Kostiantyn Maksymenko

Maureen Clerc

Theodore Papadopoulo

Data-driven cortical clustering to provide a family of plausible solutions to M/EEG inverse problem

The M/EEG inverse problem is ill-posed. Thus additional hypotheses are needed to constrain the solution space. In this work, we consider that brain activity which generates an M/EEG signal is a connected cortical region. We study the case when only one region is active at once. We show that even in this simple case several configurations can explain the data. As opposed to methods based on convex optimization which are forced to select one possible solution, we propose an approach which is able to find several "good" candidates -regions which are different in term of their sizes and/or positions but fit the data with similar accuracy.

Introduction

Human magneto-/electroencephalographic (M/EEG) [START_REF] Baillet | Electromagnetic brain mapping[END_REF] source localization aims to reconstruct the current source distribution in the brain from one or more maps of potential differences measured noninvasively from electrodes on the scalp surface (EEG), or maps of magnetic fields measured by magnetometers (MEG). A common approach is to represent the cortex as a finite set of current dipole sources. The M/EEG signal generated by such a source with a unit amplitude is called lead field and computed as a solution of M/EEG forward problem. Thus any measured signal can be modeled as a linear combination of lead fields associated to each dipole source

y = L • x + N (1)
where y ∈ R n is the signal measured by n sensors, L is the n × m lead field matrix whose columns represent lead fields of m sources, x ∈ R m is a vector of sources amplitudes and N ∈ R n is additive noise. In this work we do not take into account the time component of the signal. The inverse problem aims to find x knowing y and L.

We usually consider all vertices of a cortical mesh as possible source positions which results in m >> n. Thus recovering x from y in ( 1) is an ill-posed problem. In this work, we consider that brain activity which generates an M/EEG signal is a connected cortical region, i.e. there is a path between every pair of vertices. We study the case when only one region is active at once and each dipole in the active region has the same amplitude, i.e x i = a if i-th source is inside active region and x i = 0 otherwise.

Numerous methods were proposed to solve this problem [START_REF] Grech | Review on solving the inverse problem in EEG source analysis[END_REF][START_REF] Uutela | Visualization of Magnetoencephalographic Data Using Minimum Current Estimates[END_REF][START_REF] Ding | Reconstructing cortical current density by exploring sparseness in the transform domain[END_REF]. Most source reconstruction methods are based on convex optimization and in consequence identify a single solution. But because of ill-posedness of the problem, it is highly likely that other spatially distinct source configurations can explain the data as well as the identified solution, even under such a strong constraint of being a connected region with constant activity. We propose a method based on agglomerative hierarchical clustering [START_REF] Murtagh | Methods of Hierarchical Clustering[END_REF], whose objective is not to reconstruct one active cortical region but to find several "good" candidates -regions which are different in term of their sizes and/or positions but fit the data with similar accuracy.

Clustering algorithm

We define a cluster c i as a set of vertices of a cortical mesh and denote its size by |c i |. L(c i ) denotes the lead field of a cluster, which, by construction, is a sum of the lead fields of its dipole sources. We initialize our procedure considering each vertex as a cluster. So the vector x corresponds to the amplitudes of initial clusters. Their initial neighborhood is defined by a cortical mesh. Two vertices are neighbors if they share an edge on the mesh. For any pair of clusters c i and c j we define a potential error:

E(i, j) = min a y -a(L(c i ) + L(c j )) 2 + R(i, j) (2)
where y is the M/EEG data to fit, L(c i ) + L(c j ) represents the lead field that we would be obtained by merging the clusters. The first term of the sum represents the data fitting error that would be obtained if the clusters are merged. R(i, j) represents a regularization term which we will discuss in section 2.1. We represent the neighborhood information between clusters as a function N (i, j) = N (j, i) = 1, if clusters c i and c j are neighbors and 0 otherwise. N is initialized based on the neighborhood of vertices. We denote A as the set of current clusters. Based on this we initialize N and A and proceed with the following steps:

Step 1. Examine all inter neighbors potential error (2) and merge the clusters which minimize it:

i * , j * = arg min i,j∈A; N (i,j)=1 E(i, j); c k = c i * ∪ c j *
Step 2. Compute lead field for new cluster:

L(c k ) = L(c i * ) + L(c j * )
Step 3. Replace two merged clusters by new cluster and update neighborhood information:

A = A \ {c i * , c j * } ∪ {c k } ∀i ∈ A : N (i, k) = 1, if N (i, i * ) = 1 or N (i, j * ) = 1 0, otherwise
Step 4. Return to step 1 and repeat until the whole cortex is one cluster.

Merging two clusters can be seen as growing one region in the direction that locally minimizes the regularized data fitting error. Taking into account the neighborhood information guarantees connected regions. The way we compute a lead field for new clusters constrains these regions to have constant activity, i.e. all dipoles of active region have the same amplitude.

In the end, we obtain a dendrogram, which can be cut into a set of spatially separated growing cortical regions (Figure 2). We based the cutting criteria on the "speed" of clusters merging.

Let c k = c i ∪ c j and |c i | ≥ |c j |. c i is a cutting point if |c j | > s,
where s is arbitrary chosen merging "speed" threshold.

Regularization

Without regularization (R(i, j) = 0) we faced a kind of overfitting problem. The algorithm finds a way not only to reconstruct a region which has a good data fitting error, but also to keep growing the region without significant changes in error (Figure 1a). We belive that it is due to merging dipoles whose lead fields cancel each other out, and by merging "blind" sourcesdipoles with a low lead field norm. To solve this problem several regularization approaches can be used: penalize the size of the regions, i.e. do not allow regions to have a big size; introduce a default cortical atlas (e.g. Desikan-Killiany atlas [START_REF] Desikan | An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest[END_REF]) and allow regions to grow only inside its parcels. In this paper we introduce an approach to regularize regions' isotropy, i.e. to penalize regions with "sharp" borders and holes.

For two clusters c i and c j let us define a value B(i, j) as a number of vertices in c i which have at least one neighbor in c j . We propose following regularization term:

R(i, j) = λ • (|c i | + |c j |) 2 • min(|c i |, |c j |) B(i, j) + B(j, i) (3)
The ratio term in (3) measures the relative length of the border between clusters c i and c j . According to this measure Point 1 in Figure 1b) is more favorable than Point 2 to be merged with the cluster of black points, because it has a longer "merging border". Minimizing this measure favors regions with smooth borders.

The term λ • (|c i | + |c j |) 2 controls the importance of regularization. Being a quadratic function of a cluster size, regularization lets regions grow freely at the beginning and starts to be important for relatively big regions. The hyperparameter λ defines how fast regularization becomes important.

Results

We used the "Sample" subject from MNE-python software data set [START_REF] Gramfort | MEG and EEG data analysis with MNE-Python[END_REF] and computed its MEG forward problem. We represented source space as a cortical mesh with about 10000 vertices per hemisphere. Dipole orientations were fixed to be orthogonal to the cortical surface. We simulated one active region with additive noise and applied our reconstruction algorithm. As an output of the algorithm we obtained a set of growing regions and a data fitting error changing with respect to the region size (Figure 1c). With arbitrary chosen error threshold we can select the best regions as well as their lower and upper bound sizes (Figure 1d). As we can see, three spatially separated regions can explain the data with a high accuracy.

Conclusion

Our results show that even with a constrained model having only one active region with constant activity, we generally cannot find a unique data-driven solution which is significantly better than others.

The advantage of our method is the concept of spatially separated growing cortical regions. Compared to the methods based on convex optimization, which return a unique source configuration explaining the data, this concept provides more information about the inverse solution. It provides a relatively small number of candidate regions and estimates their size bounds.

The main directions for future work are to investigate the regularization term and the choice of hyper-parameter; to extend the method for the case when several regions are active at the same time to our clustering approach (for example, adapting MUSIC algorithm [START_REF] Mäkelä | Truncated RAP-MUSIC (TRAP-MUSIC) for MEG and EEG source localization[END_REF]) and to perform a multimodal approach (simultaneous EEG and MEG acquisition) to decrease spatial uncertainty of inverse solution.

Figure 1 :Figure 2 :

 12 Figure 1: Simulation results: a) simulated region (blue) and reconstructed one (white) without regularization. b) we have two candidates (Point 1 and Point 2) to merge with the cluster of black points. For Point 1 B(i, j) + B(j, i) = 3 + 1 = 4 and for Point 2 it is only 2. It results in smaller regularization value (3) for Point 1. Let us notice that merging Point 1 makes the cluster more isotropic compared to Point 2. c) Fitting error as a function of region size for top 3 reconstructed growing regions whith isotropy regularization. d) Localization of top 3 regions. Error threshold defines lower and upper bounds of their sizes (yellow and red colors resp.)

Acknowledgment: This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (ERC Advanced Grant agreement No 694665 : CoBCoM -Computational Brain Connectivity Mapping).


Lemenkova Polina

Current development of tourism and recreation on Baltic Sea coasts: new directions and perspectives

Keywords: Baltic Sea region, tourism development, recreation, post-Soviet Estonia

Research work analyzes current situation and development of tourism in the region of Baltic Sea. Specific case study of this paper is Pärnu Bay, Estonia. This region is known for unique environmental settings: mild maritime climate, broad beaches, coniferous pine forests on the coastal zone and high esthetic value of the surrounding landscapes. However, after the end of USSR, Estonia survived a difficult period of re-structuring of economic and social system. This affected touristic cluster, rapidly developing in new directions. Soviet touristic areas became abandoned and re-constructed, new hotels are being actively created, intensive privatization of recreation houses is actively ongoing. Main problem in the touristic cluster in Estonia consists in its specific location on the Baltic Sea with cold climate in summer period. It causes low popularity among tourists, comparing to Mediterranean. Another problem consists in ongoing development of the country, reflected in low investments into tourism, comparing to other European countries. Therefore, the main perspective for the tourism development in Estonia includes active redirection towards eco-style sustainable tourism: camping, biking, sea side recreation, construction of summer cottages for vacations, organized tours to Natural Parks. This paper, supported by fieldwork, has analytical character reviewing current Estonian tourism dynamics. Sociopolitical effects on current tourism directions are discussed, while modern touristic system in Estonia compared to Soviet. The overview of the recreation resort places was performed in Häädemeeste municipality, Pärnu district, and resulted in series of thematic author photos.

I. INTRODUCTION

Research aim

The target aim of this research is analysis of the modern trend in the development of tourism on Baltic Sea coasts with a special case of Estonia. The research topic is focused on the context of tourism resorts in Estonia generally, and of coastal Baltic seaside resorts in Pärnu region specifically. Some important issues discussed include decline of Soviet epoch and restructuring of touristic cluster that happened during the new capitalist era. This also includes case study of Pärnu area, which was traditionally a popular resort place during Russian Empire in XIX century, during the Soviet time and still keeps this position now. The touristic development of the particular resort place like Pärnu is not necessarily associated with the overall socio-economic development of the country, or its particular political-historical phase, but is rather the outcome of complex interactions between natural, climatic and sociological factors, as well as external forces (development of touristic infrastructure and available services), and cultural-historical appreciation of the place (long tradition of Pärnu resort, distinctiveness of the place, sightseeing possibilities for public, etc).

The problem of tourism development is being currently widely discussed on the European level: various workshops, seminars, conferences, discussions and lectures are organized focusing on the tourism. Main problems highlighted and investigated concern inter-relationships of man and nature: impact of the tourism on the environment, effects of the environmental, socio-political and economic conditions on the tourism development and vice versa, the impact of the tourism on the sustainability of natural ecosystems. Overview of the discussed tendencies and current problems are summarized in the relevant numerous papers (e.g. [START_REF] Smeral | Forecasting international tourism trends to 2010[END_REF][START_REF] Jansson | The Baltic Basin Case Study -towards a sustainable Baltic Europe[END_REF][START_REF] Palang | Social landscape: Ten years of planning 'valuable landscapes' in Estonia[END_REF][START_REF] Gossling | Global environmental consequences of tourism[END_REF][START_REF] Kernel | Creating and implementing a model for sustainable development in tourism enterprises[END_REF].

Estonia has its own specific characteristics in the tourism development, mostly caused by the political history. The end of the Soviet Union epoch since the 1990s caused great economical and sociopolitical reformation of the country. The disintegration of the USSR caused considerable changes in the socio-economic and political structure in many countries of Warsaw treaty from the post socialistic area, which naturally affected touristic cluster [START_REF] Berg | Writing post-Soviet Estonia on to the world map[END_REF]Oras, 2000, Light and[START_REF] Light | Romanian tourism in the post-Communism period[END_REF][START_REF] Vanwambeke | From USSR to EU: 20 years of rural landscape changes in Vidzeme, Latvia[END_REF]. Accordingly, in Estonia the system of land management, resource usage and urban development significantly changed in the past 20 years, which reflected overall socioeconomic and political situation in the country [START_REF] Roose | Land use policy shocks in the post-communist urban fringe: A case study of Estonia[END_REF]. Nowadays, the most typical processes in the coastal region of the country include suburbanization, intense construction of summer cottages (also known as "second summer houses") and creation of new, modern touristic places: hotels camping areas, hostels, etc.

Research area

The research region encompasses Baltic Sea coastal area south western part of Estonia. Spatial extent of the exact study area is limited to the surroundings of Pärnu County (Fig. 1). The region of Pärnu is valuable environmental and recreational part of Estonia. Mild climate condition and precious coniferous forests dominating in this area make it a unique environmental part of Estonian nature. Landscapes of western Estonia are rich and world-known for their diversity, variability and unique composition structure. These include, for example, mixed and broadleaved forests, traditional agricultural semi-natural landscapes, wooded meadows, plant communities, heathland, bogs and moors, complex anthropogenic areas with different land use structure, shrubland, grasslands, birch-dominating coastal areas and flooded meadows [START_REF] Zobel | Vegetation patterns and their underlying processes[END_REF]. Such environmental and geographic characteristics of the region together with advantageous location on the coastal area of Pärnu Bay and excellent facilities for the tourism make this region traditionally popular as a tourism destination place [START_REF] Ahas | Evaluating passive mobile positioning data for tourism surveys: An Estonian case study[END_REF]. Apart from the intense tourism in the study area, as it is mentioned above, the area of Pärnu county is also known for traditional agricultural activities (field crops cultivation, intensive planting, etc), as well as extensive housing development in the rural area. All these factors create additional pressure on the local ecosystems and may cause fragmentation of the landscape structure [START_REF] Mander | Coherence and fragmentation of landscape patterns as characterized by correlograms: A case study of Estonia[END_REF]. Methodologically, current study was based on the analysis of the reports of the trends in current tourism development in Estonia, and on the in-situ observations of the resort places in the study area (Baltic coastal territories, Partnu surroundings, Fig. 1), in order to analyze intensity of the local tourism development in the post-USSR time.

II. GLOBALIZATION AS THE MODERN TREND OF THE TOURISM

Globalization is a modern concept commonly used nowadays to explain variety of social, natural and economic processes. Globalization can be described as a movement in the direction of increasing world economic integration through the reduction of natural and human-made barriers to exchange and increased international flows of capital and labor [START_REF] Aramberri | The future of tourism and globalization: Some critical remarks[END_REF]. Globalization affects many aspects of the functioning of the society, and as a consequence, tourism as well, since it is an integral part of the modern social development. Currently, the tourism reached a high level of globalization in its development. The new tendency towards integration and globalization of tourism became popular in the world society in late XX-century.

The advantages of the globalization in tourism for the society consists in deep interconnection of tourist flows with various country destinations, even those not very popular earlier due to the limited natural access or climatic conditions. Other benefit of globalization is increasing world trade development, growth of various divisions of labor, internationalization of production of food, goods, hotel management system and touristic services, rapid and fast exchanges of information, computerization, standardization of guide touristic tours, etc. However, the globalization implies also a problem of maintaining the planet in global sense and tourist resort places in regional and local sense in a sustainable and nondestructive way, so that the tourism should not bring negative consequences on the surrounding landscapes and natural ecosystems. Various reports focusing on this problem have been written in this context [START_REF] Ko | Development of a tourism sustainability assessment procedure: a conceptual approach[END_REF][START_REF] Klein-Vielhauer | Framework model to assess leisure and tourism sustainability[END_REF][START_REF] Hong | Implications of potential green tourism[END_REF][START_REF] Kozak | Tourism life cycle and sustainability analysis: Profit-focused strategies for mature destinations[END_REF][START_REF] Lee | Sustainable tourism destinations: the importance of cleaner production[END_REF].

The crucial point of the globalization is that by its highest development there will still be a place for regional development as a concurrent and opposite trend. Hence, the natural geographical borders that arise when people move to the vacations will always exist. However, globalization progressively diminish and resolve potential and real borders and barriers, makes tourists and countries dependent on each other and interconnected. In Baltic post-Soviet countries like Estonia the globalization of tourism is now evident new and rapidly developing direction for the touristic industry.

III. CURRENT LOCAL TOURISM DEVELOPMENT IN POST-SOVIET COUNTRIES

Despite evident and overall trend in globalization of the tourism, there are regional and local specific nuances typical and characteristic for each country. Thus, in Estonia and other post-USSR countries, the tourism, leisure, traveling and tourism-related industry received new dimensions, rapid development and directions. Many research papers have been reported (e.g., [START_REF] Wight | Selective interpretation and eclectic human heritage in Lithuania[END_REF][START_REF] Kapaciauskaite | Environmental governance in the Baltic Sea Region and the role of non-governmental actors[END_REF][START_REF] Upchurch | Resident perceptions of tourism development in Riga, Latvia[END_REF] with focus on post-Soviet tourism development in new independent countries, as well as regional and local problems associated with global economic and social changes in these countries.

In general, the traveling moving tourist masses are not easily go beyond their national borders or, at least, further than the EU and Mediterranean. Even the most remote destinations are still encircled by Eurasia continent, and only few persons go to Australia, southern Africa or the Americas. It should be noticed also that this group includes also travel flights made by businessmen who have duties in Europe, the U.S. and Canada and Austral-Asia. The most important factor for choosing a place destination while going to vacations is individual factor and family traditions. Thus, as noticed by Daugstad (2007), personal views may differ according to age, generation, gender, place of residence, ties to urban or rural areas, etc. However, as reported in an investigation on Estonian tourism spatial locations performed by detection of mobile phone locations [START_REF] Ahas | Evaluating passive mobile positioning data for tourism surveys: An Estonian case study[END_REF], the majority of Estonians prefer national holidays vacations with some temporal seasonality variances: coastal areas are much more popular during summer tourism season, while continental inland areas are mostly being visited during the winter.

Among other nations traditionally often visiting Estonia are Russians and Finnish. Finnish tourists traditionally visit western Estonia (Baltic Sea coasts), while Russians preferably concentrate on the Estonian-Russian border, in eastern Estonia, on the Finnish Gulf. These two nations are notably the most representing tourists, while others visit Estonia significantly lesser. Hence, there are also some Latvians who made up a higher percentage in Saaremaa and Pärnu region during summer and in Otepaa and Lake Peipsi in winter [START_REF] Ahas | Seasonal tourism spaces in Estonia: Case study with mobile positioning data[END_REF]. The non-popularity of Estonia among other nations, comparing to touristic giants, like France or Spain, can be explained by various factors. First of all, it is specific climatic conditions of the territory with rather cool summers and cold waters in Baltic Sea even during summer months. Unpleasantly cold winters and lack of world-known sightseeings of UNESCO level heritage increase this aspect. Another factors consists in long Soviet history of the country, which results in bad service facilities and under-developed touristic cluster (though currently in process of gradual growth and development). It also includes still insufficient quantity of world-level hotels, possibilities for recreation and spa-centers (e.g. comparing to Finland).

Another factor which plays role in the positive development of tourism in modern Estonia is the independency of the country from the USSR. As reported in study (Gil-Pareja et al., 2007) of impact that have embassies and consulates on the touristic inflow, it has been proved that they play a positive role in attraction of potential tourists to the country. Thus, after Estonia became an independent country, the information about Estonian resort places, including brochures and maps, is available and freely distributed. This welcomes future tourists and facilitates planning a journey, which became more easy comparing to the Soviet times when certain restrictions of entrance to the USSR did exist.

Currently, it is estimated [START_REF] Worthington | Change in an Estonian resort. Contrasting development contexts[END_REF] that about 90,000 foreign tourists a year visit Pärnu, of which about 50,000 are Finns, followed by 7,200 Swedes, 4,500 Russians, 2,700 Americans, and approximately 17,100 of other nationalities.

Modern development in Estonian tourism: eco-friendly hotels and appreciation of the environment

In general, Estonian touristic sector currently transforms a gradual functional shift away from authoritative style of tourism with common Soviet guesthouses towards capitalist privately held small hotels. Nowadays, some of former hotels naturally become a bankrupts or else depopulated and lost their tourism function completely. However, as justly recommended by [START_REF] Agarwal | Restructuring seaside tourism[END_REF], such decline may be avoided in case the counter-measures are accepted and used, such as re-orientation of the hotels towards environmental eco-friendly style, enhancement of the attractions for kids and sightseeings for adults, or even the repositioning of the destination within an overall touristic market. One of the re-orientation principles of the modern tourism includes intensive development of the eco-friendly, environmentally oriented touristic resorts, or, in other words, eco-style rural tourism. Though less evident in the large cities and their suburbia, e.g. in Tallinn, eco-tourism has turned into a highly popular tendency for coastal small towns and resorts. The eco-style resorts development is currently a highly developed line in neighboring Finland, which traditionally gives following examples for Estonia. Eco-styles tourism includes not only constriction of ecologically styled buildings and hotels but also a maintenance of the surrounding landscapes, so that the houses are harmonically drawn into the natural landscape without neither esthetic nor physical disturbance and misbalance (Fig. 2).

Important trend in the development of tourism in Estonia is intensification of rural tourism. Like in other Baltic, mostly agrarian, post-Soviet countries, rural, environmentally friendly tourism is an efficient mean for further tourism development. It has evident advantages both for nature and society, thus enabling balanced co-existence of the man and environment. First, development of ecological (or, eco-style) tourism and recreation activities assists in conservation of natural and cultural heritage objects, buildings, landscapes, traditions, and customs [START_REF] Balezentis | Rural tourism development in Lithuania (2003-2010) -A quantitative analysis[END_REF]. These resources, in turn, directly affect the quality of the region, the overall appreciation of this particular place by the tourists.

In view of global popularization of the ecology, environment and natural landscapes, people tend to select most "natural" places for vacation or as tourism destinations in order to live in right environment.

Another, though may be less evident advantage of ecological tourism consists in economic support of the local infrastructure and social functioning. Namely, popularization of the places for ecological and rural tourism creates jobs opportunities for the active local population, who may receive additional income due to the increased tourist inflow.

Finally, ecological tourism is a sustainable activity which serves as a basis for conservation of sustainable and renewable natural resources, e.g. forests, landscapes, etc. Eco-style tourism depends on a wide range of natural and cultural resources, infrastructure, and service facilities, as well as provision of accommodation, food, beverages, and goods [START_REF] Cawley | Integrated rural tourism: concepts and practice[END_REF]. Therefore, for environmentally-friendly, proper regulation and functioning of tourism cluster, the development of the tourism should be in sustainable way, i.e. not affect local ecology and cause negative impacts on the quality of the natural environment, landscapes, social infrastructure and cultural sightseeings.

Tourism tradition in Pärnu: maintaining history in the present

The history of Pärnu resort goes back to the XIX century, when Estonia was under protection of Russian Empire. Domestic tourism in the Baltic Provinces including Pärnu, was largely connected with sea bathing during July month. The season always ended by August 1 due to the restricted climatic conditions [START_REF] Kohl | Provinces on the Baltic, the Steppes, the Crimea, and the Interior of the Empire[END_REF]. During the First World War the development of the resort was largely restricted, though quickly revived after the war. In 1920s the Rannapark has been restored, and a new mud bath constructed, opened for tourists. In late 1920s -1930s Estonian hotels and restaurants were one of the cheapest touristic destinations in Baltic Europe, which was advertised in the tourist literature of that time. The easy access to the Pärnu region was facilitated by good railway communication with Germany, Latvia, and Lithuania. As a consequence, this region was widely visited by various international guests with the majority of Scandinavians (e.g. Swedes, Finns), Poles, Germans and Brits [START_REF] Worthington | Change in an Estonian resort. Contrasting development contexts[END_REF]. Interior and the surroundings of the Cosmonauts Hotel -a former Soviet summer resort for workers of space industry (www.kosmonautika.ee): applying space topic and cosmos theme in hotel: soviet cosmonaut Y.Gagarin who was the guest in this hotel. Photo: author.

During the totalitarian era of Soviet Union the tourism industry in east Baltic Sea region has been diminished, since the primary goal of the state was industrial usefulness and functionality, with negative reaction towards private ownership. Evidently, the business of private hotels and restaurants has been diminished drastically. The existing touristic entrepreneurs were reconstructed to the state-controlled "Existing organizations were amalgamated into the All Union Voluntary Society for Proletarian Tourism and Excursions" [START_REF] Worthington | Change in an Estonian resort. Contrasting development contexts[END_REF], with all touristic initiatives imperatively controlled and dictated.

Development of tourism under USSR epoch has brought many new directions to this social sector. Among negative features of Soviet era were restrictions upon foreign tourism in Pärnu region, and poor management in the Soviet planned economy which reflected in bad service facilities and underdeveloped hotelier tradition. However, there were some positive consequences of this reconstruction as well: the coasts and beaches in Pärnu region were protected as "public health zone" designed for recreation, where only selected activities were permitted and vehicles were prohibited. The most precious parts and areas of the Baltic Sea were served as special places for high political leaders who took their summer vacations here, as well as for the employees from the strategic industrial sectors: spacecraft and cosmos exploration. These hotels, former restricted for politicians, prominent scientists, artists and cosmonauts, are currently being reconstructed and re-opened for public tourists (Fig. 3).

Regaining the independency of Estonia has revolutionized Baltic tourism. Consequently, the modern, "westernlooking" and quickly constructed hotels were created and the new, revitalized era for tourism industry in Estonia started, mostly based on privatization and foreign investments (from Finland or Germany).

Development of private sector and intensive building of summer cottages

The development of local-scale tourism can be of special benefit for Estonia, whose resources traditionally include small towns and villages, often of architectural interest, which are ideal for the development of tourism-related cultural and recreational services. Important way of tourism development in modern Estonia is family businesses, which often implies direct host-guest interactions in the family-runed hotel or hostel [START_REF] Getz | Family business in tourism: state of the art[END_REF]. The personal relationship and friendship are often vital to guest experiences of the tourist, his or her satisfaction, which naturally makes a place popular and thus, contributes to further tourism development in the community.

Expanding the touristic dimensions is highly profitable for the country due to the evident income of financial flows. However, as reported by Endo (2005), the overwhelming majority of foreign direct investments is so far directed to the developed countries, like France, the UK, the Netherlands, Spain, and soon. For some developing countries and for the countries that are in transitional economic situation, like Estonia after the fall of the USSR, the role played by foreign tourist investments in touristic industry is incomparable lesser in their overall economic activities.

Currently, Estonia has intensive privatization process, which is caused by serious changes in state regulations on property and ownership. Naturally it caused intensification of construction of privately hold hotels and summer cottages, built both for personal (family based) needs for spending summer vacations, and for rent to incoming tourists, domestic and international. Land management system and urban development of Estonia significantly changed in the past 20 years, which reflects overall socio-economic and political situation in the country [START_REF] Roose | Land use policy shocks in the post-communist urban fringe: A case study of Estonia[END_REF]). Nowadays, suburbanization and development of second houses become the major and most evident processes in the current urban dynamics of modern Estonia (Palang and Peil, 2010). Example of private Estonian spa hotel (Lepanina Hotell) created on the Baltic Sea coast: a successful combination of modern European hotel design, location in the nearest proximity of the sea, maritime design landscapes, and coniferous forests makes it a valuable health resort area. Photos: author.

There are multifold processes explaining this phenomena. The main triggering factor is caused by ground serious changes in the public law and ownership system of the country, which enabled to expand ownership to the immobility objects (which was largely restricted and controlled by the state during the USSR epoch). Implementation of new land reform with modest regulation of land use activated touristic and housing market in Estonia, enabled privatization, home ownership, restitution of suburban land [START_REF] Hess | Ethnic differences in housing in post-Soviet Tartu, Estonia[END_REF]. Together with accessible mortgage system developed in Estonia since 2000s, it facilitated purchase of private houses for large number of people from upper middle class, which accelerated suburban residential development. This has naturally activated privatization of real estate objects and increased size of private property and privately hold hotels (Fig. 4).

Another factor has economic character and includes development of the market economy and overall socio-economic growth in Estonia, which caused positive changes in economic sphere of the population of the country. Hence, new capitalistic, market based economy implemented in Estonia after the fall of USSR, caused gradual positive social changes: personal economic growth, well-being, new style of life, increased number of private cars, and in general, growing size of the middle class society. These factors triggered intensive construction of touristic hostels and guesthouses, private hotels, as well as second houses and summer cottages in recreation zones where families live during vacations (these homes are sometimes also referred as "dachas"). These factors, both of economic and juridic characters, have direct and positive impact on the touristic cluster of country. As a consequence, since independency of Estonia, the touristic sector changed significantly towards intensification, revitalization and overall improvements in the tourism and leisure industry. The development of tourism and overall economic growth in various developed countries have evident correlation and relationship though not necessarily linear [START_REF] Po | Tourism development and economic growth -a nonlinear approach[END_REF], since the traveling and going to resort places can only be maintained by sufficient resources. Nowadays, the development of tourism over the world leads to the strategy of cultivating an entrepreneurship and own touristic business environment. The same way of the development is now open for Estonia and other post-Soviet countries. Besides, as noticed by [START_REF] Getz | Growth and profit-oriented entrepreneurship among family business owners in the tourism and hospitality industry[END_REF], strategy of own touristic business brings advantages for the regional economy, as it requires creation of new working places which in turns brings evident advantages for the economy of the region. Privately oriented touristic business is also profitable for optimization of tourism competitiveness in the country, because the profit and growth-oriented owner (landlord or landlady) will invest products and marketing initiatives, rather than it was in USSR times in old types of guesthouses and Soviet hotels, which were mostly controlled by the state within a given business type and size.

CONCLUSION

Current research provided balanced insight into the investigations of complex processes connected to the tourism cluster development in the Estonian western region: socio-economic development, post-socialistic heritage, environmental and cultural processes. It furthermore assists to the development of sustainable appropriate future actions in touristic industry of this specific region. The paper has analytical character, and contributes to assist in further development of touristic industry in Baltic Sea area. Hence, may be used for local land and recreation management.

Presented work illustrated application of complex methods combining analytical review of the tourism development in Pärnu region with a case study of Häädemeeste municipality, and in-situ observations of touristic activities in the study area. Methodology is based on study of relevant numerous literature, statistical facts, and performed fieldwork excursions. The fieldwork monitoring and observations were aimed at studies of touristic possibilities in various selected landscapes of eastern region of Baltic Sea. The environmental aim of this paper is contribution towards landscape monitoring for sustainable development of Baltic Sea area and co-existing of man and nature. The work is aimed to demonstrate how tourism sector is successfully developing in the conditions of post-Soviet socio-economic recovering and specific climatic conditions. Furthermore, study analyzed trends and general directions for the future of tourism in post-Soviet Estonia, with focus on changes that affect this region in view of the process of globalization. Although the study is focused primarily on an Estonian context, it has wider implications for the analysis of tourism development and management of other countries with similar transitional socio-economic phase which have the same problems in tourism development: e.g. post-Soviet countries or Eastern European region, newly integrated into the EU.

That being said, it should be also highlighted that our knowledge of the real dimensions and perspectives, potential and tendencies of tourism and travel in the post-USSR region is still underestimated. The human potential and resources of the population from the post-Soviet countries have great potential for the development of tourism both in Baltic Sea area and in other regions of the world.

Figure 1 .

 1 Figure 1.

  Study area: Pärnu surroundings, Estonia. Source: xgis.maaamet.ee, modified by authors.

Figure 2 .

 2 Figure 2.

Figure 3 .

 3 Figure 3.

Figure 4 .

 4 Figure 4.

ACKNOWLEDGMENT

The financial support of this research has been provided by the DoRa Scholarship Committee of the European Social Fund (ESF). The technical support of the fieldwork was performed with kind assistance of Mrs. Irja Pede, employee from the Häädemeeste municipality, and Mrs. Merle Looring, a lecturer of the University of Tartu, Pärnu College, Department of Ecosystem Management, during the organized fieldwork company in Pärnu County.


Michaël Sdika

Daniel Pelletier

Non Rigid Registration of Multiple Sclerosis Brain Images using Lesion Inpainting for Morphometry or Lesion Mapping

Keywords: nonrigid registration, image inpainting, white matter lesions, multiple sclerosis, morphometry, lesion mapping

Morphometric studies of medical images often include a nonrigid registration step from a subject to a common reference. The presence of white matter multiple sclerosis lesions will distort and bias the output of the registration. In this paper, we present a method to remove this bias by filling such lesions to make the brain look like a healthy brain before the registration. We finally propose a dedicated method to fill the lesions and present numerical results showing that our method outperforms current state of the art method. This is the pre-peer reviewed

Introduction

Nonrigid registration is an essential tool to analyze medical images. For example, it can be used to segment images using a prelabeled atlas [START_REF] Warfield | Nonlinear Registration and Template Driven Segmentation[END_REF], to follow the evolution of brain structures in longitudinal studies [START_REF] Rey | Automatic Detection and Segmentation of Evolving Processes in 3D Medical Images: Application to Multiple Sclerosis[END_REF] or for morphometry [START_REF] Ashburner | Identifying global anatomical differences: deformationbased morphometry[END_REF].

In this paper, we will focus on the problem caused by white matter lesions in the context of multiple sclerosis (MS). MS is an immune-mediated demyelinating disease affecting both white and grey matter. White matter plaques are easily detected on current conventional images whereas grey matter lesions are still not well appreciated. When one tries to nonlinearly register a brain with MS to a brain without MS, white matter lesions will cause a strong distortion in the output transformation. Indeed, intensity driven nonrigid registration algorithms assume that the two images being registered have the same structures but these lesions are present in the patient and not in the reference image [START_REF] Brett | Spatial Normalization of Brain Images with Focal Lesions Using Cost Function Masking[END_REF]. This distortion of the transformation will be an important problem when nonrigid registration is used for morphometry.

Deformation based morphometry and tensor based morphometry allow us to analyze statistical differences in the size or shape of brain structures between two groups of subject. For these techniques, the first step is to find the (non-linear) mapping between each subject and the reference image and then to do some statistical analysis on the estimated transformations or their derivatives [START_REF] Davatzikos | A computerized approach for morphological analysis of the corpus callosum[END_REF][START_REF] Ashburner | Identifying global anatomical differences: deformationbased morphometry[END_REF][START_REF] Chung | Deformation-based surface morphometry applied to gray matter deformation[END_REF][START_REF] Studholme | Deformation tensor morphometry of semantic dementia with quantitative validation[END_REF][START_REF] Lepore | Multivariate statistics of the Jacobian matrices in tensor based morphometry and their application to HIV/AIDS[END_REF]. It is therefore important for the statistical analysis that the transformation is not distorted by the presence of lesions.

Lesions location can help in the understanding of brain disease and functions. To perform the statistical analysis of the lesions location, the lesions of each subject have to be described using a common coordinate system. Different methods have been used to do so. A manual method has been proposed in [START_REF] Damasio | Three-dimensional in vivo mapping of brain lesions in humans[END_REF] and in [START_REF] Frank | Brainvox: an interactive, multimodal visualization and analysis system for neuroanatomical imaging[END_REF]). An operator has to draw the lesions of each subject in the reference template using anatomical landmarks. The operator has to be an experienced neuro-anatomist, the process is time consuming, and as pointed out in [START_REF] Fiez | Lesion segmentation and manual warping to a reference brain: intra-and interobserver reliability[END_REF], this method is subject to a quite important inter and intra observer variability. Image registration provides an automated method to perform this task. As nonrigid registration is biased by the presence of lesions, most authors prefer to use affine registration [START_REF] Narayanan | Imaging of axonal damage in multiple sclerosis: spatial distribution of magnetic resonance imaging lesions[END_REF][START_REF] Charil | Statistical mapping analysis of lesion location and neurological disability in multiple sclerosis: application to 452 patient data sets[END_REF] or [START_REF] Enzinger | Lesion probability maps of white matter hyperintensities in elderly individuals: results of the Austrian stroke prevention study[END_REF]. Indeed, affine registration is robust to the presence of lesions in the brain but only the global shape of the brain will fit the reference.

In this paper, we propose a solution for these two problems and have a nonrigid registration that is not distorted by lesions and an automated method to map MS lesions in a reference brain taking inter subject variability into account.

State of the art of pathological brain images registration

Given two images, the aim of registration is to find the transformation that maps the voxels from one image (the reference) to the voxels of the other (the floating image). To restrict the search space and find a realistic transformation, one usually requests that the transformation be smooth and/or invertible [START_REF] Christensen | A deformable neuroanatomy textbook based on viscous fluid mechanics[END_REF][START_REF] Rueckert | Diffeomorphic Registration using B-Splines[END_REF][START_REF] Sdika | A Fast Non Rigid Image Registration With Constraints on the Jacobian using Large Scale Constrained Optimization[END_REF].

For the registration of normal brains, this requirement makes sense when both the reference image and the floating image have the same structures. An invertible transformation guarantees the preservation of the topology of the floating image before and after the transformation.

For the registration of non-healthy brains, the invertibility of the transformation is no longer a reasonable assumption as abnormal structures such as tumors or lesions can be present. Nevertheless, apart from the regions where the new structures appear, the topology should be preserved.

For the problem of tumors, a biomechanical model of the growth of the lesions can be used prior and after the registration as in [START_REF] Kyriacou | Nonlinear elastic registration of brain images with tumor pathology using a biomechanical model[END_REF]) or a "tumor seed" can be added to the atlas before the registration as in [START_REF] Dawant | Brain atlas deformation in the presence of small and large space-occupying tumors[END_REF]. These methods cannot be used here. Indeed, a tumor will grow and push the surrounding tissues of the brain, whereas multiple sclerosis will create lesions that "replace" healthy tissues without moving surrounding tissues.

Another approach consists of removing the influence of the pathological voxels during the registration process. The voxels in the lesions are removed from the similarity metric driving the registration: the cost function is masked so that only the voxels from normal structures are used. It has been applied to focal lesions in [START_REF] Brett | Spatial Normalization of Brain Images with Focal Lesions Using Cost Function Masking[END_REF] or to tumors in [START_REF] Radu | Non-Rigid Atlas to Subject Registration with Pathologies for Conformal Brain Radiotherapy[END_REF].

In [START_REF] Meier | Atlas-based anatomic labeling in neurodegenerative disease via structure-driven atlas warping[END_REF], the registration is not based on voxel intensity but works by first segmenting and parameterizing different brain structures and then finding a transformation that makes these binary structures match. In their work, they used the brain surface, the midsagittal plane and the ventricles surface. As MS lesions do not appear in these structures, they do not affect the registration, but the registration will not make the grey matter structures match either.

In general, three approaches can be distinguished: removing the lesions from the patient image and aligning, adding the lesions to the atlas and aligning, or removing the influence of the lesions during the registration.

Our method consists of inpainting white matter lesions before performing the registration: the intensity in the lesions is replaced to remove them from the original image. Usually, image inpainting is done by smoothly interpolating the image in the inpainting area while continuing the level sets as in [START_REF] Bertalmio | Image inpainting[END_REF][START_REF] Oliveira | Fast Digital Image Inpainting[END_REF]. One can also try to reproduce the surrounding texture as in [START_REF] Bertalmio | Simultaneous structure and texture image inpainting[END_REF][START_REF] Drori | Fragment-based image completion[END_REF]. We propose in this paper an inpainting algorithm dedicated to the problem of filling white matter lesions in brain images.

Our inpainting based method is adapted to the physiological process of MS, computationally efficient and fully automated once the lesions have been segmented. It allows the registration of an MS patient and the mapping of MS lesions to an atlas or a single case reference template.

In this paper, there are three contributions: the introduction of inpainting in biomedical image processing as an effective tool to remove the influence of lesion during nonrigid registration of patients, the proposition of an inpainting algorithm dedicated to this problem and the comparison between different inpainting methods and with the state of the arts method showing that our method improves the registration of MS patients

Method

Overall Approach

The method we propose in this paper applies to the nonrigid registration of multiple sclerosis brains. This disease causes the formation of lesions mostly visible in the white matter. Some lesions can also be located in the cortical or deep grey matter but are more difficult to appreciate with current images.

White matter lesions must have already been segmented either manually or with a semi-automated software as binary regions in the patient image. Then, they are removed from the image and the space left is reconstructed to make the image look like a normal brain. We can subsequently use a standard nonrigid registration algorithm that can preserve the topology of the floating image.

An Inpainting Algorithm using anatomical prior

The objective of image inpainting is to fill missing parts in a given image. Most image inpainting techniques found in the literature are applied to 2-dimensional images for scratch removal from paintings, photo restoration, object or text removal.

In general, the problem of image inpainting is ill-posed. As the intensity of the voxels in the missing regions is not known, the objective is to fill the regions in a coherent and visually acceptable way by continuing the grey level or texture of surrounding voxels.

In our case, the objective of the inpainting step was to fill the lesions to make the brain look like a healthy brain. As image inpainting will be used for a specific range of images (images of brains with a given modality) and a specific type of inpainting mask (MS lesions), a priori knowledge on the problem can be used to design dedicated inpainting algorithms. We have evaluated three inpainting methods to fill white matter lesions.

Basic Inpainting (BI)

As the inpainting areas are not textured, we have used a simple algorithm inspired from [START_REF] Telea | An Image Inpainting Technique Based on the Fast Marching Method[END_REF]. It consists of filling the inpainting region from its border to its center with an average of know neighbors voxels. So, the following iterations are applied while the inpainting region is non empty:

Ω Ω Ω n) w(x n)I(n) w(x I(x) Ω x Ω V(x) n Ω V(x) n ∂ = - - = ∂ ∈ ∑ ∑ ∩ ∈ ∩ ∈ \ : forall ,
where I is the image to inpaint, Ω is the inpainting region (initialised with the original lesion mask), , Ω its complement (the voxels outside Ω ), Ω ∂ its border (voxels of Ω having on of its 6

neighbors in Ω ), a neighborhood neighbourhood of ) x ( V
x (a 3x3x3 neighborhood neighbourhood in our implementation) and a Gaussian kernel.

w This algorithm will be denoted as BI (basic inpainting) in the rest of this paper. Note that, as some voxels are removed every iteration, this algorithm is guaranteed to terminate.

Local White Matter Inpainting (LWMI)

The restricted range of images allows us to add more a priori knowledge in the inpainting step. The lesions we want to remove from the MS patient images are located in the white matter but often have the same intensity as other tissues (grey matter or the cerebrospinal fluid). The voxel of the inpainting area should be filled only with the intensity of the normal appearing white matter. To do so, we segmented the input image into normal appearing white matter (NAWM), grey matter (GM) and cerebrospinal fluid (CSF) and inpainted the MS lesions by using only the value of the surrounding NAWM. In our implementation, the output of the FAST software [START_REF] Zhang | Segmentation of brain MR images through a hidden Markov random field model and the expectation maximization algorithm[END_REF] was used for the segmentation. The algorithm, denoted as LWMI (Local White Matter Inpainting), consists of iteratively filling the border of the unknown region using the formula:

∑ ∑ ∩ ∩ ∈ ∩ ∩ ∈ - - = NAWM Ω V(x) n NAWM Ω V(x) n n) w(x n)I(n) w(x I(x)
,

where the symbols of the BI algorithm were used. At the end of the iteration, the inpainted voxels of the border are added to the NAWM mask and removed from the inpainting mask Ω . Note that with this formula, the denominator for a given voxel x can be null. In this case, x is not inpainted and remains in Ω . So, when the lesion touches the GM or the CSF, it will automatically be filled starting from the border with the NAWM and ending with non WM structures.

If the segmentation is inexact or inaccurate, the algorithm might not start for some lesions (for example if lesion surrounded by GM). In this case, the neighbourhood V and the Gaussian kernel can be dynamically enlarged to make neighbourhoods of the border intersect the NAWM mask. w Note that, as only the NAWM is used to inpaint the lesion, enlarging V and is not problematic with LWMI and can be beneficial for the robustness of the method. Indeed, voxels not directly in contact with the lesions (and not affected with partial volume effect, fuzzy boundary or other influence of the lesion) can be used to fill the lesion area. This is another clear advantage other BI for which enlarging V means increasing the chances to use non WM structures to fill the lesions. w In our implementation, a 5x5x5 neighbourhood of x is used for . ) x ( V

Global White Matter Inpainting (GWMI)

A third possibility to inpaint the white matter lesion was to fill the MS lesions with the mean intensity of the NAWM over the whole brain. This constant is automatically found by computing the average intensity over the NAWM mask provided by FAST.

The Nonrigid Registration

Following the inpainting step, we perform a nonlinear registration using the inpainted image. As the topological changes due to lesions have been removed before the registration, constraints to preserve topology or penalization of non-smooth transformation can be used during the registration process everywhere in the image.

The algorithm used, as described in [START_REF] Sdika | A Fast Non Rigid Image Registration With Constraints on the Jacobian using Large Scale Constrained Optimization[END_REF], models the registration by a nonlinear optimization problem with nonlinear constraints to prevent the Jacobian to be negative. The constrained optimization problem is solved by using a combination of the multipliers method and the L-BFGS algorithm with a non-monotone line search. The transformation is modeled using cubic splines, making it intrinsically smooth, local, compact, and fast to compute. The cost function is the squared difference between the reference and the deformed version of the floating image, which is adapted to monomodality registration. A multiresolution approach is used to speedup the registration and to avoid local minima.

Formally, the registration problem with constraints, can be written as

( ) 2 0 2 1 min ∑ ≤ ∀ x r f x,g(c,x) (x) -I (T(c, x)) I N ,
where is the floating image, is the reference image, is the number of voxels in the reference image, T is the transformation parameterized by the spline coefficients c to be estimated. is the constraint on the transformation given by:

f I r I N x) g(c, (x)) (J - J(x) 2 1 x) g(c, 2 2 φ ∇ = ,
where is the Jacobian of the transformation and J φ is a function, negative for negative or small value of its argument. By correctly choosing φ and the stopping criterion, the Jacobian is ensured to be positive on all the voxels. Negative Jacobians are penalized between voxels by making the Jacobian derivatives small on the voxels where the Jacobian is small. The local support property of B-spline is particularly important as it ensures that a deformation in a given region of the brain have only a local effect on the transformation. More details on this registration algorithm can be found in [START_REF] Sdika | A Fast Non Rigid Image Registration With Constraints on the Jacobian using Large Scale Constrained Optimization[END_REF].

Before the nonrigid registration, a slight Gaussian smoothing ( 7 0. σ =

) is applied to both the reference and the floating image to reduce the intensity quantization effect and improve the signal to noise ratio (SNR).

Evaluation

Material

The images we used were T1 weighted 3-dimensional gradient echo images with a resolution of 1mmx1mmx1mm acquired on a 3 Tesla MR scanner. The lesion masks of the MS patients have been manually segmented by an experienced MS neurologist.

Lesion Mapping Example

To map lesions from a patient brain to a reference healthy brain using inpainting one needs to: inpaint the patient white matter lesions, perform the nonrigid registration using the inpainted image as the floating image and the healthy brain as reference and then, map the patient lesion mask using the transformation found by the registration. An example of such a mapping is shown in Figure 1. Note that on this figure, some lesions seem to be created, some others seem to disappear but if you consider them as 3D object and look at few neighbouring slices in the patient and the control, no lesions are added or lost.

Protocol for Numerical Simulation

In this section, we will evaluate quantitatively different ways to register a patient image with white matter MS lesions to a reference template. To compare the different methods, we propose an evaluation procedure similar to the one used in [START_REF] Brett | Spatial Normalization of Brain Images with Focal Lesions Using Cost Function Masking[END_REF]. Simulated datasets are created and the output transformations of the different methods are compared to a ground truth. The simulations are generated as follows. Using a healthy brain c and a patient brain p with its lesion mask , an artificial image and its lesion mask are created by mapping the lesions of the patient to the control. The registration is performed between the inpainted patient (c) and the reference image (g). The output transformation can finally be applied on the inpainted patient (d), the original patient image (e) and on the lesion mask of the patient (f ). Note that some lesions appeared and disappeared on this slice but in 3D, no lesion is added or lost.

For another control and a given registration method with lesions, a transformation T can be estimated between with its lesion mask and

c′ p c cp l c′ .
The transformation T is then compared to the ground truth computed as the output of a standard registration (control to control) between c and 0 T c′ . To measure the distance to the ground truth, we used the mean value of the transformation error on voxels:

∑ ℵ ∈ ℵ = x (x) T(x)-T N E (T ) 0 1
, where is a given mask and the number of voxels in the mask. The brain mask given by the BET software [START_REF] Smith | Fast robust automated brain extraction[END_REF] or the lesion mask are used for

ℵ ℵ N
ℵ , giving us a global error measure in the whole brain and a local measure in the lesion area. To be sure that the method used to create does not favour one of the registration methods we want to compare, three simulation datasets were created using three different lesion mapping methods. Dataset Affine was created using affine registration to transfer the lesions, Dataset Mask was created using CFM (Cost Function Masking) for the registration and Dataset Inpaint was created using LWMI before the registration. We used two sets of three control scans (one for and one for c p c c ′ ) and a set of three MS patient images.

Consequently, each of the three datasets was made of 27 simulations.

Results

The results of the evaluation are shown on Figure 2 for the error in the whole brain and on Figure 3 for the error in the lesions. Regardless of the lesion mapping method used to create the simulation set, one can see that the LWMI method gives the best results followed by BI, GWMI and CFM, the Naive method comes last. As already reported in [START_REF] Brett | Spatial Normalization of Brain Images with Focal Lesions Using Cost Function Masking[END_REF] for focal lesions or in [START_REF] Radu | Non-Rigid Atlas to Subject Registration with Pathologies for Conformal Brain Radiotherapy[END_REF]) for tumors, the cost function masking approach improves the registration compared to the Naive method. Indeed the lesions are outliers that are removed before the fit of one image to another. The experiments in this paper also show that inpainting the lesions with LWMI before the registration improves the registration over the CFM. The rationale behind the inpainting approach is to try to correct the outliers instead of removing them during the fit. A good outlier correction method provides, in this case, a better fit.

As expected, the difference between the methods is more visible in lesion area and the superiority of LWMI is clearer. Indeed, LWMI is the only method with subvoxel accuracy in the lesion area. Note also that the interval of one standard deviation around the mean do not overlap between LWMI and the second best method (CFM) for the datasets Affine and Inpaint. This emphasizes the need to pay a special attention to the registration method if the object of the study is the spatial distribution of lesions.

Results from statistical analysis show that the superiority of LWMI is highly significant. Table I and Table II present

Discussion

In this work, an original approach was proposed to perform nonlinear registration between two brain images when at least one of them has MS lesions. It consists of inpainting white matter lesions; the inpainted image is then used for non linear registration in lieu of the original patient image. Secondly, a dedicated inpainting algorithm has been proposed to fill the lesions, using the properties of the images to inpaint (images of the brain) and the inpainting mask (MS lesions). The lesions are inpainted using the intensity of surrounding normal appearing white matter voxels.

Naïve

Since our lesion inpainting approach is an easy preprocessing step before the registration, any standard nonrigid registration algorithm can be used without modification. Besides, any brain with white matter lesions can be used as the reference image or the floating image of the registration algorithm. This is not the case with the CFM method. Indeed, if a mask is used to remove the influence of a region of the floating image, the voxels of the reference mapped to this region will have a null cost. Consequently, the algorithm will tend to map voxels of the reference to the area of the floating image with no cost and the lesions in the floating image would have the tendency to attract the surrounding tissue. So, with the cost function masking approach, the brain with lesions has to be used as the reference of the registration. As for morphometry or lesion mapping, the reference image of the registration should be the reference template (a control subject or an average of a group of controls), a solution would be to do the registration with the patient as reference and the lesions masked, and then, to invert the transformation. The inpainting method does not raise this issue. The lesions of the patient are inpainted, and then, the patient image can be used as either the reference or the floating image (or both) during the registration.

The evaluation of the different methods, summarized in Figure 2 and Figure 3, favours the LWMI method over CFM. The mean error obtained with the LWMI method is clearly reduced compared to the other methods, especially in the lesion area. This is of importance when the spatial distribution of the lesions is the object of the study.

Instead of removing the outliers as the CFM method does, the inpainting method tries to reconstruct the cost function as it would be without the lesions. The registration algorithm is then driven to a better solution with this reconstruction than when no information is available at the lesion location. The GWMI method uses the a priori knowledge that the lesions are in the white matter and BI fills the lesions with surrounding voxels, using local information for the inpainting. The LWMI method combines these two properties to inpaint the lesions using the local values of the white matter and consequently, produces the best results of the evaluation. With a better reconstruction method, the solution found by the registration is also better.

The inpainting method we proposed (LWMI) uses the output of the segmentation of the brain in CSF, GM and NAWM. A high accuracy is not required for this segmentation. Indeed, we only need the intensity of the NAWM in the neighbourhood of the inpainted area. If we are not confident in the segmentation accuracy or if the lesion boundary is fuzzy or if we want to improve the robustness of the method, a good prescription would be to erode the NAWM mask and to increase the size of the neighbourhood used in the inpainting method. ) x ( V We assume in this paper that grey matter lesions have only a minor influence on the registration. If this assumption is considered too strong, grey matter lesions can also be inpainted the same way white matter lesions are inpainted, by filling them with the surrounding grey matter voxels intensity.

Our LWMI inpainting method can be applied to different contrast modalities (T 1 , T 2 , proton density...) and other neurological diseases affecting the white matter. The only requirement is that intensity in the lesions must be uniform, without details to reconstruct, create or extend from the neighborhood. The extension of our inpainting based approach to DTI images will be the object of future work.

Fig. 1 .

 1 Fig.1. Example of lesion mapping by inpainting white matter lesions before the registration. On the patient image (a), the lesions are segmented out (b) and inpainted using the LWMI method (c). The registration is performed between the inpainted patient (c) and the reference image (g). The output transformation can finally be applied on the inpainted patient (d), the original patient image (e) and on the lesion mask of the patient (f ). Note that some lesions appeared and disappeared on this slice but in 3D, no lesion is added or lost.

  the p-values of right tail T-tests between the output of LWMI and the other methods for the three datasets. With a significance threshold of 0.05 all the tests show the significance of the superiority of LWMI over the other methods presented.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Mean and standard deviation of the error in the whole brain for each set of simulations and each method.

Table I :

 I P-values of the right tail T-test between LWMI and each method for each set of simulation and for the whole brain mask.

		Naïve	CFM	BI	GWMI
	Dataset Affine	5.6e-14 2.8e-07 7.1e-08 3.2e-15
	Dataset Mask	3.7e-13 6.0e-05 1.0e-08 1.9e-13
	Dataset Inpaint 1.9e-13 6.3e-09 1.2e-11 1.9e-13
			CFM	BI	GWMI
	Dataset Affine	7.5e-08 1.9e-06 0.0011 0.00043
	Dataset Mask	7.7e-09 2.6e-06 0.0012 0.0047
	Dataset Inpaint 1.7e-08 2.1e-06 0.027	0.00092

Table II :

 II P-values of the right tail T-test between LWMI and each method for each set of simulation and for the lesion mask.

		1.4
					naive
		1.2			CFM BI
					GWMI
		1			LWMI
	Mean Error	0.6 0.8
		0.4
		0.2
		0	Dataset Affine	Dataset Mask	Dataset Inpaint

Acknoledgement

The authors would like to thank Dr Hélène Ratiney, PhD and Alan Evangelista, BA for reviewing the manuscript and Dr Roland Henry, PhD and Dr Hélène Ratiney for helpful discussion.

This work was supported in part by the grant JF-2122-A from the National Multiple Sclerosis Society (PI: Dr Daniel Pelletier).


Dominique Muller

Fabrice Gabarrot

Clémentine Bry

Daniel Priolo

Jean-Baptiste Légal

Julien Chappé

Viviane Coiffard

Audrey Villard-Forest

"Watching T.V. I start to cry; For no reason I don't know why; Could it be from messages on my TV; Which I'm getting subliminally" [START_REF] Muir | Subliminal[END_REF].

Can subliminal exposure lead people to adopt an idea, an attitude, or an action? In other words, is subliminal persuasion a myth or a fact?Subliminal influence has been a recurrent topic of debate in both scientific and popular communities since Vicary (in a press conference held in 1957) claimed (even if he finally admitted it was a hoax) that subliminal exposure to short sentences, such as "Drink coke" or "Eat pop-corn", could drastically influence people's will to consume that products. To date, evidence suggests that subliminal exposure to faces, words, or brands, can to some extent influence judgments about people (e.g., [START_REF] Bargh | Automatic information processing and social perception: The influence of trait information presented outside of conscious awareness on impression formation[END_REF], judgments about ads [START_REF] Channouf | Subliminal exposure to facial expressions of emotion and evaluative judgments of advertising messages[END_REF], people's self-evaluation (e.g., [START_REF] Baldwin | Priming relationship schemas: My advisor and my pope are watching me from the back of my mind[END_REF], their attitudes (e.g., [START_REF] Zajonc | Feeling and thinking: Preferences need no inferences[END_REF], and even their behavior [START_REF] Brasel | Red Bull "Gives You Wings" for better and worse: a double-edged impact of brand exposure on consumer performance[END_REF].

Subliminal exposure has also been used to prime goals, directly or through goal-related constructs (e.g., [START_REF] Chartrand | Automatic activation of impression formation and memorization goals: Nonconscious goal priming reproduces effects of explicit task instructions[END_REF]; for evidence about nonconscious goal-priming and pursuit, see also [START_REF] Bargh | The automated will: Nonconscious activation and pursuit of behavioral goals[END_REF][START_REF] Custers | The unconscious will: How the pursuit of goals operates outside of conscious awareness[END_REF]. In the framework of persuasion, goal-priming research has essentially focused on need-related behaviors (e.g., thirst, hunger). For instance, [START_REF] Cooper | Subliminal motivation: A story revisited[END_REF] subliminally activated a motiva-tional state of thirst using stimuli related to thirst (the word "thirsty", pictures of Coca Cola® cans, or picture of a sweating boxer) embedded in an episode of The Simpsons. Compared to a control condition, par-ticipants' ratings of thirst were significantly higher following the priming manipulation. [START_REF] Strahan | Subliminal priming and persuasion: Striking while the iron is hot[END_REF] also suggested that a message could be perceived as more persuasive when it corresponds to an active motive or need. Thus, for already thirsty participants, a relevant ad (i.e., a message about a thirstquenching beverage) could be more convincing if it was accompanied by the subliminal presentation of thirst-related words. In the same line, [START_REF] Karremans | Beyond Vicary's fantasies: The impact of subliminal priming and brand choice[END_REF] primed participants with the brand of a drink (Lipton Ice). They demonstrated that subliminal priming of a goal-related feature (i.e., the brand of the drink: Lipton Ice) affected participants' choice, as well as their intention to drink the primed brand, but only if they were thirsty.

In a way, research about subliminal persuasion only partially benefitted from findings concerning nonconscious goal pursuit. Indeed, in previous research, participants were not primed with goals directly related to features typically associated with source effects (i.e., effects produced by characteristics associated to the source of the message and that influence persuasion, such as credibility, ex-pertise, and attractiveness; see [START_REF] Petty | Attitude change: Multiple roles for persuasion variables[END_REF], but with means to accomplish the goal [START_REF] Karremans | Beyond Vicary's fantasies: The impact of subliminal priming and brand choice[END_REF] or goal-related concept [START_REF] Cooper | Subliminal motivation: A story revisited[END_REF][START_REF] Strahan | Subliminal priming and persuasion: Striking while the iron is hot[END_REF]; see also [START_REF] Dijksterhuis | Unpublished datad set[END_REF]cited in Dijksterhuis, Aarts, & Smith, 2005). In our research, we tried to use goal priming to enhance the persuasiveness of a message in a more direct way. Specifically, we attempted to use the goal "to trust" to influence participants' evaluation of the message and its source.

Previous studies have found that priming general goals could influence behavior and cognitive processing. For instance, [START_REF] Chartrand | Automatic activation of impression formation and memorization goals: Nonconscious goal priming reproduces effects of explicit task instructions[END_REF] demonstrated that a general impression formation goal could be primed; [START_REF] Albarracin | Increasing and decreasing motor and cognitive output: A model of general action and inaction goals[END_REF] also demonstrated that activating general action or inaction goals influenced behavioral outcome (doodling on a piece of paper) as well as cognitive outcomes (recall performance; problem solving). In our view, the goal "to trust" is one of these general or high order goals. Indeed, it has been proposed (e.g., [START_REF] Fiske | Social cognition[END_REF]) that motivation to trust other people is one of our most basic motivations, as people generally expect good things from other people. This inclination to trust other people would render "to trust" a rather accessible and easily activated goal.

In this study, we tried to determine whether priming the goal "to trust" could influence the way a persuasive message is processed and its influence on judgment and behavioral intentions. We hypothesized that goal-priming would lead to a better acceptance of a persuasive message, a more positive perception of the source of the message, as well as greater intentions to behave in accordance with the message.

Method

Participants and design

Ninety-three undergraduate psychology students (80 women and 13 men) participated in this study in exchange for course credits. Participants were randomly assigned to one of the two conditions: goal priming or control.

Procedure and material

We chose to use a persuasive message promoting the benefits of drinking tap water, which is a simple, an easy-to-do, and a practical daily pro-environmental behavior. Before the experimental session, participants received a questionnaire designed to assess their initial attitudes toward tap water. Participants had to indicate, on a six points Likert scale, their degree of agreement with the following statements: "I like tap water", "I think that tap water tastes bad" (reversed score), and "I think that tap-water is good for health".We computed a global score of attitude toward tap water (Cronbach's α= 0.89). Attitude scores ranged from 1 to 6, M= 3.88, and SD = 1.87.

Upon arriving to the lab, participants were informed that they would participate in two independent studies. They were then invited to start with the study on visual attention. The visual detection task they performed was actually a pretext to carry out the subliminal goal priming. Indeed, during the task in which participants had to indicate which shape ("O" or "X" displayed during 120 ms) they perceived on the computer screen, they were subliminally primed (30 ms) with "to trust" or with verbs1 closely related to this goal (e.g., to approve, to accept, to agree). Primes were flashed in the center of the screen and were immediately followed by a mask, which was displayed until participants responded. Thirty primes were flashed, half of them directly related to the goal "to trust". Participants in the control condition also performed the task; however, they were not exposed to subliminal primes. In order to check the subliminal character of our priming manipulation, a separate group of 23 participants received the task with specific instructions. They were informed that words would flash during the visual detection task and that they would have to detect these words and to report them at the end of the task. None of the participants were able to recall any word flashed during the subliminal priming manipulation, indicating that the stimuli were displayed beneath the subjective threshold.

Once the visual detection task was completed, participants were told the first study was over and that they would now complete a survey about water consumption. They were first given 80 s to read a persuasive message promoting tap-water consumption. The message was illustrated with the picture a woman, Mrs. Marie, presented as the executive head of the regional water control organization. Subsequently, participants answered questions about the message they read (agreement, clarity), the source of the message (likeable/nice, trustworthy, competent), and behavioral intentions about tap water (drinking more tap water; not buying bottled water). In the last part, a funneled questionnaire allowed us to assure that participants had not perceived subliminal primes and did not discovered the relation between the two studies.

Results

In order to control for the potential effect of participants' attitudes, ANCOVAs were used to analyze the data. Initial attitude about tap water consumption was used as a covariate. Table 1 summarizes the means, means adjusted for the covariate and standard deviations for all variables.

Message

Data analysis yielded an effect of the priming manipulation on message assessment, F(1,90) = 4.66, p b 0.05, η 2 = 0.04. Participants primed with the goal of trusting displayed a greater agreement with the message's arguments compared to the participants in the control condition (M=4.62 and M= 4.18, respectively). Attitude about tapwater was a significant covariate for this measure, F(1,90) = 48.77, p b 001. We found no differences in the evaluation of the message's clarity.

Source of the message

Goal priming influenced judgments about Mrs. Marie, who delivered the pro-tap water message. Particularly, compared to control participants, primed participants perceived Mrs. Marie as more likeable/nice, F(1,90) = 3.73, p b 0.05, η 2 =0.04 (M=4.49 and M= 4.26) and more trustworthy, F(1,90) = 5.78, p b 0.02, η 2 =0.06 (M=4.02 and M= 3.35). The covariate contributed significantly to the perception of the source as being likeable, F(1,90) = 4.63, p b 0.05, and trustworthy, F(1,90) = 5.12, p b 0.03. No effect was found for perceived competency.

Behavioral intentions

Goal priming had an effect on behavioral intentions about water consumption. Participants primed with the goal of trusting and exposed to the pro tap-water message indicated that they would drink more tap water, F(1,90) = 5.24, p= 0.02, η 2 =0.06 (M=3.74 and M=2.82) and avoid buying bottled water, F(1,90) = 9.98, p= 0.002, η 2 =0.10 (M=2.70 and M= 1.73; reversed scores). The covariate, attitude about tap water, was significantly related to both intentions with p b 0.001.

Discussion

Our study explored the possibility of using a goal priming technique to enhance persuasion by priming goals related to features typically associated with source effects. Specifically, our aim was to use goal priming to directly influence the trust in the message and its source. Results indicated that participants primed with the goal of trusting not only evaluated more positively the message and its source, but also expressed more behavioral intentions in line with the message. Results extend [START_REF] Strahan | Subliminal priming and persuasion: Striking while the iron is hot[END_REF] findings, which indicated that a message could be perceived as more persuasive even when it does not correspond to an active motive or need. In our case, activating the goal "to trust" facilitated the acceptance and enhanced the persuasiveness of the subsequently displayed message. Results are also in line with the idea that the goal "to trust" is a general goal that can influence information processing and behavioral intentions, extending Albarracin et al.'s (2008) findings.

In sum, our study demonstrated that subliminally priming a goal targeting the credibility dimension influences perception of the message and of its source as well as its consequences in terms of behavioral intentions. Potential practical implications of these findings are numerous. On the bright side, results could be used to develop pro-cedures helping to promote public health campaigns (quit smoking, safe driving). As a darker alternative, advertisers could be tempted to use them to persuade consumers to try or buy a product they weren't previously interested in. Even if many countries forbid the use of subliminal advertising, it does not mean that nonconscious influences and nonconscious goal pursuit do not occur in a natural setting or that goal priming cannot be used to enhance the per-suasiveness of a message or people's receptivity to a message. Indeed, incidental exposure (i.e., products or brands unobtrusively presented in a setting) is rather close of subliminal priming in terms of effects [START_REF] Berger | Dogs on the street, pumas on your feet: How cues in the environment influence product evaluation and choice[END_REF]. This kind of exposure is frequently manipulated in natural settings (e.g., in TV shows, websites, video games, or more generally in supermarkets and crowded places) and could allow goal priming such as the one we used to occur and operate.

Future research should address other issues that our current findings did not resolve. First, underlying processes need to be refined. How does motivation "to trust" operate? Does it work as a filter, leading people to focus only on positive/pros arguments in the mes-sage? Does it "lower people's shields" and if so, under what circumstances, if any? Moreover, motivation may be one option, but not the only possible explanation. Indeed, as our experiment did not measured motivation, we cannot exclude a non-motivational explanation for this effect. For instance, it could be that trust primes cause people to perceive the source as more trustworthy, which drives the effects. A future study will have to decide between these two possibilities. Second, priming has to be studied in combination with other classic source effects' features of persuasion, such as message framing (e.g., [START_REF] Kahneman | On the interpretation of intuitive probability: A reply to Jonathan Cohen[END_REF]. For example, goal priming could be associated with a goal framing manipulation [START_REF] Levin | All frames are not created equal: A typology and critical analysis of framing effects[END_REF] toinfluence implicit goals of "obtaining the positive consequence (i.e., positive framing)" or "avoiding the negative consequence (i.e., negative framing)". In particular, priming a goal congruent with the goal stressed in the goal-framing message should influence the evaluation of the message and, consequently, enhance its persuasiveness. Finally, we used a unilateral message concerning a quite consensual topic (drinking tap water). It might be interesting to extend this study to other types of messages, including counter attitudinal, political, or even religious.

Table 1

 1 Judgment of the message, judgment of the source, and behavioral intentions as a function of priming condition.

	Priming condition	Control		Trust
		M(M Adj. )	SD	M (M Adj. )	SD
	Message
	Agreement with the message	4.18 (4.19)	0.16	4.62 (4.59)	0.15
	Clarity	5.34 (5.35)	0.15	5.25 (5.24)	0.14
	Source
	Likeable/nice Trustworthiness	4.02 (4.05)	0.15	4.49 (4.46)	0.18
	Competency	3.35 (3.38)	0.18	4.02 (3.99)	0.18
		3.73 (3.75)	0.19	4.03 (4.01)	0.19
	Behavioral intentions
	Drink more tap water
	Not buying bottled water	2.82 (2.91)	0.24	3.74 (3.69)	0.24
		1.73 (1.80)	0.20	2.70 (2.64)	0.20

Note. M Adj. =means adjusted for the covariate.

Verbs in French are single words.