p1218 cavalcante vieira

A Biologically Inspired Generation of Virtual Characters

Roberto C. Cavalcante Vieira

Department of Computing

Federal University of Ceará

60455-760 Fortaleza, CE, Brazil

roberto@lia.ufc.br

Creto Augusto Vidal

Department of Computing

Federal University of Ceará

60455-760 Fortaleza, CE, Brazil

cvidal@lia.ufc.br

Joaquim B. Cavalcante-Neto

Department of Computing

Federal University of Ceará

60455-760 Fortaleza, CE, Brazil

joaquimb@lia.ufc.br

ABSTRACT

A number of techniques for generating geometric models of human head and body are in use nowadays. Models of human characters are useful in computer games, virtual reality, and many other applications. The complexities involved in generating such models, however, impose heavy limitations on the variety of characters produced. In this paper, diploid reproduction is mimicked to produce an unlimited number of character models, which inherit traits from two parent models. The meshes of all models are constructed based on control parameters that are distributed as genes among a group of chromosomes. Thus, the technique consists of distributing pre-selected characteristics, represented as control parameters, over a pre-determined number of chromosome pairs for both parents; followed by a simulated generation of the father’s and the mother’s gametes; which are randomly combined in a simulated fecundation. The diversity is ensured in four random processes: the random exchange of segments during crossover; the random alignment of homologous chromosomes at metaphases I and II of meiosis; and the random union of male and female gametes during fecundation.

Categories and Subject Descriptors

I.3.5 [Computational Geometry and Object Modeling]: Geometric algorithms, languages, and systems; I.6.5 [Model

Development]: Modeling methodologies.

General Terms

Algorithms, Design, Experimentation and Human Factors.

Keywords

Virtual characters modeling · Mesh generation · Genetic inheritance · Reproductive simulation

1. INTRODUCTION

Developing virtual characters requires a great deal of tedious work. This is why many systems offer only a few options of distinct corporal characteristics for the user to compose their customized character. Usually, the user is able to select different types of hair, skin colour and clothes and to apply some type of scale transformation to change the size of the character (tall or

short, fat or skinny).

In many desktop Networked Virtual Reality applications, some virtual characters represent the user inside the virtual environment, while other characters under the control of the system play specific roles in the environment. Often, the number of characters the user can select is very limited. Therefore, it seems to be desirable that the variability of characteristics of these models be close to the variability found in human populations. The problem treated in this article can be stated in the following way: “Is it possible to generate virtual characters automatically and, at the same time, ensure large variability?”

1.1 The proposed solution

Figure 1. Process of character generation simulating reproduction: (a) Definition of the parents’ chromosomes; (b) Generation of gametes; (c) Fecundation; (d) Mesh adaptation

to the information stored in the chromosomes.

The proposed solution to the problem of automatic generation of virtual characters with assurance of large variability is illustrated in Figure 1 and can be summarized in the following steps:

1. Identification of a set of descriptive characteristics of the virtual human;

2. Association of the characteristics identified in step 1 with diploid genes;

3. Distribution of the genes defined in step 2 among homologous chromosomes, determining the number of chromosomes and the number of genes per chromosome;

4. Definition of the chromosomes of the female and male generators from the definitions of step 3;

5. Simulation of the father’s and mother’s gamete generation process; and

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SAC’08, March 16-20, 2008, Fortaleza, Ceará, Brazil.

6. Simulation of the fecundation process.

The proposed method ensures automatic generation of new models, through the specified control parameters stored in the chromosomes. It also ensures diversity through four random processes: the random exchange of segments during crossover; the random alignment of homologous chromosomes at Metaphase I and Metaphase II of meiosis; and the random union of male and female gametes during fecundation.

1.2 Article’s organization

The remaining sections of this article are organized as follows. Section 2 contains the discussion of related works. Section 3 holds a brief presentation of the biology concepts of diploid reproduction. In Section 4, the concepts presented in Section 3 are mapped into an algorithmic structure for generating virtual characters. In Section 5, a case study illustrates the general process described in Section 4, focusing on the generation of faces. In Section 6, some conclusions are presented.

2. RELATED WORK

A great variety of techniques for generating geometric models of human faces and bodies have been explored already. However, the complexity of human anatomy makes it difficult to build realistic and natural models [16]. In 1998, DeCarlo et al. [9] devised a system that automatically generated facial models for virtual reality applications. His work was one of the pioneers in using anthropometric techniques [16] for the generation of faces, and inspired several other works [5, 13]. DeCarlo constructed a base model with B-Spline surface, which respected established anthropometric measures. Then, he introduced random perturbations in those measures, within predefined ranges, to generate other models. Blanz and Vetter [5] developed a model for synthesis of three-dimensional faces through morphing techniques. Thus, the appearance of the generated model is a blend of characteristics of the database models. Praun and his co-authors [17] used parameterization techniques to specify variations of characteristics, through the combination of independent parameters from two or more models. Besides, it requires much effort to define and to manipulate the parameters informations. Bui et al. [6] also used morphing for face animations. In 2002, Kähler et al. [13] built a generic model with anatomical layers (skin, muscle and bone) associated with anthropometric landmarks. Based on anthropometric information of individuals of different ages, it was possible to simulate the face changes in different stages of life, using deformation. In 2003, Allen et al. [1], based on Blanz and Vetter’s work, expanded the technique for the entire human body. The imperfect and incomplete areas of the 3D laser range scan models are filled using a base model. Seo and Thalmann [18] developed a model, based on Bézier patches, for the generation of bodies from an adaptable base model. The data used to guide the adaptation of the base model in order to generate new ones are derived from a combination of measures of available models stored in a corporal database constructed with the use of 3D scanners. Hancock et al. [11] developed a system, which generates high quality images through random recombination (using genetic algorithms) of good quality face images. Their goal was to generate faces similar to a target face. None of these works, despite the good results achieved by some of them, uses any kind of biological information or reproduction theory to generate the models. In

addition, a large variability of models is not guaranteed by most of these techniques, not to mention that the models are not automatically generated in most cases.

3. DIPLOID REPRODUCTION

3.1 Storage of genetic information

The genetic characteristics of living creatures are codified in chromosomes, which are long molecules of DNA associated with proteins. Each characteristic stored in a chromosome is called a gene (Figure 2). In diploid beings, a given trait is associated with a pair of genes (allele genes), one gene originated from the male progenitor and the other, from the female progenitor. The allele genes occupy the same position in the so-called homologous chromosomes. Consider n the total number of pairs of allele genes, which are distributed among m pairs of homologous chromosomes. Hence, the total number of genes is 2n and the total number of chromosomes is 2m.

The cells of a diploid adult is originated from only one cell, the zygote (a fecundated egg cell), through successive cellular divisions. There are two types of cells: the somatic cells (with 2m chromosomes), which form the body of the individual; and the gametes (with m chromosomes), intended for the perpetuation of the species. In the human beings, the somatic cells possess 23 pairs of chromosomes (2m = 46 chromosomes) and gametes (ovum and spermatozoid) possess 23 chromosomes (m = 23 chromosomes).

Figure 2. Chromosome illustration.

3.2 Generation of gametes

Specialized somatic cells called germinative cells suffer a process of special cellular division called meiosis that results in four gametes (haploid cells). Preceded by a phase of chromosome duplication called Interphase, meiosis occurs in eight distinct phases: Prophase I, Metaphase I, Anaphase I, Telophase I, Prophase II, Metaphase II, Anaphase II, Telophase II (Figure 3). In some of these phases, processes of random nature occur and are responsible for the diversity of the descendants.

In the first of these random processes, called crossover, which occurs in Prophase I, corresponding pieces of some of the duplicated homologous chromosomes are interchanged. Thus the new pair of duplicated homologous chromosomes is already different from the original duplicated pair (see Figure 4). In crossover, the number and size of interchanged segments are non-deterministic. Also, if crossover does occur, it is not known a priori in which of the m pairs of homologous chromosomes it will occur.

The second and the third random processes occur in Metaphase I and Metaphase II, respectively, when the alignment of the m pairs

of homologous chromosomes (Metaphase I) or m pairs of sister chromatids (Methaphase II) takes place. During the alignment, it is not known which chromosomes (or chromatids) of the m pairs will fall in one or the other cell after the cellular division (see Figure 3). In synthesis, during gamete generation, each chromosome is separated from its homologous, forming haploid cells. This process leads to a phenomenon called independent segregation of the homologous, which means that the gametes originate from independent combination of the homologous chromosomes. These three random processes are responsible for the generation of an enormous variety of gametes. Figure 3 illustrates the process of generation of gametes from a cell with two heterozygote chromosomes.

Figure 3. Gamete generation by meiosis.

3.3 Fecundation

During fecundation, two gametes (haploid cells), one from the male progenitor and one from the female progenitor, are joined to form a diploid cell which will undergo cellular divisions to form a new individual. When the homologous chromosomes from each gamete form a chromosome pair, the allele genes influence a given trait. The trait manifestation depends upon the type of allele gene combination: dominant, recessive or incomplete. If, in a pair of allele genes, one is dominant, the trait will be totally influenced by the dominant gene. A recessive gene will influence the trait, only when pairing with another recessive gene. In the incomplete dominance, both genes influence the trait. Thus, the heterozygote individual has a trait, which is intermediary of the phenotypes that would be manifested individually by each allele gene.

4. SIMULATED DIPLOID REPRODUCTON

In this section, the steps of Section 1.1 are described. These steps map the biological processes presented in Section 3 into an algorithmic structure. Some of the implementation details are left to Section 5.

4.1 Identification of the genetic

characteristics

According to estimates of the Human Genome Project, the structure of the human body and all its internal processes are specified from the information stored in some 30,000 to 40,000 genes (it has controversies on the accurate number). The genetic information describes biochemical processes, which lead to the development, in some phases, of an adult individual.

Here, the task is to identify external characteristics, such as: height, form and size of members, form and size of the head, form of the eyes, form and size of nose, mouth, ears, chin, and so on; that will be used in the construction of a virtual character. Each of these characteristics can be seen as high-level information that, respecting anthropometric limits, controls a hierarchical substructure that constructs part of the model. Thus, the set of characteristics and the associated construction structures parallels the information structure represented by genes of diploid beings. This corresponds to the two first steps of the process: 1) Identification of a set of descriptive characteristics of the virtual human; 2) Association of the characteristics identified in step 1 with diploid genes. Details of this phase are shown in Section 5.

4.2 Storage of the genetic information

Similar to diploid individuals, the total of genes is distributed in a set of chromosomes. In the human beings, for example, more than the 30,000 genes are distributed in 23 pairs of chromosomes (see Section 3.1). Thus, if n characteristics were identified, n pairs of allele genes will be distributed across m pairs of homologous chromosomes. One of the chromosomes of a pair of homologous chromosomes stores a subgroup of the n characteristics transmitted by the male ancestral and the other chromosome stores the same subgroup of characteristics originated from the female progenitor.

It is important to point out that it is not necessary to impose any restriction on how the n characteristics will be distributed among the m chromosomes. Therefore, considering C the set of pairs ci

of homologous chromosomes,

}

,

,

,

{

c

1

c

2

c

m

C

=

_L

(1)

where a pair ci is represented by

)

,

(

_iM _iF i

c

c

c

(2)

in which the homologous chromosomes

c

_iM and

c

_iF coming, respectively, from the male and the female progenitors are sequences of genes,

},

,

,

,

{

}

,

,

,

{

2 1 2 1 F F F F i M M M M i i in i i i in i i

g

g

g

c

g

g

g

c

L

L

=

=

(3)

the number ni of genes in each chromosome must obey the

relation

∑

=

=

m i i

n

n

1 . (4)

The choice of m has a direct influence on the variability of the descendants, since it contributes to the increase of combination possibilities during Metaphase I and II of meiosis (see Section 4.3). The organization of the genetic characteristics into the structure represented by equations (1) through (4) corresponds to step 3 of the proposed process. Step 4 of the process is just the instantiation of the elements of this structure (equations (1), (2) and (3)) for the parent models (Male and Female).

4.3 Gametes generation

Once the genetic information structures of the parent models are instantiated, the process of gamete generation is applied to each of these structures in order to generate the gametes of both parents (step 5). This process consists of a simulated meiosis. It is evident that, in the computational simulation, there is no need to reproduce all the biological processes that occur during meiosis (see Section 3.2). For example, it is not necessary to simulate the deterioration of the nuclear membrane, nor the creation of centrioles and microtubules, nor the process of separation that occurs in anaphase, nor the other processes of restoration of membranes. The simulation must be concentrated on the following meiosis processes:

4.3.1 Duplication of the chromosome

At this point, it is assumed that the Interphase occurred already and, therefore, all chromosomes are duplicated. That is, at the beginning of the process, there are 4m chromosomes. Thus, each pair of homologous chromosomes is transformed into four chromosomes (two identical pairs – see equation (5)). The original chromosome and its replica (called sister chromatids) are paired up with the original homologous chromosome and its sister chromatid (see Figure 4).

)

,

(

iF F i M i M i i d

c

c

c

c

c

. (5)

4.3.2 Crossover

This configuration, where the homologous chromosomes are duplicated and paired up, is the base for the simulation of the piece exchanges between the homologous chromosomes. This process is called crossover and occurs in Prophase I. If no piece exchange occurs, the sister chromatids will remain identical. However, if crossover does occur, all the four chromosomes that formed two identical pairs are distinct now.

For the purpose of crossover simulation, in a pair of duplicated chromosomes d

c

_i

(

c

_iM

c

_iM

,

c

_iF

c

_iF

)

, each chromosome

c

_iM exchanges genes with its homologous

c

_iF. Thus, if the chromosomes of pair i have ni genes, the number of possible

exchanges are given by

i i n n k i

k

n

2

0

=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

∑

= . (6)

However, since the chromosomes that exchanged genes are complementary, the number of distinct pairs that can be generated by the exchange of genes is

2

ni−1

. Thus, after crossover, the structure of the duplicated chromosome is given by

)

,

(

_{1 i}M_{2 i}M _{1 i}F_{2 i}F i d

c

c

c

c

c

(7) where the pairs

(

₁

c

_iM

,

₁

c

_iF

)

and

(

₂

c

_iM

,

₂

c

_iF

)

belong to the universe of

2

ni−1 _{possible pairs.}

Figure 4. Crossover.

4.3.3 Simulation of Metaphase I

After the simulation of crossover, the m pairs of duplicated chromosomes (see equation (7)) are lined up halfway between the two poles of the cell (Metaphase I). For this simulation, it is convenient to rewrite equation (7) as

)

,

(

d _iM d _iF i d

c

c

c

. (8) Consider the random distribution of pairs in relation to the basic alignment structure of the m pairs of chromosomes, illustrated in Figure 5, where the m chromosomes d

c

_iM are in one side and the m chromosomes d

c

_iF are in the other side of the dotted plane that represents the cellular division. Thus, the two cells generated at the end of this process, which is completed in Telophase I, belong to a universe of

2

m−1 distinct pairs of cells.

Figure 5. Chromosome alignment during Metaphase I.

4.3.4 Simulation of Metaphase II

The two cells generated at the end of Telophase I are divided once more, generating four gametes. In the simulation of phase II, only Metaphase II needs to be treated. In each of the two cells generated in Phase I of meiosis, there is a set of m pairs of sister chromatids which were modified during crossover (they are not identical anymore), that is, the i-th pair can be either

)

(

₁

c

_iM₂

c

_iM or

(

₁

c

_iF₂

c

_iF

)

. In Metaphase II, these m pairs will be lined up again in the equator of the cell, and then separated into two new cells. The simulation process is identical to the one

of Metaphase I and the random alignment is illustrated in Figure 6.

Figure 6. Chromosome alignment during Metaphase II.

Again, the new pair of cells generated from Cell 1 (Figure 6) belongs to a universe of

2

m−1 distinct pairs. Also, the new pair of cells generated from Cell 2 (Figure 6) belongs to a different universe of

2

m−1 distinct pairs. The four generated cells are gametes, that is, each cell has m chromosomes (haploid cells) instead of m pairs of chromosomes as in diploid somatic cells.

4.4 Fecundation

The process of gamete generation of Section 4.3 is applied to the genetic structure of both the paternal and maternal model. Four gametes randomly generated for each parent model can be joined in sixteen combinations. The genetic characteristics of these descendants belong to a universe of probabilities that incorporates the random nature of the crossovers that occur in the m pairs of duplicated chromosomes, and the random alignments of Metaphase I and II. In the human beings this corresponds to a universe of 10600 [19, page 273]. After the combination, the new set of genetic information is used to construct the body of the descendant character. This process is illustrated in the case study of Section 5.

5. CASE STUDY: GENERATION OF

FACIAL MESHES

In this section, a case study illustrates the general process, described in Section 4, through the generation of faces of the offspring of two characters. The simulation combined different ethnic groups (Black and Asian) (Figure 9) and a cartoon character with a human model (Figure 11).

5.1 General considerations about face

modeling

The face meshes were constructed using an in-house modelling system based on BREP (Boundary Representation Models). The geometric model used Bézier patches with continuity controls, which ensured better adjustment and smoothness in the transition between patches.

With the aid of frontal and lateral photos, the base models were constructed, using: the Euler operators implemented in the modelling system, picking resources, and auxiliary system of axes. The measures, which are used as characteristic to be

distributed in the chromosomes, are taken from face landmarks defined by Anthropometry (Figure 7) [14], and serve as references for the modelling.

The reference mesh, with standard topology, that is adjusted to the parent models’ characteristics, consists of 20×20 patches. It also serves as a base for the construction of the offspring’s meshes. The parent models’ meshes can be either constructed by manual adjustment from photos, or chosen from a database of previously generated meshes. The offspring’s meshes are generated automatically from the characteristics registered in their chromosomes. Models in the facial meshes database can be selected and have their characteristics (nose silhouette, length of nose, etc.) modified by scrollbars.

After defining the meshes of the couple (Figure 9 and Figure 11), the characteristics of the face are distributed and stored in chromosomes for posterior simulation of the reproductive process, generating possible variations of genetic inheritances in the resulting face.

5.2 Chromosome’s definitions

In this study, nine measures were defined from the anthropometric Landmarks (Table 1) and distributed as genes in three chromosomes (Figure 7). In general, a measure can be composed of different amounts of control points and can be defined by two or more landmarks. For example, genes, a, b, c, e, g and h are defined by measures comprising two landmarks while genes d and f are defined by three landmarks.

Table 1. Measures used in the case study (based in Landmarks).

Id Measure Description

a ex-en Corner of the eyes b ps-pl Height of the eyes c ch-ch Corner of the mouth d sn-prn-s Bending of the nose e g-tr Height of the forehead f ls-sto-li Labial bending g al-al Width of the nose h s-sn Height of the nose

i - General aspect of the Face

It is important to mention that the higher the number of measures (genes), the greater the variability of the combinations will be. In this work only nine measures were used to test the effectiveness of the technique. More over different forms of distribution of the characteristics among the chromosomes generate different results, since the characteristics contained in distinct chromosomes are combined independently, and genes contained in the same chromosome can be exchanged by crossover. Also, the result of the simulation can vary significantly if one modifies the probabilities of crossovers or limits the amount of crossovers that can occur in a chromosome.

The resulting characteristics are generated from the combination of pairs of genes. In this study, incomplete dominance between the alleles was adopted. Thus, weights are attributed to each gene, so that a trait in the descendant models will be defined as a weighted average of the corresponding genes of the parents.

5.3 Gametes generation

The process of gametes generation occurs as described in Section 4.3. In this case study the chromosome structure (Figure 8) is given by ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = = F M F M F M F M F M F M F M F M F M i i h h g g f f e e d d c c b b a a c c c C {₁, ₂, ₃} , , .

Figure 8. Genes' structure.

In this structure, genes are associated with weights and specific areas of the mesh defined by the measures. To ensure high variety of gametes, crossover was allowed to happen between any genes in the chromosome (Figure 4).

In this study, only one process of meiosis was executed on each chromosome structure, _CMale and _CFemale, of the parents, resulting in eight gametes (four male and four female).

5.4 Generation of the Offspring

With gametes of the parent meshes (Figure 9 and Figure 11), all the sixteen possible fecundations were generated. The meshes of the descendants are, then, constructed from the information stored in their chromosome structures. Due to space limitations, only four of these descendants of each simulation are shown in Figures 10 and 12. It is important to mention that runing several meiosis simulations on each parent model one can generate a pool of male and female gametes that can be used in fecundation. Thus, obviously the number of offspring is not limitted to 16.

6. CONCLUSIONS

This work presented a solution for the problem of automatic generation of characters, ensuring large variability. The proposed solution was based on the automatism and the great variability that occurs in the diploid reproduction. The process needs an

underlying geometric description that is adapted according to genetic information stored in the diploid artificial chromosome structure. The geometric model used in this study was composed of the union of Bézier patches. The adaptation control of the model used points, which were defined by anthropometric landmarks whose subgroupings specified the characteristics that were stored as genes in the pairs of homologous chromosomes. Through the process of simulated meiosis, applied to the chromosome structure of two parent models, gametes were generated and then used in the simulated fecundation. In the example presented here the process of meiosis was applied only once to each parent, resulting in four male and four female gametes, that after fecundation, generated sixteen descendants. The process, however, is general and can be applied to the complete model (head and body) of a character. Moreover, the process of meiosis simulation can be applied innumerable times to each parent, producing a large pool of male and female gametes that can be randomly fecundated. This method, in contrast with those presented in the literature, is more versatile, ensures automatism and great variability, and is capable of generating characters that have similar face characteristics, simulating reproduction within groups of the same family or ethnicity, as well as between individuals of distinct groups. It is also worth mentioning that the proposed method is far more versatile than the weighted average of two parent meshes similar to what happens with morphing techniques. Also, this model is different from genetic algorithms and has different goals. Genetic algorithms are used to converge to a desired result, removing some unwanted models during the process. Our approach doesn’t want to converge to specific face characteristics, but generate several possible faces from the combination of characteristics of the parents like real biological reproduction process.

7. REFERENCES

[1] Allen, B., Curless, B. and Popovic, Z. The space of human body shapes: reconstruction and parameterization from range scans, Proceedings of ACM SIGGRAPH 2003, Computer Graphics Annual Conference Series, 27-31 July 2003, San Diego, USA.

[2] Amabis, J. M. and Martho, G. R.: Biologia das populações Vol.3, 1st ed., Editora Moderna, São Paulo, São Paulo, Brasil, 1995.

[3] Blanz, V., Albrecht, I., Haber, J. and Seidel, H.-P.: Creating Face Models from Vague Mental Images, Computer Graphics Forum 25(3) pp.645-654 Eurographics 2006. [4] Blanz, V., Scherbaum, K., Vetter, T. and Seidel, H.-P.: In:

Cani, M.-P. and Slater, M. (Eds), Exchanging Faces in Images, Proceedings of EUROGRAPHICS 2004, pp. 669- 676.

[5] Blanz, V. and Vetter T.: A morphable model for the synthesis of 3D faces, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.187-194, July 1999.

[6] Bui, T.D., Poel, M., Heylen, D., and Nijholt, A. Automatic Face Morphing for Transferring Facial Animation, Computer Graphics and Imaging, Honolulu, Hawaii, USA, August 2003, pp. 19-23.

[7] Chan, M., Delmas, P., Gimel, G. and Leclercq, P., Comparative Study of 3D Face Acquisition Techniques. CAIP 2005: 740-747.

[8] Chen, T. and Fels, S. Exploring gradient-based face navigation interfaces, Proceedings of the 2004 conference on Graphics interface table of contents,Vol. 62 Pages: 65 – 72. [9] DeCarlo, D. , Metaxas, D. and Stone M., An anthropometric

face model using variational techniques, Proceedings of the 25th annual conference on Computer graphics and interactive techniques, p.67-74, July 1998.

[10] Dipaola, S. Facespace:a facial spatial-domain toolkit. In Proceedings of InfoViz 2002, 49–55.

[11] Hancock, P. J. B. and Frowd, C. D. Evolutionary generation of faces. In Proc. of AISB, p. 93--99, 1999.

[12] Kähler, K., Haber, J. and Seidel, H..: Reanimating the Dead: Reconstruction of Expressive Faces from Skull Data, ACM Transactions on Graphics (SIGGRAPH 2003 Conference Proceedings).

[13] Kähler, K., Haber, J. , Yamauchi, H. and Seidel, H. P. Head shop: generating animated head models with anatomical structure, Proceedings of the 2002 ACM

SIGGRAPH/Eurographics symposium on Computer animation, July 21-22, 2002, Texas.

[14] Kolar, J. C. and Salter, E. M.: Craniofacial Anthropometry – Practical Measurement of the Head and Face for Clinical, Surgical and Research Use. Charles C. Thomas Publisher, Ltd. Springfield, Illinois, USA.

[15] Kuo, C. J., Huang, R. and Lin T. 3-D Facial Model Estimation from single front-view facial image; IEEE transactions on circuits and systems for video technology, vol 12, No.3, March, 2002.

[16] Noh, J. and Neumann, U. A Survey of facial modeling and animation techniques, USC Technical Report 99-705, 1998. [17] Praun, E., Sweldens, W. and Schroder, P. Consistent Mesh

Parameterizations. Proceedings of ACM SIGGRAPH 2001, Computer Graphics Annual Conference Series, 179-184. [18] Seo, H. and Thalmann, N. An automatic modeling of human

bodies from sizing parameters, Proceedings of the 2003 symposium on Interactive 3D graphics Pages: 19 – 26. [19] Starr, C. and Taggart, R. Biology: The unity and diversity of

life, 7th ed., Wadsworth Publishing Company, Belmont, California, USA, 1995.

Figure 9. African and Asian parents.

Figure 10. Resultant face meshes of the fecundation of the Asian and African gametes.

Figure 11. Cartoon and Human parents.

Figure 12. Resultant face meshes of the fecundation of the Cartoon and Human gametes.