Nicole Muhlrad

Gilles Vallet

Ilona Butler

Victoria Gitelman

Etti Doveh

Emmanuelle Dupont

Pete Thomas

Rachel Talbot

Eleonora Papadimitriou

George Yannis

Luca Persia

Gabriele Giustiniani

Klaus Machata

Charlotte Bax

Analysis of road safety management systems in Europe

Keywords:

The objective of this paper is the analysis of road safety management in European countries and the identification of "good practice". A road safety management investigation model was created, based on several "good practice" criteria. Road safety management systems have been thoroughly investigated in 14 European countries on 2010, by means of interviews with both governmental representatives and independent experts, who filled in an extensive questionnaire. A reliable and accurate picture ("profile") was created for each country, allowing country comparisons. Then, statistical methods were used to make rankings of countries, and analyse the relationship between road safety management and road safety performance. The results of the analyses suggest that it is not possible to identify one single "good practice". Nevertheless, there were several elements that emerged as "good practice" criteria. On the basis of the results, recommendations are proposed at national and European level.

Résumé

L'objectif de cette étude est l'analyse de la gestion de la sécurité routière dans les pays européens et l'identification de «bonnes pratiques». Un modèle d'enquête de la gestion de la sécurité routière a été créé, en fonction de plusieurs critères de «bonnes pratiques». Les systèmes de gestion de la sécurité routière ont été examinées en détail dans 14 pays européens en 2010, au moyen d'entretiens avec des représentants gouvernementaux et des experts indépendants, qui ont rempli un questionnaire. Un tableau fiable et précis («profil») a été créé pour chaque pays, permettant des comparaisons entre pays. Ensuite, on a utilisé des méthodes statistiques pour identifier le classement de pays, et la relation entre la gestion et la performance de la sécurité routière. Les résultats des analyses indiquent qu'il n'est pas possible d'identifier un modèle unique de «bonnes pratiques». Néanmoins, il y a plusieurs éléments de «bonnes pratiques» ressortis. Sur la base de ces résultats, des recommandations sont proposées au niveau national et européen.

Mots-clé: gestion de la sécurité routière ; bonnes pratiques.

Introduction

In [START_REF] Muhlrad | Road safety management investigation model and questionnaire, Deliverable 1.2 of the EC FP7 project DaCoTA[END_REF] a road safety management system is defined as "a complex institutional structure involving cooperating and interacting bodies which supports the tasks and processes necessary to the prevention and reduction of road traffic injuries". By definition, a road safety management system should meet a number of "good practice" criteria spanning the entire policy making cycle, from agenda setting to policy formulation, adoption, implementation and evaluation, and including efficient structure and smooth processes, in order to enable evidence-based policy making.

Effective organization of road safety management is assumed to be one of the conditions for obtaining good road safety results at country level [START_REF] Dacota | [END_REF][START_REF] Elvik | Does the use of formal tools for road safety management improve safety performance[END_REF]. Moreover, as road safety is becoming more and more integrated into broader scoped transport or environment policies, and given the effects of the current economic recession on road safety resources, the need for optimization of road safety management systems becomes even more pronounced.

Within the DaCoTA research project, a road safety management investigation model proposed by [START_REF] Muhlrad | Road safety management investigation model and questionnaire, Deliverable 1.2 of the EC FP7 project DaCoTA[END_REF] is based on several "good practice" criteria, defined by an exhaustive literature review, aiming to address the need for optimized road safety management systems, leading to better road safety performance, in a changing environment.

The objective of this paper is to present the analysis of road safety management framework in European countries and the identification of "good practice" for the optimisation of road safety management processes, carried out within the DaCoTA research project.

For that purpose, road safety management systems have been thoroughly investigated in 14 European countries in 2010, by means of interviews with governmental representatives and independent experts in each country, who filled in an extensive questionnaire on the degree to which the various road safety management systems meet the "good practice" criteria. A shorter version of the DaCoTA questionnaire has also been prepared in collaboration with the European Transport Safety Council (ETSC) and dispatched to the ETSC-PIN panel of experts. The data was then analyzed by means of both quantitative and qualitative analysis. This paper is structured as follows: In section 2, the road safety management investigation model is presented, and the data collection and handling procedures are described. In section 3, the results of qualitative analysis of the data are presented, while section 4 concerns the results of quantitative analysis. Section 5 presents the conclusions of the research in terms of road safety management "good practice" in Europe. Finally, section 6 summarises the DaCoTA key messages and recommendations for the improvement of road safety management systems in Europe.

Methodology

Road safety management investigation model

The investigation model of [START_REF] Muhlrad | Road safety management investigation model and questionnaire, Deliverable 1.2 of the EC FP7 project DaCoTA[END_REF] describe road safety management structures and outputs according to the policy-making cycle (agenda setting, policy formulation, adoption, implementation and evaluation) set against the background of a typical hierarchical national government organization (Fig. 1). The most complete RS management system which would be obtained for a country fulfilling all the "good practice" criteria identified was used as a reference (Fig. 2). For each country, "good practice" elements, lack of such elements and peculiarities can be then summarised in a "diagnosis" including structures, processes, policymaking tasks and outputs according to the investigation model.

Data collection and handling

On the basis of the investigation model, an extensive DaCoTA questionnaire was developed, on the degree to which the various road safety management systems meet the "good practice" criteria. The questions related to five main areas of Road Safety Management:

 Institutional organisation, coordination and stakeholders" involvement The questionnaire was filled for 14 countries. More specifically, the DaCoTA partners represented 12 countries: Austria, Belgium, Finland, France, Greece, Israel, Italy, Latvia, the Netherlands, Poland, Spain, and the United Kingdom, and were able to collect data in the native language of a further 2: Ireland and Switzerland. In order to maximise the representativeness of the sample, questionnaires were sent by email to road safety actors in Latvia and Spain to fill in independently without an interview. However clarifications were sought when necessary.

Two groups of road safety professionals were targeted:

 Government representatives: Road safety practitioners who are or have been directly involved in policy and decision making over a long enough period of time for them to have acquired wide-ranging experience in road safety,  Independent experts: Road safety researchers or scientists who may contribute to policy but do not have a decision making role and could offer a non-partisan view of the Road Safety Management systems in place.

A shorter version of the DaCoTA questionnaire has also been prepared in collaboration with the European Transport Safety Council (ETSC). This questionnaire includes 11 key questions similar to those of the original DaCoTA questionnaire and was dispatched to the PIN panel of the ETSC, i.e. the 30 high level national experts from ETSC network of member organisations. This gave a general overview of the Road Safety Management system in 30 countries, although in much less detail than the DaCoTA data.

The combined use of the two questionnaires allowed on the one hand the coverage of basic road safety management elements for all European countries (DaCoTA/ETSC-PIN questionnaire), and on the other hand the full in-depth analysis for a subset of European countries (DaCoTA questionnaire).

Qualitative analyses of road safety management systems in Europe

Within the qualitative analysis of the DaCoTA research project, a thorough analysis and cross-checking of the questionnaire responses and related comments was carried out, for both the governmental representatives and the independent experts, in order to draw a reliable and accurate picture or "profile" for each country, and allowing in-depth country comparisons for selected key items. For details the reader is referred to Papadimitriou et al. (2012).

Road safety management profiles

Country profiles of the road safety management systems in the 14 European countries were analysed and compared to the reference "good practice" system (Fig. 2). Road safety management structures and outputs are described according to the policy-making cycle (agenda setting, policy formulation, adoption, implementation and evaluation) and set against the background of a typical hierarchical national government organization.

Because such a typical organization is not suited to managing road safety policies which involve most government sectors, specific structures have been set up in most countries, modifying or short-circuiting the typical hierarchical administration.

For each country, these structures as well as the working processes were charted to provide a graphic picture of the road safety management situation ("country profile"), as the one presented in Fig. 3 for Belgium, and the identification of "good practice" elements, as those presented in Fig. 4 for Belgium. Focus was on the national organization and the relations between national and regional/local structures and not on road safety management at the decentralized level, as it was agreed at an earlier stage of methodology building that this aspect could not be tackled in the time-frame of the DaCoTA project.

The thorough analysis of the country profiles, together with additional information from the DaCoTA/ETSC-PIN data, allowed for an in-depth analysis and comparison of countries, leading to several observations and conclusions. These are summarised in the next section 3.2.

Synthesis of country analyses

Institutional organization, coordination and stakeholders' involvement

A large variation was observed in the structures and processes at the higher level of road safety management.

The component "Lead Agency formally appointed to take responsibility for road safety" had a higher availability level among the countries. However, different types of Lead Agencies (from strong departments of ministries, to interministerial committees and road safety councils) and with different specific roles were identified. In several cases, it is not easy to identify the "lead agency". Although it is widely acknowledged that effective road safety management can be achieved with lead agencies of various structural and procedural forms [START_REF] Bliss | Implementing the Recommendations of the World Report on Road Traffic Injury Prevention. Country Guidelines for the Conduct of Road Safety Capacity Reviews and the Related Specification of Lead Agency Reforms, Investment Strategies and Safety Projects[END_REF], the results of DaCoTA suggest that road safety management systems based on strong departments of ministries, or use government agencies specifically established for this purpose, with clear responsibility for the government"s road safety policy, are more effective.

The DaCoTA results clearly indicate that the establishment of a structure and process alone is not sufficient for effective road safety management. In several countries coordination and budget are the most critical links for setting the processes going. The effectiveness of road safety management systems can also be largely affected by the degree to which regional authorities, NGOs, stakeholders or the public at large are involved via systematic

Management processes

Inter-sectoral coordination:

Effective for policy formulation and adoption, implementation is not legally binding

Monitoring:

Regular progress reports to Task Force but not formalized

Knowledge use:

Benchmarking, IBSR research

Knowledge production:

IBSR has some sustainable funding (taxes)

Policy-making tasks

Policy formulation:

Scientific and stakeholder input

Policy adoption:

Decided No specifically allocated budget Limited resources from fines for enforcement

Implementation conditions:

Training for professionals,

Implementation:

Responsibility of individual ministers

Pre-conditions

Political will: Key structures in place but the period without a Government caused delays in the adoption of a new programme Road safety climate: There are legal structures for the consultaton of key stakeholders consultation at all stages of the policy making process. Very few countries demonstrate such routine and fruitful consultation processes.

Policy formulation and adoption

Road safety policy formulation showed the largest degree of "consensus" between countries, especially as regards the presence of a road safety strategy with specific quantitative targets for fatality reduction. Nevertheless, several inconsistencies and uncertainties are involved in the adoption of road safety programmes and the participation or consultation of regional and local authorities.

Road safety visions and targets appear to be strongly influenced by either European Union proposals or road safety "leader" countries in Europe. The vast majority of countries have adopted the EU target for 2020, as they had also adopted the previous one of 2010. "Vision Zero", "Sustainable Safety" and "Safe Systems" are the main visions endorsed by several countries. Almost all European countries have road safety strategies and programmes, with the majority boasting the ambitious EU targets.

There is a lot of inconsistency in the design of the programmes, the setting of priorities and the implementation schedule. Proposals coming from regional or local authorities are hardly ever integrated into national road safety programmes. The same is the case for the allocation of resources, so that the regional or local budgets are seldom ensured or even defined at all. Finally, the formal adoption of road safety strategies and programmes takes place under quite different procedures in different countries -and in several countries it remains pending.

Policy implementation and funding

In general, implementation of programmes and measures appears to be the weakest component of road safety management systems in Europe, especially as regards the establishment of formal resource allocation procedures, the allocation of funding to evaluation, the sufficiency of funds and human resources and the drafting of plans to support implementation.

The problem of providing stable economic foundations for implementing and managing road safety programmes is the key to improved effectiveness and efficiency of road safety work. A decision is seldom taken to ensure the availability of a budget for road safety activities from the national budget. Moreover, the lack of information on measures implementation costs at national and international level, combined with a lack of knowledge on the methods appropriate to calculate these costs, makes the evaluation of the actual implementation expenses an estimation by itself.

Moreover, formal procedures for budget allocation to the various actors are seldom in place, especially for the regional or local authorities. As a consequence, the agency responsible for implementation has to rely on its own budget, and the implementation itself depends on the resources available in this agency as well as on the priority it assigns to road safety.

In countries with a clearly designated "lead agency", this agency takes over the majority of programme management duties, otherwise it is not always clear who is responsible for what part of the implementation. A lack of coordination at the operational level is clearly identifiable, resulting in some sectors being more efficient than others in performing the road safety interventions they have been assigned.

Monitoring and evaluation

A satisfactory level of availability was identified with respect to "benchmarking" for monitoring progress in the road safety situation in relation to other countries. Nevertheless, most elements related to monitoring and evaluation had a medium or lower level of availability across the countries. In the majority of cases it involves collecting information when a programme ends; only a couple of countries monitor programmes while they are still in progress.

Only in few countries, evaluation of safety measures is part of the culture and routine within the road safety programme, with a dedicated budget. In several countries, evaluation is very rare and adjusted to the available budget. Even when evaluation is consistently performed, it is usually limited to infrastructure and enforcement measures, or to specific behaviours targeted by specific measures. Formal efficiency assessment techniques are not always implemented. As regards the evaluation of the overall road safety programme, it is mostly limited to a "checklist" of the specific measures foreseen, rather than an actual evaluation.

Scientific support and information, capacity building

In most countries, a higher than medium level of availability is observed for a number of elements related to scientific support and information, such as the use of research results for formulating road safety policies, the systematic information of citizens on the national road safety policy and interventions and their effects, and the presence of articles or programmes in the media which review, criticize or challenge current road safety policies.

Moreover, in most countries, there is at least one research institute or university department performing multidisciplinary road safety research. While national road safety observatories exist in most countries, there is great variation in their type, role and operation. Only in a few countries are road safety observatories part of the lead agencies, while in most cases this role is taken over by research centres, statistical offices or the police. Capacity building and training of road safety actors is seldom a systematic procedure with a dedicated budget. A better use of the scientific capacity appears to be one of the major challenges for evidence-based road safety policy making in the European countries.

Quantitative analyses

The quantitative analyses carried out within DaCoTA used statistical methods to identify patterns and rankings of countries, as regards both the road safety management characteristics, and the relationship between road safety management and road safety performance. For details the reader is referred to Papadimitriou et al. (2012).

Clustering of countries on the basis of road safety management components

Statistical clustering techniques were used to group and rank the 14 European countries on the basis of their level of availability of the various road safety management "good practice" elements, separately for each one of the five areas of the DaCoTA questionnaire (see section 2.2). Figure 5 presents, as an example, the clustering results concerning the first area of the questionnaire, namely "institutional organisation". A ranking of countries in terms of their road safety management system, per area and as a whole, was also presented. The analyses confirmed that the complexity and variability of road safety management systems is such, that the task of ranking the countries in terms of road safety management is very demanding. It was revealed that all the countries are completely different when road safety management systems are considered as a whole, making it impossible to propose a single overall ranking of countries" road safety management systems. However, it is possible to compare the countries when parts of the road safety management system are considered separately.

However, even when examining the various parts of road safety management systems separately, no two countries were found to belong to the exact same ranking. Across all the analyses, a number of countries with a consistently higher level of availability of some road safety management components could be identified, and others with a consistently lower level of the same features. Interestingly, however, the countries that were ranked systematically at the top of road safety management components were not always those that are known to be the best road safety performing countries.

For example, according to the clustering results, Switzerland, Israel, Finland were found to be consistently ranked best in the various stages of the road safety policy making cycle, whereas UK and Netherlands were not always ranked best in road safety management components. On the other hand, the countries that were found to be consistently ranked at the lowest of the scale were Poland and Greece, which is in full accordance with these countries" ranking on the basis of fatality rates.

The inconsistencies that emerged when comparing the rankings of road safety management with road safety performance, especially for the "good" performing countries, brought forward the need for a dedicated analysis on the potential links between these two.

Statistical models linking road safety management with road safety performance

In this analysis, regression models were developed in order to test whether road safety management is associated with road safety performance. Different road safety outcomes (fatalities, reduction in fatalities, Safety Performance Indicators -the intermediate outcomes) were tested against road safety management indicators and other background variables. Composite indicators were also used both as dependent and explanatory variables [START_REF] Bax | Developing a successful Composite Index[END_REF].

The dedicated analysis of road safety management and road safety performance was based on the SUNflower pyramid [START_REF] Koornstra | SUNflower: a comparative study of the development of road safety in Sweden, the United Kingdom, and the Netherlands[END_REF] tackling the entire hierarchy from structure and culture, to programmes and measures, to safety performance indicators (intermediate outcomes), and to road safety final outcomes (i.e. fatalities and injuries). Due to the complexity of road safety management systems, as identified by the analysis of the DaCoTA questionnaire responses, this analysis was based on a shorter version of the questionnaire, namely the common DaCoTA/ETSC-PIN questions. The various models developed are summarised in Table 1. The results suggest no direct relationship between road safety management and the final outcomes of the road safety systems. However, they do suggest a relationship between road safety management and road safety performance indicators [START_REF] Papadimitriou | Is road safety management linked to road safety performance?[END_REF]. This is what is in fact suggested by the SUNflower pyramid, namely that the policy context and input will first affect the intermediate outcomes, i.e. the operational level of road safety, which corresponds to the level of road infrastructure, the maturity of road user behaviour, the protection offered by vehicles etc. These operational conditions are thought to be the result of policies and interventions, and the final outcomes are results of these operational conditions.

Of course, the fact that European countries constitute a small sample, do not allow for the identification of strong relationships, but rather to the indication of the presence of relationships. Moreover, there are some confounding factors that which could not be accounted for, such as mobility, economy, weather, long traditions etc.

Conclusions

The results of the DaCoTA analyses on road safety management systems suggest that, although a number of "good practice" elements can be established as regards road safety management structures, processes and outputs, it is not possible to identify one single "good practice" model at national level. Best performing countries are not always ranked best in terms of road safety management components. On the other hand, the proposed "good practice" criteria seem to work as regards the worst performing countries.

Despite the differences in European road safety management systems, there have been several elements that emerged as more critical "good practice" criteria, such as the presence of a strong lead agency, the efficiency of the implementationmonitoringevaluation part of the policy making cycle, the embedding of programmes in sustainable and results-focused structures and processes, and the distribution and coordination of responsibilities between federal, regional and local levels. Especially the implementation, funding, monitoring and evaluation elements showed the lowest level of availability in the European countries and appear to be the most problematic sections of the road safety management systems.

When examining the relation between road safety performance and road safety management in the different countries, road safety management was found to be associated with safety performance indicators (SPIs), reflecting the operational level of road safety in each country.

However, a factor that should be taken into account is the time of observation. In some countries, road safety management components may be so recent that they hadn"t yet had the time to deploy their full potential; or they may have been around for such a long time that their impact has already gradually faded away.

Finally, it was indicated that expert responses may reflect an independent and more objective view and that future analysis might better use experts" opinion as a prime source.

Key messages and recommendations

The improvement of road safety management systems is a key component for the improvement of road safety at national and European level, through improved structures, processes and training. The present research revealed that there is no single ideal road safety management model, but there are several good practice criteria which may be adapted to the national conditions in each case. One clear finding is that similar performance in road safety management can be achieved by means of differing structures and implementation processes. Similarly, similar road safety performance in terms of final outcomes (i.e. fatalities) may be the "result" of substantially different road safety management systems.On the basis of the DaCoTA analysis of road safety management systems in Europe, a number of key messages and recommendations are outlined in Table 2.

Table 2. Key messages and recommendations for the improvement of road safety management in Europe



  Fig.1: Government organization background

Fig. 3 .

 3 Fig.3. Structures, processes and outputs in Belgium, 2010

Fig. 5 .

 5 Fig. 5. "Institutional organization": mean values of availability of road safety management elements, by clusters of countries.

  Handle road safety management in times of recession Adopting the safe systems approach Exploiting the synergies of road safety and environmental policies Adoption of serious injury reduction targets Focusing on the essentials, leaving the details to the individual countries Strengthening the role of the European Road Safety Observatory Publication of a Road Safety Management Good Practice Manual Building on the existing framework and improving where necessary Political will and commitment from all stakeholders

National statistics Regional RS plans Regional RS plans Policy-making Knowledge base and toolbox Policy adoption: High level decision-making Policy formulation: Medium-level planning and decision-making Programming Policy implementation, evaluation Technical and scientific support Output Agenda setting Inter-Ministerial Committee for Road Safety

	Parliament
	Under the Federal Minister for
	Mobility
	Task Force Road
	Safety
	Under the Inter-Ministerial
	Committee

Federal Commission for Road Safety Medium/long term objectives/targets Medium/long term RS programme:

		Benchmarking
		European
		RS targets
	Regular
	informal progress
	reporting
	by IMC/Task Force
	members	General state of road-
		saf ety (2011-2020)
	Evaluation of
	targets
	(planned f or 2015)
	Planned
	evaluation of
	programme
	and measures
	(2020)

Belgian Road Safety Institute (IBSR) Information to citizens Multi-disciplinary RS training Rs training for professionals IBSR reports on questions asked by Parliament Scientific literature Observatorium for RS National Regional RS plans Federal Public Service for Mobility and Transport Funding of IBSR through specific taxes Funding from fines for enforcement Sectoral funding of implementation IBSR's scientific reports to the Federal Commission Road safety management structures Road safety Institutions:

	Inter-Ministerial Committee
	for Road Safety (IMC):
	Coordination (decision-making)
	Task Force for Road Safety:
	Coordination (implementation)
	Federal Commission for
	Road Safety: consultation of
	Stakeholders
	Technical
	support
	Belgium Road Safety
	Institute (IBSR)
	National road safety
	observatory

Table 1 .

 1 Summary of models linking road safety management (RSM) with road safety performance

		Model 1	Model 2	Model 3	Model 4	Model 5
	Dependent	Fatalities per	Fatalities per	% reduction in	Composite index	Composite index
	variable	million	million passenger-	fatalities 2001-	of road safety	on Safety
		inhabitants	kilometres	2010	outcomes	Performance
						Indicators (SPI)
	Dependent	rate	rate	Percentage	Values within	Values within
	variable type				[0,1]	[0,1]
	Model	Quasi-Poisson	Quasi-Poisson	Beta regression	Beta regression	Beta regression

Acknowledgements

The DaCoTA WP1 group would like to address special thanks to the governmental representatives and the independent experts of the 14 European countries analysed, for filling in the questionnaire and providing useful and insightful comments on the road safety management systems in their countries. The group is also grateful to Prof.Richard Alsop, Chairman of the ETSC PIN panel, for his useful comments and remarks on the results of this research.


A Wartelle

B Trapp

M Staňo

C Thirion

S Bochmann

J Bachmann

M Foerster

L Aballe

T O Menteş

A Locatelli

A Sala

L Cagnon

J.-C Toussaint

O Fruchart

Bloch-point-mediated topological transformations of magnetic domain walls in cylindrical nanowires

Cylindrical nanowires made of soft magnetic materials, in contrast to thin strips, may host domain walls of two distinct topologies. Unexpectedly, we evidence experimentally the dynamic transformation of topology upon wall motion above a field threshold. Micromagnetic simulations highlight the underlying precessional dynamics for one way of the transformation, involving the nucleation of a Bloch-point singularity, however, fail to reproduce the reverse process. This rare discrepancy between micromagnetic simulations and experiments raises fascinating questions in material and computer science.

Directional orders, such as nematics and ferromagnets, may give rise to topologically non-trivial textures of the order parameter. In ferromagnets, the variety of exchange interactions and host systems translates into a broad spectrum of such textures, such as non-zero Chern numbers in band structures on a kagome lattice [1], merons in coupled disks [2] or multilayers [3], chiral domain walls (DWs) [4][5][6] and skyrmions [7][8][9]. Yet, while all those have a continuous spin texture, a singular configuration was theoretically predicted in 1965[10]: the Bloch point (BP). This is a point defect for the unit magnetization vector field m, and as such the only possible topological defect in ferromagnetism [11]. It is the analogue of defects seen in nematic liquid crystals [12,13], for which the distribution of the director around the defect covers the unit sphere S 2 exactly once. For this reason, an integer called winding number [14] is associated to the BP, which is its signature as a topological defect.

The existence of the BP is crucial, as simulation suggested that the transformation from one spin texture to another of different topology is mediated by a BP expulsion or injection: in static [15] or dynamic [16] magnetization switching of vortex cores in thin films, the nucleation of skyrmions in dots [17] or of DWs in magnetically soft cylindrical nanowires [18]. The latter system appears as a textbook playground for the investigation of topological transformations and of BPs. Indeed, BPs should exist at rest, unlike those involved in the dynamical transformation processes mentioned above. In detail, two types of DWs were predicted to exist in cylindrical nanowires, with different topologies. First is the Bloch point § Institute of Engineering Univ. Grenoble Alpes ¶ Institute of Engineering Univ. Grenoble Alpes * Electronic address: alexis.wartelle@neel.cnrs.fr † Present address: CEITEC -Central European Institute of Technology, Brno University of Technology, 612 00 Brno, Czech Republic ‡ Electronic address: olivier.fruchart@cea.fr domain wall (BPW, also called vortex wall by some), hosting a BP at its center even at rest. The BPW was predicted to reach a steady-state motion with high axial velocity even at high magnetic field [19][20][21]. Second is the transverse-vortex wall (TVW, also called transverse wall by some), with fast azimuthal precession and axial mobility much lower than that of the BPW [19,22]. Both DWs have been predicted to retain their topology during motion. This makes a sharp contrast with thin strips, prone to DW transformations under both field and spin-polarized current [19,23,24]. The latter can be understood as all DWs share a single topology in strips [25], making transformations easier. As the existence of the BPW and TVW has been confirmed experimentally recently at rest [26,27], the question arises whether the different topology indeed prevents DW transformation in reality.

In this Letter, we investigate the field-driven motion of magnetic DWs in magnetically soft nanowires. Our experiments reveal that the transformation from TVW to BPW and viceversa may occur. We build a theoretical understanding of this topological transition, associated with the injection of a BP (or expulsion for the reverse process). Micromagnetic simulations partly confirm this qualitative description, highlighting how the precessional magnetization dynamics leads to the previously-overlooked possibility of TVW-to-BPW transformation. However, the BPW-to-TVW transformation is not found in the simulation, leaving open the question whether experiments or models should be blamed.

I. METHODS

Starting from nanoporous alumina templates engineered with two diameter modulations along the pores, we electroplate magnetically-soft Fe 20 Ni 80 and Co 40 Ni 60 nanowires [28][29][30]. The geometry is thus that of a cylinder with a thin section of diameter ≈ 140 nm surrounded by two wider sections of the same diameter ≈ 250 nm, all three with length 10 µm. The purpose of the modulations of diameter is


Valentin Deschaintre
email: valentin.deschaintre@inria.fr

Miika Aittala

Fredo Durand

George Drettakis

Adrien Bousseau

Single-Image SVBRDF Capture with a Rendering-Aware Deep Network

Keywords: Computing methodologies → Reflectance modeling, Image processing, material capture, appearance capture, SVBRDF, deep learning

. From a single flash photograph of a material sample (insets), our deep learning approach predicts a spatially-varying BRDF. See supplemental materials for animations with a moving light.

Texture, highlights, and shading are some of many visual cues that allow humans to perceive material appearance in single pictures. Yet, recovering spatially-varying bi-directional reflectance distribution functions (SVBRDFs) from a single image based on such cues has challenged researchers in computer graphics for decades. We tackle lightweight appearance capture by training a deep neural network to automatically extract and make sense of these visual cues. Once trained, our network is capable of recovering per-pixel normal, diffuse albedo, specular albedo and specular roughness from a single picture of a flat surface lit by a hand-held flash. We achieve this goal by introducing several innovations on training data acquisition and network design. For training, we leverage a large dataset of artist-created, procedural SVBRDFs which we sample and render under multiple lighting directions. We further amplify the data by material mixing to cover a wide diversity of shading effects, which allows our network to work across many material classes. Motivated by the observation that distant regions of a material sample often offer complementary visual cues, we design a network that combines an encoder-decoder convolutional track for local feature extraction with a fully-connected track for global feature extraction and propagation. Many important material effects are view-dependent, and as such ambiguous when observed in a single image. We tackle this challenge by defining the loss as a differentiable SVBRDF similarity metric that compares the renderings of the predicted maps against renderings of the ground truth from several lighting and viewing directions. Combined together, these novel ingredients bring clear improvement over state of the art methods for single-shot capture of spatially varying BRDFs.

INTRODUCTION

The appearance of real-world objects results from complex interactions between light, reflectance, and geometry. Disentangling these interactions is at the heart of lightweight appearance capture, which aims at recovering reflectance functions from one or a few photographs of a surface. This task is inherently ill-posed, since many different reflectances can yield the same observed image. For example, any photograph can be perfectly reproduced by a diffuse albedo map, where highlights are "painted" over the surface.

A combination of two strategies is generally employed to deal with this ill-posedness. First, ambiguity can be reduced by collecting additional measurements under different viewing or lighting conditions. While this strategy is currently the most appropriate to achieve high accuracy, it requires precise control of the acquisition process [START_REF] Xu | Minimal BRDF Sampling for Two-shot Near-field Reflectance Acquisition[END_REF]. The second strategy is to introduce a priori assumptions about the space of plausible solutions. While designing such priors by hand has challenged researchers for decades [START_REF] Dar'ya Guarnera | BRDF Representation and Acquisition[END_REF], Convolutional Neural Networks (CNNs) have emerged as a powerful method to automatically learn effective priors from data.

In this paper, we propose a deep learning approach to singleimage appearance capture, where we use forward rendering simulations to train a neural network to solve the ill-posed inverse problem of estimating a spatially-varying bi-directional reflectance distribution function (SVBRDF) from one picture of a flat surface lit by a hand-held flash. While our method shares ingredients with recent work on material capture [START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF][START_REF] Rematas | Reflectance and Natural Illumination from Single-Material Specular Objects Using Deep Learning[END_REF], material editing [START_REF] Liu | Material Editing Using a Physically Based Rendering Network[END_REF], and other image-to-image translation tasks [START_REF] Isola | Image-to-Image Translation with Conditional Adversarial Networks[END_REF], achieving high-quality SVBRDF estimation requires several key innovations on training data acquisition and neural network design.

A common challenge in supervised learning is the need for many training images and the corresponding solutions. For materials, this problem is acute: even with the most lightweight capture methods, we cannot obtain enough measurements to train a CNN. Furthermore, such an approach would inherit the limitations of the data capture methods themselves. Following the success of using synthetic data for training [START_REF] Richter | Playing for Data: Ground Truth from Computer Games[END_REF][START_REF] Su | Render for CNN: Viewpoint Estimation in Images Using CNNs Trained with Rendered 3D Model Views[END_REF]Zhang et al. 2017a], we tackle this challenge by leveraging a large dataset of artist-created, procedural SVBRDFs [START_REF] Allegorithmic | Substance Share[END_REF]], which we sample and render under multiple lighting directions to create training images. We further amplify the data by randomly mixing these SVBRDFs together and render multiple randomly scaled, rotated and lit versions of each material, yielding a training set of up to 200,000 realistic material samples.

The task of our deep network is to predict four maps corresponding to per-pixel normal, diffuse albedo, specular albedo, and specular roughness of a planar material sample. However, directly minimizing the pixel-wise difference between predicted and ground truth parameter maps is suboptimal, as it does not consider the interactions between variables. Intuitively, while a predicted map may look plausible when observed in isolation, it may yield an image far from the ground truth when combined with other maps by evaluating the BRDF function. Furthermore, the numerical differences in the parameter maps might not consistently correlate with differences in the material's appearance, causing a naive loss to weight the importance of different features arbitrarily. We mitigate these shortcomings by formulating a differentiable SVBRDF similarity metric that compares the renderings of the predicted maps against renderings of the ground truth from several lighting and viewing directions.

We focus on lightweight capture by taking as input a single nearfield flash-lit photograph. Flash photographs are easy to acquire, and have been shown to contain a lot of information that can be leveraged in inferring the material properties from one [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF][START_REF] Aittala | Two-shot SVBRDF Capture for Stationary Materials[END_REF][START_REF] Ashikhmin | Distribution-based BRDFs[END_REF] or multiple images [START_REF] Hui | Reflectance Capture Using Univariate Sampling of BRDFs[END_REF][START_REF] Riviere | Mobile Surface Reflectometry[END_REF]]. In such images, the pixels showing the highlight provide strong cues about specularity, whereas the outer pixels show diffuse and normal variations more prominently. To arrive at a consistent solution across the image, these regions need to share information about their respective observations. Unfortunately, our experiments reveal that existing encoder-decoder architectures struggle to aggregate distant information and propagate it to fine-scale details. To address this limitation, we enrich such architectures with a secondary network that extracts global features at each stage of the network and combines them with the local

Training

Data Generation

Procedural SVBRDFs (Fig. 7) Data Augmentation: random perturbations, map mixing (Fig. 8)

GT SVBRDF

Rendered Flash Image

Rendering Loss (Fig. 5)

Deep Network (Fig. 3) Predicted SVBRDF Fig. 2. Overview of our method: we use procedural SVBRDFs to generate our ground truth (GT) training data, which we augment by random perturbations of the procedural parameters and mixing of the SVBRDF maps (Fig. 7 and 8, Sec. 4). We then use physically-based rendering to synthesize the corresponding flash images. These are used to train our Deep Network (Fig. 3, Sec. 3.1 and 3.2) which compares predicted SVBRDFs and ground truth using a rendering loss (Fig. 5,Sec. 3.3).

activations of the next layer, facilitating back-and-forth exchange of information across distant image regions.

In summary, we introduce a method to recover spatially-varying diffuse, specular and normal maps from a single image captured under flash lighting. Our approach outperforms existing work [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF][START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF]] on a wide range of materials thanks to several technical contributions (Fig. 2):

• We exploit procedural modeling and image synthesis to generate a very large number of realistic SVBRDFs for training. We provide this dataset freely for research purposes1 . • We introduce a rendering loss that evaluates how well a prediction reproduces the appearance of a ground-truth material sample. • We introduce a secondary network to combine global information extracted from distant pixels with local information necessary for detail synthesis. We stress that our goal is to approximate the appearance of a casually-captured material rather than recover accurate measurements of its constituent maps.

RELATED WORK

The recent survey by [START_REF] Dar'ya Guarnera | BRDF Representation and Acquisition[END_REF]] provides a detailed discussion of the wide spectrum of methods for material capture. Here we focus on lightweight methods for easy capture of spatially-varying materials in the wild.

A number of assumptions have been proposed to reduce ambiguity when only a few measurements of the material are available. Common priors include spatial and angular homogeneity [START_REF] Zickler | Reflectance sharing: predicting appearance from a sparse set of images of a known shape[END_REF], repetitive or random texture-like behavior [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF][START_REF] Aittala | Two-shot SVBRDF Capture for Stationary Materials[END_REF][START_REF] Wang | Estimating Dual-scale Properties of Glossy Surfaces from Step-edge Lighting[END_REF], sparse environment lighting [START_REF] Dong | Appearancefrom-motion: Recovering Spatially Varying Surface Reflectance Under Unknown Lighting[END_REF][START_REF] Lombardi | Reflectance and Illumination Recovery in the Wild[END_REF], polarization of sky lighting [START_REF] Riviere | Polarization imaging reflectometry in the wild[END_REF], mixture of basis BRDFs [START_REF] Dong | Manifold Bootstrapping for SVBRDF Capture[END_REF][START_REF] Hui | Reflectance Capture Using Univariate Sampling of BRDFs[END_REF][START_REF] Ren | Pocket Reflectometry[END_REF], optimal sampling directions [START_REF] Xu | Minimal BRDF Sampling for Two-shot Near-field Reflectance Acquisition[END_REF], and user-provided constraints [START_REF] Dong | AppGen: Interactive Material Modeling from a Single Image[END_REF]]. However, many of these assumptions restrict the family of materials that can be captured. For example, while the method by [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF] takes a single flash image as input, it cannot deal with non-repetitive material samples (see Section 5.2). We depart from this family of work by adopting a data-driven approach, where a neural network learns its own internal assumptions to best capture the materials it is given for training. [START_REF] Dror | Recognition of Surface Reflectance Properties from a Single Image under Unknown Real-World Illumination[END_REF] were among the first to show that a machine learning algorithm can be trained to classify materials from low-level image features. Since then, deep learning emerged as an effective solution to related problems such as intrinsic image decomposition [START_REF] Innamorati | Decomposing Single Images for Layered Photo Retouching[END_REF][START_REF] Narihira | Direct Intrinsics: Learning Albedo-Shading Decomposition by Convolutional Regression[END_REF]] and reflectance and illumination estimation [START_REF] Rematas | Reflectance and Natural Illumination from Single-Material Specular Objects Using Deep Learning[END_REF]. Most related to our approach is the work by [START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF], who adopted an encoderdecoder architecture similar to ours to estimate diffuse reflectance and normal maps. However, their method only recovers uniform specular parameters over the material sample. In contrast, we seek to recover per-pixel specular albedo and roughness. Furthermore, they trained separate networks for different types of materials, such as wood and plastic. Rather than imposing such a hard manual clustering (which is ambiguous anyway: consider the common case of plastic imitation of wood), we train a single all-purpose network and follow the philosophy of letting it learn by itself any special internal treatment of classes that it might find useful. In addition, [START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF] introduce a strategy called self-augmentation to expand a small synthetic training set with semi-synthetic data based on the network's own predictions for real-world photographs. This strategy is complementary to our massive procedural data generation.

Since our goal is to best reproduce the appearance of the captured material, we evaluate the quality of a prediction using a differentiable rendering loss, which compares renderings of the predicted material with renderings of the ground truth given for training. Rendering losses have been recently introduced by [START_REF] Tewari | MoFA: Model-based Deep Convolutional Face Autoencoder for Unsupervised Monocular Reconstruction[END_REF] and [START_REF] Liu | Material Editing Using a Physically Based Rendering Network[END_REF] for facial capture and material editing respectively. Tewari et al. use a rendering loss to compare their reconstruction with the input image in an unsupervised manner, while Liu et al. use it to evaluate their reconstruction with respect to both the input image and a ground-truth edited image. [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF] also use a differentiable renderer to compare the textural statistics of their material estimates with those of an input photograph. However, they use this loss function within a standard inverse-rendering optimization rather than to train a neural network. In contrast to the aforementioned methods, our rendering loss is a similarity metric between SVBRDFs. The renderings are not compared to the input photograph, as this would suffer from the usual ambiguities related to single-image capture. Rather, we compare the rendered appearance of the estimated and the target material under many lighting and viewing directions, randomized for each training sample.

The need for combining local and global information appears in other image transformation tasks. In particular, [START_REF] Iizuka | Let there be Color!: Joint End-to-end Learning of Global and Local Image Priors for Automatic Image Colorization with Simultaneous Classification[END_REF] observe that colors in a photograph depend both on local features, such as an object's texture, and global context, such as being indoor or outdoor. Based on this insight, they propose a convolutional network that colorizes a gray-level picture by separately extracting global semantic features and local image features, which are later combined and processed to produce a color image. Contextual information also plays an important role in semantic segmentation, which motivates [START_REF] Zhao | Pyramid Scene Parsing Network[END_REF] to aggregate the last layer feature maps of a classification network in a multi-scale fashion. While we also extract local and global features, we exchange information between these two tracks after every layer, allowing the network to repeatedly transmit information across all image regions. [START_REF] Wang | Non-local Neural Networks[END_REF] introduced a related non-local layer that mixes features between all pixels, and can be inserted at multiple points in the network to provide opportunities for non-local information exchange. While they apply more complex nonlinear mixing operations, they do not maintain an evolving global state across layers. Finally, ResNet [START_REF] He | Deep Residual Learning for Image Recognition[END_REF]] aims at facilitating information flow between co-located features on different layers, which makes the training better behaved. Our architecture has a complementary goal of aiding efficient global coordination between non-co-located points. Our scheme also opens up novel pathways, allowing information to be directly transmitted between distant image regions.

NETWORK ARCHITECTURE

Our problem boils down to translating a photograph of a material into a coinciding SVBRDF map representation, which is essentially a multi-channel image. The U-Net architecture [START_REF] Ronneberger | U-Net: Convolutional Networks for Biomedical Image Segmentation[END_REF]] has proven to be well suited for a wide range of similar imageto-image translation tasks [START_REF] Isola | Image-to-Image Translation with Conditional Adversarial Networks[END_REF]Zhang et al. 2017b]. However, our early experiments revealed that despite its multi-scale design, this architecture remains challenged by tasks requiring the fusion of distant visual information. We address this limitation by complementing the U-Net with a parallel global features network tailored to capture and propagate global information.

U-Net Image-to-Image Network

We adopt the U-Net architecture as the basis of our network design, and follow [START_REF] Isola | Image-to-Image Translation with Conditional Adversarial Networks[END_REF] for most implementation details. Note however that we do not use their discriminator network, as we did not find it to yield a discernible benefit in our problem. We now briefly describe the network design. We provide the code of our network and its learned weights to allow reproduction of our results2 .

As illustrated in Figure 3, our base network takes a 3-channel photograph as input and outputs a 9-channel image of SVBRDF parameters -3 channels for the RGB diffuse albedo, 3 channels for the RGB specular albedo, 2 channels for the x and y components of the normal vector in tangent plane parameterization, and 1 channel for the specular roughness. We use low dynamic range images as input photographs due to the ease of acquisition, and let the network learn how to interpret the saturated highlight regions. Regardless, the dynamic range of flash photographs can still be large. We flatten the dynamic range by transforming the input image into logarithmic space and compacting it to the range [0, 1] via the formula log(x +0.01)-log 0.01 log(1.01)-log(0.01) . The input image is processed through a sequence of 8 convolutional layers that perform downsampling (the encoder), followed by a sequence of 8 upsampling and convolutional layers (the decoder). 3. Architecture of our deep convolutional network, which takes as input a single flash-lit image (left) and predicts four maps corresponding to per-pixel normal, diffuse albedo, specular albedo and specular roughness (right). Our network follows the popular U-Net encoder-decoder architecture (black), which we complement with a new global features track (green) that processes vectors instead of feature maps. Taken together, the full network consists of repeating "modules", which are detailed in the bottom part of the figure. At every stage of the network, the feature means subtracted by the instance normalization after the convolutional layer are concatenated with the global feature vector, which is then processed by a fully connected layer and a non-linearity before being added to the feature maps of the next stage. IN and FC denote instance normalizations and fully connected layers respectively. We use SELU [START_REF] Klambauer | Self-Normalizing Neural Networks[END_REF]] and leaky ReLu activation functions. In the decoder, the set of layers also includes a skip-connection concatenation and a second convolution, which we omit for clarity. We provide the code of our network to allow reproduction.

Such a hourglass-shaped network gradually reduces the resolution of the image while increasing the feature size, forcing the encoder to compress the relevant information into a concise, global feature vector. The task of the decoder is to expand these global features back into a full-sized image that matches the training target. However, while the bottleneck is critical to aggregate spatially-distant information, it hinders the reproduction of fine details in the output. Following [START_REF] Ronneberger | U-Net: Convolutional Networks for Biomedical Image Segmentation[END_REF], we mitigate this issue by introducing skip connections between same-sized layers of the encoder and decoder, helping the decoder to synthesize details aligned with the input at each spatial scale.

Prior to the decoder, we insert a single convolutional layer with 64 output feature channels. The feature counts in the encoder downscaling layers are 128, 256, 512, 512, 512, 512, 512 and 512. The downsampling is implemented by using a stride of 2 in the convolutions. In the decoder, the same feature counts are used in reverse order. At each scale, a nearest-neighbor upsampling is followed by concatenation of encoder features, and two convolutions. We use the filter size [4, 4] across all layers. For nonlinearities we use the leaky ReLu activation function with a weight 0.2 for the negative part. The final output is mapped through a sigmoid to enforce output values in the range [0, 1].

Following each convolution layer (or pair thereof), we apply instance normalization, which stabilizes training on image generation tasks [START_REF] Isola | Image-to-Image Translation with Conditional Adversarial Networks[END_REF][START_REF] Ulyanov | Improved Texture Networks: Maximizing Quality and Diversity in Feed-Forward Stylization and Texture Synthesis[END_REF]. Finally, we regularize by applying dropout at 50% probability on the three coarsest layers of the decoder.

Global Features Network

Distant regions of a material sample often offer complementary information to each other for SVBRDF recovery. This observation is at the heart of many past methods for material capture, such as the work of [START_REF] Hendrik | Image-based Reconstruction of Spatial Appearance and Geometric Detail[END_REF] where the SVBRDF is assumed to be spanned by a small set of basis BRDFs, or the more recent work of [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF]2015] where spatial repetitions in the material sample are seen as multiple observations of a similar SVBRDF patch. Taking inspiration from these successful heuristics, we aim for a network architecture capable of leveraging redundancies present in the data.

The hourglass shape of the U-Net results in large footprints of the convolution kernels at coarse spatial scales, which in theory provide long-distance dependencies between output pixels. Unfortunately, we found that this multi-scale design is not sufficient to properly fuse information for our problem. We first illustrate this issue on a toy example, where we trained a network to output an image of the average color of the input, as shown in Figure 4 (top row). Surprisingly, the vanilla U-Net performs poorly on this simple task, failing to output a constant-valued image. A similar behavior occurs on our more complex task, where visible residuals of the specular highlight and other fine details pollute the output maps where they should be uniform (Figure 4, 2nd to 4th row).

In addition, we hypothesize that the ability of the network to compute global information is partly hindered by instance (or batch) normalization, which standardizes the learned features after every convolutional layer by enforcing a mean and standard deviation . We trained a U-Net convolutional network to predict an image of the average color of the input (top row). Surprisingly, the basic U-Net fails to produce a constant image (c). Similar artifacts appear when using the U-Net for SVBRDF prediction (f). We address this issue by complementing the U-Net with a parallel network that explicitly computes and propagates global features. This approach succeeds in computing the average image (d) and reduces artifacts in SVBRDF maps (g).

learned from training data. In other words, while the normalization is necessary to stabilize training, it actively counters the network's efforts to maintain non-local information about the input image. In fact, instance normalization has been reported to improve artistic style transfer because it eliminates the output's dependence on the input image contrast [START_REF] Ulyanov | Improved Texture Networks: Maximizing Quality and Diversity in Feed-Forward Stylization and Texture Synthesis[END_REF]]. This is the opposite of what we want. Unfortunately, while we tried to train a U-Net without normalization, or with a variant of instance normalization without mean subtraction, these networks yielded significant residual shading in all maps.

We propose a network architecture that simultaneously addresses both of these shortcomings. We add a parallel network track alongside the U-Net, which deals with global feature vectors instead of 2D feature maps. The structure of this global track mirrors that of the main convolutional track, with convolutions changed to fully connected layers and skip connections dropped, and with identical numbers of features. See Figure 3 for an illustration and details of this architecture. The global and convolutional tracks exchange information after every layer as follows:

• Information from the convolutional track flows to the global track via the instance normalization layers. Whereas the standard procedure is to discard the means that are subtracted off the feature maps by instance normalization, we instead incorporate them into the global feature vector using concatenation followed by a fully connected layer and a nonlinearity.

For the nonlinearity, we use the Scaled Exponential Linear Unit (SELU) activation function, which is designed to stabilize training for fully connected networks [START_REF] Klambauer | Self-Normalizing Neural Networks[END_REF]]. • Information from the global track is injected back into the local track after every convolution, but before the nonlinearity. To do so, we first transform the global features by a fully connected layer, and add them onto each feature map like biases. Our global feature network does not merely preserve the mean signal of a given feature map -it concatenates the means to form a global feature vector that is processed by fully connected layers before being re-injected in the U-Net at multiple scales. Each pair of these information exchanges forms a nonlinear dependency between every pixel, providing the network with means to arrive at a consistent solution by repeatedly transmitting local findings between different regions. In particular, the common case of nearconstant reflectance maps becomes easier for the network to express, as it can source the constant base level from the global features and the fine details from the convolutional maps (Figure 4g).

Rendering Loss

Our network outputs a set of maps that describe BRDF parameters, such as specular roughness and albedo, at every surface point. The choice of parameterization is arbitrary, as it merely acts as a convenient proxy for the actual object of interest: the spatio-angular appearance of the SVBRDF. In fact, the parameterizations of popular BRDF models arise from a combination of mathematical convenience and relative intuitiveness for artists, and the numerical difference between the parameter values of two (SV)BRDFs is only weakly indicative of their visual similarity. We propose a loss function that is independent of the parameterization of either the predicted or the target SVBRDF, and instead compares their rendered appearance. Specifically, any time the loss is evaluated, both the ground truth SVBRDF and the predicted SVBRDF are rendered under identical illumination and viewing conditions, and the resulting images are compared pixel-wise. We use the same Cook-Torrance BRDF model [1982] for the ground truth and prediction, but our loss function could equally be used with representations that differ between these two quantities.

We implement the rendering loss using an in-network renderer, similarly to [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF]. This strategy has the benefits of seamless integration with the neural network training, automaticallycomputed derivatives, and automatic GPU acceleration. Even complicated shading models are easily expressed in modern deep learning frameworks such as TensorFlow [START_REF] Abadi | TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems[END_REF]]. In practice, our renderer acts as a pixel shader that evaluates the rendering equation at each pixel of the SVBRDF, given a pair of view and light directions (Figure 5). Note that this process is performed in the SVBRDF coordinate space, which does not require to output pixels according to the perspective projection of the plane in camera space.

Using a fixed finite set of viewing and lighting directions would make the loss blind to much of the angular space. Instead, we formulate the loss as the average error over all angles, and follow the common strategy of evaluating it stochastically by choosing the angles at random for every training sample, in the spirit of stochastic gradient descent. To ensure good coverage of typical conditions, we use two sets of lighting and viewing configurations:

• The first set of configurations is made of orthographic viewing and lighting directions, sampled independently of one another from the cosine-weighted distribution over the upper hemisphere. The cosine weighting assigns a lower weight to grazing angles, which are observed less often in images due to foreshortening. • While the above configurations cover all angles in theory, in practice it is very unlikely to obtain mirror configurations, which are responsible for visible highlights. Yet, highlights carry rich visual information about material appearance, and should thus contribute to the SVBRDF metric. We ensure the presence of highlights by introducing mirror configurations, where we only sample the lighting direction from the cosine distribution, and use its mirror direction for the viewing direction. We place the origin at a random position on the material plane, and choose independent random distances for both the light and the camera according to the formula exp(d), where d ∼ Normal(µ = 0.5, σ = 0.75) for a material plane of size 2 × 2. The net effect of these configurations is to produce randomly-sized specular highlights at random positions.

We compare the logarithmic values of the renderings using the l 1 norm. The logarithm is used to control the potentially extreme dynamic range of specular peaks, and because we are more concerned with relative than absolute errors. To reduce the variance of the stochastic estimate, for every training sample we make 3 renderings in the first configuration and 6 renderings in the second, and average the loss over them. We provide a detailed pseudo-code of our rendering loss in supplemental materials. Figure 6 compares the output of our network when trained with a naive l 1 loss against the output obtained with our rendering loss. While the l 1 loss produces plausible maps when considered in isolation, these maps do not reproduce the appearance of the ground truth once re-rendered. In contrast, the rendering loss yields a more faithful reproduction of the ground truth appearance.

Training

We train the network with batch size of 8 for 400,000 iterations, using the Adam optimization algorithm [Kingma and Ba 2015] with

PROCEDURAL SYNTHESIS OF TRAINING DATA

While several recent papers have shown the potential of synthetic data to train neural networks [START_REF] Richter | Playing for Data: Ground Truth from Computer Games[END_REF][START_REF] Su | Render for CNN: Viewpoint Estimation in Images Using CNNs Trained with Rendered 3D Model Views[END_REF]Zhang et al. 2017a], care must be taken to generate data that is representative of the diversity of real-world materials we want to capture. We address this challenge by leveraging Allegorithmic Substance Share [START_REF] Allegorithmic | Substance Share[END_REF]], a dataset of more than 800 procedural SVBRDFs designed by a community of artists from the movie and video game industry. This dataset has several key features relevant to our needs. First, it is representative of the materials artists care about. Second, each SVBRDF is rated by the community, allowing us to select the best ones. Third, each SVBRDF exposes a range of procedural parameters, allowing us to generate variants of them for data augmentation. Finally, each SVBRDF can be converted to the four Cook-Torrance parameter maps we want to predict [START_REF] Cook | A Reflectance Model for Computer Graphics[END_REF]. We first curated a set of 155 high-quality procedural SVBRDFs from 9 material classes -paint (6), plastic (5), leather (13), metal (35), wood ( 23), fabric (6), stone (25), ceramic tiles (29), ground (13), some of which are illustrated in Figure 7. We also selected 12 challenging procedural SVBRDFs (6 metals, 3 plastics, 3 woods) to serve as an independent testing set in our comparison to [START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF]. Together with two artists, we identified the procedural parameters that most influence the appearance of each of our training SVBRDFs. We obtained between 1 and 36 parameters per SVBRDF (7 on average), for which we manually defined the valid range and default values.

We then performed four types of data augmentation. First, we generated around 1,850 variants of the selected SVBRDFs by applying random perturbations to their important parameters, as illustrated in Figure 8 (top). Second, we generated around 20,000 convex combinations of random pairs of SVBRDFs, which we obtained by α-blending their maps. The mixing greatly increases the diversity of low-level shading effects in the training data, while staying close to the set of plausible real-world materials, as shown in Figure 8 (bottom). Third, we rendered each SVBRDF 10 times with random lighting, scaling and orientation. Finally, we apply a random crop on each image at training time, so that the network sees slightly different data at each epoch.

The scene we used to render each SVBRDF is composed of a textured plane seen from a fronto-parallel camera and dimensioned to cover the entire image after projection. The light is a small white emitting sphere positioned in a plane parallel to the material sample, at a random offset from the camera center. The camera has a field of view of 50 • to match the typical field of view of cell-phone cameras after cropping to a square, and is positioned at a fixed distance from the material sample. Note that there is a general ambiguity between the scale of the SVBRDF, the distance of the camera, and the strength of the light, which is why we hold the latter parameters fixed. However, since such parameters are unknown in our casual capture scenario, the albedo maps we obtain from real pictures at test time are subject to an arbitrary, global scale factor.

We used the Mitsuba renderer [Jakob 2010], for which we implemented the Cook-Torrance BRDF model [1982] with GGX normal distribution [START_REF] Walter | Microfacet Models for Refraction Through Rough Surfaces[END_REF]] to match the model used in Allegorithmic Substance. We rendered each SVBRDF as a linear low-dynamic range image, similar to gamma-inverted photographs captured with a cell-phone. We also used Mitsuba to render the parameter maps after random scaling and rotation of the material sample, which ensures that the maps are aligned with the material rendering and that the normal map is expressed in screen coordinate space rather than texture coordinate space. Our entire dataset of around 200,000 SVBRDFs took around 16 hours to generate on a cluster of 40 CPUs.

EVALUATION

We now evaluate our approach on real-world photographs and compare it with recent methods for single-image SVBRDF capture. We refer the reader to the supplemental material for an extensive set of results for hundreds of materials, including all estimated SVBRDF maps and further re-renderings. In particular, animations with moving light sources demonstrate that the solutions work equally well in a variety of lighting conditions. The supplemental material also includes additional comparisons with previous work. Fig. 10. A selection of results from our method on real-world photographs. In each image pair, the left image is a photograph of a surface, and the right image is a re-rendering of the SVBRDF inferred from that image. The illumination environment in the re-renderings is an interior space with a large window on the left. See supplemental materials for additional results and animated re-renderings.

Real-world photographs

We used regular cell phones (iPhone SE and Nexus 5X) and their built-in flash units to capture a dataset of nearly 350 materials on which we applied our method. We cropped the images to approximate the field of view used in the training data. The dataset includes samples from a large variety of materials found in domestic, office and public interiors, as well as outdoors. In fact, most of the photographs were shot during a casual walk-around within the space of a few hours. often mixed together in the same image. We found it to perform particularly well on materials exhibiting bold large-scale features, where the normal maps capture sharp and complex geometric shapes from the photographed surfaces.

Figure 9 shows our result for two materials with interesting spatially varying specularity behavior. The method has successfully identified the gold paint in the specular albedo map, and the different roughness levels of the black and white tiles. The latter feature shows good consistency across the spatially distant black squares, and we find it particularly impressive that the low roughness level was apparently resolved based on the small highlight cues on the center tile and the edges of the outer tiles. For most materials, the specular albedo is resolved as monochrome, as it should be. Similar globally consistent behavior can be seen across the result set: cues from sparsely observed specular highlights often inform the specularity across the entire material.

Note that our dataset contains several duplicates, i.e. multiple shots of the same material taken from slightly different positions. Their respective SVBRDF solutions generally show good consistency among each other. We also captured a few pictures with an SLR camera, for which the flash is located further away from the lens than cell phones. We provide the resulting predicted maps in supplemental materials, showing that our method is robust to varying positions of the flash.

Comparisons

5.2.1 Relighting. Figure 11 provides a qualitative comparison between renderings of our predictions and renderings of measured Bidirectional Texture Functions (BTFs) [START_REF] Michael Weinmann | Material Classification Based on Training Data Synthesized Using a BTF Database[END_REF] under the same lighting conditions. While BTFs are not parameterized according to the 4 maps we estimate, they capture ground-truth appearance from arbitrary view and lighting conditions, which ultimately is the quantity we wish to reproduce. Our method provides a faithful reproduction of the appearance of the leather. It also captures well the spatially-varying specularity of the wallpaper, even though it produces slightly more blurry highlights. Please refer to supplemental materials for additional results on 20 BTFs.

In addition, Figure 12 compares renderings of our predictions with real photographs under approximately similar lighting conditions. Our method is especially effective at capturing the normal variations of this wood carving. [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF]2015]. The method by [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF] is the most related to ours in terms of input, since it also computes an SVBRDF representation from a single flash-lit photograph. However, [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF] exploit redundancy in the input picture by assuming that the material is stationary, i.e. consists of small textural features that repeat throughout the image.

5.2.2

We compare our method to theirs by feeding photographs from their dataset to our network (Figure 13 and supplemental materials). Despite the similar input, the two approaches produce different outputs: whereas we produce a map that represents the entire input photo downsampled to 256 × 256, their method produces a tile that represents a small piece of the texture at high resolution. Furthermore, the BRDF models used by the methods are different. To aid comparison, we show re-renderings of the material predicted by each method under identical novel lighting conditions.

Both methods produce a good result, but show a clearly different character. The method of [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF] recovers sharp textural details that are by construction similar across the image. For the same reason, their solution cannot express larger-scale variations, and the result is somewhat repetitive. In contrast, our solution shows more interesting large-scale variations across the image, but lacks some detail and consistency in the local features. [START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF] and our method. Due to the use of different parametrizations, we cannot compute RMSE on specular terms for [START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF]. As their output albedo maps can have a different scaling than the ground truth with respect to lighting, we evaluate the re-rendering and diffuse albedo RMSE with multiple scaling factors on the albedo, and keep the best one (0.27).

Method

Li Most of our real-world test images violate the stationarity requirement, and as such would not be suitable for the method of [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF]. Our method also has the advantage in speed: whereas [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF] use an iterative optimization that takes more than an hour per material sample, our feedforward network evaluation is practically instant.

Figure 13 also contains results obtained with an earlier method by [START_REF] Aittala | Two-shot SVBRDF Capture for Stationary Materials[END_REF]. This method also assumes stationary materials, and requires an additional no-flash picture to identify repetitive details and their large-scale variations. Our approach produces similar results from a single image, although at a lower resolution. [START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF]. The method by [START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF] is based on a similar U-Net convolutional network as ours. However, it has been designed to process pictures captured under environment lighting rather than flash lighting, and it predicts a constant specular albedo and roughness instead of spatially-varying maps. We first compare the two methods on our synthetic test set for which we have the ground truth SVBRDFs (Figure 15 and Table 1). For a fair comparison, we tested the method by Li et al. on several renderings of the ground truth, using different environment maps and different orientations. We then selected the input image that gave the best outcome. We compare the results of the two methods qualitatively with re-renderings under a mixed illumination composed of an environment map enriched with a flash light, so as to ensure that neither method has an advantage. For quantitative comparison, we compute the RMSE of each individual map, as well as the RMSE of re-renderings averaged over multiple point lighting conditions; our results have systematically lower error.

5.2.3

Overall, our method reproduces the specularity of the ground truth more accurately, as evidenced by the sharpness of reflections and highlights in the re-renderings. We believe this is due to our use of near-field flash illumination, as the apparent size and intensity of the highlight caused by the flash is strongly indicative of the overall glossiness and albedo levels. The method of [START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF] must rely on more indirect and ambiguous cues to make these inferences. While such cues are available in the input images -for example, the reflections of the illumination environment are blurred to different degrees -their method has not reached an equally accurate estimate of the specular roughness.

Similarly, flash illumination highlights the surface normal variations by introducing spatially varying directional shading effects [2016; 2015]. Note that the maps (other than the normals) are not directly comparable due to different parametrization of the BRDF models. The solution of [START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF] corresponds to a small region of about 15% of the image dimension, intended to be repeated by texture synthesis or tiling. The earlier method by [START_REF] Aittala | Two-shot SVBRDF Capture for Stationary Materials[END_REF] captures the entire input image but requires an additional no-flash picture for guidance.

In contrast, our method reproduces the large-scale features well, and is applicable to non-repetitive materials captured with a single flash picture.

into the image. Such variations do also have a characteristic appearance in environment-lit images, but interpreting these cues may be more difficult due to ambiguities and uncertainties related to the unknown lighting environment. Consequently, the normal maps recovered by [START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF] are also less accurate than ours.

We then compare the two methods on real pictures, captured with a flash for our approach and without for the approach by Li et al. (Figure 16). Overall, the relative performance of the methods appears similar to the synthetic case.

Limitations

Despite the diversity of results shown, the architecture of our deep network imposes some limitations on the type of images and materials we can handle.

In terms of input, our network processes images of 256×256 pixels, which prevents it from recovering very fine details. While increasing the resolution of the input is an option, it would increase the memory consumption of the network and may hinder its convergence. Recent work on iterative, coarse-to-fine neural image synthesis represents a promising direction to scale our approach to high-resolution inputs [START_REF] Chen | Photographic Image Synthesis with Cascaded Refinement Networks[END_REF][START_REF] Karras | Progressive Growing of GANs for Improved Quality, Stability, and Variation[END_REF]]. Our network is also limited by the low dynamic range of input images. In particular, sharp, saturated highlights sometimes produce residual artifacts in the predicted maps as the network struggles to inpaint them with plausible patterns (Figure 14). We also noticed that our network tends to produce correlated structures in the different maps. As a result, it fails on materials like the one in Figure 14 (top row), where the packaging has a clear coat on top of a textured diffuse material. This behavior may be due to the fact that most of the artist-designed materials we used for training exhibit correlated maps. Finally, while our diverse results show that our network is capable of exploiting subtle shading cues to infer SVBRDFs, we observed that it resorts to naive heuristics in the absence of such cues. For example, the normal map for the wool knitting in Figure 14 suggests a simple "dark is deep" prior.

In terms of output, our network parameterizes an SVBRDF with four maps. Additional maps should be added to handle a wider range of effects, such as anisotropic specular reflections. The Cook-Torrance BRDF model we use is also not suitable for materials like thick fabric or skin, which are dominated by multiple scattering. Extending our approach to such materials would require a parametric model of their spatially-varying appearance, as well as a fast renderer to compute the loss. Finally, since our method only takes a fronto-parallel picture as input, it never observes the material sample at grazing angle, and as such cannot recover accurate Fresnel effects.

CONCLUSION

The casual capture of realistic material appearance is a critical challenge of 3D authoring. We have shown that a neural network can reconstruct complex spatially varying BRDFs given a single input photograph, and based on training from synthetic data alone. In addition to the quantity and realism of our training data, the quality of our results stems from an approach that is both aware of how SVBRDF maps interact together -thanks to our rendering lossand capable of fusing distant information in the image -thanks to its global feature track. Our method generalizes well to real input photographs and we show that a single network can be trained to handle a large variety of materials. As the methods produce output data using different BRDF models, the values of the maps of [START_REF] Comparison | [END_REF] should not be compared directly to ours or the ground truth. We show them to aid qualitative evaluation of the the spatial variation. To facilitate comparison, we rendered the ground truth and each result under novel illumination conditions (right). The renderings for the results of [START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF] were made with a lower exposure due to different albedo magnitudes predicted by the methods. The input images (left) were rendered under flash lighting for our method and under environment lighting for the method by Li et al., in agreement with the type of input assumed by each method.

  Fig.3. Architecture of our deep convolutional network, which takes as input a single flash-lit image (left) and predicts four maps corresponding to per-pixel normal, diffuse albedo, specular albedo and specular roughness (right). Our network follows the popular U-Net encoder-decoder architecture (black), which we complement with a new global features track (green) that processes vectors instead of feature maps. Taken together, the full network consists of repeating "modules", which are detailed in the bottom part of the figure. At every stage of the network, the feature means subtracted by the instance normalization after the convolutional layer are concatenated with the global feature vector, which is then processed by a fully connected layer and a non-linearity before being added to the feature maps of the next stage. IN and FC denote instance normalizations and fully connected layers respectively. We use SELU[START_REF] Klambauer | Self-Normalizing Neural Networks[END_REF]] and leaky ReLu activation functions. In the decoder, the set of layers also includes a skip-connection concatenation and a second convolution, which we omit for clarity. We provide the code of our network to allow reproduction.

  Fig.4. We trained a U-Net convolutional network to predict an image of the average color of the input (top row). Surprisingly, the basic U-Net fails to produce a constant image (c). Similar artifacts appear when using the U-Net for SVBRDF prediction (f). We address this issue by complementing the U-Net with a parallel network that explicitly computes and propagates global features. This approach succeeds in computing the average image (d) and reduces artifacts in SVBRDF maps (g).

Fig. 5 .

 5 Fig. 5. Our rendering loss compares the appearance of the predicted SVBRDF and ground truth by rendering both under the same random lighting and viewing configurations.

Fig. 6 .

 6 Fig.6. When trained with the l 1 loss (b), the SVBRDF predicted by the network for a test input image does not accurately reproduce the appearance of the target material when rendered. A network trained using the rendering loss (c) produces an SVBRDF that, while not necessarily identical in terms of the parameter values, reproduces the ground truth rendered appearance well (last row).

Fig. 7 .Fig. 8 .

 78 Fig. 7. Example parametric SVBRDFs for each original material class. We produce our final training set by perturbing and mixing such SVBRDFs.

Fig. 9 .

 9 Fig. 9. Based on the input photographs (left), our method has recovered a set of SVBRDF maps that exhibit strong spatially varying specular roughness and albedo effects. The gold-colored paint (top) and the highly glossy black tiles (bottom) are clearly visible in the re-renderings of SVBRDF under environment illumination (right).

  Fig. 11. Comparison between relighting of our predictions and of measured BTFs [Weinmann et al. 2014].

Fig. 13 .

 13 Fig. 13. Comparison with[START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF] 2015]. Note that the maps (other than the normals) are not directly comparable due to different parametrization of the BRDF models. The solution of[START_REF] Aittala | Reflectance Modeling by Neural Texture Synthesis[END_REF] corresponds to a small region of about 15% of the image dimension, intended to be repeated by texture synthesis or tiling. The earlier method by[START_REF] Aittala | Two-shot SVBRDF Capture for Stationary Materials[END_REF] captures the entire input image but requires an additional no-flash picture for guidance. In contrast, our method reproduces the large-scale features well, and is applicable to non-repetitive materials captured with a single flash picture.

Fig. 14 .

 14 Fig.14. Failure cases and performance on materials violating our assumptions. Our method generally struggles with otherwise uniform surfaces exhibiting structured albedo detail, such as the text and the photograph on the product packaging (top). Highly concentrated specular highlights are sometimes missed and result in overestimated roughness and occasional highlight removal artifacts (top). Materials outside the scope of the training data (e.g. anisotropic brushed metal, center) cannot be reproduced properly, and result in an undefined assignment of the apparent shading effects (the streak of the specular highlight) into the various maps of the SVBRDF. Nevertheless, the method can produce reasonable approximations for materials violating the assumptions, with varying degrees of success, as seen on the fuzzy wool (bottom).

[Fig. 15 .

 15 Fig. 15. Comparison with[START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF] on synthetic data. As the methods produce output data using different BRDF models, the values of the maps of[START_REF] Comparison | [END_REF] should not be compared directly to ours or the ground truth. We show them to aid qualitative evaluation of the the spatial variation. To facilitate comparison, we rendered the ground truth and each result under novel illumination conditions (right). The renderings for the results of[START_REF] Li | Modeling Surface Appearance from a Single Photograph using Self-augmented Convolutional Neural Networks[END_REF] were made with a lower exposure due to different albedo magnitudes predicted by the methods. The input images (left) were rendered under flash lighting for our method and under environment lighting for the method by Li et al., in agreement with the type of input assumed by each method.

Table 1 .

 1 RMSE comparison between

https://team.inria.fr/graphdeco/projects/deep-materials/ ACM Transactions on Graphics, Vol. 37, No. 4, Article 128. Publication date: August

https://team.inria.fr/graphdeco/projects/deep-materials/ ACM Transactions on Graphics, Vol.

37, No. 4, Article 128. Publication date: August 2018.

ACM Transactions on Graphics, Vol. 37, No. 4, Article 128. Publication date: August 2018.

ACKNOWLEDGMENTS

We thank the reviewers for numerous suggestions on how to improve the exposition and evaluation of this work. We also thank the Optis team, V. Hourdin, A. Jouanin, M. Civita, D. Mettetal and N. Dalmasso for regular feedback and suggestions, S. Rodriguez for insightful discussions, Li et al. [2017] andWeinmann et al. [2014] for making their code and data available, and J. Riviere for help with evaluation. This work was partly funded by an ANRT (http://www.anrt.asso.fr/en) CIFRE scholarship between Inria and Optis, by the Toyota Research Institute and EU H2020 project 727188 EMOTIVE, and by software and hardware donations from Adobe and Nvidia. Finally, we thank Allegorithmic and Optis for facilitating distribution of our training data and source code for non-commercial research purposes, and all the contributors of Allegorithmic Substance Share.