Fuzzy Similarity of Facial Expressions of Embodied Agents
Contents
1. Fig 7 Examples of expressions a disappointment and b disappointment masked by a happiness 6 Conclusion In this paper we have presented how fuzzy similarity can be used to compare facial expressions of an embodied agent In our approach any facial expression is described by a set of fuzzy sets Using our algorithm we are able to compare expressions i e the vague and imprecise objects described by certain labels The main advantage of this approach is that slightly different facial displays can be described by one significant label Then using fuzzy similarity we compare these imprecise definitions and establish the degrees of similarity between them We are unaware of any other applications of the fuzzy similarity for the purpose of comparing facial expressions We have also conducted a test to measure the perception of similarity between facial expressions We checked if the perception of similarity between computer generated facial expressions is consistent with the values that are obtained with Fuzzy Similarity of Facial Expressions of Embodied Agents 97 our algorithm The results of the test showed that the algorithm based on the fuzzy similarity meets our expectations Finally we have also presented an ap plication of our algorithm for generating facial expressions It is important to stress that in a more realistic model of similarity one should take into consideration also the probability of occurrence of certa2. all facial displays that belong to one category like happiness anger or embarrassment have some common features Therefore any category can be defined by a set of fuzzy sets that corresponds to these features Our approach follows the results from the psychological theory and experi ments It is based on the discrete emotion approach represented among others by Paul Ekman 7 10 According to this theory there is only a discrete number of expressions that can be universally recognized by humans Ekman focuses his research on the six facial expressions mentioned above We decided not to restrict ourselves to this small set Thus our algorithm of similarity should work properly with any facial expression as for example those described in 13 18 19 Thus we aim at building an algorithm that is coherent with the discrete emotion approach and with the results of the experiments about the perception of facial expressions works for any facial expression preserves the fuzziness of the concept of facial expression preserves the different degrees of similarity between facial expressions The remaining part of this paper is structured as follows In next section we present some theoretical aspects of comparing facial expressions In section 3 we present our algorithm and in section 4 the evaluation study The section B is entirely dedicated to the applications of our algorithm Finally conclusi
3. S defined by M AN B S A B _ 1 where A and B are two fuzzy sets ua is membership function of A and M is the fuzzy measure on 2 M A J pa e de 2 This choice was made mainly because of practical consequences This concrete measure is easy to implement and the process of computation is relatively simple As aresult we obtain the value of comparison x 0 1 for each pair of attributes Following the approach proposed in we use Ordered Weighted Averaging OWA operator to aggregate all values x1 xXn The OWA hy 0 1 0 1 is defined as hw 5 wibi 3 i 1 where b be i th biggest value between x1 Xn and W w1 Wn is a set of weights with w 0 1 and such that X w 1 23 Finally we use trape zoid fuzzy sets in order to describe the features of facial expressions as shown in Figure 1 This shape renders the experimental results about perception of facial expressions 2 27 On the other hand it is characterised by computational facility Fuzzy Similarity of Facial Expressions of Embodied Agents 89 3 Similarity of Facial Expressions in an Embodied Conversational Agent In order to implement and test our algorithm we used an existing ECA archi tecture called Greta 4 Facial expressions of Greta are described in terms of facial animation parameters FAPs 21 Originally Greta did not offer fuzzy definitions of facial expressions The static expressions u
4. and the values of fuzzy similarity FS see section B are in the interval 0 1 Let the vector a contains the values of our fuzzy similarity FS such that a FS A B and let the vector b be such that bj y p First of all we measured the correlation between a and b The overall value of correlation r is 0 89 The average similarity index yag i e subjects answers is more or less proportional to the fuzzy similarity values see Figure 5 The higher the index value is the higher the fuzzy similarity value is as well On the other hand certain pairs were evaluated significantly higher by the participants than by the fuzzy similarity For this reason we measured also the discrepancy between values b and a The mean difference between b and a gt b ai 7 n YAB is 0 09 At the same time the standard deviation of the difference a and b is 0 15 Finally the average value of yap is 0 35 4 4 Discussion The aim of our experiment was to verify if the degrees of the similarity of com puter generated facial expressions established by our algorithm are consistent with human perception of this phenomenon Firstly we compared the weighted average of the subjects answers with the values of our algorithm We found that the human s answers and our algorithm results are positively correlated and that the correlation coefficient is high 0 89 Also other results show that the human percepti
5. of contempt or of disappointment we look to which expression of the six elements set mentioned above it is the most similar to and we use the associated rule Thus masked Fig 6 The partition of the face 96 R Niewiadomski and C Pelachaud inhibited or fake facial expressions of two similar facial expressions are created using the same rules Figure presents the agent displaying the expression of disappointment masked by a fake happiness Our rules describe the expression of masked sad ness but they do not define masked disappointment We applied algorithm fuzzy similarity and found that disappointment has a facial expression very similar to sadness According to Ekman the features of felt sadness that leak over the masking expression are forehead brows and upper eyelids In our model these elements of expression are represented by the facial areas F forehead and brows and F upper eyelids As a consequence they can be observed in masked sad ness On the other hand the expression of disappointment Figure 7h is very similar according to the algorithm described in section 3 to the expression of sadness and so the rules of sadness will be applied also in the case of disappoint ment expression Indeed in the expression of disappointment masked by fake joy Figure b we can notice the movement of brows which is characteristic of disap pointment On the other hand the mouth area displays a smile sign of happiness
6. 2005 IST 5 References 1 Albrecht I Schroder M Haber J Seidel H Mixed feelings expression of non basic emotions in a muscle based talking head Virtual Reality 8 4 201 212 2005 2 Bartneck C Reichenbach J Subtle emotional expressions of synthetic characters International Journal Human Computer Studies 62 2 179 192 2005 3 Bassili J N Emotion recognition the role of facial movement and the relative importance of upper and lower areas of the face Journal of Personality and Social Psychology 37 11 2049 2058 1979 4 Bevacqua E Mancini M Niewiadomski R Pelachaud C An expressive ECA showing complex emotions In Proceedings of the AISB Annual Convention New castle UK pp 208 216 2007 5 Bouchon Meunier B Rifqi M Bothorel S Towards general measures of com parison of objects Fuzzy sets and systems 84 2 143 153 1996 6 Constantini E Pianesi F Prete M Recognizing Emotions in Human and Syn thetic Faces The Role of the Upper and Lower Parts of the Face In Proceedings of the 10th International Conference on Intelligent User Interfaces San Diego California USA January 10 13 pp 20 27 2005 7 Ekman P The Face Revealed Weidenfeld amp Nicolson London 2003 8 Ekman P Darwin deception and facial expression Ann N Y Acad Sci 1000 205 221 2003 98 10 11 12 13 14 15 16 17 18 19 20 21 22 23
7. 24 20 26 Die R Niewiadomski and C Pelachaud Ekman P Friesen W V The Repertoire of Nonverbal Behavior s Categories Origins Usage and Coding Semiotica 1 49 98 1969 Ekman P Friesen W V Unmasking the Face A guide to recognizing emotions from facial clues Prentice Hall Inc Englewood Cliffs New Jersey 1975 Etcoff N Magee J Categorical perception of facial expressions Cognition 44 3 227 240 1992 Frank M G Ekman P Friesen W V Behavioral Markers and Recognizability of the Smile of Enjoyment In Ekman P Rosenberg E L eds What the Face Reveals Basic and Applied Studies of Spontaneous Expression Using the Facial Action Coding System FACS Oxford University Press Oxford 1995 Gonzaga G C Keltner D Londahl E A Smith M D Love and commitment problem in romantic relation and friendship Journal of Personality and Social Psychology 81 2 247 262 2001 Gosselin P Kirouac G Dor F Y Components and Recognition of Facial Ex pression in the Communication of Emotion by Actors In Ekman P Rosenberg E L eds What the Face Reveals Basic and Applied Studies of Spontaneous Expression Using the Facial Action Coding System FACS pp 243 267 Oxford University Press Oxford 1995 Haidt J Keltner D Culture and facial expression Open ended methods find more expressions and a gradient of recognition Cognition and Emotion 13 3 225 266 1999 Izard C E
8. 5 persons did not specify their gender 4 3 Results The total number of answers was 2760 First of all we found that different labels were used by subjects with different frequency The first label 1 Not at all that corresponds to the lowest degree of similarity occurred in nearly half of all answers 46 Other labels occurred from 10 to 16 of all responses In order to interpret the subjects answers we compared them with the values returned by our algorithm For this purpose we changed the responses given by the subjects into numeric values Then we compared them with the values of fuzzy similarity We translated a discrete set of answers given by participants to one value in the interval 0 1 We assumed that labels are evenly placed along this interval and for each degree of similarity we associated a weight More formally for the purpose of measuring the answers of participants we introduced the average similarity index Let A B be a pair of expressions in which A is the reference and B is the compared object Then u is the number of answers using a given label i e uy corresponds to the label 1 Not at all and us to the 5 Equal The average similarity index yAB is Fuzzy Similarity of Facial Expressions of Embodied Agents 93 5 5 gt wins w dui 6 w5 wy dui where w t is the weight that corresponds to u Let us notice that the values of yap
9. Fuzzy Similarity of Facial Expressions of Embodied Agents Radostaw Niewiadomski and Catherine Pelachaud IUT de Monreuil Universit Paris 8 France niewiadomski pelachaud iut univ paris8 fr Abstract In this paper we propose an algorithm based on fuzzy similar ity which models the concept of resemblance between facial expressions of an Embodied Conversational Agent ECA The algorithm measures the degree of visual resemblance between any two facial expressions We also present an evaluation study in which we compared the users percep tion of similarity of facial expressions Finally we describe an application of this algorithm to generate complex facial expressions of an ECA Keywords Embodied Conversational Agents facial expressions fuzzy similarity 1 Introduction The mystery of the human face inspired artists and psychologists for centuries Recently it has become also an object of interest of computer scientists Em bodied conversational agents ECAs programs that focus on multimodal communication between humans and machines display facial expressions to communicate In this paper we focus on modelling the concept of similarity be tween any two facial expressions of emotion of an ECA Despite facial expressions are complex objects it is quite natural and easy for human beings to decide if any two facial expressions are similar or not Our aim is to build an algorithm that simulates this human s skill Establis
10. Human emotion Plenum Press New York 1977 Katsyri J Klucharev V Frydrych M Sams M Identification of synthetic and natural emotional facial expressions In ISCA Tutorial and Research Workshop on Audio Visual Speech Processing AVSP 03 St Jorioz France pp 239 244 2003 Keltner D Signs of appeasement Evidence for the distinct displays of embarrass ment amusement and shame Journal of Personality and Social Psychology 68 441 454 1992 Matsumoto D More evidence for the universality of a contempt expression Mo tivation and Emotion 16 4 363 368 1992 Niewiadomski R A model of complex facial expressions in interpersonal relations for animated agents Ph D thesis University of Perugia 2007 Ostermann J Face Animation in MPEG 4 In Pandzic I S Forchheimer R eds MPEG 4 Facial Animation The Standard Implementation and Applica tions pp 17 55 Wiley England 2002 Poggi I Interacting bodies and interacting minds In 2nd lInternational Society for Gesture Studies ISGS Conference Interacting Bodies Lyon pp 15 18 2005 Rifqi M Mesures de comparaison typicalit et classification d objets flous th orie et pratique Ph D Thesis 1996 Scozzafava R Vantaggi B eds Fuzzy Relations in a Coherent Conditional Probability Setting 7th International Conference on Information and Management Sciences IMS Chengdu China pp 496 500 2006 Teknomo K Similarity Measurement tut
11. ach object or feature that does not have a precise definition can be described by a fuzzy set Fuzzy similarity allows for the comparison of any two fuzzy sets It takes into consideration the various features of objects that characterise them at least partly Various measures have been proposed to compare any two fuzzy sets 5 For the purpose of comparing computer generated facial expressions we de cided to use fuzzy similarity It allows us to define attributes of an object by fuzzy sets instead of using precise values On the other hand according to many researchers e g LO 16 each distinct and labelled expression of emotion like expression of anger or expression of contempt is rather a class or a set of different but similar configurations of facial muscles actions or a set of differ ent facial displays Indeed there is not one precise smile or a frown Each smile is a little bit different but all smiles have some characteristics in common The boundary between smiling and not smiling is also imprecise Different facial displays of different intensities are classified as smiles Indeed in many exper iments e g 2 11 different facial displays involving the same group of muscle contractions were described by subjects with the same label so an expression of an emotion e g expression of anger is not a precise concept It has an im precise fuzzy definition see also 26 On the other hand
12. d of felt emotions inhibited masking the expression of emotion with the neutral expression suppressed de intensifying the expres sion of an emotion or exaggerated intensifying the expression of an emotion see for detailed discussion We called complex facial expressions expres sions that are combinations of several facial displays It was shown that humans can distinguish the expression of felt emotion from the expression of fake emo tion or from a masked one 9 12 14J22 In fake expressions some elements of the Fuzzy Similarity of Facial Expressions of Embodied Agents 95 original expression are missing 10 while certain elements of expression of the felt emotion can be still visible even if that expression is masked or inhibited 8 We proposed a model to generate complex facial expressions e g fake ex pression of anger or expression of sadness masked by joy on the basis of simple expressions e g sadness joy This model of complex facial expressions is based on Ekman s results We model complex facial expressions using a face partitioning approach The face is divided in eight facial areas F i 1 8 i e Fi brows F upper eyelids F3 eyes Fy lower eyelids F s cheeks Fg nose F7 lips movement Fs lips tension see Figure 6 Each facial expression is a composition of these facial areas each of which can display signs of emotion For complex facial expressions different emotions as in an
13. expression masked another one can be expressed on different areas of the face in the example of sadness masked by anger anger is shown on the eyebrows area while sadness is displayed on the mouth area In our model complex facial expressions involving one or more emotions are composed of the facial areas of the input expressions using a set of rules Our model can be used to generate different displays for the facial expressions of masking as well as fake and inhibited expressions These complex facial expressions involving the six emotions anger disgust fear joy sadness and surprise are described in the literature 7 10 For each type of expression we have defined a set of fuzzy rules that describes its characteristic features in terms of facial areas To each emotion corresponds a rule Thus we have defined six rules for each type of complex facial expression In case an input expression for which the deceptive facial expression is not defined explicitly by our rules e g expressions of contempt or disappointment our fuzzy similarity based algorithm presented in the previous sections is used in order to establish the degree of similarity between the input expression and the expressions whose complex facial expressions are described by our rules Once the most similar expression chosen among the 6 ones is known we can apply the corresponding rules to our input expression For example when we want to compute the complex facial expression
14. expressions we want to compare Thus we want to establish fuzzy similarity between two static expressions Exp E and Exp E Each Exp E is associated with a number of fuzzy sets such that all plausible facial displays 90 R Niewiadomski and C Pelachaud 0 not similar 1 equal Fig 2 Fuzzy similarity of facial expressions of Greta agent a b c Fig 3 The example of comparing facial expressions in the sense of muscle contractions for the emotion E are defined That is for each parameter k of an expression of E there is a fuzzy set FAP that specifies its range of plausible values Then the value of fuzzy similarity for each param eter of Exp E and Exp E is established The M measure of resemblance S is used to find these similarity values Finally in the third step all values are combined by means of the aggregation operator h 3 Let us compare the three facial expressions shown in Figure The values of similarity between them are S A B 0 6 and S B C 0 4 That is the expression A is more similar to B than C is to B In Figure Bh the lips are extended with greater intensity than in Figure Bb When comparing Figure Bb and Figure 3k the eye aperture in Figure Bb is more closed than in Figure Bp Moreover in these two images the eyebrows have different shapes This explains why the similarity between B and C is less than between A and B The areas of the facial expressions that vary among the th
15. hing the degree of similarity between facial expressions can be very useful for an ECA designer Often the knowledge about facial expressions is restricted only to some particular cases Despite the evidence that many facial expressions exist most of researchers e g 3 10 11 limit their research only to six of them namely anger disgust fear joy sadness and surprise Other facial expressions were rarely studied and as consequence they are difficult to model We used the algorithm presented in this paper to model different types of facial expressions like fake or inhibited expressions for the expressions like embarrassment disappointment or contempt see section Generally similarity is very difficult to measure It is a quantity that reflects the strength of relationship between two objects The similarity between two objects is measured by comparing their attributes Two cars are similar if both have the same number of doors are about 4 meters long and both are red C Pelachaud et al Eds IVA 2007 LNAI 4722 pp 86498 2007 Springer Verlag Berlin Heidelberg 2007 Fuzzy Similarity of Facial Expressions of Embodied Agents 87 Traditionally the similarity between two objects is expressed through a distance function In this geometrical tradition two objects are similar if the distance between them is small 25 On the other hand fuzzy similarity 5 is used to work with objects characterised by loose description E
16. in values for a FAP It means that even if a fuzzy set defines plausible values for a certain expression it does not mean that all these values occur with the same frequency The similarity between two objects has to take into account the probability of occurrence of the values from the given interval see 24 to avoid for instance that two attributes become similar because of similar values but that occur very seldom Unfortunately we do not have the data of this type for facial expressions In this situation we assumed that all values are equi probable In the future we aim to create fuzzy definitions of facial expressions based on empirical data Consequently the shapes of the fuzzy sets that describe the features of facial expression will be uniquely defined for each expression see 26 All parts of the face are considered as equi important in our similarity algorithm at current stage of development However it is known that each face areas of the face can have a different role in the perception of emotion 3 6 We want to test if it is also the case for the perception of similarity Acknowledgement We are very grateful to Giulianella Coletti and to Andrea Capotorti for their help on fuzzy methods We also thank Elisabetta Bevacqua and Maurizio Mancini for implementing the Greta system Part of this research is supported by the EU FP6 Network of Excellence HUMAINE IST 2002 2 3 1 6 and by the EU FP6 Integrated Project Callas FP6
17. l expressions follows the same setting each image presents one facial expression of Greta only the face is visible in the image the face is directed at the observer a black background was used Each image was saved in jpeg format An example of the image is presented in Figure 4 In the experiment we used 22 different facial expressions Each expression is defined by a different combination of FAP parameters and by their values The expressions are created according to the descriptions presented in the literature Among others we used all six facial expressions proposed by Ekman as universally recognized expressions of emotions 7 10 We used other distinct facial expressions e g as well as some variations of one expression like low intensity joy and high intensity joy The neutral expression is also included see Fig 4 An example of facial expression used in the evaluation study 92 R Niewiadomski and C Pelachaud 4 2 Procedure In our evaluation study we asked participants to rate the degree of similarity between different facial expressions For this purpose we ascribed the images prepared according the procedure presented in the previous section to ten sets Each set s 1 10 is composed of one reference expression and six facial expressions that have to be compared with the reference one It means that each experiment session consists of 60 operations of comparison i e ten sets
18. of six comparison pairs each To have access to a greater number of participants we set up our experiment on the web One experiment session consists in passing through 10 different web pages Each of them presents one set of images s i e seven facial expressions The reference image is signalled by a yellow border and it is placed in the first row The next two rows contain expressions to be compared with the reference one After deciding the similarity degrees for all six pairs subjects can pass to another set They cannot come back to the preceding sets i e s s 1 and they cannot jump to the next set sj without providing answers to the current one The single images as well as sets of images s were displayed in a random order Images were not labelled The participation in the experiment was anonymous For each pair of images i e reference object compared object subjects had to choose the degree of similarity by using a set of predefined expressions defined in natural language five point Likert scale ranging from not similar to equal In the experiment we decided to avoid the use of numerical description of the level of similarity as it is not used by people to refer to similarity Sixty persons participated in the experiment but only 46 of them went through all ten sets of images We focused only on complete responses Twenty three participants from the 46 classified were women the other 18 men The remaining
19. on and future work are presented is section 6 88 R Niewiadomski and C Pelachaud 2 Fuzzy Similarity Fuzzy similarity offers a set of methods to compare two objects As opposed to distance based similarity each feature of an object is represented by a fuzzy set Two fuzzy sets can be compared using M measure of comparison 5 It expresses the strength of the relationship between the features of two objects There are different types of the M measures of comparison For our application we chose the M measure of resemblance 5 It is used for comparing objects of the same level of generality Using this M measure it is possible to check whether two objects have many characteristics in common 5 It is often used in case based reasoning systems Each M measure of resemblance S has also two other properties reflexivity S A A 1 symmetry S A B S B A These properties characterise also the process of comparing facial expressions First of all comparing facial expressions means to compare objects of the same level of generality Following Ekman s theory all expressions are equi important and distinct Moreover in it was found that the perception of similarity between unlabelled facial expressions is symmetrical i e expression A is similar to expression B to the same degree as B is similar to A 20 In different M measures of resemblance are proposed For our application we chose the measure of resemblance
20. on of the resemblance of facial expressions is modelled cor rectly by our algorithm The average similarity index for 80 of the considered pairs is different from the perfect value represented by the main diagonal by 0 2 at most Moreover the mean difference between subjects responses and our algorithm results is relatively small i e 0 09 It is less than half of the distance between any two neighbouring degrees of similarity on the scale used by subjects in this experiment Thus we can say that the values of fuzzy similarity tend to be proportional to the subjects answers The coarse grained scale of similarity used in this experiment probably influenced this result negatively Subjects had to choose from a discrete set of labels as a consequence their answers can only approximate the values of FS The result is also influenced by the choice of the method of ranking the subjects answers i e yap In particular we assumed arbitrally that the distance between any two degrees of similarity was constant 94 R Niewiadomski and C Pelachaud correlation similarity index fuzzy similarity value Fig 5 Correlation between the fuzzy similarity and the average similarity index On the other hand the mean difference between subjects responses and our algorithm results is positive It means that the algorithm has a tendency to eval uate certain pairs of expressions as less similar in comparison with
21. orial Similarity index html Tsapatsoulis N Raouzaiou A Kollias S Crowie R Douglas Cowie E Emo tion Recognition and Synthesis Based on MPEG 4 FAPs In Pandzic I Forch heimer R eds MPEG 4 Facial Animation The standard implementations applications John Wiley amp Sons UK 2002 Young A W Rowland D Calder A J Etcoff N L Seth A Perrett D I Facial expression megamix tests of dimensional and category accounts of emotion recognition Cognition 63 3 271 313 1997
22. ree images are marked by a circle 4 Evaluation We have conducted an evaluation study to check if our algorithm models ad equately the concept of the resemblance of static computer generated facial Fuzzy Similarity of Facial Expressions of Embodied Agents 91 expressions We are unaware of any similar experiment made on computer gen erated expressions of emotions Previous evaluation studies of embodied agents 2 6 17 mainly analysed the perception of emotions from the computer gen erated facial expressions Instead we focus on the process of comparison of any two facial expressions i e the perception of the common features and the dif ferences between them We avoid considering the problem of interpretation of these facial expressions Our main aim is to verify if the values of the similarity established by our al gorithm are consistent with human perception of the resemblance between facial expressions Our hypothesis was that values of fuzzy similarity are proportional to those found by human s perception In particular we expected to find that our algorithm and human perception are concordant not only in evaluating if any two expressions are similar to each other or not but also that different degrees of resemblance perceived are adequately modelled in our algorithm 4 1 Objects of Comparison Our objects of comparison are images the emotional facial expressions of the Greta agent Each image depicting facia
23. sed by Greta needed to be fuzzified For each FAP of each expression we have defined the fuzzy set of plausible values First we have established for each facial feature i e single FAP the amplitude of values that preserves the reliability and plausibility of a particular movement It means that for any feature we have established the minimum z and the maximum z plausible values for any expression Beyond this range the movement is perceived as unnatural Each fuzzy set FAP of a particular facial expression depends on this amplitude of plausible values We have established that membership is a symmetrical trapezoid with the centre in the point v where v is a value of the original expression see Figure I The dimensions of the trapezoid depend on the absolute value of the difference x2 x Using fuzzy definitions of facial expressions we count the value of sim Heap x 1 V X Fig 1 A fuzzy set of FAP ilarity between them For that purpose we use the procedure described in the previous section Let FS Exp E Exp E be the value of similarity between two expressions Exp E and Exp E For each FAP of Exp E and Exp E we have M FAP Ei 0 FAP E fsk MU AP E U FAP E 4 where k 1 n Then PS Bap E Exp Bj hu fs1 f5n 5 where h is OWA operator with the weights wk 4 see section 2 Recapitulating our algorithm works as follow let E and E be two emo tions whose
24. the subjects choices Indeed we noticed certain pairs that have the fuzzy similarity value in the interval 0 3 0 5 were evaluated as relatively more similar than our algorithm indicates Indeed as shown in Figure 5 more points in this interval are situated above the diagonal than under it 5 Application In the previous section we have presented an innovative algorithm which allowed us to compare any two facial expressions of an embodied agent In this section we present an example of its application We use it to generate different types of fa cial expressions e g expressions of masking or fake expressions Previous mod els of facial expressions deal with the display of emotional states They are based on the assumption that emotions which are similar for instance in terms of valence or arousal values have also similar expressions On the contrary we pro pose that the visual resemblance between two facial expressions is the measure that can be used in order to generate a new expression We used our fuzzy sim ilarity based algorithm in order to generate different types of facial expressions There is a large amount of evidence in psychological research that human s repertoire of facial expressions is very large 9 15 22 Facial expressions do not always correspond to felt emotions but they can be fake showing an expression of an unfelt emotion masked masking a felt emotion by an unfelt emotion su perposed showing a mixe
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