional test. D2 [START_REF] Brickenkamp | Aufmerksamkeits-Belastungstest (Test d2-R). 9[END_REF] task allows a brief assessment of selective attention (5 minutes with a tablet, see Figure 1). TAP battery [START_REF] Zimmermann | Test batterie zur Aufmerksamkeitsprüfung : (TAP)[END_REF] allows a complementary assessment of sustained attention, divided attention and alertness (see Figure 2). Attention disorder determinants in adults with epilepsy ILAE recommends to assess AD in adults with epilepsy [START_REF] Wilson | Indications and expectations for neuropsychological assessment in routine epilepsy care: Report of the ILAE Neuropsychology Task Force, Diagnostic Methods Commission, 2013-2017[END_REF]. Attention is modulated by several positive and negative factors. Some are specific and others not specific to epilepsy (cf Figure 3).

Non-specific determinants of attention

Attention is required to process external stimuli, so it depends very strongly on changes in the environment (noise, fatigue, etc.). AD's determinants not specific to epilepsy are motivation, sleep, mood, age, and/or neuropsychological profile. Depression and anxiety are associated with poorer performances across multiple domains, including attention, executive functioning, memory, and processing speed [START_REF] Rock | Cognitive impairment in depression: a systematic review and metaanalysis[END_REF][START_REF] Castaneda | A review on cognitive impairments in depressive and anxiety disorders with a focus on young adults[END_REF].

Aging is accompanied by a decrease in attentional resources, and a greater sensitivity to interference, which leads to a decrease of behavioral performance in the elderly facing multiple simultaneous tasks [START_REF] Anderson | 50 years of cognitive aging theory[END_REF]. Importantly, attention is also linked to the global neuropsychological profile of the patient reflecting a reciprocal interdependency.

Specific to adults with epilepsy?

ADs are frequent in epilepsy, and have been reported in idiopathic generalized epilepsy (IGE), focal epilepsy, and new onset epilepsy [START_REF] Elger | Chronic epilepsy and cognition[END_REF]. However most of these studies have assessed only one of the four dimensions of attention. Seizure recurrence, inter-ictal activity, anti-epileptic drugs, focus location and disease duration can be considered as potential specific determining factors of AD.

In a recent study focusing on IGE, 36 patients with IGE, 38 first-degree relatives, and 40 healthy controls were examined using a battery of neuropsychological tests sensitive to sustained attention and frontal lobe dysfunction (executive function, nonverbal reasoning, verbal generativity, response inhibition, and working memory) [START_REF] Chowdhury | Revealing a brain network endophenotype in families with idiopathic generalised epilepsy[END_REF]. Patients with IGE showed deficits predominating in sustained attention but involving also various executive functions (nonverbal reasoning, verbal generativity and working memory). Interestingly, nonepileptic and untreated relatives exhibited a parallel profile of cognitive abilities, with significant but less pronounced deficits. Authors suggested that this common cognitive profile could result from a common genetic trait independent of seizures or antiepileptic drugs.

Conversely, the tendency of patients to demonstrate greater impairment in these tasks could be due to a combination of greater genetic contribution and/or factors related to seizures and/or treatment.

A study [START_REF] Hudson | Attentional control in patients with temporal lobe epilepsy[END_REF] proposed to assess AD in focal epilepsy (Temporal Lobe Epilepsy: TLE) with an exhaustive assessment including sustained attention, selective attention and short-term memory. Fourteen TLE surgery candidates (4 left TLE, 10 right TLE) achieved the comprehensive neuropsychological assessment. Impairment was reported in short term memory, and selective attention, with a preservation of sustained attention. These findings suggest that attentional impairment in TLE was not global and could be limited to a single dimension, for instance selective attention. The greatest deficits appear to be on tasks that require a high load of processing resources. In contrast, sustained attention is less compromised and the capacity to allocate cognitive resources appears to be normal in patients with TLE.

Impact of side of lesion, seizure outcome and interictal epileptiform discharges (IEDs) on attention after surgery were explored with 94 patients with left (n=50) and right (n=44) intractable mesial TLE [START_REF] Wisniewski | Impact of side of lesion, seizure outcome and interictal epileptiform discharges on attention and memory after surgery in temporal lobe epilepsy[END_REF]. Selective attention was evaluated with Go/No-Go test (TEA), divided attention with TEA subtest and focused attention with a cancelation task (D2). In selective attention, RTLE patients produced significantly more errors. In divided-attention, postoperatively seizure-free patients were significantly faster than patients with recurring seizures. In addition, patients who continued to present IEDs in the one-year postoperative routine EEG tended to have a slower performance and a higher omission rate, regardless of the time of examination and their seizure outcome. Results in focused attention showed a significant effect of seizure outcome, and a significant two-way interaction between side of surgery and time of examination. The LTLE group, but not the RTLE group improved postoperatively. Results could suggest that AD may not only be attributed to unfavorable seizure outcome after surgery, but also to the persistence of IED activity. In addition, variables measuring basal selective attention reflect the importance of the functional integrity of the non-dominant temporal lobe and its interaction with the large, right-sided frontoparietal network which underlies basal sustained and selective attention. This study suggested a link between several variables on post-surgical attention outcome (persisting IED activity, seizure outcome, location side …). Post-surgical improvement of attention was also described in other studies using cancellation task [START_REF] Helmstaedter | Differential effects of temporal pole resection with amygdalohippocampectomy versus selective amygdalohippocampectomy on material-specific memory in patients with mesial temporal lobe epilepsy[END_REF], and interpreted as the result of a general cognitive improvement, as mentioned in a previous report [START_REF] Helmstaedter | Chronic epilepsy and cognition: a longitudinal study in temporal lobe epilepsy[END_REF]. Surprisingly a study the neuropsychological profile of FLE and TLE showed a greater impairment of executive functions but not of selective attention in FLE than in TLE suggesting that ADs are not specific to a single epileptogenic zone localization [START_REF] Helmstaedter | Neuropsychological aspects of frontal lobe epilepsy[END_REF] Therapeutic strategy Therapeutic strategies include a drug and a psychotherapeutic approach. The drug approach corresponds to AED and anti-depressive drug therapy. The psychotherapeutic approach corresponds to cognitive rehabilitation and psychotherapy.

Anti-epileptic drug therapy

Combination of antiepileptic drugs contributes to the emergence of cognitive effects [START_REF] Helmstaedter | The longer-term cognitive effects of adjunctive antiepileptic treatment with lacosamide in comparison with lamotrigine and topiramate in a naturalistic outpatient setting[END_REF], and difference of these effects according to the molecules are observed. Each molecule has a specific profile. Epitrack [START_REF] Helmstaedter | The longer-term cognitive effects of adjunctive antiepileptic treatment with lacosamide in comparison with lamotrigine and topiramate in a naturalistic outpatient setting[END_REF] is the most common tool to assess cognitive impact of AED. Some molecules have no interaction with cognitive performance, some could improve it, or could impair it in a specific field. Potential attentional effects of AED are summarized in table 1 [START_REF] Helmstaedter | The longer-term cognitive effects of adjunctive antiepileptic treatment with lacosamide in comparison with lamotrigine and topiramate in a naturalistic outpatient setting[END_REF][START_REF] Brissart | Neuropsychologie des épilepsies de l'adulte: Approche clinique et pratique[END_REF].

Cognitive risk is also major with combinations of multiple AED [START_REF] Mula | The role of hippocampal sclerosis in topiramaterelated depression and cognitive deficits in people with epilepsy[END_REF]. Witt et al. [START_REF] Witt | Adverse cognitive effects of antiepileptic pharmacotherapy: Each additional drug matters[END_REF] suggested that numerous AEDs appears to impair all cognitive functions, especially attentional / executive functions and, to a lesser extent, memory functions. These results are observed with Epitrack score, but Epitrack does not specifically measure patients' attentional capacities. The benefit/risk balance of AED is very difficult to assess. Some drugs may cause direct negative effects, but in contrast, the control of epileptic seizures may have a positive effect on mood and associated psychiatric disorders and could also independently lead to an improvement of attention. Some molecules may have a direct positive effect on cognitive performance by improving alertness and cognitive abilities [START_REF] Helmstaedter | The longer-term cognitive effects of adjunctive antiepileptic treatment with lacosamide in comparison with lamotrigine and topiramate in a naturalistic outpatient setting[END_REF]. Negative effects of AED on attention could depend on the used posology and can therefore be improved by pre and posttreatment introduction monitoring and trying to find the lowest efficient dosage. In any case, cognitive side effects of AED in adults have been shown to be reversible after cessation [START_REF] Dodrill | Neuropsychological abilities before and after 5 years of stable antiepileptic drug therapy[END_REF][START_REF] Kwan | Effectiveness of first antiepileptic drug[END_REF].

Antidepressive drug therapy

The incidence of depression is five to 20 times higher in patients with epilepsy than in the general population [START_REF] Evans | Mood disorders and medical illness: a major public health problem[END_REF]. Numerous studies have investigated cognitive functions in depression, including attention, processing speed, executive function, and verbal memory.

Effects of antidepressive drug therapy (ADT) on attention in patients with epilepsy are not reported. Effects of ADT on cognition are described in depressed patient [START_REF] Prado | A meta-analysis of the effects of antidepressants on cognitive functioning in depressed and non-depressed samples[END_REF], more precisely in attention, improvement is reported but with no specific task. Altogether AD, depression, and epilepsy are confused, and care of these three axes is crucial. Close collaboration between psychiatrists, neurologists and neuropsychologists is necessary in order to stop the vicious circle of mutual aggravation of one pathology by the other. One must not be resigned to one's disorders in order to progress towards a satisfactory therapeutic balance. In epilepsy, despite the knowledge of cognitive disorders and the large number of patients, very few studies have been conducted. A first study [START_REF] Engelberts | The effectiveness of cognitive rehabilitation for attention deficits in focal seizures: a randomized controlled study[END_REF] mentioned that "a comprehensive cognitive rehabilitation approach involves the increment of the individual's awareness of his or her cognitive deficits and the subsequent retraining of those cognitive functions that were specifically impaired, or the teaching of compensatory strategies". Two cognitive methods have been proposed in patients with focal seizure, according to their cognitive impairment: restorative method for AD, compensatory method for verbal memory impairment. Here, the first approach is presented. Attentional assessment was exhaustive, with visual alertness, acoustic alertness, focused attention, divided attention, selective attention, and vigilance. Enrolled patients included had a poor performance on at least two of the six attentional dimensions. Divided attention capacity was affected in most patients. Six weekly sessions were administered. Positive effects on neuropsychological outcome related to the Retraining Method were reported in divided-attention (on omissions). Six months later, remaining effects were found, suggesting that benefits were sustained over a long period of time after the intervention. This might indicate that patients have incorporated these new methods into their daily-life functioning. Supplementary analyses demonstrated that patients who still had seizures benefited more from either program than the seizure-free patients.

Authors suggest that cognitive rehabilitation programs are effective for patients with focal seizures and attention deficits should be added into comprehensive care programs.

In a second study [START_REF] Helmstaedter | The effects of cognitive rehabilitation on memory outcome after temporal lobe epilepsy surgery[END_REF], two groups of patients who underwent temporal lobe resection, were assigned to two arms with (n = 55) and without (n = 57) postoperative rehabilitation.

They were evaluated with respect to memory and attention before and three months after temporal lobe surgery. Rehacom software was used for rehabilitation of AD. The study showed that attentional performance improved independent of cognitive training. Previous research has demonstrated that nonmemory function deficits obviously have the potential to recover after surgery without any interventions, an effect that has been interpreted in terms of a release due to control of epileptic activity. So, CR in AD with epilepsy is not really developed, and more studies should be considered, to assess CR effects in patients with epilepsy, and to determine which patients are best responsive to these interventions (focal seizure?) and when as regard as the time of surgery (pre or postoperatively).

Psychotherapy

As previously mentioned, depression and anxiety are associated with cognitive impairment including attention, executive functioning, memory, and processing speed [START_REF] Rock | Cognitive impairment in depression: a systematic review and metaanalysis[END_REF][START_REF] Castaneda | A review on cognitive impairments in depressive and anxiety disorders with a focus on young adults[END_REF]. The principles of depressive and anxious comorbidities care are similar in patients with epilepsy and in patients without epilepsy, with a combination of pharmacological therapies and psychotherapy such as cognitive and behavioral therapies (CBT).

CBTs have been shown to be effective in anxiety and depressive disorders on these symptoms but not on the frequency of seizures. CBTs of anxiety disorders focus on the perception of stress and their interpretation of anxiety symptoms. Thus in epilepsy, they are particularly interesting in the treatment of the specific phobia of epileptic seizures in order to reduce the anticipatory anxiety seizures and improve the level of anxiety, depressive symptoms and quality of life [START_REF] Kotwas | Self-control of epileptic seizures by nonpharmacological strategies[END_REF].

Conclusion

Cognitive disorders such as verbal memory and language have been extensively described in patients with epilepsy. In contrast, few studies have specifically explored AD, separately from executive functions and speed processing. ADs have been reported in new onset epilepsy, idiopathic generalized epilepsy, and in focal epilepsy. AD seems to decrease after successful surgery. In focal epilepsy, ADs predominate on selective attention and divided attention. More studies are needed to specify prevalence and nature of AD, related to epileptic status.

In the field of therapeutic strategies, anti-epileptic drugs show an impact on AD. More studies should be conducted to explore specifically their specific impact on the four dimensions of attention. The efficacy of antidepressants as well as psychotherapy on attention have not been specifically studied but a benefit can be expected through the indirect effect on depressive and anxiety disorders. Cognitive rehabilitation of attention disorder seems promising but additional studies are mandatory to demonstrate its efficacy.

  Cognitive rehabilitation Cognitive rehabilitation (CR) is developed in neurological pathologies. AD rehabilitation programs have been developed mostly on numeric supports implementing restauration technics. The main objectives of such software (Rehacom, CogniPlus, PRESCO,…) are to manage intensity and specificity of attention.

Figure 3 .

 3 Figure 3. Determinants specific or not to epilepsy

Conflicts of interest

The authors declare that they have no conflict of interest concerning this article.

Selective attention

D2

Test duration: 5 minutes