Laure Gossec
email: laure.gossec@aphp.fr

Francis Berenbaum

Pierre Chauvin

Christophe Hudry

Gabrielle Cukierman

Thibault De Chalus

Caroline Dreuillet

Vincent Saulot

Sabine Tong

Françoise Russo-Marie

Jean-Michel Joubert

Alain Saraux

Development and application of a questionnaire to assess patient beliefs in rheumatoid arthritis and axial spondyloarthritis

Keywords: Rheumatoid arthritis, outcome measures, spondyloarthritis, behavior, patient attitude to health

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

Method

All beliefs reported by >5% of 50 patients in a previous study were reformulated with a partnering patient organization into statements with which participants could rate their agreement on a scale of 0-10 (totally disagree to totally agree). The resulting Questionnaire for Arthritis Dialogue (QuAD) was made available to patients with RA or axSpA. A score ≥7 was considered a strongly-held belief. Associations between patient characteristics and individual lifestyle beliefs were assessed using multiple logistic regression.

Results

The 21-item QuAD was completed by 672 patients (432 RA, 240 axSpA; mean [±SD] age: 54.2 [±14.2]; 63.7% female). The most widely held beliefs were related to uncertainty about progression (n=354, 54.0%), heredity (n=309, 47.8%) and flare triggers (n=283, 42.7%). The unwarranted belief that physical activity is deleterious to disease activity was associated with markers of psychological distress and lower educational levels.

Conclusions

INTRODUCTION

Chronic inflammatory rheumatic diseases (CIRDs), of which rheumatoid arthritis (RA) and axial spondyloarthritis (axSpA) are the most frequent, are progressive diseases that evolve with an unpredictable and fluctuating course over the patient's lifetime.

The chronic nature of these diseases, the heterogeneity of physical manifestations between patients, and the difficulty in foreseeing disease flares and long-term progression create uncertainty and stress for the patient. In addition, they make it difficult for patients to develop a valid internal representation of their disease [START_REF] Lutze | The impact of arthritis on daily life with the patient perspective in focus[END_REF].

This may in turn lead to misplaced disease perceptions and treatment expectations [START_REF] Carr | Rheumatology outcomes: the patient's perspective[END_REF][START_REF] Goodacre | Factors influencing the beliefs of patients with rheumatoid arthritis regarding disease-modifying medication[END_REF], and the development of inappropriate behaviors for managing disease manifestations and coping with their consequences [START_REF] Vriezekolk | Longitudinal association between coping and psychological distress in rheumatoid arthritis: a systematic review[END_REF][START_REF] Groarke | The role of perceived and actual disease status in adjustment to rheumatoid arthritis[END_REF]. For example, patients who believe that disease flares are triggered by physical activity may actively pursue a sedentary lifestyle, with detrimental consequences for their CIRD and their general health [START_REF] Ehrlich-Jones | Relationship between beliefs, motivation, and worries about physical activity and physical activity participation in persons with rheumatoid arthritis[END_REF]. The erroneous assumption that diet has an impact on disease may also lead the patient to make poor nutritional choices [START_REF] Salminen | Female patients tend to alter their diet following the diagnosis of rheumatoid arthritis and breast cancer[END_REF]. In addition, expectations about the benefits and risks of treatment with disease-modifying antirheumatic drugs (DMARDs) may influence treatment adherence [START_REF] De Thurah | Compliance with methotrexate treatment in patients with rheumatoid arthritis: influence of patients' beliefs about the medicine. A prospective cohort study[END_REF] or perceptions of tolerability [START_REF] Nestoriuc | Prediction of nonspecific side effects in rheumatoid arthritis patients by beliefs about medicines[END_REF]. Therefore, it is important for physicians to understand their patients' beliefs about their disease, and to initiate a dialogue with the patient about unwarranted beliefs, with the goal of modifying behavior and thereby improving overall health. However, very little research has been published relating to the beliefs and apprehensions of patients with CIRDs [START_REF] Gossec | Reporting of patient-perceived impact of rheumatoid arthritis and axial spondyloarthritis over 10 years: a systematic literature review[END_REF].

In order to gain more information about disease perceptions in patients with CIRDs, a research program was initiated, with the aim of developing a questionnaire to evaluate these beliefs. The specific objectives of this study were to develop a questionnaire to assess beliefs in patients with RA or axSpA regarding their disease and its treatment, and to identify patient characteristics associated with these beliefs.

MATERIALS AND METHODS

Development of the Questionnaire for Arthritis Dialogue

A previous qualitative study of disease perception in patients with RA or axSpA was performed in 50 patients (25 with RA and 25 with axSpA) [START_REF] Berenbaum | Fears and beliefs in rheumatoid arthritis and spondyloarthritis: a qualitative study[END_REF]. Based on data from this study [START_REF] Berenbaum | Fears and beliefs in rheumatoid arthritis and spondyloarthritis: a qualitative study[END_REF], all items reported by >5% of patients were rephrased as assertions, with help from a partnering patient organization. This questionnaire covered the most widely-held perceptions about disease and treatment. Other questions related to patient fears and beliefs are reported elsewhere [START_REF] Gossec | Development and Validation of a Questionnaire Assessing the Fears and Beliefs of Patients Suffering from Chronic Rheumatic Diseases[END_REF]. Each item was scored on a 10-point numerical rating scale (NRS) ranging from 0 (totally disagree) to 10 (totally agree).

The questions were tested in a sample of 10 patients for linguistic validation and cognitive debriefing. The original French questionnaire was translated into English through two independent forward translations (French to English) followed by two independent back translations (English to French), with reconciliation of the translated texts [START_REF] Wild | Principles of Good Practice for the Translation and Cultural Adaptation Process for Patient-Reported Outcomes (PRO) Measures: report of the ISPOR Task Force for Translation and Cultural Adaptation[END_REF]. The questionnaire took around 25 minutes to complete.

Application of the Questionnaire for Arthritis Dialogue to a wide sample

This cross-sectional, prospective study included patients with RA or axSpA in everyday practice in France, and was implemented by hospital and community rheumatologists between July 2014 and October 2015. The study was performed in accordance with Good Epidemiological Practice [START_REF]International ethical guidelines for epidemiological studies[END_REF] and relevant French guidelines for patient surveys. Verbal informed consent was obtained from all participating patients. The study protocol was considered by the Ethics Committee of the St Antoine Hospital, Paris, to be both ethical and outside the scope of French legislation restricting biomedical research (session of 7 th October 2014). The study was also declared to the National Advisory Committee on Medical Research Information (CCTIRS) and the French national data protection agency (CNIL).

All rheumatologists currently practicing in France were invited to participate in the study though post and email. Each participating rheumatologist was expected to invite all consecutive patients with RA or axSpA during routine outpatient visits who fulfilled the eligibility criteria (up to 20 patients per investigator). Adult patients (aged >18 years) with a diagnosis of RA according to the American College of Rheumatology/European League Against Rheumatism (ACR/EULAR) classification criteria [START_REF] Aletaha | 2010 Rheumatoid arthritis classification criteria: an American College of Rheumatology/European League Against Rheumatism collaborative initiative[END_REF], or of axSpA according to the Assessment in Spondyloarthritis International Society (ASAS) classification criteria [START_REF] Zeidler | The Assessment in Spondyloarthritis International Society (ASAS) classification criteria for peripheral spondyloarthritis and for spondyloarthritis in general: the spondyloarthritis concept in progress[END_REF], were eligible and were enrolled if they agreed to participate. Patients who were unable to complete a questionnaire in French were excluded.

Data collection

Patients were asked to complete both the beliefs questionnaire and other questions relating to fears (44 items in total) [START_REF] Gossec | Development and Validation of a Questionnaire Assessing the Fears and Beliefs of Patients Suffering from Chronic Rheumatic Diseases[END_REF], the Hospital Anxiety and Depression Scale (HADS) [START_REF] Zigmond | The hospital anxiety and depression scale[END_REF], the Arthritis Helplessness Index (AHI) [START_REF] Nicassio | The measurement of helplessness in rheumatoid arthritis. The development of the arthritis helplessness index[END_REF], the Patient Global Assessment (PGA) of overall disease activity (scored between 0-10), and for patients with axSpA, the Bath Ankylosing Spondylitis Disease Activity Index (BASDAI) [START_REF] Garrett | A new approach to defining disease status in ankylosing spondylitis: the Bath Ankylosing Spondylitis Disease Activity Index[END_REF]. All questionnaires were in French. Patients also provided information on sociodemographic indicators, health insurance coverage and disease duration.

In parallel, rheumatologists provided information on their own age, gender, type of practice (hospital, community or mixed) and geographical region, in addition to information about the patient on current treatment, disease activity measured with the 28-item Disease Activity Score calculated with erythrocyte sedimentation rate (DAS28[ESR]) [START_REF] Prevoo | Modified disease activity scores that include twenty-eight-joint counts. Development and validation in a prospective longitudinal study of patients with rheumatoid arthritis[END_REF] for RA, and an overall assessment of disease activity scored from 0-10.

Statistical analysis

Data were analyzed for all patients for whom both patient and physician questionnaires were available. For each item of the questionnaire, mean value ± standard deviation (SD) and the percentage of patients with scores ≥7 were determined both for the total population, and for the RA and axSpA subgroups.

Comparisons were performed with the χ² test (corrected for continuity) or Fisher's exact test, as appropriate. A score of ≥7 was taken to indicate strong agreement with the opinion presented. This cut-off was chosen on an empirical basis; in the absence of any known disease characteristic with which these beliefs are correlated, we did not feel that it was realistic to attempt psychometric calibration of the VAS.

In order to identify variables associated with a score ≥7 for a given item, we performed a univariate regression analysis for all patient and physician variables documented in the study. Variables with an association at a probability threshold of 0.20 (χ² test) were entered into a backwards stepwise multiple logistic regression analysis. A threshold of 0.05 was used for retention of variables in the model.

Multiple imputation methods (Markov chains using Monte Carlo simulations) were used for missing data when this concerned >5% of all patients. When this proportion was ≤5%, missing data were replaced with the median value of the full study sample. All statistical analyses were performed using SAS® Version 9.2 (SAS Institute, Cary, NC, USA).

Role of the funding source

reviewed the text to ensure that from a UCB Pharma perspective, the data presented in the publication are scientifically, technically and medically supportable, that they do not contain any information that has the potential to damage the intellectual property of UCB Pharma, and that the publication complies with applicable laws, regulations, guidelines and good industry practice. The authors approved the final version to be published after critically revising the manuscript for important intellectual content.

RESULTS

Characteristics of the Questionnaire for Arthritis Dialogue

The Questionnaire for Arthritis Dialogue (QuAD) includes 44 items in total, 21 of which cover beliefs on the cause of disease, disease flares and treatments. The remaining 23 items concern fears that are described in detail elsewhere. [START_REF] Gossec | Development and psychometric validation of a patient-reported outcome measure to assess fears in rheumatoid arthritis and axial spondyloarthritis: the Fear Assessment in Inflammatory Rheumatic diseases (FAIR) questionnaire[END_REF]

Participants in the validation study

Of the 1618 rheumatologists in France who were contacted, 134 agreed to participate in the study (including 20 who were exclusively community-based, 51 exclusively hospital-based and 29 with a mixed practice), and 100 enrolled at least one patient.

A total of 796 patients were enrolled, of whom 672 (84.4%) were available for analysis (Table 1). The remaining patients were excluded, due to either missing physician (n=98) or patient (n=12) questionnaires, or because the diagnostic criteria for RA/axSpA were either not fulfilled (n=5) or not documented (n=10). The median number of patients enrolled by each center was six. Patients with RA were more frequently female, and older on average than those with axSpA. Both physician and patient global assessments were higher for patients with axSpA than for those with RA. In both groups, around three-quarters of patients were undergoing treatment with biological DMARDs.

Beliefs of patients with rheumatoid arthritis and axial spondyloarthritis

The 21 relevant items in the QuAD (Table 2) included beliefs about psychological factors (2 items), genetic factors (2 items), physical activity (4 items), diet (4 items), and other lifestyle factors (3 items). The remaining items were categorized as miscellaneous beliefs (6 items). Mean (±SD) scores for each item of the QuAD ranged from 0.7 (±1.6) for "I think that drinking alcohol (even moderately) triggered my disease" to 6.3 (± 3.2) for "I don't know how my disease will progress (and that worries me)". The proportion of patients rating each item of the QuAD with a score ≥7 is presented in Figure 1.

Overall, beliefs appeared to be more strongly held in patients with axSpA than in those with RA. The three most widely held beliefs were: "I don't know how my disease will progress (and that worries me)" (n=354, 54.0%), "I am afraid of passing my disease on to my children" (n=309, 47.8%), and "I think that my flare-ups are triggered by fatigue" (n=283, 42.7%).

Characteristics of patients with specific lifestyle beliefs

A comprehensive listing of patient characteristics associated with individual lifestyle beliefs, identified from the univariate and multivariate analyses, is provided in Online Resource 1 (physical activity items), Online Resource 2 (food and diet items) and Online Resource 3 (other lifestyle items).

Findings from the multivariate analysis are presented in Table 3. The belief that 'eating certain foods could reduce disease flares' had more acceptance in women than in men. The belief that 'physical activity could reduce disease flares' had more acceptance in patients with higher education, while fewer patients in this subgroup believed that their disease may have been caused by physical overload. In contrast, more patients with high HADS scores for anxiety or depression (or both) believed that 'their disease was caused by physical overload' and that 'flares were triggered by physical effort', whereas fewer held the opposite belief that 'physical activity could reduce flares'. Similarly, more patients with high AHI scores believed that disease flares could be triggered by physical activity, or that their disease may have been caused by environmental factors such as pollution. The belief that 'drinking alcohol or smoking caused the disease' was more widely accepted among financially deprived patients (those eligible for an income subsidy from the state). Some differences were observed between patients with RA and those with axSpA.

Compared to patients with RA, those with axSpA were more likely to believe that taking physical exercise could reduce disease flares, and less likely to believe that their disease was caused by smoking.

These multiple logistic regression analyses were reiterated twice: firstly, by introducing age and gender as forced variables in the models, and then with patientreported disease activity (visual analogue scale, VAS) and disease duration as forced variables. Although these adjustments altered the odds ratios minimally, the variables retained in the models were not changed (data not shown).

DISCUSSION

The aim of this study was to develop a questionnaire to evaluate the beliefs of patients with RA and axSpA, and to identify patient characteristics associated with these beliefs. In a large sample of patients with RA or axSpA, our study identified a wide range of patient opinions on their disease and its treatment, and a number of demographic, socioeconomic and psychological factors associated with these opinions.

No individual belief was strongly held by more than half of patients overall. However, more than one-third of patients attributed their disease to psychological or genetic causes, whereas less than ten percent attributed it to causes that have little support from medical opinion, such as diet, pollution, smoking, infection, vaccination or alcohol consumption. In contrast, beliefs about lifestyle and CIRDs were often erroneous, perhaps due to inadequate patient education, or because of psychological distress. These beliefs need to be explored by physicians and discussed with the patient to ensure that the patient maintains as healthy a lifestyle as possible.

The diversity of beliefs identified include those that are consistent with current medical opinion, such as the belief that axSpA may have a genetic cause; those that are inconsistent with medical opinion, such as the belief that CIRDs may be caused by vaccination, and those for which there is limited medical consensus or where medical opinion is evolving. In general, the beliefs held were similar between patients with RA and those with axSpA, which may be explained by the similarly unpredictable course of the two diseases, the common core symptoms, and the fact that these patients will usually be cared for in the same healthcare facilities and thus be exposed to the same sources of information. However, patients with axSpA were around twice as likely as those with RA to attribute their disease to a genetic origin, likely reflecting awareness of a strong association between SpA and HLA-B27 [START_REF] Brown | Genetics of ankylosing spondylitis--insights into pathogenesis[END_REF].

In contrast, when asked to suggest possible causes for their disease, patients with RA were more likely to cite emotional factors. Moreover, patients with axSpA, who were on average younger and had a higher level of education than those with RA, were more likely to believe that physical activity could be beneficial to their disease (in agreement with current medical thinking) and less likely to believe that their disease was caused by smoking.

In this study, we focused on beliefs relating to lifestyle. This choice reflects the fact that these beliefs may be modifiable, potentially leading to changes in lifestyle.

Investigation of a patient's beliefs about lifestyle, and a dialogue about unwarranted beliefs, may help modify behavior and improve health. For example, patients who are convinced of the benefits of physical activity might adopt a regular exercise routine. In addition, dispelling unwarranted fears about the risks of vaccination may encourage patients to be vaccinated against infectious diseases.

In some cases, different groups of patients held opposing beliefs, such as those relating to the impact of physical activity or diet on disease flares. For example, the proportion of patients who believed that physical activity triggered their disease flares (35.5%) was comparable to the proportion of those who held the opposite opinion, that physical activity reduced their flares (36.5%). It should be noted, however, that the two items are not wholly comparable, since they are phrased somewhat differently: the deleterious belief referring to 'physical effort' (passive) and the beneficial belief referring to 'doing sport or physical activity' (active).

Nevertheless, the characteristics of these two groups of patients were different: those who considered physical activity to be detrimental were more frequently anxious or depressed and expressed a high helplessness score, possibly indicating that this belief was associated with psychological distress. In contrast, patients who believed that physical activity was beneficial tended to be better educated, less depressed, and to rate their disease activity as low. With respect to this particular belief, it is noteworthy that medical opinion has evolved over recent years -whereas in the 20 th century many physicians had a conservative approach to exercise in patients with CIRDs, a consensus has now emerged that exercise and sports activities are helpful in the short-and long-term management of disease, which is reflected in current practice guidelines [START_REF] Gaujoux-Viala | Recommendations of the French Society for Rheumatology for managing rheumatoid arthritis[END_REF][START_REF] Braun | 2010 update of the ASAS/EULAR recommendations for the management of ankylosing spondylitis[END_REF].

The study has a number of limitations that should be considered when interpreting the results. Firstly, participation of rheumatologists was voluntary and not remunerated, and physicians with a hospital practice were over-represented. This may have influenced the representativeness of the patient sample included.

However, the age and gender distributions of enrolled patients were similar to those of the overall RA [START_REF] Fautrel | Characteristics and management of rheumatoid arthritis in France: Analysis of a representative French national claims database resulting in an estimated prevalence of 0.35[END_REF] or axSpA [START_REF] Claudepierre | Prevalence, Comorbidities and Burden of Severe Spondyloarthritis In France: Analysis of A National Public Health Insurance Database In 2012 In France[END_REF] populations. Nevertheless, the proportion of patients in this study who were undergoing treatment with biological DMARDs was much higher than national figures (75%, versus 14% of all French RA patients [START_REF] Fautrel | Characteristics and management of rheumatoid arthritis in France: Analysis of a representative French national claims database resulting in an estimated prevalence of 0.35[END_REF] and 26% of all axSpA patients [START_REF] Claudepierre | Prevalence, Comorbidities and Burden of Severe Spondyloarthritis In France: Analysis of A National Public Health Insurance Database In 2012 In France[END_REF]). Another factor to be considered in interpretation of these data relates to the choice of the cut-off value for the identification of 'strongly held' beliefs (≥7 on the VAS). This choice was purely empirical and, in the absence of any known disease characteristic with which these beliefs are correlated, we do not believe that it is realistic to attempt any psychometric calibration of the VAS. Use of a threshold lower than 7 would clearly generate higher percentages of 'believers'. Finally, it is important to note that the items of the QuAD were derived from a qualitative survey of French patients [START_REF] Berenbaum | Fears and beliefs in rheumatoid arthritis and spondyloarthritis: a qualitative study[END_REF]. It is possible that patients in other countries or cultures would have different concerns [START_REF] Putrik | In wealthier countries, patients perceive worse impact of the disease although they have lower objectively assessed disease activity: results from the cross-sectional COMORA study[END_REF][START_REF] Nikiphorou | Patient global assessment in measuring disease activity in rheumatoid arthritis: a review of the literature[END_REF], which would be interesting to evaluate in future studies.

We believe that exploring patient beliefs about disease and treatment with a questionnaire such as the QuAD is useful for the physician in several ways; for example, to facilitate dialogue with the patient and to help patients understand their disease and form realistic treatment expectations. In particular, we believe that physicians should discuss lifestyle beliefs with their patients in order to dissipate unwarranted concerns and unfounded beliefs, and to encourage the adoption of healthy lifestyles. Facilitating physician-patient dialogue in this way would be expected to improve the overall quality of care, and to encourage the patient to become an active partner in setting and achieving treatment goals. In addition, the questionnaire may be a useful component of therapeutic education programs for structuring debate about disease perceptions. Finally, patients may feel that their perceptions and concerns about their disease are not considered important or discussed by their physician, and the availability of the QuAD might help to address this need. At a population level, the questionnaire could also describe shifts in beliefs over time (following awareness campaigns, for example).

In conclusion, it is important to understand and discuss patients' beliefs about inflammatory rheumatic diseases in order to optimize the quality of care. The QuAD provides a simple tool to help achieve this, and merits further assessment.

ETHICAL STATEMENT

The study was performed in accordance with Good Epidemiological Practice [START_REF]International ethical guidelines for epidemiological studies[END_REF] and relevant French guidelines for patient surveys. Verbal informed consent was obtained from all participating patients. The study protocol was considered by the Ethics Committee of the St Antoine Hospital, Paris, to be both ethical and outside the scope of French legislation restricting biomedical research (session of 7 th October 2014).

The study was also declared to the National Advisory Committee on Medical The codes for the questionnaire items correspond to those listed in Table 2. Data are presented as odds ratios (OR) with 95% confidence intervals (CI). AHI: Arthritis Helplessness Index; axSpA: axial spondyloarthritis; HADS: Hospital Anxiety and Depression Scale; QuAD: Questionnaire for Arthritis Dialogue; RA: rheumatoid arthritis.

FIGURE LEGENDS

Fig. 1 Proportion of patients with strongly held beliefs (QuAD score ≥7)

The codes for the questionnaire items correspond to those listed in Table 2.

: patients with RA (n=432); : patients with axSpA (n=240).

QuAD: Questionnaire for Arthritis Dialogue.

Table 1

 1 TABLES Patient characteristics

	RA	axSpA	TOTAL
	[n= 432]	[n= 240]	[N=672]

Table 2

 2 The QuAD questionnaire and mean scores for each item in patients with RA or axSpA

	QuAD Item

Scores are presented as mean scores (standard deviation) on a scale from 0-10, where 10 indicates full agreement. axSpA: axial spondyloarthritis; QuAD: Questionnaire for Arthritis Dialogue; RA: rheumatoid arthritis.

Table 3

 3 Principal associations between patient variables and strongly held beliefs (QuAD score ≥7)

		QuAD Item	Patient variable	Reference		OR [95% CI]
	F4	Physical activity reduces flares	Diagnosis	RA	axSpA	2.15 [1.50-3.08]
	O2	Disease caused by smoking	Diagnosis	RA	axSpA	0.60 [0.36-0.96]
	D4	Certain foods reduce flares	Gender	Men	Women	2.22 [1.18-4.20]
	F1	Disease caused by physical overload	Education	Higher	High school	2.14 [1.30-3.53]
	F4	Physical activity reduces flares	Education	Higher	High school	0.42 [0.29-0.60]
	O2	Disease caused by smoking	Social deprivation Not	Deprived	2.04 [1.15-3.62]
				deprived
	D2	Disease caused by alcohol	Social deprivation Not	Deprived	4.18 [1.19-14.6]
				deprived
	F1	Disease caused by physical overload	Anxiety	HADS-A ≤8 HADS-A >10 2.87 [1.67-4.92]
	F2	Flares triggered by physical effort	Anxiety	HADS-A ≤8 HADS-A >10 1.59 [1.03-2.45]
	F4	Physical activity reduces flares	Depression	HADS-D ≤8 HADS-D >18 0.58 [0.38-0.88]
	F2	Flares triggered by physical effort	Depression	HADS-D ≤8 HADS-D >8	1.49 [1.00-2.23]
	F2	Flares triggered by physical effort	Helplessness	AHI <20	AHI ≥20	1.77 [1.23-2.54]
	O3	Disease caused by environmental factor Helplessness	AHI <20	AHI ≥20	2.93 [1.38-6.18]

The authors thank the patients, the investigators and their teams who took part in this study. The authors also acknowledge Susanne Wiegratz (UCB Pharma GmbH, Monheim am Rhein, Germany) for publication coordination, and Sam Fraser, PhD (Costello Medical, Cambridge, UK) for medical writing and editorial assistance in preparing this manuscript for publication, based on the authors' input and direction.

The study was initiated and funded by the Fondation Arthritis and the Laboratoires UCB France, who delegated operational management of the study to a contract research organisation (AXONAL-BIOSTATEM, Nanterre, France).

Research Information (CCTIRS) and the French national data protection agency (CNIL).

CONFLICT OF INTEREST

LG, PC, CH, CD, ST and AS report non-financial support from UCB Pharma and Fondation Arthritis during the conduct of the study; FB reports non-financial support from UCB Pharma during the conduct of the study; GC and J-MJ are employees of UCB Pharma; TdC was an employee of UCB Pharma at the time of the study; VS and FR-M declare that they have no competing interest. The authors have full control of all primary data and agree to allow the journal to review these data if requested.


MD Andreas Hartmann
email: andreas.hartmann@aphp.fr

Bruno Millet

Repetitive movements and behaviors in neurologic and psychiatric practice : Distinctions and similarities between Tourette Disorder and Obsessive-Compulsive Disorder

Keywords: Tics, Tourette disorder, obsessive-compulsive disorder, repetitive behaviors, differential diagnosis Abbrevations : OCD = obsessive-compulsive disorder, SSRI = selective serotonin reuptake inhibitor, TD = Tourette disorder

Repetitive movements are a hallmark of chronic tic disorders such as Tourette disorder (TD) while repetitive behaviors characterize Obsessive Compulsive Disorder (OCD). Both disorders tend to frequently co-occur as a substantial number of patients with TD also suffer from OCD and vice versa. The clinical distinction between tics and OCD is usually easy but borderline forms exist. Also, correct symptom recognition is vital to chose the appropriate treatment modalities in both disorders, either pharmacologic, psychotherapeutic (behavioral therapy) or using brain stimulation (deep brain stimulation or repetitive transcranial magnetic stimulation).

Introduction

Both neurologists and psychiatrists have to cope with abnormal movements and behaviors. However, while neurologists primarily treat movement disorders, psychiatrists deal more frequently with behavioral disorders. Movement is defined by the act of moving, whereas behavior defines the way how one acts, especially toward others. This is the main distinction between tics, where symptoms are characterized by a movement dysfunction generally resulting from an urge-to-move or urge-to-do, and Obsessive Compulsive Disorder (OCD) in which a repetitive behavior responds to an obsessive and irrepressible set of thoughts.

However , in certain forms of chronic tic disorders such as Tourette disorder (TD), repetitive complex movement can mimic OCD, while early-onset OCD is frequently associated with complex tics.

From a semiologic viewpoint, repetitive behaviors can occur in a large number of neurologic and psychiatric conditions. Generally, these movements will be labelled as abnormal (dystonia, parkinsonian tremor, catatonia etc), specifically movements or postures that appear non-physiological just by observing the patient. However, one can also witness movements that, when taken as such, are physiological but occur with an abnormal frequency and/or in an abnormal context : tics, stereotypies, mannerisms, compulsions. Regarding compulsions, we speak of behaviors rather than specific movements. Here, contextual anxiety is paramount, and in the majority of these cases clinical evaluation allows to identify obsessive phenomena underpinning the behavior.

Tics

Tics are the cameleons in the world of movement disorders : they may correspond to any kind of movements (motor tics) or vocalisations (vocal tics) occurring naturally, i.e. in everyday life. Depending on their complexity, they are labeled as simple (involving a single muscle or muscle group) or complex (involving several muscle groups). As a rule, simply observing the patient will not suffice : he or she must be interrogated about the presence (or absence) of a premonitory sensation (urge to do, urge to move) which precedes the tic and which is relieved by ticking, since premonitory sensations are usually experienced as uncomfortable. Note, however, that premonitory sensations are rarely present before the age of 10 [START_REF] Banaschewski | Premonitory sensory phenomena and suppressibility of tics in Tourette syndrome: developmental aspects in children and adolescents[END_REF]. Another feature of tics is that they can be repressed but only for limited periods (ranging between seconds and hours) and that tic suppression requires an effort .

When multiple motor and vocal tics occur in a chronic manner, we are confronted with Tourette disorder (TD). TD is defined by the DSM-5 [START_REF]APA. Diagnostic and Statistical Manual of Mental Disorders (DSM-5)[END_REF] as the association of at least two motor tics and one vocal tic over a period of at least 12 months with an onset before age 18 (Table 1). Tics usually start in childhood between the age of 5-7 years and are thus initially pediatric [START_REF] Leckman | Course of tic severity in Tourette syndrome: the first two decades[END_REF].

OCD

OCD can be characterized by abnormal behaviors rather than movements. Compulsions are defined as repetitive and excessive behaviors the person is obliged to perform in response to intrusive and incoercible ideas ; performing the compulsion will temporarily alleviate or interrupt these ideas which are labelled obsessions. Regarding the first DSM and ICD classifications, OCD was initially embedded into the category of anxiety disorders. Anxiety was considered as an essential dimension which mainly allowed to explain the relationship between obsessive thoughts and compulsive behaviors (for instance, "I am obsessed by the dirtyness, this causes anxiety, so I should wash my body" or on the other hand " not washing my hands causes a huge anxiety which might eventually initiate obsessive thoughts"). Today, the DSM-5 classification considers OCD as a distinct disorder, as part of the category of Obsessive Compulsive and Related Disorders, containing Body Dysmorphic Disorder, Hoarding Disorder, Trichotillomania, Excoriation Disorder and Substance/Medication-Induced Obsessive-Compusive and Related Disorder.

The major types of OCD are now well identified. The DSM-5 [START_REF]APA. Diagnostic and Statistical Manual of Mental Disorders (DSM-5)[END_REF] (Table 2) distinguishes : (i) obsessions related to cleanliness or fear of contamination which are associated with washing rituals ; (ii) obsessions linked to the fear to harm oneself or close ones associated with checking rituals ; (iii) obsessions of symmetry or order associated with counting rituals or repetition compulsions ; (iv) obsessive ideas linked to taboos such as sexuality or religious blasphemy associated with checking behaviors or purification rituals. It is crucial to understand the distinction between normal rituals and compulsive behaviors within the frame of OCD. While rituals, in children as well as in adults, correspond to rules and habits that contribute to the structuration of the individual's daily life, compulsions in OCD are defined by excessive and repeated behaviors that the patients must accomplish in order to alleviate anxiety and /or the frequency of obsessive thoughts. In that sense, OCD should be distinguished from stereotypies which should be considered as repetitive behaviors without a goal directed behavior.

Subjects suffering from OCD describe an intense and overwhelming anxiety when forced to confront their obsessions. They describe a feeling of discomfort and malaise driving the realization of the corresponding compulsion. This behavioral ritual, when appropriately accomplished, can provide a temporary feeling not only of respite but of satisfaction.

Another manifestation of OCD is avoidance behavior by trying to circumvent the obsession trigger. For instance, patients with contamination obsessions will avoid public toilets whereas those fearing to provoke a catastrophe will not drive their cars anymore.

Considering the clinical specificities of both OCD and tics, behavior on one hand, movement on another, it sounds -in principle -easy to establish a differential diagnosis.

However, because both disorders sometimes present with excessive rules or habits sequences which lead to adjustment difficulties in daily life, the overlap between both syndromes is not rare and differential diagnosis tricky.

Borderline forms

Despite the obvious differences between tics and OCD, their border can be permeable, even more so since both conditions are frequently associated. For instance, some OC symptoms such as repetitive rituals of touching, obsessions of symmetry may look like complex tics.

Additionally, in patients with TD, it is estimated that 60% also suffer from OCD [START_REF] Hirschtritt | Lifetime prevalence, age of risk, and genetic relationships of comorbid psychiatric disorders in Tourette syndrome[END_REF].

Conversely, around 30% of patients suffering from OCD also display tics [START_REF] De Vries | Tic-Related Versus Tic-Free Obsessive-Compulsive Disorder: Clinical Picture and 2-Year Natural Course[END_REF]. This temporal and symptomatic overlap might argue for a continuity between both syndromes.

In a large French study on adult patients suffering from TD, two thirds had repetitive behaviors [START_REF] Worbe | Repetitive behaviours in patients with Gilles de la Tourette syndrome: tics, compulsions, or both?[END_REF]. These behaviors were analyzed both by a psychiatrist and a neurologist with an equal proportion of tics and OCD, but one fourth of patients also displayed mixed forms which could correspond either to tics or to OCD. From a phenomenological viewpoint, behaviors linked to washing/cleaning and checking could be attributed unequivocally to OCD.

In borderline forms, symmetry and counting behavior as well as touching and just right behaviors were predominant.

Of note, the age of onset for tics and OCD is different. Tics usually start in childhood whereas OCD begins to manifest in late adolescence or early adulthood. Even though OCD can be considered a neurodevelopmental disorder, it is striking to see that tics are predominantly observed with early-onset OCD, while late-onset OCD is much less frequently associated with tics [START_REF] Millet | Phenomenological and comorbid features associated in obsessive-compulsive disorder: influence of age of onset[END_REF]. This might be in line with the different stages of the neurodevelopmental processes of habit procedures (learning skills) which, when becoming dysfunctional, could concern different deep brain structures [START_REF] Rosenberg | Toward a neurodevelopmental model of of obsessive--compulsive disorder[END_REF].

Appropriate differential diagnosis is paramount in choosing the appropriate therapeutic course. With regard to pharmacologic interventions, tics usually respond to antipsychotics (typical and atypical), whereas OCD is targeted by using selective serotonin reuptake inhibitors (SSRI) as first choice treatments, and is treated with antipsychotics only in cases of lack of insight or delusional beliefs.

When using psychotherapeutic approaches, both tics and OCD can be treated by behavioral therapies with a common principle, exposure with response prevention [START_REF] Van De Griendt | Behavioural treatment of tics: habit reversal and exposure with response prevention[END_REF][START_REF] Lewin | Cognitive behavior therapy for obsessivecompulsive and related disorders[END_REF]. In both disorders, this technique is destined to help the patient escape from pathological habits in which he or she is incarcerated. Nonetheless, it is essential to clearly identify the major symptom(s) in order to obtain an optimal result.

Pathophysiology

Anatomically, both tics and OCD have been linked to two cerebral structures interacting with each other : the cortex and the basal ganglia. The main hypothesis postulates dysfunctional loops of the cortico-striato-thalamo-cortical circuitry. The basal ganglia comprise the striatum (caudate nucleus and putamen), the pallidum (external and internal segment), the substantia nigra pars reticulata and the subthalamic nucleus. These nuclei receive afferences from the cortex and are subdivided into distinct loops : (i) sensori-motor (originating from the sensorimotor cortex), (ii) associative (originating from the dorsolateral prefrontal cortex and supplementary and pre-supplementary motor areas) and (iii) limbic (originating from the the orbitofrontal and anterior cingulate cortex) [START_REF] Krack | Deep brain stimulation: from neurology to psychiatry?[END_REF]. Each of these loops either commands movements (sensorimotor loop) or behaviors (associative and limbic loops) which can be altered variably both in TD and OCD depending on the symptoms and their severity.

Although both TD and OCD initially appear as goal-directed movements (to alleviate premonitory sensations) and behaviors (to alleviate obsessions and anxiety), they eventually transition into habits with time. For instance, in TD, habit formation has been shown to be enhanced in unmedicated patients due to aberrant reinforcement signals to the sensorimotor striatum which underly the formation of stimulus-response associations [START_REF] Delorme | Enhanced habit formation in Gilles de la Tourette syndrome[END_REF]. In OCD patients, excessive habits have been associated with hyperactivation of the caudate nucleus, previoulsy implicated in goal-directed behavior, which suggests that habit formation in OCD may result from impairments in this system, rather than differences in the buildup of stimulus-response habits as such [START_REF] Gillan | Functional neuroimaging of avoidance habits in obsessivecompulsive disorder[END_REF]. Certainly, the coming years will allow to fine tune our understanding of the balance between goal-directed behaviors and habit formations in TD and OCD as well as other disorders (i.e. addictions), and the anatomical substrates involved [START_REF] Gillan | The role of habit in compulsivity[END_REF].

Understanding neuronal circuitry also informs about available neuromodulation brain stimulation treatments, i.e. deep brain stimulation for severe pharmaco-resistant TD, and deep brain stimulation and repetitive transcranial magnetic stimulation in OCD. Whereas in TD motor circuits such as the globus pallidus (internal segment) or the thalamus (centromedian/parafascicular nucleus) are preferentially targeted [START_REF] Baldermann | Deep Brain Stimulation for Tourette-Syndrome: A Systematic Review and Meta-Analysis[END_REF], limbic targets are favoured in OCD such as the ventral striatum and the medial part of the subthalamic nucleus [START_REF] Alonso | Deep Brain Stimulation forObsessive-Compulsive Disorder: A Meta-Analysis of Treatment Outcome and Predictors of Response[END_REF] as well as the orbitofrontal cortex OFC when using repetitive transcranial magnetic stimulation [START_REF] Nauczyciel | Repetitive transcranial magnetic stimulation over the orbitofrontal cortex for obsessive-compulsive disorder: a double-blind , crossover study[END_REF].

Take home messages

Similarities between tics and OCD are repetitive movements and behaviors which make a precise clinical differential diagnosis necessary. A special situation arises in France where the terms « tics » et « tocs » are often used interchangeably. Also, many patients suffering from chronic tics / TD also suffer from OCD and vice versa. In most cases, however, the clinical distinction will be relatively easy when exploring the physical, mental and emotional landscape of the patients when it comes to symptom manifestation (premonitory sensations / anxiety / mental imagery). The age of onset is also an important differentiator between TD and OCD. Finally treatment response, in case of doubt, might also be helpful (antipsychotics vs. SSRI).


Alexandre Bléron

Thomas Hurtut

Joëlle Thollot

Motion-coherent stylization with screen-space image filters

Keywords: Computing methodologies → Computer graphics, Rendering, Non-photorealistic rendering, Screen-space lter, temporal coherence, GPU

Stylized result

Coherent under motion Figure 1: Using standard G-bu ers and auxiliary bu ers (noise, shading) as input, our pipeline can reproduce stylization e ects that extend outside the original rasterized footprint of the object. Visual features produced by the lters stay coherent under motion or viewpoint changes.

INTRODUCTION

Expressive rendering strives to reproduce artistic styles by designing algorithms to mimic the artistic creation process with a computer. Depending on the application, these algorithms can use various inputs ranging from photographs, where the only available information is a at color image, to full 3D scenes, with geometry, animation and lighting information. In this paper our goal is to stylize 3D scenes by taking advantage of image lters traditionally used in image manipulation software and in the post-processing pipeline of animated movies and video games.

Stylizing animated 3D scenes is challenging, since desired properties (temporal continuity, motion coherence and atness) cannot all be satis ed at once [START_REF] Bénard | State-of-the-Art Report on Temporal Coherence for Stylized Animations[END_REF]. For instance, following the motion eld of a scene while keeping a 2D visual impression leads to an inherent contradiction: when style marks are attached to the surface of 3D objects (e.g. using mapped textures or anchored strokes), the resulting motion is coherent but the atness is broken because the density and size of style marks will vary in screen-space depending on the location of the camera (zooming) or of the surface orientation (foreshortening). Conversely, attaching style marks to the 2D screen ensures all these statistics to be stable, but also leads to the well known shower-door e ect, breaking the motion coherence.

In this work, we present a new compromise, where style marks are applied in screen space with behaviors controlled by 3D scene properties (stored in G-bu ers), to ensure a high level of temporal continuity, motion coherence and atness. The style marks are created with kernel-based 2D image lters that allow a wide range of digitally painted 2D at looks to be obtained. In contrast to manyprimitive methods, such as stroke-based rendering, they are well suited to per-pixel parallel evaluation on a GPU, which makes this approach very e cient and usable in interactive contexts.

Working in image space with G-bu ers is a well-studied and widespread technique. One of its advantages is that no modi cation of the original geometry of the scene is required. This makes such an approach easily compatible with any compositing pipeline. However, a current limitation with image lters is that they cannot easily alter the rasterized silhouette of an object in a coherent way. Yet, irregular silhouettes contribute greatly to the perceived atness of the look, and are a key aspect of some styles: a plausible painted fur should extend outside the silhouette of the object.

When targeting contours, lters usually alter them incoherently with respect to the motion of individual objects. As such, they are subject to the shower-door e ect. Motion coherence can be improved by using 3D geometric information available in G-bu ers (e.g. orient the marks according to surface normals, colorize them according to the shading color, etc.). However, current techniques that exploit this information are limited to lling the inside of the rasterized footprint where the geometric data is well-de ned, and cannot a ect the contours.

In this paper, we address this limitation by proposing a way to in ate the data contained in G-bu ers with a controllable radius in order to have motion-coherent data outside the original footprint of the object, which is then used to drive stylization lters. This combination of motion coherence and footprint extension necessitates a careful handling of internal silhouettes because di erent styles can overlap at these locations. The proposed approach explicitly deals with this issue, avoiding visual artifacts. To summarize our contributions, we propose a method to stylize animated 3D objects that:

• Uses only screen-space data contained in G-bu ers;

• Is fully evaluated on the GPU;

• Ensures strong motion coherence;

• Enables the design of various styles that extend beyond the rasterized footprint of the object.

RELATED WORK

Stylization of 3D animated objects is a widely studied subject among the expressive rendering community. We refer the reader to [START_REF] Bénard | State-of-the-Art Report on Temporal Coherence for Stylized Animations[END_REF] for a state-of-the-art on this topic. Depending on the use of the geometrical information, stylization methods can operate in image-space -where no 3D information is available -or in object-space. While a vast amount of image lters are available for image stylization, they do not extend easily to animated objects. In image-space the only way to compute the object motion is to compute the optical ow of the animation. This information can then be used to control the change of the lters over time to ensure some motion coherence (e.g. [START_REF] Bousseau | Video Watercolorization using Bidirectional Texture Advection[END_REF][START_REF] Lu | Interactive Painterly Stylization of Images, Videos and 3D Animations[END_REF]). Yet it su ers from the di culty to compute a correct and noise-free optical ow.

On the other hand, operating in object-space gives access to the 3D geometry and thus to the exact motion eld of the object. However working directly in 3D space can be costly as the computation time depends on the geometrical complexity of the 3D object. That's the reason why several methods have been designed to work in 2.5D space allowing for an access to 3D information but at the image resolution. Saito & Takahashi rst introduced this class of methods [1990] with G-bu ers, screen-space images containing geometry information about the scene, and demonstrated their usefulness for various rendering purposes, such as shading or contour extraction and enhancement. G-bu er based methods have since been ported to GPU architectures, as rst demonstrated by Nienhaus and Döllner [2004a], and are now widely used in the industry, in the compositing stage of most animation software. Our approach ts in this category: it does not require any modi cation of the base geometry but rather relies only on G-bu ers and can consequently be easily integrated in existing deferred renderers or compositing software as a simple set of post-processing operations.

Stylizing outside the object contours

Stylizing a 3D object mostly consists in adding visual details, such as brush strokes, pigment or paper grain, fur, glow, etc. We focus in this paper on region stylization as opposed to the stylization of contours. Still our approach will allow to produce e ects located near the silhouettes but we do not target styles that need contour parameterization.

Stroke-based approaches. Stroke-based approaches have been introduced by [START_REF] Meier | Painterly Rendering for Animation[END_REF]. They rely on distributed anchor points on the 3D objects used to render small 2D primitives in image-space. The coherence of the motion of the strokes with the motion of the depicted object is directly ensured by the anchoring in 3D. However, maintaining constant density and size of strokes in image-space requires to add or remove strokes along the animation, leading to temporal discontinuities. Most of the previous works in this category try to improve the continuity by carefully distributing the anchor points, and by blending strokes that appear or disappear in a meaningful way [START_REF] Kalnins | WYSIWYG NPR: Drawing Strokes Directly on 3D Models[END_REF][START_REF] Michael | Art-Based Rendering of Fur, Grass, and Trees[END_REF][START_REF] Lu | Interactive Painterly Stylization of Images, Videos and 3D Animations[END_REF][START_REF] Vanderhaeghe | Dynamic Point Distribution for Stroke-based Rendering[END_REF]]. The Overcoat system, proposed by [START_REF] Schmid | OverCoat: an implicit canvas for 3D painting[END_REF] circumvents this issue by allowing an artist to embed entire brush strokes anywhere in 3D space around a proxy object. These stroke-based approaches are well-suited for painterly styles but are costly when the number of strokes increase to reproduce higher frequency e ects such as watercolor.

Texture-based approaches. To avoid temporal discontinuities and decrease the cost, texture-based approaches rely on texture mapping. The added details are contained in the texture and the mapping ensures a perfect motion coherence without temporal discontinuity. The drawbacks of these approaches are rst their strong 3D look due to perspective distortion, and second, the impossibility to add textured details outside the object contour. Most of the previous works in this category try to augment the perceived atness of the texture-mapped objects [START_REF] Bénard | Dynamic Solid Textures for Real-Time Coherent Stylization[END_REF][START_REF] Bénard | A Dynamic Noise Primitive for Coherent Stylization[END_REF]. A possible solution that allows stylization to extend outside object boundaries is to use 3D volumetric textures rendered with ray-marching [START_REF] Kajiya | Rendering Fur with Three Dimensional Textures[END_REF][START_REF] Perlin | Hypertexture[END_REF]. Later works focus on improving the performance of this approach to real-time frame rates by approximating volumes with layers of additional geometry [START_REF] Decaudin | Volumetric Billboards[END_REF][START_REF] Lengyel | Real-Time Fur over Arbitrary Surfaces[END_REF][START_REF] Meyer | Interactive Volumetric Textures[END_REF]. We refer the reader to the survey of Koniaris et al. [START_REF] Koniaris | Survey of texture mapping techniques for representing and rendering volumetric mesostructure[END_REF]] for a comprehensive overview of this type of approaches. A similar technique specialized for painterly appearances has been proposed by [START_REF] Imhof | Fin Textures for Real-time Painterly Aesthetics[END_REF], for accelerating the rendering of Overcoat paintings. However, these methods retain a strong 3D look, and are poorly suited to reproduce at styles.

Geometry modi cation.

Another option is to modify the geometry on the y. In [START_REF] Botkin | Painting with polygons: non-photorealistic rendering using existing tools[END_REF]], perturbation of the vertices of a 3D model is used to simulate a painterly e ect. Displacement mapping techniques, combined with hardware tessellation, can also be used to e ciently add surface details to a 3D object. Nienhaus and Döllner [2004b] propose to render an in ated version of the geometry to allow coherent warping e ects outside an object's silhouette.

In this paper we propose a similar method to extend geometrical information away from the silhouettes. Yet unlike the previously described techniques, our approach does not need to rasterize any additional geometry. Our technique relies solely on image-space lters operating on G-bu ers to produce di erent styles that are coherent outside the footprint of the object.

Noise textures

We employ an approach based on solid procedural noise to generate motion-coherent random variations. However, unlike previous methods, the noise is not composited directly onto the object but instead is used as an auxiliary map that drives the 2D image lters. Most texture-based stylization methods use textures as a layer composited on top of a rst rendering of the 3D object. Several layers of textures can be composited on top of each other, as was previously done in watercolor rendering [START_REF] Bousseau | Interactive watercolor rendering with temporal coherence and abstraction[END_REF]] but the range of resulting e ects remains limited. However textures, and especially noise textures, have been widely used in photorealistic rendering to modulate not only the object color but also normals, positions, etc. A detailed survey of procedural noise functions has been conducted by Lagae et al. [2010]. Of particular interest to us are noise models presenting thin elongated features that can be used to mimic the appearance of brush strokes or fur. To synthesize those kind of textures, 2D techniques such as sparse convolution noise can be used. However, they cannot be used reliably with a 3D parameterization. Instead, image ltering techniques have been used to lter noise patterns in order to obtain these elongated features. For instance, [START_REF] Lum | Non-photorealistic rendering using watercolor inspired textures and illumination[END_REF] used line integral convolutions [START_REF] Cabral | Imaging Vector Fields Using Line Integral Convolution[END_REF] to reproduce watercolor washes. A variant of this technique has also been used to generate glass patterns [START_REF] Papari | Continuous Glass Patterns for Painterly Rendering[END_REF], which have also been remarked for their painterly quality. We demonstrate the use of such lters in our pipeline, in combination with 3D solid noise, and driven by geometrical data from G-bu ers. We show how they can be used to reproduce "digitally painted" styles, that range from visible discrete strokes to more continuous appearances.

To summarize, our system can be seen as a hybrid between a texture-based and an image-space approach: we use procedurally generated motion-coherent random variations both as a base for subsequent ltering in image-space and also as a way to control certain aspects of the lters. This hybrid approach allows us to strike an advantageous balance between atness and motion coherence. lters, is also evaluated on each cluster using the necessary input data (in ated normals, colors, etc) as guidance. Note that the stylization is then evaluated multiple times on pixels that overlap di erent parts of an object. The last step consists in a compositing pass, where overlapped styles are blended to obtain the nal result.

MOTIVATION AND OVERVIEW

To illustrate the motivation behind the pipeline proposed in this paper, let's consider a basic stylization of spheres, as shown in Figure 2. In this example, the paint strokes are obtained by simply applying a Line Integral Convolution (LIC) [START_REF] Cabral | Imaging Vector Fields Using Line Integral Convolution[END_REF] on colored spots distributed on the object surface. The spots are created using a thresholded 3D cellular noise, parameterized by surface positions (stored in a G-bu er), to ensure robust motion coherence. The LIC is then guided by screen-space surface normals to transform the spots into elongated paint strokes. The whole process is evaluated locally: the result of the lter for one pixel at location p is a function of all pixels under a neighborhood centered on p that we call the lter window.

With a naive approach (a), the stylization stops abruptly outside the object: the lter cannot be evaluated because normals are not de ned at these image locations. Our rst contribution is to ll the missing information in such a way that the object looks in ated (b).

To that end, we propose a new image lter that locally extends any G-bu er whithout breaking the motion coherence of the original 3D scene. Once the necessary information is available everywhere under the window of the stylization lter (noise and normals in this example), the strokes can naturally extend outside the rasterized footprint of the object.

However, this in ation is ambiguous when parts of an object are overlapping each other (e.g. when dealing with internal contours). This is illustrated with two spheres in Figure 2(c), where we extend the front-most surface information of the G-bu ers. In that case, the red strokes are coherent, but the green ones produce a spatial discontinuity because the lters do not have access to the information from the second sphere behind. Our solution (d) is to keep track, at each pixel, of all the in ated surface parts that overlap. We then perform the stylization separately for each of those. For that we propose a local segmentation method, based on soft K-means [Bauckhage 2015], that nds and classi es the surface parts that will overlap when in ated. This information is handed over to the in ation and stylization passes so that they can lter each surface part independently.

Figure 3 provides an overview of our pipeline. In the following sections, we detail the local segmentation and screen-space in ation algorithms, and how to integrate image lters into our pipeline.

INFLATION AND SEGMENTATION

In this section, we show how G-bu ers can be locally in ated and segmented to provide motion-coherent data inside and outside the footprint of the rasterized objects to the stylization pass.

Object In ation

We extend G-bu er data by mimicking a real in ation of the original 3D object, that is, displacing vertices along their associated normals before rasterization. Let us consider a pixel p 0 , being the center of a circular neighborhood of radius r (the lter window) in a G-bu er. Our goal is to look for pixels p in the neighborhood that would be at the p 0 position if the corresponding object had really been in ated before being rasterized. Intuitively, this can be done by checking if, when a point p is displaced along the projected screen-space normal with a given radius, the point equals p 0 . In other words, for every pixel p 0 , we look for points p such that p 0 = p + r n(p), where n(p) is the projected screen-space normal at point p. Points p that satisfy this equation can be seen as anchor points as they can be used to in ate any G-bu er (by simply fetching the data at point p instead of p 0 ).

In practice, we work on discrete bu ers, and this equation is usually not satis ed. Instead, we assign a weight w p to each point under the lter window that evaluates the tness of the point for in ation. We de ne it as a Gaussian of the distance between the

w p = exp -p 0 , p + r n(p) 2 σ 2 , ( 1
)
where σ controls the tolerance towards the displacement error.

The in ated data at p 0 is then calculated by averaging the data under the lter window S, weighted by w p :

I in ated = p∈S w p I (p) p∈S w p , (2)
where I (p) represents the bu er data being in ated (depth, normals, colors, etc.). A visualization of weights and in ated data is provided in Figure 4.

Weighted Clustering

When di erent parts of the surface are overlapping in the in ated version (due to internal contours, multiple silhouettes, T-junctions, etc.), the relation p 0 = p + r n(p) can be satis ed by more than one anchor point p under the lter window. This is shown in Figure 5, where several clusters of weighted points stand out. In that case, we would like Equation 2 to be applied independently on each cluster to ensure that each part is correctly in ated. Figure 5 illustrates what happens with naive approaches, in contrast to our solution, on a style similar to the one shown in Figure 2, where a LIC is oriented along surface normals to "smudge" colors outside the silhouettes of the object. In the second row, the normals of all clusters are averaged together, resulting in an unnatural direction eld for guiding the style. In the third row, only the weights of the top-most surface are considered. As a unique direction is computed per pixel, only the front surface will be correctly stylized, producing discontinuities when styles of front and back surfaces should overlap. Our solution is presented in the last row, where we locally segment and stylize each overlapping part independently before recomposing the nal result.

Our segmentation is done locally over each lter window. It is based on a weighted soft K-means [Bauckhage 2015] since it is relatively fast and well suited to parallel GPU evaluation. The data to be segmented takes the form d(p) = (x, , z), where (x, ) is the position of the pixel and z is the depth of the surface at this position. Note that all components are remapped into the range [-1; 1] so that they have the same impact on the segmentation. Each data point is weighted by w p (Equation 1). Intuitively, the K-means will segment di erent clusters of weights (using w p ) and thus clearly distinguish pixels that belong to di erent parts of a surface in a lter window. Adding z enforces this segmentation and separates parts that contain the same normal with di erent depths.

Initialization. The initial clusters are distributed linearly along the z dimension inside the lter window:

µ (0) i = 0, 0, z min + i z max -z min K , (3)
where µ

i , i ∈ [0, K -1] is the cluster i at step 0 and z min/max are the minimal and maximal surface depths under the lter window. We found this simple and fast initialization to work well in most cases, as overlapping in ated parts usually tend to have signi cantly di erent depths.

Class membership weights. Each data point is soft-assigned to a cluster, meaning that each of them can partially belong to all classes. The class membership weight of the data point at p to class k is noted m k (p), with K -1 k =0 m k (p) = 1. It can be interpreted as the probability that p e ectively belongs to cluster k. We de ne the membership weights m k (p) for the data point d(p) as the softmax distance from the point to the class centroid, as suggested in [Bauckhage 2015]:

m k (p) = e -β d (p)-µ k 2 K -1 k =0 e -β d (p)-µ k 2 , (4)
β being the sti ness parameter, controlling the segmentation sensitivity: a higher sti ness value will result in more clearly separated classes, but with an increasing risk of over-segmentation of nearby points.

Centroid update. For each iteration of the algorithm, we update the class centroids µ k ∈ R 3 from the weighted data points under the lter window S using the following formula:

µ (t +1) k = p∈S w p m (t ) k (p)d(p) p∈S w p m (t ) k (p) . (5)
We stop the process when a speci ed maximum number N of iterations is reached. We used N = 8 for all the examples shown in the paper. The result of the clustering is a xed K number of classes represented by their centroid µ k = (µ k,x , µ k, , µ k,z ), each representing a local surface part. We nally sort those clusters by depth, µ 0 being the closest to the camera, and µ K -1 the farthest.

In ation. Following the clustering, the in ated G-bu er data for class k can be calculated by modifying Equation 2 as follows:

I in ated,k = p∈S m k (p)w p I (p) p∈S m k (p)w p . ( 6
)
Figure 6 shows the result of our segmentation on three local windows. We used K = 3 in all the results shown in this paper as there is rarely more than 3 distinct surface parts under the lter window, but more clusters could be used if needed (especially when using very large neighborhoods). Thanks to the soft assignement used in the K-means algorithm, multiple clusters can overlap when the number of surface parts is less than K. For instance, this is shown in 6(a). All clusters are located at the same place then all pixels equally belong to the three of them. The corresponding in ation on a normal map is shown on the right, where we α-blend the resulting normals when multiple parts were overlapping.

STYLIZATION

In this section, we describe how 2D image lters used for stylization are integrated in our pipeline.

Assigning clusters to individual pixels

We want to apply sylization lters independently for each distinct surface part under the lter window. So we need to be able to mask out all pixels not belonging to the surface part being considered, as otherwise data belonging to di erent surface parts may be averaged together (e.g. the color of two di erent surfaces may bleed onto each other, which is not the desired result).

Our K-means segmentation locates anchor points on these surface parts, but the class membership weights m k do not allow us to directly say whether a pixel belongs to a given surface part. Indeed, as seen in Figure 4, the weights quickly decrease according to the distance between the pixel and the class centroid. For most pixels we have w p ≈ 0, meaning that their normals are all pointing "away" from the window center p 0 . Still it does not mean that they do not belong to a surface part, it rather means than when in ated they do not reach the window center. However, the class membership weights m k cannot be relied upon for pixels with a low weight in the segmentation (i.e. w p ≈ 0).

Instead of using the class membership weights m k , our strategy for deciding whether a pixel belongs to a surface part detected by the K-means is to simply consider the unnormalized depth di erences and the normal deviations between the current pixel and the centroid that corresponds to the surface part. The pixel is considered as belonging to the surface part if this di erence is under a certain threshold. In the end, pixels not assigned to any previously detected surface part are put in a so-called residual class, and treated separately in the stylization.

The depth and normal deviations ∆ z,k (p) and ∆ n,k (p) for a given point p with respect to centroid µ k are de ned as follows:

∆ n,k (p) = exp (-σ n acos (n(µ k ) • n(p))) , (7) ∆ z,k (p) = exp (-σ z |z(µ k ) -z(p)|) , (8)
with n(µ k ) the approximate normal associated with class k, and z(µ k ) the screen-space depth of the centroid. We note n(p) the screen-space normal at p. As either ∆ n,k or ∆ d,k may be more suited to discriminate between classes, depending on the shape of the object in the lter window, we take the minimum of the two:

∆ k (p) = min(∆ n,k (p), ∆ z,k (p)). (9)
The σ n and σ z parameters control the tolerance of the classication to depth and normal di erences, respectively. They are scene-wide parameters and can be adjusted by the user as needed. Note that one of σ n and σ z can be set to zero to disable the in uence of the normal variations and depth variations, respectively. The membership of a pixel to class k, noted m k , is obtained by thresholding the nal weight ∆ k :

m k = 0 if ∆ k < 0.5 1 otherwise (10)
It is important for the lters that as much pixels as possible under the lter window are properly assigned to a matching surface part. It is up to the user to ensure that the surface parts are properly segmented by adjusting the σ n and σ z parameters. Figure 7 illustrates this process. In Section 7, we discuss guidelines on the input geometry and lter window size to avoid over-segmentation. Note that, as with the K-means segmentation, the resulting classes can overlap (a pixel under the lter window can belong to more than one class), and thus

K -1 k =0 m k (p) 1.
Residual class. Pixels that have not been assigned into any previously detected class (i.e. ∀k, m k = 0) are put in the residual class. They represent all pixels for which we could not assign a surface part previously detected by the K-means segmentation. Still, this residual class needs to be taken into account by the lters to avoid holes in the stylized result, so it is treated similarly to the classes detected by the segmentation. We de ne the membership weight of a pixel p to the residual class, m residual (p), as:

m residual (p) = max 0, 1 - k m k (p) . ( 11
)
The residual class holds all surface parts that contain no anchor point under the lter window (often, because their anchor points are occluded). Thus, we cannot obtain coherent data for those surfaces by in ation. Nevertheless, extended G-bu er data for the residual class, required by the lters, is still calculated as the average of all its pixels:

I in ated,residual (p) = p∈S m residual (p)I (p) p∈S m residual (p) . ( 12
)

Stylization lters

In this section, we describe several concrete examples of stylization lters that we use to generate the results presented in Section 6. We show how these lters can be made motion-coherent and silhouetteaware with relative ease inside our pipeline. The stylization lter is calculated separately for each class, meaning all pixels that do not belong to the surface part being considered are masked out during evaluation. The stylization lter is also calculated for the residual class, resulting in a total of K + 1 evaluations per pixel. The nal result will be obtained by blending each stylized class on top of each other.

Auxiliary bu ers. Our styles are based on several bu ers commonly used in image-space stylization approaches. The simplest one is the color I color (p) ∈ [0; 1] 4 . Depending on the desired style it can be a at color, a texture mapped on the object, a simple shading, or a more complex result obtained with standard procedural texturing techniques. All color values in the pipeline are considered to be in premultiplied alpha space: given a color C = (c r , c , c b , c a ) of opacity c a , wC = (wc r , wc , wc b , wc a ) is the same base color with opacity wc a .

In most styles, we use 3D procedural noises I noise (p) ∈ [0; 1] as a basis for generating motion-coherent procedural details. It is generated in post-processing from the object-space position bu er and relieves the users of the burden of providing their own noiselike texture on the object, although this work ow is also possible. Finally we use 2D direction ows I ow (p) derived from available G-bu ers (normals, tangents, curvature, etc.).

All these bu ers can be in ated when needed, allowing to compute lters in a controllable radius outside the original rasterized footprint of the object, with correct overlaps.

Line Integral Convolution lter. A typical stylization lter is the Line Integral Convolution (LIC) [START_REF] Cabral | Imaging Vector Fields Using Line Integral Convolution[END_REF] that can be used to produce bers like textures for fur or brush strokes. This class of lter has previously been used for stylization purposes [START_REF] Lum | Non-photorealistic rendering using watercolor inspired textures and illumination[END_REF][START_REF] Papari | Continuous Glass Patterns for Painterly Rendering[END_REF].

To reproduce a painterly appearance, we multiply the color input I color by the noise texture I noise , modulating the opacity of the color input. The intent is to mask out colored spots in the original color input, that are then spread along the provided ow eld by the LIC lter, creating elongated color ats reminiscent of brush strokes.

For the lter window centered at p 0 , the resulting ltered value for class k is de ned by:

C k (p 0 ) = L s=-L f (s/L)m k (κ(s))I noise (κ(s))I color (κ(s)) f (s/L) , ( 13
)
with L being the length of the convolution path, and f : [-1; 1] → [0; 1] a convolution pro le used to control the spread of the colored spots. The per-pixel class membership weights m k (κ(s)) are used to mask out all pixels outside of the considered classes. The convolution path κ(s) is de ned as:

κ(s) = p 0 + s × I ow in ated,k (p 0 ), (14)
i.e. a straight line oriented along the in ated ow. The length of the convolution path should be chosen so as to avoid going outside the lter window. Modi ed Line Integral Convolution lter. Due to the opacity modulation of the color input, the result of the LIC is semitransparent. Standard procedural texturing techniques can be used to process the opacity of the result in order to produce less washed-out strokes. Alternatively, we propose a minor variation in the normalization term in Formula 13 to ll the opacity gaps between the strokes, producing a more continuous painterly appearance:

C k (p 0 ) = L s=-L f (s/L)m k I noise (κ(s))I color (κ(s)) f (s/L) (1 -m k ) + m k I noise (κ(s)) (15)
with m k = m k (κ(s)). A comparison of the resulting appearances is shown in Figure 8.

LIC control. The number of strokes and their weights can be controlled through the noise parameters. In practice, we used a thresholded cellular noise [START_REF] Worley | A Cellular Texture Basis Function[END_REF]] to reproduce most stroke-like appearances. This noise masks out round colored spots that serve as "seed points" for stroke generation. Their size and smoothness are controlled through the thresholding parameters. The resulting aspect of the strokes can also be controlled through the integration pro le function f . In combination with the modi ed LIC lter in Equation 15, we found that a gaussian integration pro le with an user-adjustable width α (i.e. f (x) = e -x 2 α 2 ) provides intuitive control over the resulting appearance: low values of α tend to produce more clearly separated color ats, while increasing α results in a atter pro le that tends to blend the color of neighboring strokes together, resulting in a more continuous appearance.

Brush convolution lter. The LIC previously described can be generalized by replacing the integration path by an arbitrary user-provided footprint. This is inspired by Implicit Brushes [START_REF] Vergne | Implicit Brushes for Stylized Line-based Rendering[END_REF], and sparse convolution noise [START_REF] Lewis | Texture synthesis for digital painting[END_REF]]. When used in tandem with thresholded cellular noise, the brush pattern is replicated on every cell, and can be used to reproduce a variety of di erent styles with proper handling of silhouettes. Examples of such styles are given in Figure 12. The result of those lters can be processed afterwards with standard procedural texturing techniques to re ne the style (thresholding, color mapping, etc.).

Blending of intermediate lter results

The lter results for each individual class C k , k ∈ [0; K -1], and the lter result for the residual class, C r , need to be composited together in depth order to get the nal stylized result. The classes k ∈ [0; K -1] are sorted by depth. As the presence of a residual class is often due to occlusions by classes on top, we consider that the residual class is behind all other classes during compositing. Thus, the nal compositing order should be rst C K -1 composited over C r , then C K -2 composited over the previous result, and so on up to C 0 .

However, as the segmentation algorithm may produce overlapping classes when the number of e ective surface parts are less than K under the classi cation window, we must avoid compositing twice lter results that correspond to the same surface part, since it may result in wrong colors for semitransparent styles. A robust way to handle this is to rst identify sets of overlapping classes, average the lter results that belong to a set of overlapping classes and then blend the result of each set.

To detect if a class k overlaps with another, we consider m µ k = m k (µ k ), the class membership weights of the centroids. If m µ k < 1 then the centroid is also partially assigned to another class, meaning an overlap. We therefore can consider m µ k as the contribution weight of class k. Due to classes being sorted by depth, overlaps can only happen between successive classes. Note that the residual class never overlaps with any other class, so it is unconditionally composited.

We describe here for K = 3, but generalizable to higher values of K, an enumeration of all the possible class con gurations using the middle class weight m µ 1 to distinguish between the four cases, shown in Figure 9. Let C f be the nal composited result,

• if m µ 1 ≈ 1 then all classes are likely distinct, and all intermediate results should be composited on top of each other:

C f = C 0 over C 1 over C 2 over C r
• if m µ 1 ≈ 1/2 then m µ 1 is overlapping either m µ 0 or m µ 2 :
if m µ 0 < m µ 2 then m µ 1 is likely overlapping m µ 0 , and m µ 2 is a distinct class:

C f = m µ 0 C 0 + m µ 1 C 1 m µ 0 + m µ 1 over C 2 over C r -if m µ 2 > m µ 0 then m µ 1 is likely overlapping m µ 2 ,
and m µ 0 is a distinct class:

C f = C 0 over m µ 1 C 1 + m µ 2 C 2 m µ 1 + m µ 2 over C r
• nally, if m µ 1 ≈ 1/3 then all three classes are likely overlapping:

C f = m µ 0 C 0 + m µ 1 C 1 + m µ 2 C 2 m µ 0 + m µ 1 + m µ 2 over C r
In practice, the class membership weight m µ 1 may take intermediate values between 1, 1/2 and 1/3. To avoid discontinuities, we calculate the blending result for all four cases and interpolate between those according to the value of m µ 1 . Note that the standard "over" compositing operator can be replaced by other blend modes for more exibility in the resulting style.

RESULTS

Figures 1, 10 and 11 present several styles using our line integral convolution, showing that it can create discrete stylization marks that extend outside the original object. The accompanying video shows them in motion demonstrating the coherence of the motion of the marks. Unless speci ed otherwise, all results presented in this section have been made with N = 8 K-means iterations, and with σ = 1.

In Figure 11(a), a LIC is directed by a constant ow, whereas in Figure 1, solid gradient noise is used to locally perturb the orientation of the directing ow (surface tangents). This produces a wavier appearance. Auxiliary maps that drive the stylization lters can also vary over time, as shown in Figure 10 where a gradient noise is animated to evoke a fur moved by the wind.

Figures 11(b,c,d,f,g) illustrate various painterly appearances obtained with our modi ed LIC lter. In Figure 11(d), the lter is directed by the in ated surface tangents; whereas in Figures 11(c,f,g), the lter is directed by the in ated screen-space normals. These lters can be used in various ways to create novel styles: in Figure 11(b), we introduce perturbations in the directing ow, but also introduce color variations along the integration path, producing a fur-like e ect.

More geometrical e ects can also be emulated with image lters, such as the wobbled silhouette of Figure 11(e). Here, the integration pro le f of the modi ed LIC lter is designed to simulate a displacement along the directing ow (normals). The length of the integration path, and thus the amount of displacement, is locally modulated by a low-frequency solid noise that has been in ated outside the original object footprint. In Figure 11(h) a low-frequency solid gradient noise is applied on the object, slightly in ated, then processed in the stylization step to extract isolines. The result is composited on top of the original object. The accompanying video also shows this style with an animated solid noise.

Finally, Figure 12 shows several examples obtained with the brush convolution lter. The ability to choose any arbitrary brush footprint provides great artistic freedom.

Performance: our pipeline was implemented as a set of (nonoptimized) OpenGL fragment shaders in the Gratin software [START_REF] Vergne | Designing Gratin, A GPU-Tailored Node-Based System[END_REF]. Its performance is mainly a ected by the radius of the lter window as well as the target resolution. The stylization lter complexity also has an impact on performances. The following table provides the number of frames per second for varying radii, resolutions and style modes. These numbers were measured on the "bunny" object, on the styles in Figures 1 (LIC Figure 12: Styles obtained with the brush convolution lter over a thresholded cellular noise. By varying the brush pattern, a variety of di erent appearances can be reproduced. In the "grass" example, the brush patterns are oriented by the in ated screen-space normals. For these results β = 11, σ z = 10, σ n = 2.

(d) (e) () (g) (h) β =11 σn =2 σz =10 β =15 σn =2 σz =20 β =15 σn =0 σz =20 β =11 σn =2 σz =10 β =11 σn =2 σz =8 β =22 σn =3 σz =20
σn =0 σn =3 σn =1.5 σn =6 σn =13
Under-segmentation Over-segmentation

DISCUSSION

Segmentation quality. Our local segmentation produces best results when the lter window contains enough data to cluster and with objects having rather smooth geometry. Local oversegmentation and per-pixel classi cation errors tend to occur in regions with large variations of depth or normal orientations, such as heavily slanted areas or regions with high curvature. In such cases, noticeable visual artifacts or holes may appear in the result. A good rule of thumb is to choose a lter window smaller than the smallest geometrical feature in the G-bu ers but large enough to have enough data (e.g. r > 10). This, however, limits the size of the stylized features, and the amount of geometric detail in the original geometry. However, the impact of the latter is rather low, since the ne geometric features of highly detailed meshes would be lost anyway after applying the stylization lters, as shown in Figure 14.

Large lter windows are more likely to contain more overlapping in ated surface parts, and may require increasing K. As shown in Figure 15, if the e ective number of distinct surfaces parts is higher than K, some of them will be grouped in the resulting classes, which may lead to undesirable artifacts in the in ated bu ers. By following the rule of thumb above and limiting the lter window size, we found that smooth objects with low geometrical detail rarely need more than K = 3 classes for a correct detection of overlaps in in ation.

Finally, the segmentation is a ected by the amplitude of depth discontinuities at silhouettes. It is sometimes necessary to increase the sti ness parameter β and/or adjust the per-pixel classi cation weights σ z and σ n to increase the sensitivity to depth di erences, and, if necessary, increase the weight given to normal di erences. Figure 13 shows visual artifacts that might appear in case of undersegmentation and oversegmentation, for varying values of σ n . It shows a simple visual style consisting of marks directed by the surface normals. For high values of σ n , the per-pixel segmentation may become too conservative and assign fringe pixels to the residual class. As the residual class spans unrelated surface parts, the corresponding in ated data blends two con icting orientations, resulting in a distracting interaction at the boundary between the two spheres (σ n = 13). Conversely, low values of σ n or outright disabling the contribution of normals by setting σ n = 0, can lead to undersegmentation: the surface parts are not properly segmented during ltering and the color of di erent surface parts may bleed onto each other (σ n = 0, σ n = 1.5).

In ation of concave surface parts. The in ation result is not well de ned in concave surface parts, as an in nite number of surface points may overlap when in ated. In those con gurations, the weights w p form elongated clusters with no local maximum, and are hence not easily detected as a single cluster by the local segmentation. The K-means algorithm will distribute class centroids along the cluster, splitting it into multiple classes in an unpredictable way. This is an inherently di cult case for stylization, as it is di cult to nd a coherent anchor point on the surface. It is not handled in our pipeline, but we found that in practice those cases are rare and easily identi able.

Undetected surface parts and residual class. Some surface parts under the lter window are missed by the K-means segmentation pass when no pixel belonging to the surface part has an adequate screen-space normal that displaces it towards the window center. In most cases, this happens because the corresponding anchor point for in ation is occluded by another surface. Signi cant complexity is needed during per-pixel segmentation to account for missed surface parts. Our solution, which is to manually separate all pixels not belonging to a detected class into a residual class, cannot accurately preserve motion coherence, as the extended data for this class is not obtained by in ation. More generally, it can be seen as a limitation of screen-space algorithms: information about occluded surfaces are lost, but is sometimes needed to get coherent data. However, this slight incoherence is usually not noticeable as it is often occluded by the stylization of other classes.

Disocclusions. A pervasive issue in stylized rendering techniques based on stroke primitives is how to handle disocclusions when a primitive becomes visible during camera or object motion. Our pipeline is not based on stroke primitives, but instead uses a combination of solid noise, 2D ltering, and standard procedural texturing techniques to achieve a similar appearance. Yet, this process is also subject to visual artifacts due to disocclusions. Depending on the stylization lter, noise features that become suddenly visible can introduce large changes in the results from one frame to another. This is particularly prevalent with the styles based on cellular noise and the modi ed LIC lter, as they tend to spatially "amplify" the point-like cells, producing noticeable popping artifacts with large lter sizes. This could be improved as a future work by pre ltering the noise at disocclusion boundaries (silhouettes).

Pipeline parameters. In addition to the parameters of the stylization lters, which are out of the scope of our contribution, the user may have to adjust several parameters of the segmentation (σ , β, σ n , σ z , lter window radius r ) to obtain an accurate result for a given object. This can be a tedious process as some segmentation failure cases may only appear under certain viewpoints. Currently, a visualization of the local segmentation results under a lter window is provided to ease this process, but an improvement would be to infer some of those parameters, either from the geometry if it is available, or from a global analysis of the G-bu ers contents.

Comparison with object-space in ation. Our approach does not require modi cation of the input geometry or the rendering pipeline. An alternative to our screen-space in ation algorithm could be done during the vertex processing stage, as in [Nienhaus and Döllner 2004b], and overlapping surface parts could be recovered using a depth peeling technique. Such an approach may be more e cient for high in ation radii at the cost of a more complex rendering pipeline. However our per-pixel classi cation stage would still be necessary in order to assign each pixel to a surface part within a ltering window.

CONCLUSION

We presented a post-processing stylization pipeline that allows stylization that extends outside object boundaries. Our main contribution in this paper is a post-processing technique to extend image lters that depend on G-bu er data outside the rasterized object boundaries in a motion coherent way, and with proper handling of overlaps at silhouettes. This pipeline only requires standard G-bu ers as input (normal map, depth map), allowing it to be embedded in the compositing stage of most rendering software. This technique was then put to the test by integrating several wellknown image ltering techniques. Instead of striving to reproduce a particular artistic style, our intent is to provide a generic way to make arbitrary image lters motion-coherent and silhouette-aware. We impose a very limited amount of restrictions on the image lters, thus providing a exible stylization method capable of reproducing a wide variety of appearances. In the future, we would like to integrate more image ltering techniques into our pipeline, and further experiment to discover novel styles. In the process, we plan to take inspiration from styles found in digital paintings as we feel that such styles have not yet been widely explored in the context of the interactive rendering of 3D scenes.

Figure 2 :Figure 3 :

 23 Figure 2: Overview of stylization challenges in screen-space. (a) A lter requiring data contained in G-bu ers will produce discontinuities as this information is not available outside the silhouettes. (b) Locally inflating G-bu ers along the normals allows extending the lter e ect beyond the original object footprint. (c) When dealing with internal contours, a naive screen-space in ation fails where overlapping surfaces occur because a single surface is considered for each pixel. (d) Our approach uses a local segmentation in order to in ate and stylize each overlapping surface part.

Figure 4 :

 4 Figure 4: In ation: (top) e ect of σ on the size of the clusters, (middle) in ated normal map, (bottom) in ated color. Low σ values make the averaged region more localized, as few normals are considered t for in ation. Conversely, higher σ values result in a wider region being averaged when inating G-bu er data. This can lead to more stable animations, at the price of a loss of detail on high-frequency data, as shown with the noisy color image in the bottom row.

Figure 5 :

 5 Figure 5: Handling overlapping in ated data on a style guided by screen-space normals. (Top) normals and weights obtained on two lter windows. (Second) averaging all data leads to unnatural direction elds. (Third) averaging only front-most surfaces produces discontinuities in the resulting stylization. (Bottom) in our approach the weight maps are rst segmented into clusters to stylize each part independently before compositing them.

Figure 6 :

 6 Figure 6: (Left) K-means segmentation results with K = 3. Under lter windows where only one or two distinct surface parts are present, the clustering associates multiple centroids to the same surface part. (Right) visualization of the in ated normal map. Regions with overlapping in ated normals are represented by blending them on top of each other.

Figure 7 :

 7 Figure 7: Extending the initial segmentation to all pixels under the lter window. Red: class 0; green: class 1; blue: class 2. (a) The initial K-means segmentation is only reliable for pixels with signi cant weights w p . (b) Prior to adjusting σ n and σ z to the current scene, the class assignments may be imprecise or incomplete (black parts are unclassi ed regions). (c) Adjusted σ n to increase the tolerance to normal variations with respect to the normal at the cluster center. The distinct surface parts are properly detected and classi ed.

Figure 8 :

 8 Figure 8: Comparison of the original and our modi ed formulation of the LIC lter.

Figure 9 :

 9 Figure 9: Contribution weights for K = 3 under 3-cluster (a), 2-cluster (b) and single (c) con gurations. Class 0,1 and 2 associated colors are respectively red, green and blue. The contribution weight of the middle class m µ 1 can be used to identify the current con guration.

Figure 10 :

 10 Figure 10: Random variations introduced by solid noise can be animated, such as in this example with a fur-like style. See the accompanying video for the full animation. Segmentation parameters: β = 15, σ z = 20, σ n = 2

  ) and 12 (brush), using K = 3 and with a Nvidia GeForce GTX 1080 Ti graphics card.Resolution Filter r = 15 r = 20 r = framerates are usually obtained with simple styles and small screen resolutions. Optimizations necessary to improve performances and allow our pipeline to be included in real-time applications such as video-games are left for future works.

Figure 11 :

 11 Figure 11: Various results obtained with LIC based lters. Model (b) by Sketchfab user Katerina Novakova (CC-BY-SA). Bunny model (d,e,f) by Sketchfab user Bernardo 3D (CC-BY). Octopus model by Lukáš Marek (CC-BY).

Figure 13 :

 13 Figure 13: In uence of σ n on the segmentation and ltered result. Pixels assigned to the residual class are shown in black in the classi cation result (lower-right windows). For these results β = 11, σ z = 10.

Figure 14 :

 14 Figure 14: Geometry details ner than the lter size are lost during the stylization process, and can lead to visual artifacts as K-means does not handle the many small overlapping surface parts.

✗Figure 15 :

 15 Figure 15: Segmentation failure for K = 3 classes. Under the lter window, 4 distinct surface parts overlap when in ated. The K-means algorithm merged two unrelated surface parts in the same class (blue class), impacting the in ated result.