Individual

Keywords: Empathy, Infancy, Emotion regulation, Self perception Social Development empathy, infancy, emotion regulation, self perception Page 1 of 39 Social Development

differences in infant's emotional resonance to a peer in distress.

Individual differences in infant's emotional resonance to a peer in distress. Self-other awareness and emotion regulation.

Empathy related responses are essential for children's developing abilities to respond to their social partners in an altruistic manner [START_REF] Eisenberg | Consistency and development of prosocial dispositions: a longitudinal study[END_REF]. Once developed, these abilities tend to be manifested with consistency across time [START_REF] Knafo | The developmental origins of a disposition toward empathy: genetic and environmental contributions[END_REF]. Empathy as an emotional response stems from the comprehension of another's emotional state or condition, similar to what the other person is feeling or would be expected to feel [START_REF] Eisenberg | Empathy-related responding and cognition: A "chicken and the egg[END_REF]. It is associated with at least minimal awareness that the source of one's own affect is the emotion observed in the other person [START_REF] Decety | The functional architecture of human empathy[END_REF][START_REF] Hoffman | Empathy and Moral Development. Implications for Caring and Justice[END_REF]. The "functional architecture" of human empathy encompasses several components, including affect sharing, self-other awareness, regulatory processes, and perspective taking [START_REF] Decety | The functional architecture of human empathy[END_REF]. Among these, affect sharing or the ability to emotionally resonate to other's emotions seems to represent the core element of empathy [START_REF] De Waal | Morally evolved: primates social instincts, human morality, and the rise and fall of "Veneer Theory[END_REF].

Emotional resonance is the first element of empathy to appear during ontogeny. It can be seen in the newborns' contagious crying reactions to the cry of another newborn [START_REF] Field | Depressed mothers' newborns show less discrimination of other newborns' cry sounds[END_REF]Sagi & Hoffman, 1985;[START_REF] Simner | Newborn's response to the cry of another infant[END_REF]. It has been hypothesized that later in development, this initial pure emotional contagion becomes associated with a growing differentiation between self and other, allowing for reactions that are more tuned into the other's state than one's own. Also, the infant is increasingly able to use regulatory strategies for modulating this emotional response to an adaptive level for both the self and conspecifics [START_REF] Hoffman | Empathy and Moral Development. Implications for Caring and Justice[END_REF].

In general, it is considered that only around the age of 18-24 months children manifest such mature empathic reactions [START_REF] Hoffman | Empathy and Moral Development. Implications for Caring and Justice[END_REF]. One of the main arguments is that at this age children pass the classic test of mirror self-recognition which may index the existence of a self concept. In support of this argument, Zahn-Waxler, [START_REF] Zahn-Waxler | Development of concern for others[END_REF] provide some indirect evidence by showing that 23-to 25-month-olds who have higher levels of mirror self-recognition manifest more prosocial behaviors. In the same vein, [START_REF] Kärtner | Influences of contingent responsiveness on the development of self-recognition and empathy with 18 months[END_REF] show that a large percent of those 19-month-old children who manifest helping behaviors toward a distressed adult also recognize themselves in the mirror.

However, the perception of other's emotions induces in the observer a matching affective state as early as few days after birth, with newborns manifesting increased facial and vocal distress in response to the cry sound of another infant [START_REF] Field | Depressed mothers' newborns show less discrimination of other newborns' cry sounds[END_REF][START_REF] Martin | Distress crying in neonates: Species and peer specificity[END_REF][START_REF] Simner | Newborn's response to the cry of another infant[END_REF].

Later in infancy, these affective resonance responses to others' emotions seem to persist. [START_REF] Haviland | The induced affect response: 10-week-old infants' responses to three emotion expressions[END_REF] have shown that the perception of mother's expressions of joy and anger induces in 10week-old matching affect states. Importantly, in this study, the perception of persistent anger, but not positive emotion, resulted in increased affect sharing in half of the sample. Other's negative emotions (e.g., the pain cry of another infant) induce facial anger and sadness in 1-, 3-, 6-, and 9-month-old infants [START_REF] Geangu | Contagious crying beyond the first days of life[END_REF], and toddlers (Spinrad & Stifter, 2006). Similarly, this type of stimulus triggers negative emotional reactions evident in both facial expressions and cardiac reactivity in kindergarten and school age children as well [START_REF] Fabes | The relations of children's emotion regulation to their vicarious emotional responses and comforting behaviors[END_REF][START_REF] Zahn-Waxler | Children's emotions and behaviors in response to infants' cries[END_REF].

Independent of empathy research, investigations concerning the ontogenesis of a sense of self suggest that well before the age of 2, children develop a perceptual protorepresentation of the body which allows them to differentiate between self and others [START_REF] Rochat | Perceived self in infancy[END_REF]. Infancy is also the time for important developments of regulatory mechanisms [START_REF] Calkins | The emergence of emotion regulation: Biological and behavioral transactions in early development[END_REF][START_REF] Kopp | Antecedents of self-regulation: a developmental perspective[END_REF].

One might thus reasonably think that the emotional resonance to another's distress as it is documented in infants might be interconnected with these other abilities. Scattered evidence supports this line of thought. Newborns discriminate between their own cry and the cry of another [START_REF] Dondi | Can newborns discriminate between their own cry and the cry of another newborn infant?[END_REF], and express more emotional contagion in response to the cry sound of a peer than in response to their own cry [START_REF] Simner | Newborn's response to the cry of another infant[END_REF]. Further, infants who better regulate their emotional arousal at the age of 4-months, show reduced affect sharing in response to a peer's distress at the age of 12 months [START_REF] Ungerer | The early development of empathy: self-regulation and individual differences in the first year[END_REF]. It thus seems that early emotional arousal is not pure contagion, rather it is associated with an awareness of the source of distress, and it might be regulated. The present study is designed to further investigate possible relations between emotional resonance to another's distress, self-other differentiation, and emotion regulation during infancy.

The development of a sense of self is a very dynamic process that starts early in infancy, and encompasses several aspects related to forming a primary representation of the bodily self and having a sense of self as a physical agent, as well as differentiating between self and others as intentional agents [START_REF] Gergely | The development of understanding self and agency[END_REF][START_REF] Rochat | Perceived self in infancy[END_REF]. The early ability to discriminate the bodily self from others is based on an implicit intermodal body schema [START_REF] Rochat | Perceived self in infancy[END_REF] that integrates information related to bodily space [START_REF] Bahrick | Detection of intermodal proprioceptive-visual contingency as a potential basis of self-perception in infancy[END_REF][START_REF] Schmuckler | Visual-proprioceptive intermodal perception using pointlight displays[END_REF], intermodal timing [START_REF] Rochat | Self-perception and action in infancy[END_REF][START_REF] Rochat | Spatial determinants in the perception of self-produced leg movements in 3-to 5-month-old infants[END_REF], and intermodal forms of action (Rochat & Striano, 1999a).

Newborns are successful in discriminating between self and other produced tactile stimulation [START_REF] Rochat | Differential rooting responses by neonates: evidence for an early sense of self[END_REF], and in altering self-produced action in order to obtain a certain outcome (i.e., to hear or see their mother) [START_REF] Decasper | Of human bonding: Newborns prefer their mothers' voices[END_REF]. By the age of 2 months, infants become sensitive to the relative matching of proprioception with other perceptual modalities, and seem to detect links between their sucking actions and the auditory consequences of this action, based on spatial and temporal matching [START_REF] Rochat | Emerging self-exploration by 2-month-old infants[END_REF].

Around the age of 5-months there are signs of intermodal matching between proprioceptive and visual determinants of limb movements. At this age infants prefer to watch a video display of their own or of another infant non-contingent hand or leg movements, but not a video display of their own contingent hand or leg movement [START_REF] Bahrick | Detection of intermodal proprioceptive-visual contingency as a potential basis of self-perception in infancy[END_REF][START_REF] Rochat | Spatial determinants in the perception of self-produced leg movements in 3-to 5-month-old infants[END_REF]. Seven-and 9month-old infants seem to require less information about motion [START_REF] Schmuckler | Visual-proprioceptive intermodal perception using pointlight displays[END_REF], and less perfect timing [START_REF] Zmyj | Discrimination between real-time and delayed visual feedback of self-performed leg movements in the first year of life[END_REF] for establishing such a contingency, and they manifest a propensity for social initiatives towards others compared to their own image in the mirror.

In conjunction, these data suggest that infants at this age do show a perceptual discrimination between self and others, even if they don't necessarily construe a representation of their own image [START_REF] Rochat | Who's in the mirror? Self-other discrimination in specular images by four-and nine-month-olds infants[END_REF]. It is also around the age of 9-months, that children begin to understand others as having different intentional states than their own and to act upon them [START_REF] Tomasello | Joint attention as social cognition[END_REF].

Little is known about if or how this increased self-other differentiation relates to the early observed emotional resonance. Importantly, work with newborns show that they selectively manifest contagious crying in response to another baby's cry, but not to their own cry [START_REF] Simner | Newborn's response to the cry of another infant[END_REF][START_REF] Field | Depressed mothers' newborns show less discrimination of other newborns' cry sounds[END_REF], suggesting that a relation between affect sharing and an incipient sense of self might be already present. Apart from work on infants, studies investigating the neural mechanisms of empathy in adults have shown that the temporoparietal junction, an area also involved in the multisensory processing of body-related information and the phenomenological and cognitive aspects of self [START_REF] Blanke | The out-of-body experience: disturbed self-processing at the temporoparietal junction[END_REF], is also activated during the perception of pain in others [START_REF] Jackson | To what extent do we share the pain of others? Insight from the neural bases of pain empathy[END_REF]. It seems thus that aspects of bodily self are related to affect sharing. Mature sense of self is crucial for empathic responses, as it allows the observer to go beyond affect sharing, appraise the other's emotional state in relation to oneself and engage in intersubjective exchanges [START_REF] Decety | The functional architecture of human empathy[END_REF]. This further motivates investigation of these relations in infancy, when important aspects of self begin to develop.

It is also crucial that the initial affect sharing reaction to another's distress is modulated to an adaptive level through the use of various regulatory strategies that lead to its inhibition, activation or graded modulation. In children, for example, reduced emotion regulation abilities are related to increased arousal to an infant cry [START_REF] Fabes | The relations of children's emotion regulation to their vicarious emotional responses and comforting behaviors[END_REF].

Significant developments in emotion regulation take place during infancy, with younger infants using more primitive self-soothing strategies (e.g., digit or hand sucking) [START_REF] Derryberry | Emotion, attention, and temperament[END_REF]Hornick & Gunnar, 1987), while withdrawal and escaping behaviors characterize more 3-to 6month-old infants [START_REF] Shapiro | Infants' emotional and regulatory behaviors in response to violations of expectancies[END_REF]. Also, attention based strategies become more frequent during the second half of the first year [START_REF] Shapiro | Infants' emotional and regulatory behaviors in response to violations of expectancies[END_REF], when object distraction becomes more involved in regulating emotions [START_REF] Braungart-Rieker | Infants' responses to frustrating situations: continuity and change in reactivity and regulation[END_REF][START_REF] Mangelsdorf | Developmental and temperamental differences in emotion regulation in infancy[END_REF][START_REF] Shapiro | Infants' emotional and regulatory behaviors in response to violations of expectancies[END_REF]. This is probably due to development of endogenous attention, with older 7-month-olds being more reliably efficient to shift attention than the 3-or 4-month-olds [START_REF] Colombo | Infant visual attention in the pairedcomparison paradigm: test-retest and attention-performance relations[END_REF], while very young infants tend to have difficulties in disengaging attention, especially in stimuli competing situations [START_REF] Hood | Adult's eyes trigger shifts of visual attention in human infants[END_REF]. Fearfulness, as an index of inhibition of approach, increases as well [START_REF] Carranza | A longitudinal study of temperament in infancy: Stability and convergence of measures[END_REF][START_REF] Gartstein | Studying infant temperament via a revision of the Infant Behavior Questionnaire[END_REF], being relevant for regulating the affective arousal [START_REF] Grolnick | Age-graded change in initiation of positive affect[END_REF], although mainly by withdrawal and disengagement from a distressful or challenging situation (Liew et al., in press).

The early emotional resonance responses seem to be regulated. In Haviland and Lelwica's study (1987), only half of the infants reacted with intense distress as evidenced by uncomforted crying to their mother's persistent angry face and voice. It seems thus that the rest of them, who showed less intense distress, were employing some regulatory strategies. But, what exactly are those emotion regulation strategies that relate to infant's emotional resonance is still a matter of further investigation.

The goal of this paper is to investigate possible concurrent relations between infant emotional resonance and the emerging abilities for regulation and self-other differentiation. Infants' emotional reactions to the cry of another infant have been systematically used in previous studies as a sign of emotional resonance in both very young infants and older children (e.g., [START_REF] Dondi | Can newborns discriminate between their own cry and the cry of another newborn infant?[END_REF][START_REF] Eisenberg | Vicarious emotional responsiveness and prosocial behavior -their interrelations in young children[END_REF][START_REF] Simner | Newborn's response to the cry of another infant[END_REF]. In the current study we aimed to investigate the individual differences for these particular reactions in 3-, 6-, and 9-month-old infants.

With respect to emotion regulation, we have chosen to analyze both infants' regulatory behaviors triggered by the perception of the cry sound, and parents' report of their babies' daily use of regulatory strategies. We have particularly focused on those aspects of emotion regulation that are specific for this age interval: comforting (i.e., thumb sucking/mouthing) and escape behaviors, as well as those temperamental elements that index regulatory strategies (e.g., attention based). We predict less emotional resonance when self-soothing behaviors are used, especially in younger infants, while for older age groups we would expect that infants with higher scores on temperamental dimensions that index attentional strategies will manifest less affect sharing reactions in response to another infant cry sound.

For self-other differentiation, we aim to analyze if the emergence of an implicit intermodal body schema is related to infants' emotional resonance. Previous studies have successfully employed visual preference paradigms to show that 7-to 9-month-old infants discriminate between their own body and that of others based on intermodal matching of sensorial information [START_REF] Schmuckler | Visual-proprioceptive intermodal perception using pointlight displays[END_REF][START_REF] Zmyj | Discrimination between real-time and delayed visual feedback of self-performed leg movements in the first year of life[END_REF]. Older, but not younger infants (2-month-old), prefer visual exploration of novel stimuli [START_REF] Wetherford | Developmental changes in infant visual preferences for novelty and familiarity[END_REF], and the underlying attentional processes also seem to be consistently present up to the age of 8-months [START_REF] Colombo | What habituates in infant visual habituation? A psychophysiological analysis[END_REF]. Visual preference for the image of another body is therefore regarded as an index of self-other discrimination. In our study, we expect that infants with better abilities to differentiate self from other as reflected in longer looking duration towards the video image of another infant body will also manifest reduced personal distress in response to the observed negative affect.

Method Participants

The final sample consisted of: 34 3-month-old infants (16 males, mean age: 96.23 days); 44 6-monthold infants (17 males, mean age: 182.47 days); and 44 9-month-old infants (18 males, mean age: 271.76 days). Additional 9 3-month-olds, 3 6-month-olds, and 4 9-month-olds responded to the invitation to participate but were not included because they became distressed shortly before the beginning of the procedure or when seated in the infant chair. Some infants completed only part of the procedure or parents did not return the questionnaire. In order to retain as much data as possible, subjects with only one set of data where included in the analysis for that task. All subjects were living in a mid-sized city in Europe. Infants were rewarded with a small toy for their participation, and, if necessary, parents received payment for car parking.

Procedures and Measures

Infants were assessed with two tasks in laboratory settings. At home, parents completed a questionnaire about their infant temperamental characteristics. The order of the laboratory tasks was the same for all participants: the self-other differentiation task first, followed after a ten minutes break by the affect sharing task. This order was determined by the nature of the affect sharing task, which is expected to induce negative emotional reactivity (e.g., [START_REF] Haviland | The induced affect response: 10-week-old infants' responses to three emotion expressions[END_REF]. In order for the response to self-other differentiation task not to be influenced by the potential negative affect, this task was always first.

1. The emotional resonance task. To measure the affect sharing responses, infants were presented with the cry sound of a peer. The stimulus was represented by the sound of a 3-month-old male infant crying, recorded during a blood sampling procedure, in a nearby hospital unit. The blood sampling triggered a cry from first to last vocalization of 199 s. During the procedure, this cry sound was played continuously twice, for a maximum duration of 360 s. The task consisted of a baseline and a test episode as per previous work in this area [START_REF] Dondi | Can newborns discriminate between their own cry and the cry of another newborn infant?[END_REF][START_REF] Field | Depressed mothers' newborns show less discrimination of other newborns' cry sounds[END_REF]. During the 60 s baseline episode, in the absence of any auditory or visual stimulation, the infant's behavior was recorded. The test episode consisted of the presentation of the cry stimulus, and varied in duration as follows: 300 s for those infants who did not manifest cry vocalizations during this interval; maximum 360 s for those participants who started crying after the first 290 s from the stimulus onset. If the infant started to cry, a maximum of 30 s continuous cry was allowed until the parent was requested to start soothing him/her.

During the entire procedure, the infant was seated in an infant chair (reclined 65 º ). One camera (~100 cm in front of the child) recorded the infant behavior, and a speaker (~200 cm away from the infant, hidden by a dark curtain) played the stimulus. The parent sat approximately 100 cm away to the infant's left, and the experimenter sat behind the camera, partially occluded by it.

Infants' emotional resonance responses were coded in terms of different dimensions of facial expressivity and vocal reactions that match the perceived crying. Intensity of distress vocalizations, latency to signs of distress, facial expression patterns characteristic to anger and sadness are all considered to be parameters of emotional reactivity [START_REF] Kochanska | Individual differences in emotionality in infancy[END_REF][START_REF] Rothbart | Temperament and self-regulation[END_REF]) and so we reasoned they will be good indicators of affect sharing. The recordings were divided in 10 seconds units. For reliability, a second coder analyzed 20% of the data.

Intraclass correlation based on absolute agreement is presented in parentheses for each dimension.

The following behaviors were coded as present or absent for each unit. Facial expressivitycriteria derived from AFFEX were used for coding expressions of anger (.976) and sadness (.875) as described by [START_REF] Goldsmith | The Laboratory Temperament Assessment Battery (Prelocomotor Version, Edition 3.1)[END_REF]. For either facial expression to be coded, specific movements in at least two of the following face regions should be displayed: forehead/brows regions; eyes/nose/cheek regions; mouth/lips/chin regions. Facial movements that are specific for anger and sadness can appear simultaneously, leading to mixed facial expressions [START_REF] Sullivan | Emotional expressions of young infants and children -a practitioner's primer[END_REF]. If this was the case, expressions of both anger and sadness were coded as present for the same 10-second unit. Also, in cases where a facial expression started in one unit and continued for more than one unit, it was coded as present for each of them.

Cry vocal reactions were defined as audible, intermittent vocalization of distress [START_REF] Simner | Newborn's response to the cry of another infant[END_REF]. We scored the presence of the cry vocalizations (.911) and the intensity of the cry (.958) for each unit. The intensity was rated on a scale from 1 to 5 (1 -mild protest verbalization that may be difficult to identify as negative, 5 -full intensity cry/scream [START_REF] Goldsmith | The Laboratory Temperament Assessment Battery (Prelocomotor Version, Edition 3.1)[END_REF]. Where a cry was elicited in one unit and lasted for more than one unit, the cry was scored as present for each of them, and the intensity was rated separately for each unit. The latency to the onset of crying (.960) was recorded as the number of units from the beginning of stimulus presentation to the onset of the first bout of cry. We coded this dimension only in the test phase, where we could establish with precision the beginning of the stimulation.

2. The self-other discrimination task. We used the task described by [START_REF] Bahrick | Detection of intermodal proprioceptive-visual contingency as a potential basis of self-perception in infancy[END_REF], indexing aspects of the implicit intermodal body schema. The participant was seated in an infant high chair, adjusted so that infant's view of his/her own legs was occluded. In front of the participant, approximately 100 cm away, 2 TV monitors were placed at the same level as the head and torso of the infant. These were set side by side, 15 cm away from each other and turned inward by an approximate 15ْ angle. A dark curtain masked them, so that only the screens were visible to the participant. A camera situated above the infant, 165 cm high, recorded on-line the subject's own legs movements. This video recording represented the self stimulus and it was displayed on-line on one monitor. Prior to the session, the leg movements of another infant of the same age with the participant (either 3-, 6-or 9month-old) were recorded in the same position/setting. This recording represented the other stimulus, had a length of approximately 120 s, and it was displayed off-line on the other monitor (Figure 1).

Both the participant in the self condition and the infant in the other condition were wearing identical white trousers in order to increase physical appearance similarity between conditions. The presentation of the stimuli on the two monitors was counterbalanced across participants.

-Figure 1 -A camera recorded the participant's head and torso for off-line coding. Participant's gazing was coded in terms of duration of the total fixation toward each TV monitor. Preferential looking for either the self or the other stimulus was indicated by greater fixation towards the corresponding TV monitor [START_REF] Dannemiller | Detection of relative motion by human infants[END_REF]. Also, we coded the subject's response in term of self leg movement. Subjects who did not manifest leg movement during testing were eliminated from the analysis for this task, since disproportionate leg motion for one stimulus compared to the other would represent a confound for preferential looking analysis. A second coder analyzed 20% of the data for reliability, with intraclass correlation based on absolute agreement .969.

3. Emotional regulation was measured as the infant's observed performances in a potentially distress inducing situation (i.e., the situation created by the emotional resonance task) and via parental reports.

Observed measures of infant emotion regulationthumb-sucking and escaping behaviors have been previously reported as being successfully employed by infants for regulating emotional arousal in various distress provoking tasks [START_REF] Goldsmith | The Laboratory Temperament Assessment Battery (Prelocomotor Version, Edition 3.1)[END_REF][START_REF] Weinberg | Beyond the face: an empirical study of infant affective configurations of facial, vocal, gestural, and regulatory behaviors[END_REF]. For thumb-sucking (.959), any sucking actions applied to hand or any other parts of the body that lasted more than 1 second were coded. For escaping behaviors (.753), we coded the presence or absence of any attempts to escape from the seat by mild turning away, back arching, twisting away, leaning away, and kicking. Both behaviors were coded as present or absent for every 10 s unit, and a score was computed consisting of the percentage of time it was present from the total amount of time of stimulus presentation.

Parental reports of infant's emotional regulation abilities were obtained using the Infant Behavior Questionnaire -Revised (IBQ-R) [START_REF] Gartstein | Studying infant temperament via a revision of the Infant Behavior Questionnaire[END_REF]. IBQ-R is a widely used measure that has been developed for assessing both reactivity and regulation dimensions of temperament. For the current study we used those subscales that are theoretically related to selfregulatory processes (Cronbach's alpha coefficients are reported in parentheses): Duration of Orienting (α = .738; attention to and/or interaction with a single object for extended periods of time), Falling Reactivity (α = .703; rate of recovery from peak distress, excitement, or general arousal; ease of falling asleep), Fear (α = .876; startle or distress to sudden changes in stimulation, novel physical objects or social stimuli; inhibited approach to novelty), and Sadness (α = .731; lowered mood and activity related to personal suffering, physical state, object loss, or inability to perform a desired action; general low mood).

Results

The duration of the test phase varied for each participant, therefore for further analysis we computed the percentage of units each infant spent crying, manifesting facial expressions of anger and sadness.

Descriptive data for the affect sharing task for each age group are presented in Table 1. A twoway 2 (condition: baseline vs. test phase) x 3 (age: 3-vs. 6-vs. 9-month-old) mixed ANOVA, with repeated measures on the first variable (Greenhouse -Geisser correction for the violations of the assumptions of variance homogeneity) indicate that infants manifested significantly more cry vocalizations (F(1, 102) = 126.465, p < .001), anger (F(1, 102) = 110.749, p < .001), and sadness (F(1, 102) = 97.00, p < .001) during the test phase compared to baseline. Also, the cry was more intense during the test phase (F(1, 102) = 160.954, p < .001). We found significant age effects for the cry vocalizations (F(2, 102) = 3.26, p < .05), with 6-month-olds crying more than the 3-month-olds (Mean difference = 9.94, p < .05). Also, 6-month-olds manifested more sadness (F(2, 102) = 5.68, p < .05) than both 3-(Mean difference = 6.85, p < .05) and 9-month-olds (Mean difference = 5.56, p < .05).

There was a marginally significant age effect for cry intensity (F(2, 102) = 2.62, p = .07), with a tendency for 6-month-olds to cry more intensely than the 3-month-olds (Mean difference = .46, p = .07). A one way ANOVA (age x latency) revealed significant age effects (F(2, 102) = 4.181, p < .05) with 6-(Mean difference = -6.90, p < .05) and 9-month-olds (Mean difference = -7.17, p < .05) having a faster onset of cry vocalizations than the 3-month-old infants. There was no significant difference between the 6-and the 9-month-old infants (p > .05). Independent t-tests suggest that boys and girls manifest similar levels of emotional resonance for each dimension included in the study (ps > .10).

-Table 1 -

Interrelations of observed measures of self-regulatory behaviors and emotional resonance measures

Thirteen (40.63%) 3-month-old infants manifested thumb sucking behavior while perceiving the cry of another infant in distress, while only 7 (20.59%) of the 6-month-olds and 7 (19.44%) of the 9-month-olds exhibited the same behavior. Jonckheere-Terpstra test suggests a significant trend of decreased use of thumb sucking from age 3-to 9-months (Std. J-T statistic = -2.302, p < .05), while infants from all age groups manifested similar levels of escaping behaviors (Std. J-T statistic = -1.231, p > .05).

Because the 3-month-old group significantly used more thumb-sucking, we further analyzed whether the presence of this behavior was successful in altering the emotional response to another infant pain cry. We split this age group by the presence of thumb sucking. Independent samples t-test shows that infants who used thumb-sucking manifested less vocal distress (t(32) = 2.19, p < .05), with a lower intensity (t(32) = 2.86, p < .05), and less sadness (t(32) = 3.29, p < .05). Also, marginally significant, when thumb sucking was used, infants tended to have a delayed onset of crying (t(32) = -1.919, p = .065) (Figure 2). No significant differences were found for the percentage of time they manifested angry facial expressions (t(32) = 1.32, p = .195). For older infants, thumb-sucking did not relate significantly with measures of contagious crying (ps > .05).

Scores for escape behavior did not relate significantly with any of contagious cry measures at the age of 3-or at the age of 9-months (ps > .05), while for the 6-month-olds it correlated significantly and positively only with facial expression of anger (r(34) = .352, p = .041), suggesting that increased attempts to escape a situation where this is not possible, is actually associated with increased levels of anger.

We also explored the independence of these behaviors from negative affect, by looking at their patterns of relations with temperamental fear. Neither thumb-sucking or escape behaviors related significantly with fear for both 3-(r(25) = -.240, p = .249; r(25) = .265, p = .201) and 6-month-old infants (r(23) = .228, p = .296; r(23) = .276, p = .203). For the 9-month-old there was a significant, but negative, relation between thumb-sucking and levels of fear (r(29) = -.422, p = .022).

-Figure 2 -

Interrelations of temperamental characteristics and emotional resonance measures

Pearson correlations (2-tailed significance) for contagious crying measures and temperamental dimensions are presented in Table 2. Duration of Orienting and Falling Reactivity related significantly and consistently across dimensions with contagious crying.

-Table 2 -Six-month-old infants with higher scores for Duration of Orienting cried with lower intensity (r(23) = -.49, p = .019) and expressed less anger (r(23) = -.43, p = .043) in response to the cry sound.

There was also a tendency for 6-month-olds with higher scores on this subscale to manifest fewer cry vocalizations (r(23) = -.38, p = .071) and to have a longer latency to the first bout of cry (r(23) = .40, p = .062), but did not reach significance.

Three-month-olds' Duration of orienting correlated significantly solely with the intensity of vocal distress (r(25) = .42, p = .036) and marginally significant with cry vocalizations (r(25) = .35, p = .090). Interestingly, the direction of the relation is positive, and significantly different than the ones for 6-month-olds (based on Fisher Z transformation, p = .001 and p = .010, respectively).

Falling Reactivity related negatively with 3-month-olds' emotional resonance measures. Higher abilities to recover from a state of distress were associated with less vocal distress (r(25) = -.40, p = .046), and with a longer delay of onset (r(25) = .44, p = .030). Three-month-old infants high on falling reactivity also tended to express less sadness, although this trend was marginally significant (r(25) = -.35, p = .083).

Fear as an index of inhibition, was not found to relate significantly with the contagious cry measures for any of the age groups included in the study.

Self-other discrimination

For the self-other discrimination task, the total amount of time subjects spent gazing to both stimuli was computed. Based on this score, we obtained the percentage of time subjects gazed to either the self or the other stimuli.

-Figure 3 -Discrimination between conditions, based on preferential looking, is indicated by a significantly greater proportion of gaze fixation time on the other condition [START_REF] Dannemiller | Detection of relative motion by human infants[END_REF] (Figure 3). For each age group, significance related to chance for both the self and the other conditions were analyzed via two-tailed t-tests. Three-month-old and 6-month-old participants did not manifest a greater proportion of fixation toward the other stimulus when compared to chance (50%): t(34) = .584, p >.05 and t(44) = .375, p >.05, respectively. For the 9-month-olds, the mean proportion of fixation toward the noncontingent other stimulus was found to be greater than chance (50%): t(44) = 8.59, p < .05.

Possible age and gender effects on fixation toward the other stimulus were explored by 3 x 2 ANOVA. Individual analyses suggest significant effects for age (F(2,121) = 10.213, p = .001), but not for gender (F(1,121) = .350, p = .555). Also, there were no significant interactions between age and gender (F(2,121) = .757, p = .471). Post-hoc Games-Howel tests for unequal variances show that 9month-olds manifested a significantly greater percentage of looking fixation for the other stimulus than both the 3-month-olds (mean difference = 18.931, p = .005) and the 6-month-olds (mean difference = 20.567, p = .001). The 6-month-olds' percentage of looking toward the other stimulus did not differ significantly from that of the 3-month-old infants (mean difference = -1.636, p = .962).

All participants who successfully completed both the emotional resonance task and self-other discrimination task were further included in the analysis. Simple linear correlations were performed for analyzing possible covariations between data sets (Table 3).

-Table 3 -We found significant relations between self-other discrimination, as a percentage of looking fixation towards the non-contingent other, and the parameters of contagious crying with the 9-monthold sample, but not for younger ages. Those 9-month-old participants with preferential looking toward the other, also manifested fewer cry vocalizations (r(35) = -.342, p < .05) and reduced anger (r(35) = -.366, p < .05) in response to the perception of another infant cry. Also, those 9-month-olds who gazed longer at the other condition tended towards a delayed first bout of cry (r(35) = .333, p = .051).

For the 6-month-old group there was a marginally significant relation. More specifically, those 6-month-olds looking longer towards the other stimulus also tended to express more sadness in response to the cry stimulus (r(34) = .301, p = .083).

Discussion

The present paper aimed to explore the relation between emotional resonance responses triggered by the perception of another's distress and the abilities to self-regulate and to differentiate self from others in infants 3-to 9-months of age. We bring evidence that young infants use regulatory strategies for modulating the emotional resonance response to another infant cry, and that self-other differentiation is related to low personal distress.

Previous studies have explored the relation between inhibition, attentional mechanisms of self-regulation, and infants' emotional arousal provoked by another person's distress, and have shown that 4-month-old regulatory abilities significantly predict later empathic distress (12-and 24-months) [START_REF] Ungerer | The early development of empathy: self-regulation and individual differences in the first year[END_REF][START_REF] Young | The relations between temperament and empathy in 2-year-olds[END_REF]. For the present study, we used an experimental paradigm known to trigger affect sharing in infants. With a carefully selected auditory stimulus (the pain cry of a 3-months-old infant), we have shown that the observed individual variability in infants' emotional reactions is concurrently related with self-regulation.

Different regulatory strategies were employed by infants, according to their age group. Threemonth-olds used more thumb sucking and this behavior proved successful in down-regulating their emotional resonance responses, leading to a less intense vocal distress, which had also a longer latency. This is in agreement with previous studies that documented the efficiency of thumb-sucking in regulating emotional reactivity in younger infants [START_REF] Campos | Emergent themes in the study of emotional development and emotion regulation[END_REF]Tronick, 1989).

Our findings are consistent across different but related measures of the emotional response.

Importantly, thumb-sucking was not found to be related at this age to infants' tendencies to respond with negative affect in everyday life situations. This further suggests that it is an independent index of regulation rather than a correlate of negative affect, as has been previously mentioned [START_REF] Ungerer | The early development of empathy: self-regulation and individual differences in the first year[END_REF].

A similar pattern of findings was obtained for the temperamental regulatory dimension of falling reactivity. It refers to the rate of recovery from peak distress, excitement or general arousal, and reflects the infant's ability to regulate his/her own state [START_REF] Gartstein | Studying infant temperament via a revision of the Infant Behavior Questionnaire[END_REF]. We found that 3month-old's better abilities to regulate peak emotional reactions is associated with reduced contagious crying in response to another infant sound of distress. This temperamental dimension might not represent a specific regulatory strategy, but more likely points to the use of some regulatory strategies, other than thumb-sucking, specific to this age group. This is because we found no significant relation between them (r = -.278, p > .05), although both were associated with decreased emotional resonance.

Duration of orientation indexes attentional abilities as important regulatory processes [START_REF] Emde | The first two months: Recent research in developmental psychobiology and the changing view of the newborn[END_REF][START_REF] Rothbart | Self-regulation and emotion in infancy[END_REF]. We found that this ability was efficient in regulating infants' emotional reactions to another's distress, and this relation was consistently significant only for the 6-month-old group. This is in line with data showing that from 6-to 9-months of age, duration of orientation decreases significantly [START_REF] Carranza | A longitudinal study of temperament in infancy: Stability and convergence of measures[END_REF], and that usually 6-montholds use more gaze aversion than both 12-and 18-month-old infants in a distressful social situation [START_REF] Mangelsdorf | Developmental and temperamental differences in emotion regulation in infancy[END_REF]. Similarly, [START_REF] Hay | Responses of six-month-olds to the distress of their peers[END_REF] have shown that 6-month-olds tend to become distressed by their peer's negative affect when there are fewer toys in the environment.

In our current study we assessed infant's attention orientation abilities in everyday life contexts which limits our understanding of the particular way these strategies are used when affect sharing reactions arise. However, the combined data from these separate studies, suggest that most likely, 6-month-olds disengage attention from the distress of their peer and reorient towards a distracting stimulus. In contrast, three-month-olds with higher levels of duration of orientation manifested more intense vocal distress in response to the cry sound. One possible explanation is that very young infants' attention is more exogenously driven by the stimulus properties, while they are not yet fully efficient in disengaging attention [START_REF] Hood | Adult's eyes trigger shifts of visual attention in human infants[END_REF]Johnson, Dziurawiec, Ellis, & Morton, 1991). In our particular case, the high salience of the negative stimulus might retain 3-month-olds' concentration of attention, while their incipient abilities for attentional shifting may not be sufficient for reorienting to another distracting and comforting stimulus.

We did not find any relationships between self-regulatory abilities and contagious crying in 9month-olds. There are several possible explanations. First, this age group manifested similar levels of distress to the perception of another infant pain cry with the 6-month-old group, which suggests that they also employ some regulatory strategies. Since for older infants there is a tendency toward specialization of certain regulation strategies for specific situations and stimuli [START_REF] Cicchetti | Contributions from the study of high-risk populations to understanding the development of emotion regulation[END_REF], and for specific emotions [START_REF] Buss | Fear and anger regulation in infancy: Effects on the temporal dynamic of affective expression[END_REF], they might not have been captured by the global measure based on parental report we used (IBQ-R). The observed measures of emotion-regulation (thumb-sucking and escape behavior) proved to be either specific for one age (i.e., thumb-sucking for 3-month-olds) or not associated with emotional reactivity (i.e., escaping behaviors).

More refined assessments of regulation that include psychophysiological recordings in addition to parental report and observational measures (see for example [START_REF] Hastings | Links among gender, inhibition, and parental socialization in the development of prosocial behavior[END_REF]) could be used in future research for an in-depth analysis of its relation with emotional resonance reactions.

Second, the relation between emotional reactivity and regulation might follow a more complex pattern than simple one way and unmediated causality [START_REF] Buss | Fear and anger regulation in infancy: Effects on the temporal dynamic of affective expression[END_REF]. This may be the case especially for older infants, where both emotional reactivity and regulation register an increase [START_REF] Gartstein | Studying infant temperament via a revision of the Infant Behavior Questionnaire[END_REF], and start to influence each other in determining the child's reactions to emotion inducing situations [START_REF] Eisenberg | Prediction of elementary school children's externalizing problem behaviors from attentional and behavioral regulation and negative emotionality[END_REF]. This line of explanation is also consistent with our findings for the 6-months-olds, where, although there was a significant down-regulatory effect from attentional mechanisms, the levels of emotional reactivity triggered by the perception of another infant pain cry were on certain dimensions higher than those for 3-month-olds. Also, as the pattern of social interactions becomes increasingly complex towards the end of the first year of life, other factors, like the parenting style, may start playing a role in how emotionality and regulatory mechanisms are related to affect sharing and empathic behaviours [START_REF] Hastings | Links among gender, inhibition, and parental socialization in the development of prosocial behavior[END_REF].

In general, the present study brings evidence for the relation between affect sharing and selfregulation abilities in infancy. Models of empathy [START_REF] Decety | The functional architecture of human empathy[END_REF][START_REF] Eisenberg | Empathy: Conceptualization, measurement, and relation to prosocial behavior[END_REF] stipulate that pure emotional contagion/sharing triggered by the perception of another distress must be controlled in order to afford emotions and behaviors that are prosocial in nature. Previous studies have shown that toddlers, preschoolers and school age children self-regulation is associated with reduced personal distress and increased prosocial behaviors [START_REF] Fabes | Behavioral and physiological correlates of children's reactions to others in distress[END_REF][START_REF] Fabes | The relations of children's emotion regulation to their vicarious emotional responses and comforting behaviors[END_REF][START_REF] Kochanska | Inhibitory control as a contributor to conscience in childhood: From toddler to early school age[END_REF][START_REF] Rothbart | Temperament and social behavior in childhood[END_REF][START_REF] Zahn-Waxler | Children's emotions and behaviors in response to infants' cries[END_REF][START_REF] Valiente | Prediction of children's empathy-related responding to their effortful control and parents' expressivity[END_REF][START_REF] Young | The relations between temperament and empathy in 2-year-olds[END_REF]. Our results add to the existent body of research by showing that even infants regulate the vicariously induced emotional reactions.

One important aspect of empathy is the minimal awareness that the shared emotional reaction is triggered by the observed affective state of another person [START_REF] Eisenberg | Emotion, regulation, and moral development[END_REF][START_REF] Hoffman | Empathy and Moral Development. Implications for Caring and Justice[END_REF][START_REF] De Vignemont | The empathic brain: how, when and why?[END_REF]. Our data suggests that already by the age of 9-months, there is a significant link between the developing sense of self and emotional resonance to another's distress. We found that 9-month-old infants, who manifest greater preference for perceiving another infant's body than their own, produce fewer cry vocalizations and fewer facial expression of anger in response to the cry of another infant. Also, they tended to have a longer latency to the onset of crying.

Self awareness is regarded as a top-down process that restricts the tendency to fully share the emotions of others [START_REF] Decety | The functional architecture of human empathy[END_REF], potentially explaining its positive relation with prosocial behavior [START_REF] Zahn-Waxler | Development of concern for others[END_REF] and its negative relation with affect sharing reactions like the emotional resonance in the present study. However, [START_REF] Zahn-Waxler | Development of concern for others[END_REF] did not find a significant relationship between self-awareness and sympathetic concern. Several explanations may account for these findings. First, parental reports were used to assess toddlers' sympathetic concern.

While prosocial behavior is easier to conceptualize and to observe, facial and vocal expressions of emotion can be easily missed or misinterpreted when not explicitly investigated. Second, the emotional reactions to the distress of another were assessed globally. We measured emotional resonance in infants 3-to 9-months of age by looking at different aspects of emotional expressivity (both facial and vocal). Although the relation with self-other awareness was consistent across some of these measures, it did not apply to all of them. Therefore, a more componential conceptualization of affective sharing response as a component of empathy is more informative than a global assessment, especially when investigating its relation with other processes.

Another important aspect refers to how different dimensions of self development such as the sense of self as agent (either social or physical); the self as a set of intermodal integrated sensorial information about own body; the representations of self based on external features (either of the face or of the legs) relate with other components of empathy, and emotional sharing in particular, during infancy. This is also because little is known regarding the relation between these dimensions of self development as facets of the same concept. The present study, along with the studies of [START_REF] Zahn-Waxler | Development of concern for others[END_REF] and [START_REF] Kärtner | Influences of contingent responsiveness on the development of self-recognition and empathy with 18 months[END_REF], show that both the sense of self as a set of intermodal integrated sensorial information about own body and the representation of self relate with empathic responses (emotional sharing and prosocial behavior).

We have shown that self-other awareness, as indexed by the manifested visual preference for the moving legs of another, is related to emotional sharing reactions in 9-month-old infants. This may be further involved in the elaboration of prosocial behavior as suggested by studies with older children.

Since self-other awareness related to reduced affect sharing only for the oldest infants in our study, while even 2-month-olds show some signs of discrimination between one's own body and others (Rochat & Striano, 1999a), it suggests that a certain level of maturity within this skill is required. It is difficult to infer how the findings in our study could predict further relations between affect sharing and a sense of self, as the relation between early forms of self-awareness that rely mostly on intermodal perception of one's own body, and the later more representational ones, is still only marginally understood [START_REF] Nielsen | Mirror self-recognition beyond the face[END_REF]. There seems, however, to be an agreement that increased self-awareness is related with affect sharing modulation. Importantly affect sharing experiences might influence the development of sense of self, as it has been proposed that it is within interpersonal exchanges that the infant acquires information about both self and the others [START_REF] Tomasello | Joint attention as social cognition[END_REF]. It could be therefore speculated that, by resonating to other's affect, infants learn about themselves as emotional agents.

The current cross-sectional design limits our interpretation regarding how different dimensions of infants' emotional resonance to another distress relate to the fully developed empathy. For example, [START_REF] Zahn-Waxler | Development of concern for others[END_REF] argued that sadness in response to another's distress is a sign of empathy, while anger is more a sign of self-distress. Our study shows that both crying and sadness relate to regulation and self-other awareness in a way consistent with their interpretation as precursors of empathy. However, the current data does not allow for such a rich interpretation. One possible solution could be to follow the same infants at different ages and investigate the predictive value of different dimensions of emotional resonance for later more mature forms of empathy.

Impairments in empathic abilities are specific for a series of mental disorders, including autistic spectrum disorders [START_REF] Decety | The empathic brain and its dysfunction in psychiatric populations: implications for intervention across different clinical conditions[END_REF]. By toddlerhood, atypical patterns of responses to another's distress are already evident in autistic individuals [START_REF] Charman | Infants with autism: an investigation of empathy, pretend play, joint attention, and imitation[END_REF]. A better understanding of the mechanisms underlying empathy development in infancy could prove crucial for early detection of autistic symptoms, and facilitate the application of specifically designed intervention programs (Roth-Hanania, Busch-Rossnagel, & Higgins-D'Alessandro, 2000).

Affect sharing, along with self-other awareness and regulation are processes particularly important for early development of empathy. We found important evidence that affective resonance to another's distress is modulated by emotion regulation mechanisms and self-awareness at different age points in infancy. Further studies that address the predictive nature of these early abilities to the later empathic responses and prosocial behaviors will be particularly important for validating them as early precursors of empathy development. Table 1 Means, standard deviations, and percentages of emotional resonance responses to the perception of the cry sound for each age group.

Tables

Figure 1 .

 1 Figure 1. Example of video output used for offline coding of preferential looking for self or other

Figure 2 .

 2 Figure 2. Emotional resonance responses (with SEs) during the presentation of the cry sound for 3-

Figure 3 .

 3 Figure 3. Mean percentage looking time (with SEs) towards "self" stimulus and "other" stimulus

  Note. % column refers to the percentage of children who manifested that behavior during the presentation of the cry stimulus. Percentages were not established for those variables that cannot be quantified in terms of frequency (i.e., intensity of cry vocalizations and latency to onset of cry).

			Social Development				Page 32 of 39
					Age groups
		3-months-olds	6-months-olds	9-months-olds
			(N=32)			(N=34)			(N=36)
		M	SD	%	M	SD	%	M	SD	%
	Cry vocalizations	24.62 29.98 59.38 43.04 34.78 76.47 38.03 29.20 77.77
	Mean intensity of cry	1.57	1.61	NA	2.41	1.80	NA	2.00	1.33	NA
	Latency to onset of
		19.81 11.40	NA	12.91 11.97	NA	12.64 10.87	NA
	cry
	Facial expression of
		32.63 32.40	84.37 41.52 37.47 73.53 37.58 29.95 77.78
	anger
	Facial expression of
		3.45	6.11	34.37 16.90 24.23	50.0	6.26	15.68 27.78
	sadness

Table 2

 2 Interrcorelations of measures of emotional resonance and temperament by age groupNote. 1 -Mean intensity of cry; 2 -Cry vocalizations; 3 -Latency to onset of cry; 4 -Facial expression of sadness; 5 -Facial expression of anger † p < .10; *p < .05; ** p < .01Correlations between time looking towards "other" stimulus and parameters of contagious crying for all age groupsNote. † p < .10 (2-tailed); *p < .05 (2-tailed); **p < .01 (2-tailed)

	Emotional resonance measures
	Age groups

Social Development

Social Development Social Development


Pierre Bénard

Forrester Cole

Aleksey Golovinskiy

Adam Finkelstein

Self-Similar Texture for Coherent Line Stylization

Keywords: Non-photorealistic rendering, line drawing, temporal coherence, artmap

Figure 1: Shapes drawn with stylized lines using self-similar textures. The bird (above) is a purely 2D figure, while lines are extracted from a 3D model of a horse (below). At different scales the lines appear qualitatively similar, and transitions exhibit temporal coherence.

Introduction

Stylization is an integral part of effective line rendering. Artists vary effects such as width, texture, and precision to convey weight, shape, motion, or abstraction. A dotted line might suggest an invisible object, while an oversketched contour might indicate emphasis or movement. A common approach for simulating these effects in computer graphics is to define a parameterized space curve (known here as a brush path), and apply a stroke texture along its length. Applied textures may include dots, dashes, or captured images of marks made with pen, pencil, or other natural media. Stroke textures create attractive imagery that can appear as though it was drawn by hand.

There are two simple policies for texture mapping a brush path with a stroke texture. The first approach, which we call the stretching policy, stretches or compresses the texture so that it fits along the path a fixed number of times. As the length of the path changes, the texture deforms to match. The second approach, called the tiling policy, establishes a fixed pixel length for the texture, and tiles the path with as many instances of the texture as can fit.

The two policies are appropriate in different cases. The tiling policy is necessary for textures that should not appear to stretch, such as dotted and dashed lines. Because the tiling policy does not stretch the texture, it is also usually preferred for still imagery. Under animation, however, the texture appears to slide on or off the ends of the path and be very distracting. In contrast, the stretching policy provides intuitive behavior under animation, but the stroke texture loses its character if the path is stretched or shrunk too far.

A third approach is the artmap method [START_REF] Klein | Nonphotorealistic virtual environments[END_REF]], which uses a set of N textures (an artmap), where each texture has a particular target length in pixels. At each frame, the texture with target length closest to the current path length is selected and drawn. This ensures that the brush texture never appears stretched by more than a constant factor (often 2×). Of course, if the path length extends beyond the length of the largest texture in the artmap, stretching artifacts will still appear. A more troublesome problem is that artmap construction is a time-consuming and painstaking process. As a result, current artmap implementations such as "Styles" in Google SketchUp [Google 2008] use as few as four textures.

This paper presents a new artmap-based approach called selfsimilar line artmaps (SLAMs). A SLAM is similar to a conventional artmaps, but has two additional properties: it is self-similar and smoothly varying. In this context, self-similarity implies that the same texture is repeated at two separate levels of the artmap, a property that allows for infinite zoom without visible interruption. The smooth variation property means that nearby levels of the artmap are similar in appearance, and ensures that animations using SLAMs are temporally coherent. This paper makes two technical contributions for creating and rendering with SLAMs. First, we present an example-based synthesis approach that creates an arbitrarily dense set of textures that satisfy the SLAM conditions. We note that parametric texture synthesis (e.g. [START_REF] Portilla | A parametric texture model based on joint statistics of complex wavelet coefficients[END_REF]) is superior to non-parametric synthesis for this purpose, because small changes in the synthesis seed tend to produce small changes in the output texture. Second, we present a method for parameterizing view-dependent 3D lines (such as contours and suggestive contours) for rendering with SLAMs. The method is simpler than the coherent line parameterization approach of [START_REF] Kalnins | Coherent stylized silhouettes[END_REF] because we explicitly target arc-length parameterization for the textures.

Related Work

In this section we describe work related to the two main technical contributions of this paper.

Self-similar textures. With the goal of stylizing shaded regions of NPR imagery (e.g., canvas, watercolor, hatching or painterly rendering), many texture-based approaches have been proposed to maintain a quasi-constant size of the texture pattern in screen-space. Both the artmaps approach proposed by [START_REF] Klein | Nonphotorealistic virtual environments[END_REF] and the subsequent "tonal art maps" of [START_REF] Praun | Real-time hatching[END_REF] rely on a specific set of mip-maps which offer coherence transitions between scales. Nevertheless, these methods can only handle a restricted range of zoom imposed by the depth of the mipmap, and exhibit noticeable blending artifacts when transitioning between levels. To address these limitations, the method of [START_REF] Cunzi | Dynamic canvas for immersive non-photorealistic walkthroughs[END_REF] introduces an infinite zoom mechanism which dynamically regenerates the pattern by alpha-blending multiple scaled versions of the original texture. Following this approach, Bénard et al. [2009a] dynamically compute a self-similar texture for each object, which is used as a base-layer for many styles. However, they subsequently demonstrate [Bénard et al. 2009b] that this general approach perceptually degrades high-contrast structured patterns -the very kind of stylization we would like to use for lines. To better preserve the original pattern, [START_REF] Han | Multiscale texture synthesis[END_REF] propose a 2D example-based non-parametric synthesis algorithm that generates new texture elements at multiple scales on the fly during the zoom. With their method, multiple scales of texture elements appear at every level of the zoom. Our approach also relies on texture synthesis, but uses the parametric method of [START_REF] Portilla | A parametric texture model based on joint statistics of complex wavelet coefficients[END_REF]. We precompute a continuous self-similar pyramid of textures, allowing for infinite continuous zoom while maintaining similar appearance to the original exemplar at every scale, as described in Section 3.

Coherent line stylization. Many researchers have focused their efforts on extraction and rendering of lines (see the annotated bibliography of [START_REF] Rusinkiewicz | Annotated bibliography: Published research on line drawings from 3D data[END_REF]). Nevertheless, temporal coherence for stylized lines remains a challenging problem. The state of the art system by [START_REF] Kalnins | Coherent stylized silhouettes[END_REF] built on the seminal work by [START_REF] Masuch | Animating frame-to-frame consistent line drawings for illustrative purposes[END_REF] and [START_REF] Bourdev | Rendering Nonphotorealistic Strokes with Temporal and Arc-Length Coherence[END_REF], generalizing their approaches to provide temporal coherence for stylized lines drawn over a broad class of computer graphics models. The three key ideas of the Kalnins et al. system were: (1) propagating the line parameterization from one frame to the next to provide temporal continuity, (2) splitting screen-space continuous paths into possibly multiple brush paths corresponding to the paths used in previous frames, and (3) optimizing an energy function that includes the competing goals of uniform screen-space arc-length parameterization, coherence on the object surface, and attempting to merge multiple paths where possible. The Kalnins et al. approach is somewhat complex and brittle, largely due to the combination of optimization and splitting and merging of paths. In this work we observe that some of this complexity may be omitted for the case of line styles explicitly targeting arc-length parameterization. Coupled with the use of the SLAM datastructure described above, our system need only to compute two numbers -scale and phase -for each path in order to fully parameterize it. This leads to a simpler optimization, described in Section 4.

L max

A(0.15,0.6,1.1) A(0.2,0.7,0.4) A(0.1,0.35,0.8) Horizontal distance corresponds to length in screen-space, vertical distance to scale. The shaded region is where A(u1, u2, l) is defined. Paths with scale l < 0.5 or l > 1.0 (dotted lines) are mapped to coordinates with 0.5 < l < 1.0 under the mapping function g (solid lines). Each level of the pyramid tiles seamlessly with itself, so long lines may safely be wrapped (e.g., solid red line).

A(0.3,1.2,0.55) g() g() l = 0.5 l = 0 u = 0 u = 1 l = 1

Self-Similar Line Art Maps

This section describes the construction of our self-similar line artmaps (SLAMs) and their relationship to conventional artmaps.

In the conventional artmap approach the number of textures required is O(log σ Lmax), where Lmax is the length of the longest path and σ is the maximum stretch factor allowed. Unfortunately, Lmax is effectively unbounded for several interesting cases, including continuous zoom. Our new artmap construction (Section 3.1) is self-similar, allowing a small number of textures to smoothly texture paths of arbitrary length.

When σ is large, visible pops may appear at transitions. Blending adjacent artmap levels reduces popping, but tends to produce a blurry result. The solution is to create a dense artmap, with many textures and a small σ. We propose an example-based artmap synthesis approach (Section 3.2) that generates an arbitrarily dense artmap based on a single exemplar. Our synthesis approach also guarantees that each artmap level blends seamlessly into the next.

We will describe the implementation first using 1D textures. The extension to stroke textures with width is discussed in Section 3.2.2.

SLAM Definition

A line artmap can be visualized as a pyramid, with base width Lmax and each level shrinking in size by a factor of σ. For convenience, define the artmap as a function A(u1, u2, l), where u1 and u2 are the left and right texture coordinates and l is the level in the artmap, normalized such that l = 1.0 corresponds to texture length Lmax. For example, A(0, 1, 0.5) corresponds to the entire texture with target length 0.5Lmax, and A(0.5, 1.0, 0.2) corresponds to the right half of the texture with target length 0.2Lmax. For concise notation, let A l = A(0, 1, l).

In order to support paths of arbitrary length with infinite zoom, the full artmap domain u1 ∈ R, u2 ∈ R, l ∈ R + must be mapped somehow onto a finite set of textures (Figure 2). To accommodate arbitrary u1 and u2, we assume that every texture in the artmap tiles seamlessly with itself. This leaves the problem of l > 1. The naive solution is to simply tile the path with the longest texture available (A1), but this policy has all the negative aspects of the tiling policy.

* = Seed Pyramid Exemplar Seed Generation Output Pyramid W source W f W f 0.5 W f + 0.5 [ W f W f ] [ W f W f ]
Our approach is to change the problem by placing an additional constraint on the artmap: it must be self-similar. Precisely, there must exist at least one pair of textures Ax and Ay such that Ax = [AyAy] (the concatenation of Ay with itself). If such a pair exists, then arbitrary stretching or shrinking can be handled by looping between the two similar textures. Figure 3 shows an example of such artmap for a dotted line. Note that the bottom texture is visually equivalent to a tiled version of the top texture. For simplicity, we will use x = 1.0 and y = 0.5. The mapping from the full domain to the self-similar domain is then defined by a mapping function g(u1, u2, l) ∈ R 3 :

g(u1, u2, l) = (2 t u1, 2 t u2, 2 -t l) t = log 2 l (1)
If the path to render has length s in pixels, the texture used is A(g(0, 1, κs/Lmax)), where κ is a user-defined scaling parameter. This parameterization may tile the texture, but will not cause the texture to slide on and off the path as it grows or shrinks.

L max /2 L max 0.5 1 l Figure 3:
Example SLAM for a dotted line texture. This set includes eight levels, but an arbitrary number may be generated. As the scale grows, the dots tend to stretch out. When they grow too large, they split into two smaller dots. Irregularly sized dots are necessary for temporal coherence; other small imperfections are the consequence of texture synthesis.

Artmap Synthesis by Example

Given the definition of a SLAM, the challenge is to construct one without a huge amount of manual effort. The two necessary conditions for a well-behaved SLAM are that A1.0 = [A0.5A0.5] (selfsimilarity), and that A l ≈ A l+ (smooth variation). A desirable third condition is that any texture extracted from the SLAM closely resembles the exemplar. Our synthesis approach satisfies the first two conditions and, for many types of textures, the third condition as well.

The basis of our approach is the parametric texture synthesis (PTS) method of [START_REF] Portilla | A parametric texture model based on joint statistics of complex wavelet coefficients[END_REF]. Each artmap texture A l is the result of PTS applied to a filtered white noise seed W l . We notice that the PTS method seems to have the vital property that small changes in the seed result in small changes in the output. We exploit this property by constructing a set of seeds W l that satisfy the SLAM conditions of self-similarity and smooth variation. Because of the continuous behavior of PTS, if the W l satisfy the SLAM conditions, then A l should also satisfy the conditions.

Using PTS, the quality of each individual A l is less than what might be achieved using a modern non-parametric synthesis method (e.g. [START_REF] Lefebvre | Appearance-space texture synthesis[END_REF]). However, non-parametric methods tend to lack the property that small changes in the synthesis seed produce small changes in the output texture. This property arises because parametric methods are based on iteratively adjusting statistics of a random noise seed, and each of these adjustments (e.g., histogram matching) is a continuous operation. By contrast, non-parametric methods are based on iterative neighborhood matching, which produces a chain of discrete decisions that can change drastically with small perturbations to the input.

Note, however, that we do not have a formal proof of this desirable behavior of PTS. In our experiments, PTS provides continuous behavior for a variety of textures, but there may still be cases for which PTS fails to create smooth variation.

Construction of Synthesis Seeds

The seeds W l are scaled and filtered versions of a fixed white noise texture Wsource, which has length Lmax. Ideally, all W l have perfect white noise statistics, but perfect white noise is not necessary as PTS will coerce the statistics to match the exemplar. We therefore only need to ensure that the W l satisfy the self-similarity and inria-00472673, version 3 -Jul 2011

(a) (closeup images) (b) (c) (c) (b) (a)
Figure 5: Zoom sequence on a 2D vector-art flower. Note that at every frame the screen-space size of the scribbles is well preserved and that no alpha-blending artifacts are noticeable. See especially the inset closeups of the upper left three flowers for continuity, and shown in motion (with dot pattern) on the accompanying video. smooth variation conditions, and have roughly white noise statistics. In practice, we start from a single filtered version of Wsource, and scale and linearly interpolate to produce each W l (Figure 4).

The original white noise texture Wsource is filtered with a small Gaussian filter (we use a width of 5 pixels) to produce a smoothed version W f . This smoothing is necessary to avoid aliasing when the seed is scaled. The smoothed seed W f is then adjusted using histogram matching to restore a uniform distribution across the range (0, 1). The top level of the seed pyramid W0.5 is simply W f scaled to half its original length. The bottom level of the pyramid is W1.0 = [W0.5W0.5], or the concatenation of W0.5 with itself. The interior levels of the pyramid are generated by scaling W0.5 and W1.0 to the proper length, then linearly interpolating:

W l = αW1.0 + (1 -α)W0.5 α = 2l -1 (2)
The seed pyramid satisfies the self-similarity condition by construction, since W1.0 is a tiled version of W0.5. The smooth variation condition is satisfied by the linear interpolation of the top and bottom of the pyramid.

Extension to 1.5D Textures

So far, we have considered only 1D textures in our description. However, all the results in this paper were generated with stroke textures with width between 8 and 32 pixels. We call these brush textures 1.5D, since they are essentially 1D textures with a finite width. A few modifications to the synthesis algorithm are necessary to accommodate 1.5D textures.

The construction of the seed pyramid is similar to the 1D case.

Wsource becomes a d × Lmax white noise texture, where d is the number of rows. The initial filtering operation from Wsource to W f is only performed in 1D (the horizontal direction in Figure 4), because W f is only scaled in one dimension. The remaining operations to produce the seed pyramid are identical to the 1D case.

The largest changes are required in the texture synthesis, because our 1.5D stroke textures violate the stationarity assumption of the PTS method. More specifically, the statistics of each row of a 1.5D texture are not identical: the top and bottom rows are usually dark (transparent), while the middle rows are usually bright (solid). Our approach is to apply different statistics to each row of the texture. While the PTS method stores and applies many different statistics of the source texture, through experimentation we found that varying only the mean and variance by row sufficed to produce good results. We therefore modify the PTS method to gather and apply the mean and variance per-row, and all other statistics per-texture. This modification is only a few lines of MATLAB code.

As illustrated by Figure 1 (top row) and Figure 5, applying 1.5D SLAMs to 2D vector-art animations ensures a strong temporal coherence of the stylization, while preserving the 2D characteristics of the stroke textures. Note in particular the quasi-constant size of the scribbles at each zoom level, and the absence of blending artifacts. This approach can also be used for fixed 3D segments, such as the edges of a cube (see the accompanying video for an example in motion).

Coherent Line Parameterization

Applying Self-Similar Lines Artmaps to complex curved pathsrepresented as a list of segments -requires the definition of a parameterization T . The most straightforward choice for T is the screen-space arclength of the path s. However, for any viewdependent feature lines (silhouettes, suggestive contours, apparent ridges, etc.) this approach produces "swimming" artifacts, as no temporal coherence is ensured from one frame to the next.

To solve this problem, we propose a simple three step screen-space parameterization scheme, which finds the parameters (ρ, φ) such that T (s) = ρs + φ best fits the parameterization of the previous frame. Section 4.1 describes how we propagate the parameterization from frame f to f + 1 using splatting. Section 4.2 and 4.3 detail how these parameters are updated and combined with SLAMs to render strokes. Figure 6 gives an overview of the whole process.

Propagating Parameters

The first step is to propagate the parameterization of all the paths at frame f to the next frame f + 1. At frame f we evenly sample each visible path in screen-space at a user-defined sampling rate δ. Each sample is parameterized by its 2D arclength si and the current parameters of the path (ρ, φ).

Observing that view-dependent lines are moving in a rather smooth and continuous way in screen-space, the key idea of our approach is to extend the size of each sample and splat its corresponding parameterization into a screen-space buffer (the parameterization buffer).

View-dependent lines at frame f + 1 can thus look up their closest correspondent at frame f , and the contributions of overlapping paths are added, tending to unify their parameterization. If the paths shift too far between frame f and f + 1 the lookup will fail, but coherence of the stylization may be unnecessary or even undesirable in that case. : Three steps pipeline for coherent line parameterization. At frame f , the parameterization of all the visible brush paths is splatted into a screen-space buffer. At frame f +1, this buffer is read back, and parameterization votes are recorded for each path. The new scale factor s and phase φ that best fit these votes are robustly estimated using RANSAC. Finally, paths are rendered according to this parameterization, choosing the appropriate level in a pre-computed SLAM. The sample parameterization ti = ρsi + φ is written as a textured sprite of radius δ in a floating point off-screen buffer (inset left).

Each location p at a distance d from the center si of the sprite determines a weight for the splatted parameterization ti by:

wi = clamp(1 - d δ , 0, 1)
We keep track of the weight by splatting wi in another color channel. Thus, at the end of this step, each pixel of the buffer covered by j overlapping samples contains ( P j wjtj, P j wj). Note that by design this weighting scheme corresponds to the exact linear interpolation of the parameterization along the spine of the line, if no paths overlap. The weight of the splat can be varied with the partial visibility [START_REF] Cole | Two fast methods for high-quality line visibility[END_REF] of the sample, or the z-depth of the sample at that point.

Unlike that of [START_REF] Kalnins | Coherent stylized silhouettes[END_REF], our method does not rely on an ID image (item buffer). The item buffer approach can introduce aliasing artifacts, and requires a local neighborhood search for each sample. Our splatting approach avoids this search, and also allows the additional control of varying the sprite size to trade-off coherence of parameterization against parameterization overlap. Increasing the size of the sprite makes it less likely that a path will move outside the sprite radius in a single frame, but increases the chance that separate lines will interfere with each other.

Updating Parameters

At frame f + 1, we uniformly sample the new visible brush paths in screen-space and reproject each sample to the previous frame's parameterization buffer, using the camera from frame f . If P j wj is defined at this pixel location, we record a vote:

v k = " P j wjtj P j wj , s k « (3)
which is a pair of values that associates the averaged parameterization at screen-space location j in frame f with the current arclength parameter s k of this sample.

For each path, we compute the scale factor ρ and the phase φ that best fit the votes in the least-square sense. As the input votes can be very noisy when paths overlap, we use the RANSAC algorithm [START_REF] Fischler | Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography[END_REF] to robustly estimate these two parameters. This iterative method allows a trade-off between speed and accuracy: the user estimates the proportion of outlying votes (refined according to data during the computation) and a target probability for inlying votes, which control the number of required iterations.

If fewer than two votes have been recorded for a path, we parameterize the path by T (s) = s/L where L is the path length, such that T ranges in [0, 1]. The same default parameterization is used to initialize the first frame rendering.

Note that this approach is similar in spirit to the mixed policy described in [START_REF] Bourdev | Rendering Nonphotorealistic Strokes with Temporal and Arc-Length Coherence[END_REF]] and used by [START_REF] Kalnins | WYSIWYG NPR: drawing strokes directly on 3D models[END_REF]. As this policy mixes information from multiple paths, popping can occur when two paths merge. Our method shares this limitation, however the robust fitting operation reduces sensitivity to outlying votes, allowing paths to quickly find a common parameterization. We thus avoid the fragmentation problem encountered by [START_REF] Kalnins | Coherent stylized silhouettes[END_REF]].

Stroke Rendering

In the last stage, we use the path parameters to determine the appropriate SLAM level l and render the final textured stroke. To ensure that paths moving off-screen remain at the same level in the SLAM, we define l as a function of the scaling factor ρ. Unlike the length of the path, ρ does not change as the path is clipped. Taking into account the self-similarity of the SLAM, the formula is:

d = ρkLmax l = 8 < : ω/d if d > 2 1/d if d ∈ [1, 2] 1/(dΩ) if d < 1 ˛∈ [0.5, 1] with: ω = 2 log 2 (1/d) and Ω = 2/d
where Lmax is the length of the longest texture in the SLAM and k is a user-defined scaling factor. When looping from one end of the truncated pyramid to the other, the path parameterization T has to be scaled by 1/ω and Ω respectively.

A SLAM can be simply represented as a 3D texture, allowing us to make use of trilinear filtering on the GPU. We assign 3D texture coordinates to each segment according to the path parameterization and SLAM level (w = 2l -1).

Exemplar Synthesized Result

Figure 7: Texture synthesis results. The method of [START_REF] Portilla | A parametric texture model based on joint statistics of complex wavelet coefficients[END_REF]] produces good results for many types of brush textures, especially small or simple textures (top half). More complex textures (bottom half) are reproduced credibly, but have imperfections in detail. Other approaches to SLAM generation may be possible to improve the results further (Section 6.1).

Results

Our SLAM construction process leverages the texture synthesis code of [START_REF] Portilla | A parametric texture model based on joint statistics of complex wavelet coefficients[END_REF], and our implementation is available for download. 1 Results for several different brush textures are shown in Figure 7. For simple textures, the PST algorithm produces results almost indistinguishable from the exemplar. For more complex textures such as the scribble and the jumbled lines (bottom of Figure 7) the overall impression of the synthesized result is similar, but some details are lost. High quality SLAMs are composed of 17 gray-scale images of 1024 × 32 pixels (100 to 300 KB in PNG). Synthesis typically takes a few minutes.

We implemented the entire coherent line parameterization method on the CPU without fine optimizations. We use the segment atlas data-structure describe in [START_REF] Cole | Two fast methods for high-quality line visibility[END_REF] to compute the visibility of the paths and perform the final rendering of the strokes on the GPU. Nevertheless, our approach could be used with any system that renders lines as textured quads, such as [START_REF] Mcguire | Hardware-determined feature edges[END_REF][START_REF] Kalnins | WYSIWYG NPR: drawing strokes directly on 3D models[END_REF][START_REF] Isenberg | Stylizing silhouettes at interactive rates: From silhouette edges to silhouette strokes[END_REF][START_REF] Markosian | Real-time nonphotorealistic rendering[END_REF]. Our system runs at interactive framerates for scenes of moderate complexity on a commodity PC with an Intel Core 2 Duo 2.4GHz CPU and 4 GB RAM. The bottleneck of our approach is the RANSAC algorithm, which varies in performance depending on the number of visible segments and the number of outliers. However, this algorithm is intrinsically parallel since the parameterization of each path can be fitted independently.

Our system uses OpenMP to accelerate this step on the CPU. Although we currently do not have a GPU implementation of this algorithm, we believe it should be practical and would significantly improve performance for complex models.

Figure 8 illustrates the wide variety of styles which can be achieved applying different SLAMs on lines extracted from 3D models. Note that creating new styles only requiers to synthesis new SLAMs by example. We refer the reader to the accompanying video to appreciate the temporal coherence of this stylization during the animation. Even if some popping is noticeable when brush paths merge, our simple parameterization scheme in conjunction with SLAMs provides a convincing screen-space behavior for most textured lines.

1 http://www.cs.princeton.edu/gfx/proj/dpix/

Conclusion

Self-similar line artmaps help address one of the principal challenges in stylized rendering: how to animate strokes with strong textures such as dots, scribbles, or brush marks. While SLAMs are a special case of conventional artmaps, we believe that the additional conditions of self-similarity and smooth variation extend the usefulness of SLAM textures to areas where artmaps have not seen much popularity, such as 2D animation and rendering of smooth 3D models.

The two additional conditions make an automatic method for SLAM creation more important than for conventional artmaps, since self-similarity cannot be easily obtained by just progressively simplifying a texture. Our texture synthesis scheme creates selfsimilar artmaps of arbitrary density, and produces good results for a range of texture types.

Our parameterization approach for rendering smooth 3D models with SLAM textures is similar in spirit to [START_REF] Kalnins | Coherent stylized silhouettes[END_REF]], but includes several simplifications and improvements. It handles partial visibility, which has been shown to be important for temporal coherence [START_REF] Cole | Two fast methods for high-quality line visibility[END_REF]. Since we only consider SLAM textures, we do not require a complex, piece-wise fitting scheme.

Limitations and Future Work

Our system does not satisfactorily handle several types of applications that we hope to address in future work.

We believe the quality of our synthesized textures is more than sufficient for many styles of rendering, but the quality is not perfect. As shown in Figure 7, complex textures may not be reproduced faithfully. Conventional non-parametric synthesis does not satisfy the condition of smooth variation (Section 3.1), but texture advection techniques [START_REF] Kwatra | Texture optimization for example-based synthesis[END_REF][START_REF] Bousseau | Video watercolorization using bidirectional texture advection[END_REF]] may provide an alternative for synthesis. In our experiments, however, the animation of the PTS textures was more visually appealing than basic advection. We believe a more promising route to higher-quality is to use the synthesized textures themselves as seeds for a final rendering pass using procedural strokes. For example, our synthesized dotted line texture could be used as a guide for the size and placement of particle sprites.

While our parameterization method for 3D models provides a good trade-off between performance and implementation complexity, the general problem of temporally coherent line parameterization remains unsolved. In particular, neither our method nor previous work (e.g. [START_REF] Kalnins | Coherent stylized silhouettes[END_REF]) works well for complex models with many overlapping lines. Satisfactory results for complex models will likely require a new approach that does not rely solely on a screen-space buffer to propagate parameterization from frame to frame.

Figure 2 :

 2 Figure 2: Parameterization space of a self-similar line artmap.Horizontal distance corresponds to length in screen-space, vertical distance to scale. The shaded region is where A(u1, u2, l) is defined. Paths with scale l < 0.5 or l > 1.0 (dotted lines) are mapped to coordinates with 0.5 < l < 1.0 under the mapping function g (solid lines). Each level of the pyramid tiles seamlessly with itself, so long lines may safely be wrapped (e.g., solid red line).

Figure 4 :

 4 Figure4: Synthesis of a self-similar line artmap. An initial white noise seed Wsource is slightly filtered to produce a filtered seed W f . The filtered seed W f is scaled to half its original length and placed at the top of the seed pyramid. The scaled W f is concatenated with itself and placed at the bottom of the pyramid. Interior levels of the pyramid are created by linearly interpolating the top and bottom. Finally, each seed is used to synthesize the corresponding level of the artmap pyramid.

  Figure6: Three steps pipeline for coherent line parameterization. At frame f , the parameterization of all the visible brush paths is splatted into a screen-space buffer. At frame f +1, this buffer is read back, and parameterization votes are recorded for each path. The new scale factor s and phase φ that best fit these votes are robustly estimated using RANSAC. Finally, paths are rendered according to this parameterization, choosing the appropriate level in a pre-computed SLAM.

Figure 8 :

 8 Figure 8: Various styles obtained by applying SLAMs on lines extracted from 3D models. The bottom row shows the line texture of one level of the associated SLAM.

Acknowledgements

Thanks to Georges Winkenbach and the stylization team at Google SketchUp for helpful discussions. This work was sponsored in part by Adobe, Google, and the ExploraDoc program of the region Rhône-Alpes. Many of the images shown in this paper are rendered from 3D models courtesy of Georgia Tech, Viewpoint, Aim@Shape, and the Google 3D Warehouse.