Jade Georis-Creuseveau
email: jade.georis-creuseveau@univ-brest.fr

Joep Crompvoets
email: joep.crompvoets@soc.kuleuven.be

Roger Longhorn
email: rlonghorn@gsdi.org

The intensity of current changes that characterize marine and coastal areas demand the implementation of collective processes and tools to enhance knowledge and management of these territories. To contribute to these goals, Spatial Data Infrastructures (SDIs) aim to facilitate the sharing and the use of spatial data between a broad range of stakeholders by promoting data and metadata harmonization and services interoperability.

This paper describes the first results of an international Web survey undertaken to assess the developments of existing national marine and coastal geoportals of SDIs or similar Web services. A Web survey done in October 2014 led to an inventory of 81 national operational geoportals. Based on the survey results, a preliminary typology can be made. Four types of geoportals can be distinguished: (1) National Oceanographic Data Centre (NODC) geoportals, (2) Marine/Coastal Atlas geoportals and (3) Hydrographic Office geoportals, (4) Hybrid geoportals.

Introduction

Marine and coastal areas are complex and vulnerable territories, home to many diverse human activities and complex environmental oceanic and meteorological events. For the past fifty years, marine and coastal areas all over the world have been in crisis, through over-exploitation of resources and related use conflicts (UNEP, 2012). The intensity and magnitude of current changes that characterize marine and coastal areas demand the implementation of collective processes and tools to enhance knowledge and management of these territories [START_REF] Cicin-Sain | Integrated coastal and ocean management: concepts and practices[END_REF].

Progress over the past three decades in the field of Geographic Information Sciences and Technologies provides an enabling framework for the monitoring and management of these territories [START_REF] Bartlett | GIS for coastal zone management[END_REF][START_REF] Gourmelon | SIG et littoral[END_REF][START_REF] Wright | Coastal informatics: web atlas design and implementation[END_REF]. Since the 1990's, the role of spatial data and information in decision making in many sectors (including the marine and coastal environment) has led to the development of SDIs to better manage and share spatial data and information [START_REF] Crompvoets | Assessing the worldwide developments of national spatial data clearinghouses[END_REF]. The development of SDIs responds to the international needs to facilitate access, exchange, and share of spatial data and information held by many stakeholders to maximize its use and re-use, while reducing the cost of management and production. SDIs include components such as data, policy, access networks, standards, and people [START_REF] Rajabifard | Future directions for SDI development[END_REF] to support these goals.

Coastal and Marine SDIs have been gradually implemented in order to improve the accessibility and the availability of spatial data and information related to marine and coastal areas at various levels [START_REF] Longhorn | Coastal spatial data infrastructure[END_REF][START_REF] Canessa | Spatial Information Infrastructure for Integrated Coastal and Ocean Management in Canada[END_REF]. While these initiatives are not always labelled "SDI" (e.g. Atlas, Information System...), they share SDI objectives and concepts. They provide the user community (decision makers, planners, scientists and citizens in general) with real time observations and multi-thematic data (biophysical, human uses, biodiversity…) collected through research, monitoring and observation [START_REF] Wright | Coastal informatics: web atlas design and implementation[END_REF].

A favourable context for increasing efficiency in spatial data production and improving availability and accessibility is being put into place to support the international concepts of Integrated Coastal Zone Management (ICZM) [START_REF] Cicin-Sain | Integrated coastal and ocean management: concepts and practices[END_REF] and maritime spatial planning (MSP) [START_REF] Douvere | The importance of marine spatial planning in advancing ecosystem-based sea use management[END_REF]. These concepts aim to deliver a sustainable approach to the management of the coastal zones, oceans and seas, across sectors, between different levels of government, and across jurisdictional boundaries. These concepts and related regulations (e.g. European Commission (2008), European Commission (2013), European Commission (2014)) act as the catalyst for increasing production, access, sharing, use and integration of coastal and maritime geo-information in order to inform IZCM/MSP decision making [START_REF] Iho | Spatial Data Infrastructures[END_REF]. The needs for coastal and marine SDIs are becoming a priori evident.

Within this context, an international Web survey aims to assess the worldwide developments of existing national marine and coastal geoportals of SDIs or similar Web services, as such inventory does still not exist.

The geoportal is the central web gateway targeting the facilitation of spatial data discovery, access, and related added-value services [START_REF] Crompvoets | Assessing the worldwide developments of national spatial data clearinghouses[END_REF][START_REF] Maguire | The emergence of geoportals and their role in spatial data infrastructures[END_REF]. The existence and status of such portals represents one of the ways to assess the processes implemented by the country to enable the access and use of coastal and marine geographic data and information. This article presents the first preliminary results of the international survey undertaken. Given the diversity of the geoportals inventoried, the first step of the survey is to establish a typology to guide the ongoing analysis of the different characteristics of the geoportals.

Scope and methodology

The survey focuses on geoportals implemented by national public bodies enabling the access and the use of geographic data specifically related to marine and/or coastal zones. Within the framework of the survey, the term "data" encompasses a broad range of items such as real-time observations, time series data, GIS data layers, digital maps, etc. The data can be related to different domains (physical or biological environments, human uses, topography, bathymetry, management or legislative aspects) and different scales (local, national, supranational, global).

The survey was conducted in October 2014. The required information was collected from the Web. The survey of geoportals was gathered by browsing of the Internet with the help of specific monitoring tools: Google alert, Mention and Netvibes. Based on a literature review, the following keywords were utilized in English, Spanish and French to parameterize the tools in order to encompass the diversity of vocabulary used: "coastal", "marine", "ocean", "sea", "portal", "geoportal", "clearinghouse", "spatial data infrastructure", "atlas", "data centre" and "information system". The approach also encompassed a scan of various types of information sources related to geomatics and coastal/marine domains, including international networks and events such as GSDI, ICAN, IHO, IODE, INSPIRE, COASTGIS conference, Seadatanet, FIG.

In order to provide a general overview of the geoportals, the following characteristics were sourced from the geoportal Web pages. They allow a general description of the first elements that the user can discover online: (1) Name, (2) Geographical distribution, (3) Language used, (4) Data thematic, (5) Data access policy, (6) Search data mechanisms, (7) Access data mechanisms. The first three characteristics correspond to the general description of the geoportal. The four others characteristics provide information on the discipline and the topic of the data accessible on the geoportals (4) and on different means to discover and access these data (5-7).

At the time of the submission, 128 geoportals were assessed from 72 coastal countries (48 % of the total number of coastal countries). Out of these, 23 geoportals were not operational (18 %), 24 out of the scope of the survey (19 %) , and 81 were implemented by national public organizations providing access to coastal and/or marine spatial data (63 %). These latter were included in the survey and are the basis of the main results presented later in this paper. These geoportals are implemented by 46 countries. With the exception of major maritime countries (USA, France, Australia, Canada) that manage several geoportals (from 4 to 5), the large majority of the countries have only one or two geoportals. It appears that the geoportals of the non-English countries provide information in two or more languages.

The comparison of the characteristics 4, 5, 6 and 7 enables to suggest a preliminary typology resulting into the following four types of geoportal: (1) National Oceanographic Data Centre (NODC) geoportals, (2) Atlas-like geoportals and (3) Hydrographic Office geoportals, (4) Hybrid geoportals.

NODC geoportals

In the first category, 34 geoportals were identified (42 % of the total number of surveyed geoportals). They correspond mainly to National Oceanographic Data Centres. These data centres have been progressively implemented by the International Oceanographic Data and Information Exchange (IODE) since the 1960's. Their missions are to gather, control quality, process and disseminate oceanographic data. As of 2012, there were 80 NODCs active worldwide (IODE, 2013).

They enable access to data related to physical and chemical oceanography, marine biology or geology (e.g. data from marine cruises, buoys, tide gauge stations, satellites). The data are freely accessible or through a request form. The search page is in the form of a list of data or a catalogue interface based on criteria such as parameters, geographic extent, time period, etc. The data can be viewed, downloaded or transferred by the data centre.

Atlas-like geoportals

Within the framework of the International Coastal Atlas Network (ICAN), a coastal web atlas (CWA) is defined as "a collection of digital maps and datasets with supplementary tables, illustrations and information that systematically illustrate the coast, often with cartographic and decision support tools, all of which are accessible via the Internet" [START_REF] Cummins | Report on Coastal Mapping and Informatics Trans-Atlantic Workshop 1: Potentials and Limitations of Coastal Web Atlases[END_REF].

This second type gathers the 8 geoportals of national atlases of the ICAN network together with 13 other atlas-like geoportals. The main differences with NODC are the diversity of the data thematics and the type of data available. These 21 geoportals (26 % of the total number of surveyed geoportals) enable access mainly to GIS data layers and digital maps from different sources and suppliers describing biophysical aspects of the coastal and marine zones along with human uses, biodiversity, pollution related topics, etc. Although personal registration may be required for the portal, access to the data is mostly free. The registration enables the user to have access to various additional functionalities (e.g. online map saving, search request saving). To consult the data, the user has access to map search mechanisms and catalogue interface. Data access services are mainly based on viewing, downloading and other web services which allow the user to have direct access to the geographic data, maps and metadata from a GIS desktop or for online applications. Some of the geoportals provide access to decision support tools (spatial analysis, indicator, barometer tools).

Hydrographic Office geoportals

The third type includes 19 geoportals (23 % of the total number of surveyed geoportals) that are mainly implemented by national Hydrographic Offices. The main data accessible on these geoportals are related to Nautical Charts. These latter are mainly digital maps accessible via a list of products in hypertext. Access to the products is generally fee-paying through online payment mechanisms. The data can be then accessed in the online cart.

Hybrid geoportals

In addition to the 74 geoportals classified into these three first types, 7 geoportals (9 % of the total number of surveyed geoportals) were identified as hybrid geoportals sharing the characteristics of the types 1 and 2 (3 geoportals) or these of the types 1 and 3 (4 geoportals).

The table 1 presents the main characteristics of the four types of geoportal.

Preliminary conclusion

The preliminary results suggest that worldwide developments are underway for geoportals enabling users to have access to various data concerning coastal and marine zones. At the present stage of the study, the 81 geoportals assessed can be classified in four types: (1) National Oceanographic Data Centres or similar, (2) Atlas-like geoportals and (3) Hydrographic Office geoportals, (4) Hybrid geoportals. Each type enables access to different kinds of data through various mechanisms.

Despite the integrated approach promoted by IZCM and MSP concepts and related regulations, platforms allowing access to a wide range of data related to marine, coastal and land territories are not frequent. True data harmonisation and services interoperability which are the underpinning principles for SDIs, need to be improved.

In the near future, the proposed typology will be complemented by the measurement of about twenty characteristics related to the five components as proposed by [START_REF] Rajabifard | Future directions for SDI development[END_REF] to describe SDIs: data (e.g. number of dataset), access network (e.g. data search mechanism type), people (e.g. number of data suppliers), standards (e.g. metadata standard type), and policy (e.g. level of openness, pricing). The choice of these characteristics is based on similar geoportals assessment studies [START_REF] Crompvoets | Assessing the worldwide developments of national spatial data clearinghouses[END_REF]EUROGI/eSDI-Net+, 2011) and on specificities recognized as useful for IZCM and MSP processes [START_REF] Dwyer | Potentials and limitations of Coastal Web Atlases[END_REF][START_REF] Wright | Coastal informatics: web atlas design and implementation[END_REF]. These characteristics will be measured a second time in April 2015 in order to monitor the current developments.

Table 1 .

 1 Characteristics of the geoportal

	Geoportal	Number	Data		Data access policy	Search data		Access data
	Class		thematic		mechanism		mechanism
	NODC	34	Oceanography Free or request	List	or/and	View, download or
					form	catalogue		transfer
	Atlas	21	Biophysical	Free	Map	and	View, download or
			and	human		catalogue		Web services for
			environment				GIS desktop or
								online application
	Hydro. Dept.	19	Nautical	Fee-paying	List		View and online
			Charts					cart
	Hybrid	7	Various		Various	Various		Various

Survey of National Coastal and Marine SDI geoportals: a first typology of the worldwide developments


Renaud Hédouin

Olivier Commowick

Elise Bannier

Benoit Scherrer

Maxime Taquet

Simon K Warfield

Senior Member IEEE Christian Barillot

Block-Matching Distortion Correction of Echo-Planar Images with Opposite Phase Encoding Directions

Keywords: Block-Matching, Echo Planar Imaging, Registration, Diffusion MRI

By shortening the acquisition time of MRI, Echo Planar Imaging (EPI) enables the acquisition of a large number of images in a short time, compatible with clinical constraints as required for diffusion or functional MRI. However such images are subject to large, local distortions disrupting their correspondence with the underlying anatomy. The correction of those distortions is an open problem, especially in regions where large deformations occur.

We propose a new block-matching registration method to perform EPI distortion correction based on the acquisition of two EPI with opposite phase encoding directions (PED). It relies on new transformations between blocks adapted to the EPI distortion model, and on an adapted optimization scheme to ensure an opposite symmetric transformation. We present qualitative and quantitative results of the block-matching correction using different metrics on a phantom dataset and on in-vivo data. We show the ability of the blockmatching to robustly correct EPI distortion even in strongly affected areas.

I. Introduction

In recent years, single-shot Echo Planar Imaging (EPI) has been increasingly used as it is substantially faster than most other acquisition sequences. The high speed of this acquisition comes from the fact that the image is acquired within a single-shot instead of multiple shots (single or multiple echoes) in other classical sequences (Gradient Echo, Spin Echo...). In regard of the required relaxation time between each shot, the single-shot method saves a considerable acquisition time. By shortening the acquisition time of every single time frame, EPI enables the acquisition of a larger number of images than other methods while respecting the same clinical constraint. This is particularly useful for diffusion-weighted imaging (DWI) wherein the acquisition of several scalar images is required to represent the underlying microstructure of the brain (white matter mainly) [START_REF] Ferizi | A ranking of diffusion MRI compartment models with in vivo human brain data[END_REF], [START_REF] Zhang | NODDI: Practical in vivo neurite orientation dispersion and density imaging of the human brain[END_REF], [START_REF] Stamm | A new multi-fiber model for low angular resolution diffusion MRI[END_REF], [START_REF] Taquet | A Mathematical Framework for the Registration and Analysis of Multi-Fascicle Models for Population Studies of the Brain Microstructure[END_REF]. For this reason, EPI is the most common sequence used for DWI [START_REF] Johansen-Berg | Diffusion MRI: From quantitative measurement to in-vivo neuroanatomy[END_REF]. For similar speed reasons, EPI is also used for functional imaging [START_REF] Huettel | Functional magnetic resonance imaging[END_REF], which requires the fast acquisition of many brain images while a task is executed by the subject.

The high velocity of EPI acquisitions comes at the cost of a high sensitivity to magnetic field inhomogeneities. Affected areas, often located at the tissue interfaces with different magnetic susceptibilities such as bone or air, are either contracted or dilated along the phase encoding direction (PED) [START_REF] Jezzard | Correction for geometric distortion in echo planar images from B0 field variations[END_REF] (moreover, measured tissue intensities in these regions change due to the local transformation). Therefore the brain anatomy in EPI does not match with structural images that are much less sensitive to distortions. Such a correspondence is however critical as a joint analysis is often performed for these modalities: 1for diffusion imaging, structural images are used to define regions of interest for fiber tracking or to extract lesions that are to be linked to brain microstructure properties ; 2-for functional MRI, activations are computed on low resolution EPI to speed up acquisition time and need to be aligned with a high resolution T1w image at least for interpretation and visualization of activated regions in the brain. In both cases, it is therefore necessary to perform EPI distortion correction as non linear anatomy mismatch between the modalities will lead to biased results. Computing such a distortion correction is still an open problem, especially in regions where large deformations occur.

As the distortion in EPI acquisitions comes from the B 0 field inhomogeneities, the first technique for distortion correction relies on the acquisition of a B 0 field map [START_REF] Jezzard | Correction for geometric distortion in echo planar images from B0 field variations[END_REF], [START_REF] Reber | Correction of off resonance-related distortion in echo-planar imaging using epibased field maps[END_REF]. This map is in turn used to infer the local contractions and dilations, and correct EPI intensities. This field map however needs to be smoothed to avoid noise corruption and may therefore be unable to provide sufficient correction in severely distorted areas [START_REF] Holland | Efficient correction of inhomogeneous static magnetic field-induced distortion in echo planar imaging[END_REF], [START_REF] Wu | Comparison of EPI distortion correction methods in diffusion tensor MRI using a novel framework[END_REF].

Other techniques have considered new sequences using point spread functions to obtain acquisitions with no distortion. This category includes works by Robson et al. [START_REF] Robson | Measurement of the point spread function in MRI using constant time imaging[END_REF], Chung et al. [START_REF] Chung | An improved PSF mapping method for EPI distortion correction in human brain at ultra high field (7T)[END_REF] and Zaitsev et al. [START_REF] Zaitsev | Point spread function mapping with parallel imaging techniques and high acceleration factors: Fast, robust, and flexible method for echo-planar imaging distortion correction[END_REF]. Unfortunately such sequences are not currently available on all scanners.

A third class of methods considers the acquisition of two EPI sequences with opposite phase encoding directionsone anterior-posterior and one posterior-anterior for exam-ple -to correct for distortion. This class of techniques, initially proposed by Chang and Fitzpatrick [START_REF] Chang | A technique for accurate magnetic resonance imaging in the presence of field inhomogeneities[END_REF] and Bowtell et al. [START_REF] Bowtell | Correction of geometric distortion in echo planar images[END_REF], relies on the computation of a distortion field from the two images to correct the EPI. Several methods use this technique: Andersson et al. [START_REF] Andersson | How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging[END_REF] used a pair of reversed EPI in conjunction with a discrete model of image formation for spin-echo EPI. An implementation called TOPUP is available in the FSL package 1 . Voss et al. [START_REF] Voss | Fiber tracking in the cervical spine and inferior brain regions with reversed gradient diffusion tensor imaging[END_REF] introduced an algorithm to estimate, from the two images, the correction displacement field based on cumulative intensity distributions along each line in the PED. This simple method strongly reduces the distortion, however it is sensitive to noise and the computed transformation needs to be smoothed, leading to a trade-off between regularity and precision. Other methods in this category include Morgan et al. approach [START_REF] Morgan | Correction of spatial distortion in EPI due to inhomogeneous static magnetic fields using the reversed gradient method[END_REF], using continuously alternating phase encoding, Weiskopf et al. method [START_REF] Weiskopf | Singleshot compensation of image distortions and BOLD contrast optimization using multi-echo EPI for reltime fMRI[END_REF] using a modified multi-echo EPI acquisition with reversed phases, or Holland et al. algorithm [START_REF] Holland | Efficient correction of inhomogeneous static magnetic field-induced distortion in echo planar imaging[END_REF] which performs an intensity-based registration (each line being considered independently). As for Voss et al. algorithm, the obtained displacement field is sensitive to noise, especially when large displacements are present. More recently a new method has been proposed to combine EPI with opposite PED with Point Spread Functions (PSF) [START_REF] In | Distortion correction in EPI using an extended psf method with a reversed phase gradient approach[END_REF] however costing additional acquisition time. Finally a registrationbased method has been proposed by Irfanoglu et al. [START_REF] Irfanoglu | DR-BUDDI (diffeomorphic registration for blipup blip-down diffusion imaging) method for correcting echo planar imaging distortions[END_REF] requiring a non distorted image such as a T2 image (in addition to the reversed PED image) which is used as the central point where the two images with reversed PEDs are transformed. It minimizes a cost function to compute a transformation which has no a priori restriction with respect to EPI image formation. The transformation is instead projected after each step of the minimization to follow a distortion model (with distortions appearing uniquely along the PED).

This last category of techniques has the advantage of requiring only a short additional acquisition time to correct for distortion: if we assume no patient movement occurred during the acquisition and that the magnetic field inhomogeneity stays constant during the acquisition [START_REF] Vovk | A review of methods for correction of intensity inhomogeneity in mri[END_REF], only one supplemental EPI image with reversed PED is necessary to correct the entire EPI series (e.g. fMRI or DWI acquisition). We therefore present a new algorithm for distortion correction falling in the same category. Block-matching based registration has been successfully proposed for registration in medical imaging both for rigid [START_REF] Ourselin | Block matching: A general framework to improve robustness of rigid registration of medical images[END_REF] and non-linear registration [START_REF] Commowick | Automated diffeomorphic registration of anatomical structures with rigid parts: Application to dynamic cervical MRI[END_REF]. As a registration framework, block-matching has the advantage of being very generic and easily adaptable to different transformation priors, both to match blocks in the floating image [START_REF] Commowick | Blockmatching strategies for rigid registration of multimodal medical images[END_REF] and for the global transformation (linear or non-linear). Moreover, this framework is also robust to outliers in the local matches. We therefore propose in this work a new approach towards distortion correction of EPI based on block-matching. It is designed to register two images ac-1 http://fsl.fmrib.ox.ac.uk/fsl/fslwiki quired with opposite PED without requiring an additional structural image. To do so, we introduce a new symmetric block-matching registration algorithm, optimizing local affine transformations constrained a priori in the PED to match the expected distortions in EPI. In addition, the transformation is computed as opposite symmetric to match the distortion model in EPI [START_REF] Jezzard | Correction for geometric distortion in echo planar images from B0 field variations[END_REF]. The implementation of our algorithm is available in our open source medical image processing toolbox Anima2 .

We evaluate our new algorithm qualitatively and quantitatively on two datasets in Section IV. First, we present results on EPI acquisitions of a phantom, where the geometry of the image is known. We also perform evaluation on in-vivo diffusion-weighted EPI of five subjects for which images with four different PED (anterior-posterior (AP), posterior-anterior (PA), left-right (LR), right-left (RL)) were acquired. We present our results in contrast to two state-of-the-art methods using the same inputs: TOPUP from Andersson et al. [START_REF] Andersson | How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging[END_REF] and Voss et al. method [START_REF] Voss | Fiber tracking in the cervical spine and inferior brain regions with reversed gradient diffusion tensor imaging[END_REF]. Results demonstrate the ability of our algorithm to compute a robust EPI distortion correction.

II. Methods

A. Distortion Model

We assume that two images have been acquired: I F is the EPI forward image acquired with a classical PED (AP for example), and I B is the EPI backward image acquired with a reversed PED (PA in this case). The goal of EPI distortion correction is to estimate a distortion transformation field from these two images. Then, from this field, it is possible to recover a corrected image C from these two images, but also an entire serie of EPI acquired with AP or PA PED. Jezzard et al. [START_REF] Jezzard | Correction for geometric distortion in echo planar images from B0 field variations[END_REF] have demonstrated that deformations due to B 0 field inhomogeneities appear mainly along the PED and are negligible in other directions. More precisely, we follow the distortion model as expressed previously in [START_REF] Voss | Fiber tracking in the cervical spine and inferior brain regions with reversed gradient diffusion tensor imaging[END_REF], [START_REF] Morgan | Correction of spatial distortion in EPI due to inhomogeneous static magnetic fields using the reversed gradient method[END_REF] which assumes that I F and I B are generated from the theoretical corrected image C using a displacement field parallel to the PED:

C(x) = J T+ (x)I F (T + (x)) C(x) = J T-(x)I B (T -(x)) (1)
where

T + (x) = x + U (x) and T -(x) = x -U (x)
. J T+ and J T-denote the Jacobian determinants of the local deformations which account for intensity changes in the distorted areas. It will lead to an increased intensity in the contracted areas and a decreased intensity in the dilated areas. U corresponds to the distortion displacement field which is parallel to the PED, e.g. if the PED is along the y-axis then U (x) = [0 U y (x) 0] T . It is assumed in this model that T + and T -are opposite symmetric, i.e. that they share the same U up to a minus sign along the PED.

B. Block-Matching for Distortion Correction

Different approaches may be considered to match the two images. In the distortion model, the corrected image C is generally unknown. It could be replaced (as suggested in [START_REF] Irfanoglu | DR-BUDDI (diffeomorphic registration for blipup blip-down diffusion imaging) method for correcting echo planar imaging distortions[END_REF]) by a non distorted similar acquisition (such as a T2 weighted acquisition). However, this is not always available in clinical acquisitions. We therefore consider the case where C can be at best estimated and choose a registration approach that does not rely on it. A registration method has been introduced by Avants et al. [START_REF] Avants | Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain[END_REF] allowing to estimate the corrected image C without having it directly appear in the algorithm. The idea, instead of looking for the transformation T between two images, is to seek the half-transformation T 1/2 so that the two images registered from I F and I B match as much as possible:

I F • T 1/2 ≈ I B • T -1/2 ≈ C (2)
We adapt this approach to a block-matching algorithm [START_REF] Ourselin | Block matching: A general framework to improve robustness of rigid registration of medical images[END_REF], [START_REF] Commowick | Automated diffeomorphic registration of anatomical structures with rigid parts: Application to dynamic cervical MRI[END_REF] by constraining the transformation to be aligned with the PED as assumed in the distortion model. The block-matching algorithm enables a simple and effective incorporation of this constraint on the deformation field.

First we present the global scheme of the block-matching algorithm, then we detail each part separately. We consider an initial transformation U 0 which can be null or coming from another coarse correction algorithm. We use a classic multi-resolution pyramidal scheme [START_REF] Burt | The laplacian pyramid as a compact image code[END_REF] to process images from coarse to fine resolution. At each level of the pyramid, from the transformation at the previous pyramid level, we proceed as described in Algorithm 1 and illustrated as a diagram in Fig. 1.

Algorithm 1 Block-Matching Algorithm for EPI Distortion Correction 1: for p = 1...P , iteration on pyramid levels, do 2:

for l = 1...L, iterations, do

3:

Resample images to get I F,l-1 and I B,l-1

4:

Estimate local transformations for each block on I B,l-1 : A + ← block-matching(I B,l-1 , I F,l-1 )

5:

Estimate local transformations for each block on

I F,l-1 : A -← block-matching(I F,l-1 , I B,l -1 ) 6:
Extrapolate asymmetric dense SVF updates from A + and A -:

δS + ← extrapolate(A + ), δS -← extrapolate(A -) 7:
Compute a symmetric SVF update: δS, and compose it with current transformations 8:

Ensure T +,l and T -,l are opposite symmetric 9:

Regularize (elastic-like) T +,l and T -,l

At each step, we first resample the original images with the current transformation. Then we estimate pairings between the images in the forward and backward directions (A + = { Â+,1 , .., Â+,N } and A -= { Â-,1 , .., Â-,N }) using a block-matching algorithm. We utilize A + and A -to extrapolate two asymmetric stationary velocity fields (SVF) δS + and δS -which are combined into a symmetric SVF update δS (Section II-C). We then compose this update with T +,l-1 and T -,l-1 , and ensure that T + and T -still share the same displacement field U . Finally, the current displacement field is regularized using a convolution with a Gaussian kernel (standard deviation σ E ). The following sections detail the block-matching, extrapolation and composition steps of this algorithm and their specificities for distortion correction of EPI.

1) Block-Matching of Distorted EPI:

At each iteration, we define blocks B +,i , which are patches centered at x i with size (2N +1) 3 , regularly placed on image I B,l-1 (every V voxels in each direction). We also define blocks B -,i with the same characteristics on I F,l-1 . For each of those blocks, we look for an adapted transformation best matching them respectively to I F,l-1 and I B,l-1 . Let L be the set of allowed transformations for matching blocks. Frequently, in other applications, the transformation sought between blocks is a simple 3-dimensional translation. In the case of EPI distortion, the set L can be further adapted to match a priori the expected features of the distortion at the block level and thus obtain a more robust transformation estimation. First the model assumes that distortions appear uniquely along the PED: a one-dimensional translation along the PED (modeled by one parameter t .,i ) is therefore sufficient. At the scale of the block, a single translation is however not enough to account for local contractions and dilations due to the distortion at different points of the block. We account for this by adding three parameters to the transformation. The first one accounts for the change of scale due to the global contraction or dilation inside the block (s .,i ). This scale parameter solves the problem of global scaling inside the block, however different lines along the PED will have different distortions generating skewness at the block level. To consider this, we define two skew components (k .,i and m .,i ) for the two directions complementary to the PED. Assuming the PED is the yaxis, A .,i can be expressed as a 4 × 4 matrix:

A .,i =     1 0 0 0 k .,i s .,i m .,i t .,i 0 0 1 0 0 0 0 1     (3)
Note that having the PED on an other axis will result in the line of parameters being displaced on the first or third line of the matrix. A few interesting properties are associated to this transformation. The Jacobian determinant of the transformation is simply computed as the scaling parameter s .,i , and this parameter is therefore utilized directly for modeling the intensity changes due to distortion at the block level. In addition, this transformation has an analytic form for its matrix logarithm, and may therefore be directly estimated in the log-Euclidean space to speed up the global SVF extrapolation process (see Section II-C).

The block-matching step then amounts to estimate the four log-parameters of each block transformation in L to compute the set of optimal transformations Â+,i and Â-,i (respectively for blocks B +,i and B -,i ) optimizing a similarity measure S between I F,l-1 and I B,l-1 :

At the L-th iteration

Original I F Current forward transform T +,l-1 Current backward transform T -,l-1 Original I B Resample I F,l-1 Resample I B,l-1 δS + δS -
Block-matching in the log-Euclidean space Symmetrize the transform Go back to the regular space Â+,i = arg max

δS = 1 4 (δS + -δS -) δT + , δT - Exponential T +,l = T +,l-1 • δT + T -,l = T -,l-1 • δT -
A+,i S J A+,i I F,l-1 • A +,i , I B,l-1 (4) Â-,i = arg max A-,i S I F,l-1 , J A-,i I B,l-1 • A -,i (5)
This optimization is performed using the BOBYQA algorithm for gradient free optimization with parameters within predefined bounds [START_REF] Powell | The BOBYQA algorithm for bound constrained optimization without derivatives[END_REF]. It proceeds by successively computing quadratic approximations to the cost function to find its local maximum.

2) Confidence weights:

We have computed for each block B .,i the local transformation Â.,i that optimizes the similarity measure S. We then assign to this transformation a weight w .,i to estimate the confidence in the block match. To do so, we use a combination of two different terms. The first one is the similarity itself Ŝ.,i assuming it belongs to the range [0, 1], 1 being the best result (if not, a function of Ŝ.,i can be used). The second one, w d (B .,i ) gives an index of the local structure of the reference block along the PED. If the block structure is parallel to the PED, all tested transformations A .,i for that block may get the same similarity score, thereby introducing uncertainty in the matches. Actually, the algorithm will always find a solution due to small variations of intensities or computing precision. However the quality of such solutions will be random. We therefore want to avoid as much as possible such random solutions which can propagate important errors. Only considering the optimal similarity is therefore not enough and we introduce the index w d to give a low weight to these uncertain blocks and their corresponding local transformations. w d is defined as a function of the structure tensor inside the reference block B .,i :

w d (B .,i ) = c l D B.,i < vD B .,i , g > (6)
• D B.,i is the average structure tensor of block B .,i

• c l (D B.,i
) is a linear coefficient which quantifies the anisotropy of the tensor [START_REF] Westin | Processing and visualization for diffusion tensor MRI[END_REF] -

c l (D B.,i ) = λ 1 -λ 2 λ 1 , with λ 1 λ 2 λ 3 the eigenvalues of D B(.,i) -c l (D B.,i ) is close to 0 if D B.
,i has a planar or circular structure and close to 1 if it has a very anisotropic one

• vD B .,i is the principal eigenvector of D B.,i
• g is the unit vector along the PED w d will be 0 if the structure tensor is perpendicular to the PED (image structure parallel to g) or planar/spherical (c l = 0) giving a structure based confidence to the matches. Finally, the weight for the match of block B .,i is defined as the geometric mean of the similarity index and the structural index:

w .,i = w d (B .,i ) Ŝ.,i (7)

C. Transformation Extrapolation and Composition

From the block-matching algorithm, two sets of block pairings have been constituted: one for I F , Â+ = ( Â+,1 , . . . , Â+,m ), and one for I B , Â-= ( Â-,1 , . . . , Â-,n ). Each pairing is defined by the center of its corresponding block B .,i , a transformation Â.,i , and a weight w .,i . We then extrapolate two update SVFs from the sparse weighted transformation logarithms: δS + = extrapolate( Â+ ) and δS -= extrapolate( Â-). This extrapolation aims at computing a dense field of transformation logarithms R.,i (i = 1, ..., M representing each voxel) from the sparse Â.,j . This is performed utilizing an Msmoothing algorithm in the log-Euclidean space on affine transformations [START_REF] Arsigny | A fast and log-euclidean polyaffine framework for locally linear registration[END_REF] as proposed in [START_REF] Commowick | Automated diffeomorphic registration of anatomical structures with rigid parts: Application to dynamic cervical MRI[END_REF]:

( R.,1 , . . . , R.,M ) = arg min R.,1,...,R .,M M i=1 j∈Ni w B.,j ρ ||R .,i -log Â.,j || 2 d |x i -x j | 2 (8)
where log denotes the matrix logarithm, x j is the spatial position of pairing, N i is the neighbourhood of x i , ρ is a robust error norm to account for outliers in the set of sparse transformations Â. (here the Welsh function), d is a function of the Euclidean distance -here d(b 2 ) = exp(-b 2 /2θ 2 ) -giving more importance to spatially close reference pairings. This cost function is optimized through an iterative scheme, more detailed in [START_REF] Commowick | Automated diffeomorphic registration of anatomical structures with rigid parts: Application to dynamic cervical MRI[END_REF]. The obtained transformation logarithms R.,i are then applied to their respective positions x i to compute the SVFs δS + and δS -: δS . (x i ) = R.,i x i . Extrapolating update SVFs using this Msmoothing algorithm, we incorporate an outlier rejection framework, mainly coming from the ρ function in Eq. ( 8), that removes from the resulting SVF erroneous block transformation logarithms due for example to artifacts or other effects in I F,l-1 and I B,l-1 . In addition, the extrapolated fields are SVFs and therefore encode diffeomorphic and invertible transformations. A symmetric δS is then computed, following Vercauteren et al. approach [START_REF] Vercauteren | Symmetric log-domain diffeomorphic registration: A demons-based approach[END_REF], as a quarter of the subtraction of asymmetric incremental updates δS + and δS -:

δS = 1 4 (δS + -δS -) (9)
While the half difference of the two asymmetric incremental updates is sufficient to compute a symmetrized field, δS is computed as a quarter of the difference as we are seeking the transformation bringing the two input images towards an unknown middle image C. As such only the half symmetric SVF is needed. The final step of each iteration then amounts to composing the updates with the current transformations and ensure that the resulting T +,l and T -,l transformations still share the same displacement field U at the l-th iteration U l . To do so, δT + and δT -are first obtained by exponentiating δS: δT + = exp(δS) and δT -= exp(-δS) [START_REF] Arsigny | A fast and log-euclidean polyaffine framework for locally linear registration[END_REF], and composed with the current transformations:

T +,l = T +,l-1 • δT + and T -,l = T -,l-1 • δT -.
As the composition and inverse operations do not ensure the opposite symmetry condition, we finally compute the shared displacement field

U l as U l (x) = 1 2 (T +,l (x) -T -,l (x)) such that T +,l (x) = x + U l (x) and T -,l (x) = x -U l (x).

III. Experimental Design

A. Image acquisitions

Imaging was performed on a Siemens Verio 3T scanner. The approach was evaluated on in vitro and in vivo data:

• In vitro: A grid phantom with known geometry developed by the UNIRS group from the CEA Neurospin for the CATI Consortium for image acquisition and processing3 was imaged : b 0 images (AP, PA, LR and RL) were acquired with a 12 channels coil, a 128×128×60 matrix size and a 2×2×2mm 3 voxel size. • In vivo: 5 healthy volunteers were imaged after approval from the local institutional review board. For each volunteer, two pairs of b 0 EPI images with opposite PED (AP/PA and LR/RL), 128×128×60 matrix size and 2×2×2mm 3 voxel size were acquired with a 32 channels head coil. The EPI images were acquired using the parallel imaging method GRAPPA with an acceleration factor of 2 (T E = 82ms and an echo space 0.69ms). Regular clinical DWI were also acquired (30 gradient directions, b = 1000s.mm -2 ) with identical geometry and AP PED.

B. Experimental methods 1) Evaluation strategy:

In order to estimate the quality of the distortion correction we follow the process illustrated in Fig. 2. We first estimate a corrected image C AP/P A from one pair of reversed b 0 EPI (AP/PA). Then, independently, we estimate a corrected image C LR/RL from the other pair of reversed b 0 EPI (LR/RL). Each pair of reversed EPI has a PED following the same orientation but with an opposite direction. However the two pairs have a PED following a different orientation. This means that distortions will affect different areas of the brain in a different way depending on the orientation of the PED. We thus consider the quality of the match between C AP/P A and C LR/RL as an index to estimate the general quality of the distortion correction (see Fig. 2). If the two pairs of images are perfectly corrected, they will match after correction. In the following, we compare three different distortion correction methods with different metrics.

2) Method 1: Voss: The first evaluated method was proposed by Voss et al [START_REF] Voss | Fiber tracking in the cervical spine and inferior brain regions with reversed gradient diffusion tensor imaging[END_REF]. Their approach amounts, for each line in the PED, for both images, to do:

• Compute normalized cumulated intensities N i (y) = 1 α i y 0 L i (x)dx for i = 1, 2 (10)
• L 1 and L 2 are line intensities of images I F and I B , α 1 and α 2 are normalization constants:

α i = ∞ 0 L i (x)dx for i = 1, 2 (11)
• For a large number n of values x n between 0 and 1, find by cubic interpolation [START_REF] Schoenberg | Cardinal spline interpolation, ser. Regional conference series in applied mathematics[END_REF] y 1,n and y 2,n such that

N 1 (y 1,n ) = N 2 (y 2,n ) = x n • At each position y n = (y 1,n + y 2,n )/2, the transforma- tion map is computed as U (y n ) = y 1,n -y n = y n -y 2,n (12)
This algorithm has the advantage of being very fast and simple. However, it is highly sensitive to noise and lines registrations are purely independent which may lead to unrealistic transitions between consecutive lines. Therefore, a 3D Gaussian smoothing with a standard deviation σ is performed on the obtained transformation T , which leads to a trade-off between transformation precision (small Gaussian σ) and transformation regularity (high Gaussian σ). In our experimentations, we have set σ to one pixel.

3) Method 2: TOPUP: In addition to Voss et al. method, we also evaluated the distortion correction obtained from the TOPUP algorithm, available within the FSL package 4 . This correction method is based on the work from Andersson et al. [START_REF] Andersson | How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging[END_REF]. It uses a model of EPI image formation and, together with the two images with opposite PEDs, reconstructs a deformation field to obtain a corrected EPI. More details are provided in Andersson et al. publication or on the FSL documentation page. We utilized the default parameters of this method for all of our experiments.

4) Method 3: Proposed block-matching technique: Distortion correction involves finding very large and local displacements between the images, displacements that may be extremely difficult to recover for registration approaches. We tackle this problem using a coarse-to-fine approach to recover EPI distortion and using Voss et al. method with a large σ smoothing value as an initial transformation, which is then further improved with our block-matching strategy.

Aside from transformation initialization, the blockmatching implementation has different parameters, that are set as follows. First, we use three levels on the multiresolution pyramid and 10 iterations at each level. The size of each block is 3 × 3 × 3 (i.e. N = 1). These blocks are placed regularly every two voxels in each direction (V = 2). The initial search radius for BOBYQA is set to 2 voxels, the initial skew radius is set to 0.1, and the initial scale radius to 0.1. We use a squared correlation coefficient as the similarity measure between blocks. At the end of each iteration, the elastic regularization is made with a σ E value of 2 voxels. These parameters were set to the same values for each distortion correction experiment.

C. Evaluation Metrics

1) Phantom Evaluation: point-based metric: Contrary to brain images, the phantom acquisition has a known grid structure on which landmarks are easily identifiable. For each uncorrected image (AP, PA, LR and RL), 20 landmarks were carefully and manually selected at voxels representing crossing points. To evaluate quantitatively distortion correction, we have then applied the following steps for each evaluated method. First, images AP and PA, respectively LR and RL, were used to correct their distortion and estimate two deformation fields (one for AP/PA and one for LR/RL). For this specific evaluation, they were applied independently to the spatial landmark positions in AP, PA, LR and RL giving 4 corrected images. If the distortion correction is perfect, the transformed points should then match after transformation. We evaluate this match by computing an average of the one to one Euclidean distances between the landmarks:

d i = 1 6 4 j=1 4 k>j ||p i,j -p i,k || (13)
where p i,j denotes the transformed i-th landmark on image j (one of the four images with different PEDs, AP, PA, LR and RL). d i is a distance in millimeters characterizing at which point the four images are distorted after correction around the specific locations of the p i,j : the closer d i is to 0, the closer the four input images are around the i-th landmark.

2) Brain images evaluation: intensity-based metrics: To compare images from the brain database after correction, we define a similarity measure computed between the two corrected images (C AP/P A and C LR/RL ).

This evaluation similarity measure (Sim) is defined as a sum of local correlation coefficients normalized between two images. To compute this metric only on relevant areas, masks are computed on four images, the two corrected by TOPUP and the two corrected by BM using the brain extraction tool of the FSL package 5 . Then the union of these four masks is used to obtain the global mask M and therefore compute the similarity measure:

Sim(I, J, M) = 1 Card(M) p∈M C(I Np , J Np ) ( 14
)
where I Np and J Np are neighborhoods of p in I and J, defined as a cube centered on p of size (2q + 1) 3 , in the result part q = 3. C is the local correlation between I Np and J Np . Card(M) denotes the cardinal of the set to ensure that Sim belongs to the range [0,1]. Sim characterizes well if the images match after correction and is defined between 0 and 1 which is useful to keep the same stable index between several subjects.

IV. Results

A. Results on the Phantom

We first compare the different distortion correction algorithms on the phantom acquisition. We present in Fig. 3 a visual example of the phantom images before and after correction. The BM corrected images are really close and appear visually as being well corrected for distortion. TOPUP images are also properly corrected. Phantom images however do not represent a realistic anatomy and the distortion correction quality may vary depending on the methods. For example, Voss method is not adapted for this kind of bicolor images and gives visually poorer results. In addition to visual inspection, we computed landmark position errors based on the distance presented in Section III-C1, Eq. ( 13). These results are illustrated in Fig. 4, showing the box-plots of d i distances over all i. Voss performs slightly and significantly better than uncorrected images (paired t-test, p = 3 × 10 -3 , average error of 2.09 mm compared to 3.46 mm untouched), illustrating its modest performance on this specific dataset. TOPUP also significantly reduces the distance errors, to an average of 1.54 mm, with respect to both uncorrected images (paired

B. Results on in-vivo Data 1) Qualitative Results:

We first present in Fig. 5 results of our distortion correction method by visualizing b 0 , corresponding color fractional anisotropy (CFA) images and their corresponding T1 (not distorted) image. The color in CFA map depends on the principal direction of the tensor (red is Left/Right, green Anterior/Posterior and blue Foot/Head) and the intensity of the color is proportional to the FA value. The two lines correspond to a different phase encoding orientation to show distortion in different orientations. It can clearly be seen on Fig. 5 that left-right PED images suffer from large deformations around the falx cerebri (see arrows on Fig. 5.a,c), and on anterior-posterior acquisition the brainstem has a spatial displacement (see arrows on Fig. 5.f,h). On the contrary, our distortion correction method allows for a good matching of the structures in the T1 image and both b 0 and color FA images. Such a good correction will then allow, for example, for a better definition of regions of interest from the T1 image to seed fiber tracts on the diffusion image, or to study diffusion model properties in specific anatomical regions.

We then illustrate on Fig. 6 distortion correction results of the different evaluated methods on a pair of EPI with opposite PED (anterior-posterior and posterior-anterior). On this strongly affected area, we compared the three different distortion correction methods with respect to a structural image (T1 image). We first noticed that the three corrected images are more similar to the structural image than the original ones, suggesting that each method is able to strongly reduce the distortions. However the image corrected using Voss et al. method (Fig. 6.d) still presents a mismatch around the lateral ventricles (see arrow on Fig. 6.b). TOPUP and BM both obtain a corrected image very close to the structural T1 image.

2) Quantitative Results: We performed experiments on an Intel Xeon 2.5 Ghz computer on 20 cores. The mean time per subject is very short (about 5s) for the Voss algorithm, 170s for the BM and 500s for TOPUP. Unlike TOPUP, BM is multi-threaded, allowing a faster computation time which may be useful in the clinic.

To obtain a quantitative evaluation of the quality of the corrected images, the similarity metric (Sim) introduced in Section III-C2 was computed on the dataset of 5 subjects after correction by the different methods. The Sim metric results between the two corrected images C AP/P A Between BM and TOPUP, the best score depends on the subject, the average similarity for the 5 subjects is better for BM than TOPUP however it is not statistically significant (Wilcoxon signed-rank test, p = 0.69).

V. Discussion and Conclusion

We have presented a new block-matching based algorithm for EPI distortion correction using an additional EPI with reversed PED. To this end, we have developed specific linear transformations constrained to fit a priori with the distortion model at the block level. This transformation definition, integrated into a symmetric blockmatching algorithm, ensures a robust computation of an opposite symmetric transformation.

We have tested our distortion correction and two stateof-the-art methods on a phantom with a known ground truth shape. Our results perform significantly better than Voss et al. correction, which is not adapted for images with uniform intensity regions. Moreover BM performs significantly better than TOPUP algorithm but at a sub-voxel level (though one should not over interpret this difference). Then, we have evaluated the BM registration on 5 subjects with 2 pairs of b 0 EPI. A similarity measure based on local correlation between the 2 corrected images C AP/P A and C LR/RL show a significant improvement between the Voss initialization and the BM correction. TOPUP algorithm and BM obtain similar levels of similarity. Our BM algorithm is implemented in a multi-threaded fashion using ITK allowing for faster computation time than TOPUP.

A common problem with reversed PED methods is motion since the a priori distortion model is not true any more in that case. The best way to avoid motion problems is to perform an acquisition with continuously alternating PEDs and to correct all pairs independently. For clinical use it is also possible to acquire only one PA and a series of AP and then correct the entire series from the deformation field estimated. This is more subject to the motion issue but also reduces the acquisition time, which is crucial.

The intensity of distortion in EPI is related to susceptibility-induced fields and eddy current-induced fields. The general trend to increase the scanner field strength increases distortions [START_REF] Wang | Propeller epi: an mri technique suitable for diffusion tensor imaging at high field strength with reduced geometric distortions[END_REF]. Thus it is essential to have efficient tools to correct these distortions. With that goal, we proposed a new simple and robust method, computationally efficient, ready for a clinical use. We studied its application for diffusion MRI, however it can be used for other modalities based on EPI acquisitions such as functional MRI.

Fig. 1 .

 1 Fig. 1. Graphical illustration of one iteration of the block-matching algorithm.

Fig. 2 .

 2 Fig.2. Illustration of the evaluation process for two pairs of EPI images with different reversed PEDs. On the left side, the AP (Top) and the PA (Bottom) images corrected by BM (Middle). On the right side, the LR (Top) and the RL (Bottom) images corrected by BM (Middle). A similarity measure between the 2 corrected images is performed to estimate the quality of the corrections.

Fig. 4 .

 4 Fig. 4. Landmark position errors on the phantom. Errors (in mm) box-plot before and after distortion correction with the Voss correction method, TOPUP and the proposed technique. Error differences are all significant (paired t-test see text for more details).

Fig. 3 .

 3 Fig. 3. Distortion correction results on a phantom. Illustration of EPI distortion corrections with the evaluated methods on images acquired with opposite PEDs along the anterior-posterior axis (first line) and the left-right axis (second line). (a-b, f-g): uncorrected b 0 images, (c,h): correction with Voss et al. method, (d,i): correction with TOPUP, (e,j): correction with BM algorithm (proposed technique).

Fig. 5 .

 5 Fig. 5. Block-Matching distortion correction results compare to original images. Illustration of Block-Matching EPI distortion corrections on b 0 images acquired with opposite PEDs. The distortion field is computed from the two b 0 images and applied to an entire DWI volume with a left-right PED for the first line and a anterior-posterior PED for the second one. The fractional anisotropy (FA) is then estimated from the original and the corrected DWI. (a-f): uncorrected b 0 images, (b,g): block-matching corrected b 0 images, (c,h): uncorrected FA, (d,i): block-matching corrected FA, (e, j): structural T1 reference.

Fig. 6 .

 6 Fig. 6. Registration results on a subject according different distortion correction methods. First row : (a) b 0 acquired with anterior-posterior PED; Mean of opposed PEDs corrected images : (b) by Voss; (c) by TOPUP; (d) by BM; (e) T1 structural reference. Second row (f) to (i) : zoom on the lateral ventricles of the corresponding colored FA; (j) T1 zoomed.

TABLE I

 I Correlation results (Sim measure) between AP/PA and LR/RL images. Columns from left to right: no correction, M 1 , M 2 and M 3 .

	Sim	Untouched Voss	BM	TOPUP
	Subject 1	0.842	0.901 0.916	0.927
	Subject 2	0.818	0.904 0.918	0.937
	Subject 3	0.812	0.875 0.894	0.859
	Subject 4	0.886	0.923 0.939	0.954
	Subject 5	0.872	0.913 0.921	0.898
	Mean	0.852	0.903 0.918	0.915

https://github.com/Inria-Visages/Anima-Public

http://cati-neuroimaging.com

http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/TOPUP

http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FSL

Acknowledgments

Renaud Hédouin PhD is partially funded by the Brittany Council. MRI data acquisition was supported by the Neurinfo MRI research facility from the University of Rennes I. Neurinfo is granted by the the European Union (FEDER), the French State, the Brittany Council, Rennes Metropole, Inria, Inserm and the University Hospital of Rennes. The grid phantom was developed by the UNIRS group from the CEA Neurospin for the CATI Consortium for image acquisition and processing.


Marie-Amélie Coste

Christine Huguet

Nathalie Vanfasse

Dickensian

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

Introduction

Marie-Amélie Coste, Lycée Jules Ferry Christine Huguet, Université de Lille, CECILLE, EA 4074 Nathalie Vanfasse, Aix Marseille Univ, LERMA, Aix-en-Provence, France Though Dickens is best known for his unique characters, he is also associated with unforgettable descriptions of London. These memorable cityscapes will be used here as a springboard to conduct an in-depth analysis of Dickensian landscapes in general. In the wake of Malcolm Andrews's study of Landscape and Western Art, the word landscape is understood here as a twofold process in which land is not just perceived as landscape but actually built into art; in other words landscape is defined here as land "aesthetically processed" (Andrews 1, 7), or to paraphrase Simon Schama in Landscape and Memory, as a way of elaborating on land as raw matter (10). 1 It is this complex construction of landscapes-which in this instance are made of words-that the following collection of articles brings to light. They consider how Dickens combined what he saw with imaginary constructions, to build the unique cityscapes we all know so well. They show that Dickens's landscapes were informed by other artistic landscapes as well as by actual views of Victorian scenery.

Unravelling the cultural influences, myths and memories that influenced his writing in the building of such landscapes, they tackle the question of mental landscapes.

Mindscapes feature in fact prominently in this selection of articles.

These papers show how Dickens framed the scenery that he chose to depict and how his landscapes provide a setting for other views. Far from being mere backdrops, however, these landscapes always complement what they frame or foreground in subtle and complex ways. Some of them even seem to exist in their own right and not as mere frameworks for other subjects. This collection of essays examines the very nature of Dickens's response to his surroundings. The reader's experience of Dickensian landscapes is scrutinised and their sensory, personal but also spiritual and aesthetic dimensions are explored in detail. Following a pictorial model, the very composition of these landscapes is also taken into account-that is to say their subject matter, framing, foreground, middle ground and background. The feeling of unity that each landscape does or does not convey is also considered.

The articles further highlight how Dickens contributed, through his writing of landscapes, to making their surroundings more intelligible to readers. Dickens thus shed new light on Victorian scenery. His literary representation of contemporary landscapes recomposed reality and produced aesthetic emotions that made it possible for his readers to take a step back, to apprehend and appreciate their environment differently. Victorian urban or industrial areas must indeed have seemed disconcerting, baffling, inhospitable and even hostile. In this respect, such areas could be compared to a "new wilderness" (Andrews 18). Through his writing, Dickens endeavoured to make sense of this modern wilderness.

Last but not least, the contributions to this collection examine the opposition between cityscapes and landscapes and its implications. They show that this opposition dissolves, in the last analysis, into a set of complex issues that both polarise the dichotomy between urban and rural areas, and paradoxically enough connect them even more narrowly. This involves what the geographer Denis Cosgrove has defined as the insider/outsider opposition, in which insiders experience the landscape without seeing it as such, while outsiders admire it without noticing the experience of its inhabitants. 2 In keeping with Malcolm Andrews's approach, the first section of this collection, entitled "Constructing Land into Landscape", is devoted to the transformation of land into landscape. Marianne Camus underlines the modernity of Dickensian landscapes. She demonstrates how Dickens's insights seem to foreshadow artistic movements such as impressionism and cubism, as well as new media like the cinema-since his landscapes are often "on the move", as seen as it were, through the eye of a camera.

What stands out most clearly in Camus's contribution is the construction of landscape and its framing by the senses-all the senses and not simply sight-feelings and memories of the perceiver. Dickens thus draws our attention to the predominant role of perception in the transformation of land into landscape. He also highlights the distortions and limitations of perception by debunking the superimposition onto landscapes of fashionable concepts, such as the picturesque, which eliminates people and their real sufferings from the pictures. A most interesting discussion arises in this respect between Camus's article and the next ones by Nathalie Jaëck and Xavier Amelot on the one hand, and Mark Frost on the other.

Geographical input is brought to bear by Jaëck and Amelot who describe how

Dickens understood the rhetoric of landscape and developed strategies to resist it. Indeed Dickens deconstructs typical romantic country scenery, showing their literal as well as metaphorical emptiness, and shifts the focus on the people living in the landscapes, themselves to be understood more often than not as cityscapes, or more precisely as "cityscopes". He is not interested in the falsely idyllic country pictures enjoyed by the happy few, but in the workers and the newly born cities, seen from a viewpoint that is no longer panoramic and stable but mobile and fragmented.

According to Mark Frost, it is precisely Dickens's urban gaze, alive to the unjust sufferings and exploitation of the people, which accounts for his apparent wooden descriptions of the countryside. Focusing more particularly on The Old Curiosity Shop, he shows how the novel's quest for "a pastoral idyll (a site of peaceful retreat and natural plenty, in which humans engage harmoniously with their environment, providing an effective alternative to debased urban existence)" fails, leading the novel "into the territory of pastoral elegy (in which the lost idyll is recalled with regret) and anti-pastoralism (in which scepticism about the possibility of idylls becomes prominent)". The countryside is only an extension of the city; Nell is struggling to escape from Quilp, the monster spewed out by the city; and Dickens's novel betrays the anxieties caused by the blurring of the radical distinction between the rural and the urban.

Moving from the transformation of real land into landscapes, the second part of this collection of essays, "Landscapes and the Mind" focuses on the internalisation of landscapes and the way they can give rise to various mindscapes. Françoise Dupeyron-Lafay offers a detailed and most subtle analysis of Bleak House, which she opposes to earlier novels such as Oliver Twist and The Old Curiosity Shop, to highlight how sharp distinctions have broken down and given way to an all-pervasive corruption and "an uncanny similarity between London and the country". In a way that echoes Camus, Dupeyron-Lafay suggests that we understand landscapes in Bleak House not only as "mindscapes", but as the projection of the characters' unconscious, and even as places bearing simultaneously signs of the past, the present and the future in "a foreshortening of the diachronic perspective [which] produces a sense of constriction akin to claustrophobia. Everything merges and converges in this world where evil, corruption and suffering are as diffuse, elusive and ubiquitous as the unhealthy London fog".

Sara Gazo offers another take on Dickensian mental scapes, which she approaches from the angle of dreamscapes. Her article shows that Dickens used dreamscapes to explore geographical spaces differently but also to connect these spaces to the space of the mind. Gazo traces the evolution of Dickensian dreamscapes from the 1830s until the 1860s through three short texts, namely an essay from Sketches by Boz entitled "Early Coaches", a section from Pictures from Italy on Venice and another essay from The Uncommercial Traveller bearing the title "Night Walks". Gazo relates the dreamscapes described in these texts to interactions between external stimuli and the innermost self. Besides analysing such phenomena in detail, she alludes to the scientific theories underlying them as well as to various mental states and external elements triggering them. The article shows that dreamscapes are characterised by shifting perspectives rendered narratively by the use of references to optical devices like the magic lantern or the diorama. From these dreamscapes emerge scenes infused with mystery and eeriness typical of the sensations, thoughts and impressions experienced during sleep, ranging from daydreaming to nocturnal dreamscapes. Atmospheric cityscapes pervade almost all of these dreams; they do so, however, in altered forms that connect urban geography and the geography of the mind in complex manifestations involving projections of the self. In these alternative urban environments, the limits between the inner self and the world become blurred. The maze of the city comes to mirror the labyrinth of the mind.

In the last section of this collection of articles, "Man, Place and Landscape", Diana Archibald, Norbert Lennartz and James Cutler explore further connections between man, place and landscape. Norbert Lennartz deals with landscape through the turbulent relations between man and nature. His article mentions the destructions wrought by man upon nature and, by extension, upon the landscape. Lennartz depicts the opposition between nature and cities as a violent clash in which one does not know the victim from the victimiser. Treacherous cities repress nature and monstrous nature, incubate the foulest miasma that are not just to be found and left to stagnate in the distant swamps of America but encroach upon the very heart of London, via the Thames. This article situates Dickensian landscapes somewhere in between those depicted by Wordsworth and Byron. Dickens is not so reluctant as the former to present the conflicts brought about by the imbalance between man and nature, nor as thoroughly pessimistic in his depiction of nature as the latter is, although his optimism rests on somewhat blinkered views, much to some critics' woe-Lennartz notably recalls how Allan MacDuffie complains that Dickens leaves his readers "with the unsatisfying idea that middle-class marriage makes possible some kind of clean, untapped, uncompromised energy source".

Landscapes of liminality where in-betweenness prevails is the subject of Diana Archibald's article, devoted to the Dickensian portscapes of Boston and Boulogne.

These harbour scenes are characterised by a sense of transition related to those who go through them on their way from one country to another. Archibald argues that these areas "dis-locate Dickens and facilitate transition to a new phase of his life and career". Reaching these ports from the sea implies a view upon the shore, the islands and the mainland, all of which awaken anticipations on the part of the traveller and prepare for the transition between two worlds, the Old and the New World in the case of Boston, England and the Continent in the case of Boulogne.

What strikes us in Diana Archibald's article is that Dickens's writing even seems to have anticipated the definition of landscapes as "imagined worlds" or as extensions of what Benedict Anderson calls "imagined communities",3 in which landscapes are the imaginary projections or constructions of a group of people. In this respect, Archibald shows that in the mind of many British travellers, Boulogne was precariously balanced between a sense that it was an extension of Britain and the idea that it had no character, being neither British nor continental.

The link between landscapes and the idea of travel is taken up again in James Cutler's article, which tackles Dickensian landscapes through the idea of thanatourism, in connection with Dickens's propensity to explore sites related to death and to introduce them into his novels. Thanatourism introduces two novelties in the perception of landscapes. It stresses the fact that landscapes can be travelled past or through, and it emphasises the possibility of being immersed in a landscape.

Cutler aptly shows that Dickens's preoccupation with deathly landscapes is not just a sign of his fascination mixed with horror for such sights, but also a symptom of his preoccupation with his own death and the afterlife of his art. The depiction of landscapes related to death was paradoxically part and parcel of strategies aimed at overcoming oblivion and complete erasure. Cutler centres his paper around Our Mutual Friend and highlights the role of riverscapes in connection with death in this novel. He shows that the 1998 film adaptation refrains from offering large vistas of the river in period-drama style. The close-up views of the river are used as a backdrop to foreground the corpses that the Thames washes up. Similarly, views of urban landscapes in the novel are also at times limited by the eye's incapacity to see through the London fog, whose elaborate colour-scheme is described in the novel with the outmost detail. Here the eye is forced to hover above the surface of the landscape and to appreciate only its coating or, so to speak, veneer of fog.

Of course, Dickens is not free from contradictions and nostalgic wishful-thinking: thus in the foreword to this selection of articles, Paul Schlicke's overview of Dickens's corpus shows that in Dickens's work pastoral idylls are closely associated with memories of childhood, tenacious but never allowing the idyll to be retrieved. In the afterword to this collection, Michael Slater describes Dickens vainly searching for the sublime during his first American tour in 1842, though he later leaves David Copperfield utterly unmoved by views of the Swiss sublime, as though such hackneyed scenes failed to provide him with the solace he is seeking, a solace he only finds by going down into the valley and looking at the men working there.

All in all, these articles argue that the concept of landscape never goes unchallenged in Dickens's writing. It is never simply or simplistically seen as the easy transposition of empirical reality-it is, precisely, a concept, created from ideals or ideology, involving and reflecting the characters' subjectivity, thick with the representation of their past, present and even future, at the same time as it is utterly "other" and cannot ever be entirely caught in any representation. Dickens was aware of the plasticity and evolving quality of landscapes. In his work, the word landscape shifts from its predominantly pastoral acceptance, with occasional variations like the seascapes in David Copperfield, to the description of increasingly urban environments in the form of townscapes or cityscapes, with their own distinctive and striking sound and olfactory scapes. Dickens clearly understood landscapes as not being "objectively given" but as perspectival constructs. His novels even seem to anticipate very recent and postmodern forms of landscapes, defined by the sociologist Arjun Appadurai as ethnoscapes, technoscapes, mediascapes and ideoscapes. 4 Dickens's landscapes anticipate "ethnoscapes" in the form of unstable flows of restless characters and communities on the move, epitomised by Little Nell and her grandfather, Pip, the Dorrit family or the French revolutionaries, to mention but a few. All these characters belong to changing worlds whose boundaries are becoming more and more uncertain and fluid and therefore impossible to pin down.

Dickens's very work fits into what is now called a "mediascape"-the growing network of sources used to produce and disseminate information on an increasingly large scale and at increasing speed. At times, Dickens even seems to foresee the emergence of "technoscapes", namely the mechanical and informational fluidity of technology across boundaries. Thus, in Little Dorrit the rumours about Merdle's investment schemes and then about the financial collapse of his ventures spread through society and especially through Bleeding Heart Yard like wildfire, and this propagation somehow foreshadows today's social networks and tweets. Moreover, the whole of Dickens's work sets up a constantly evolving imaginary world or "ideoscape", both quintessentially English and increasingly transnational, as his work travels across frontiers and becomes part and parcel of the imaginary constructions of other communities. In short, Dickens had already realised and shown in his work how powerful a tool the notion of landscapes and its declensions could be to understand the self and the world. 4 See Arjun Appadurai, "Disjuncture and Difference in the Global Cultural Economy", in Modernity at Large: Cultural Dimensions of Globalization, Minneapolis: University of Minnesota Press, 1996. 27-47.

See Malcolm Andrews, Landscape and Western Art, Oxford: Oxford University Press, 1999 and Simon Schama, Landscape and Memory, New York: AAKnopf, 1995.

See Denis Cosgrove, Social Formation and Symbolic Landscape, 1984, Madison: University of Wisconsin Press, 1998.

See Benedict Anderson, Imagined Communities: Reflection on the Origin and Spread ofNationalism, 1983, New York: Verso, 1991.