DIRECT TEXTURE SYNTHESIS OF FEATHER

PIGMENTATION PATTERNS

C. G. Franco and M. Walter

Masters in Applied Computing, Unisinos

Centro de Informatica, Universidade Federal de Pernambuco, Brazil

Keywords:

Natural Phenomena, Texture Synthesis, Feather Pattern Modeling, Feather Rendering.

Abstract:

Feathers present exquisite shapes and visual patterns. Just recently feathers have been addressed in computer

graphics with realistic-looking results. Current solutions, however, make use of texture mapping for adding

the visual patterns seen on feathers. In this paper we present an integrated model for direct texture synthesis

of feather pigmentation patterns. The model uses B´ezier curves to model the feather shape and procedural

MCLONE patterns for the synthesis of feather pigmentation patterns. We show that the Clonal Mosaic model

(MCLONE) is a viable option for direct texture synthesis of the many pigmentation feather patterns found in

Nature.

1 INTRODUCTION

The modelling of natural phenomena is one of the

most challenging ﬁelds in computer graphics, due to

the intrinsic complexity of natural phenomena and

the familiarity we have with them. In the Animal

Kingdom, feather formation is one of the most fas-

cinating and intriguing process, which has attracted

little attention in computer graphics and it is still a

not clearly understood process in Biology (Prum and

Williamson, 2002). In addition, feather pigmentation

patterns exhibit a large range of visual diversity.

In the work presented so far on this subject, this

visual diversity is achieved through texture mapping

real world images. Although powerful, this method

lacks ﬂexibility and we are restricted to real images.

Not to mention the usual problems of texture mapping

such as distortion and the mapping itself. The main

investigation problem in this work are visual patterns

of feathers. We propose a procedural model based

on the MCLONE model (Walter et al., 1998) which

is able to synthesize feather pigmentation patterns di-

rectly on the feather shape, avoiding the difﬁculties

associated with texture mapping. Besides, MCLONE

patterns capture the large range of visual diversity

found in feathers, as illustrated in Figure 1. We ini-

tially present related work on the topics explored in

this paper, followed by a background section on the

biology of feathers and the MCLONE model. Our so-

lution is presented in Section 4. Finally, we present a

few results with our approach and the conclusions.

Figure 1: Example of pattern and shape diversity of real

feathers. From (Prum and Williamson, 2002).

2 PREVIOUS WORK

As our main goal is the direct texture synthesis

of feather pigmentation patterns, we present related

work on direct texture synthesis and on feather mod-

elling.

277

G. Franco C. and Walter M. (2007).

DIRECT TEXTURE SYNTHESIS OF FEATHER PIGMENTATION PATTERNS.

In Proceedings of the Second International Conference on Computer Graphics Theory and Applications - GM/R, pages 277-283

DOI: 10.5220/0002076602770283

 SciTePress

2.1 Procedural Methods

In 1991 Turk (Turk, 1991) generated animal skin pat-

terns with Reaction-Diffusion (RD) mechanisms, in-

troduced by Turing (Turing, 1952). Instead of map-

ping the generated pattern onto a polyhedral or para-

metric model, Turk’s approach simulated the RD sys-

tem on the surface of the model, without the inter-

mediate mapping from texture space to object space.

Fleischer et al. also presented an approach (Fleischer

et al., 1995) for texturing with direct simulation on the

surface of an object. The surface of the object is cov-

ered with cells that are constrained to remain on an

iso-surface computed from the original model. The

whole approach is general, and can in principle gen-

erate many interesting organic-liketextures, including

RD ones. Their results show an organic quality to the

generated textures, but they did not present any results

simulating real-life patterns.

2.2 Direct Texture Synthesis From

Samples

The following four approaches are variations on the

basic idea of texture synthesis from samples on arbi-

trary surfaces, and therefore extensions of (Wei and

Levoy, 2000).

Turk presented an approach where the texture syn-

thesis on the surface is achieved through a hierarchy

of points on the surface (Turk, 2001). A user-deﬁned

vector ﬁeld indicates the orientation of the texture.

The mesh vertices are then sorted in such a way that

visiting the points in order will follow the vector ﬁeld

and will sweep across the surface from one end to the

other. The color of a particular point is deﬁned by

examining the color of neighboring points and ﬁnd-

ing the best match to a similar neighborhood in the

given texture sample. Wei and Levoy (Wei and Levoy,

2001) also presented an approach based on search-

ing strategy to solve the texture synthesis problem on

arbitrary surfaces. The difference between this ap-

proach and Turk’s one is that in this work there is no

need to specify a vector ﬁeld, since it is obtained on

the ﬂy.

In 2002, Soler et al. (Soler et al., 2002) presented

an approach that, instead of searching the whole sur-

face point by point, it progressively covers the tex-

ture surface with texture patches, of several sizes, se-

lected from a single input image. One of the ad-

vantages of this approach is that there is no need of

generation of a intermediary geometry, and the ini-

tial geometry is preserved. In another work in 2002,

Tong et al. (Tong et al., 2002) presented a solution

that enables the synthesis of BTFs (Bidirectional Tex-

ture Functions) (Dana et al., 1999), on arbitrary sur-

faces. This solution performs the synthesis of the

BTF’s samples directly on the surface, avoiding dis-

tortions and discontinuities. The results show that this

approach achieved the main goal of maintaining de-

tails of the mesostructure, represented by the BTF, in

all viewing and lighting directions.

2.3 Feather Modelling

The ﬁrst published model targeted speciﬁcally for

feathers was presented in (Dai et al., 1995). The feath-

ers were modelled as line segments branching from

a main structure. The textures were computed from

simulations of dynamical systems.

The work in (Chen et al., 2002) uses paramet-

ric L-systems for the modelling of the feathers and

texture mapping and customized BTF for the render-

ing. In (Streit and Heidrich, 2002), the feathers are

modeled as a collection of B´ezier curves. The over-

all shape of the individual feathers is achieved by the

user specifying key barbs from which the other barbs

are derived by interpolation. The rendering uses tex-

ture mapping to add color to the barbs. Recently in

Biology (Prum and Williamson, 2002) proposed an

approach addressing pattern formation for feathers.

They used Reaction-Diffusion (RD) mechanisms to

build the pattern of the feathers. The results are inter-

esting, but since their work is not focused in computer

graphics, the visual aspects were not privileged. Fur-

thermore, there is no universal RD system capable of

generating all patterns, and therefore distinct RD sys-

tems are used or even sometimes a new one must be

developed.

Our work advances the idea of direct texture syn-

thesis, using a procedural model targeted to visual

patterns of feathers. In this sense we make contribu-

tions on procedural texture generation, feather mod-

eling, and direct texture synthesis.

3 BACKGROUND

Since our model derives its inspiration from real

feathers, we brieﬂy review in this section basic infor-

mation on the biology of feathers.

Feathers are a type of branching structure, ﬂexible

and yet strong (Freethy, 1982). They present a main

rigid structure called calamus at the base (with no

branching structures) and the rachis where the main

body of the feather develops (see Figure 2). From the

rachis a variable number of barbs are originated. The

collection of barbs at each side of the feather’s body

is known as vanes. Each barb is built from two sets

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278

Figure 2: Structure of a typical feather.

of interconnected barbules: the anterior and the pos-

terior barbules. For some feathers each barbule has in

turn microscopic barbicles (not labeled in the ﬁgure),

structures with small hooks that connect the anterior

barbule of one barb to the posterior barbuleof the next

barb. This connection helps maintaining the feather

overall shape.

There are 5 types of feathers. The most famil-

iar type is the contour feather. The semiplume has

a structure between the contour and the plume. The

plume type is soft and the length of the barbs is typ-

ically longer than the length of the rachis itself. Fi-

nally, the ﬁloplume and the bristles are very small

specialized feathers.

Most recent theories (Prum, 1999) present the

feather as a tubular structure that growsfrom a follicu-

lus. Barbs grow around this folliculus, and as they ap-

proach the anterior part of that, they are joined to form

the rachis, creating the branching structure (Prum,

2001). Melanin, one of the key elements for pro-

ducing the colors, come from melanocytes, that mi-

grate through this structure during feather develop-

ment. Currently, there is no universal theory on

how a speciﬁc pigmentation pattern is deﬁned. An

accepted concept today is that within-feather pig-

ment patterns are determined by differential pigmen-

tation of keratinocytes within independent barb ridges

during feather development (Prum and Williamson,

2002).

3.1 The Clonal Mosaic Model

The Clonal Mosaic theory (Walter et al., 1998), pro-

poses that the typical yellow-black stripped and spot-

ted patterns occurring in several species of mammals,

reﬂect a spatial arrangement – a mosaic – of ep-

ithelial cells which derive from a single progenitor,

i.e., they are clones. Hence the name Clonal Mo-

saic (MCLONE). The basic idea of the Clonal Mo-

saic model is that the pattern on mammals is obtained

from simulation of the interaction between cells with

different properties, such as color, division rate, ad-

hesion, and others (Walter et al., 1998). One of the

main advantages of the MCLONE model is its gen-

erality, since in the last years it has been explored in

different domains, ranging from pattern modelling in

butterﬂies (Lied and Walter, 2002) up to simulation of

growth of tumors (dos Reis et al., 2003). Although the

MCLONE has been initially designed for simulation

of mammalian patterns, it is general enough to handle

also visual patterns of feathers.

4 THE PROPOSED MODEL

The approach introduced here is an extension

of (Franco and Walter, 2002). For completeness, we

start this section with a brief review of that work.

In order to model a single feather, the user initially

deﬁnes a cubic B´ezier, which represents the rachis,

and two B´ezier curves that deﬁne the boundaries of

the overall feather structure (the vanes). From the

rachis the technique generates a variable number of

barbs, controlled by a set of parameters. Each barb

is itself a B´ezier segment with 4 control points. Even

though this scheme uses cubic segments, the result-

ing B´ezier in practice has enough ﬂexibility to repre-

sent a wide range of possible barb shapes. The model

has 7 main parameters which allow real time gener-

ation of many feather structures, from contour feath-

ers to semiplumes, plumes, and even ﬁloplumes. To

get a detailed description of the meaning and playing

role of each parameter we suggest the reader to con-

sult (Franco and Walter, 2002).

4.1 Modelling the Pattern

This step consists in synthesizing the texture rep-

resenting a determined feather pattern, using the

MCLONE. At this point, we have the feather repre-

sented only by its barbs, that are a collection of B´ezier

curves. In order to simulate the MCLONE model

we used a process analogous to the one described

in (Walter et al., 2001). This process has two main

steps described next.

4.1.1 Generation of the Mesh Representing the

Feather Structure

The MCLONE model is applied directly onto the ob-

ject’s surface. Since we only have curves in our

model, in this step we derive a triangular mesh from

the original structure of the feather modelled by the

user, as we can see in Figure 3.

This derivation process is quite simple. The sur-

face represented by the rachis and the vanes forms the

DIRECT TEXTURE SYNTHESIS OF FEATHER PIGMENTATION PATTERNS

279

(a) Generated Mesh (b) Algorithm’s de-

tail

Figure 3: Visualization of the mesh generation algorithm.

superior part of the volume. Then, this surface is tri-

angulated, using a simple interpolation mechanism,

with a level of detail deﬁned by the user. As we can

see in Figure 3, the rachis and the vanes are divided

into n sections, where n is the user-deﬁned level of de-

tail. From there we build a quadrilateral covering this

section, and this is divided into two triangles (marked

red in the ﬁgure). In order to build the posterior part

of the feather, we project the faces using the inverted

normal vectors as guidelines. The user speciﬁes the

thickness of the feather. After this step, the two sur-

faces are connected by the borders, which will be tri-

angulated using the same process (represented in blue

in the ﬁgure). At the end, we have a closed mesh rep-

resenting the overall shape of the feather, able to be

submitted to the simulation by the MCLONE. This

structure is only required for MCLONE simulation,

so this 3D model will not be used for the rendering of

the feather.

4.1.2 Simulating the Pattern

In this step we run a MCLONE simulation onto the

3D feather generated by the previous step, in order to

create the desired visual pattern. We run the simu-

lation, and as output we have the desired pattern de-

scribed in a ﬁle that contains all the cells of the pat-

tern, with respective positions and types. The graph-

ical representation of these cells is illustrated in Fig-

ure 4(a), while the ﬁnal pattern is presented in Fig-

ure 4(b). This pattern is obtained by computing the

Voronoi diagram for all cells in Figure 4(a). The use

of the Voronoi Diagram to represent the pattern and

the number and meaning of parameters is fully ex-

plained in (Walter et al., 1998).

4.2 Rendering

Once the structure for one feather is built, we can (i)

render it in a non-realistic way; (ii) render it with tex-

ture that can be acquired from feather pictures (di-

rect texture mapping), or (iii) we can generate textures

procedurally using the MCLONE model (transferring

(a) Cells (b) Final Pattern

Figure 4: Graphical representation of cells.

the pattern to the barbs). The last 2 approaches use

BTF to improve the realism.

For each feather, we maintain a set of control

points deﬁning the rachis and the barbs in each vane

(left and right). Sampling on B´ezier curves is user

driven and allow us to generate feathers in multi-

ple levels of resolution, from coarse (few sampling

points) to ﬁne (many sampling points). This feature

could be used, for instance, to adjust rendering ac-

cording to distance from camera to feather. Results in

this paper were generated using 30 sampling points.

The way the feather is constructed allows us to eas-

ily compute texture map coordinates, since the B´ezier

curves (rachis and barbs) are already parameterized in

the [0,1] interval.

4.2.1 Transferring the Generated Pattern to the

Barbs

In case we are using the pattern generated by the

MCLONE, we have a pattern simulated directly on

the surface derived from the structure of the feather

built by the user. In this context, the rendering step

needs to transfer this pattern onto the barbs of the

feather. During the rendering of the segments describ-

ing the barbs, we need to ﬁnd out the color indicated

by the pattern. In a intuitive way, we must ﬁnd the

nearest cell in the pattern for that segment, obtaining

type and consequently color, ﬁnally rendering the seg-

ment using this color. We solve this problem using a

kd-tree. Figure 5 illustrates the problem.

Figure 5: Searching for the nearest cell, when transferring

the pattern to the barbs. Dotted line in the picture represents

the barb.

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280

4.2.2 Generating and Mapping a Btf

Bidirectional Texture Functions (BTFs) are used to

capture the mesostructure’s details of an object and

represent those details in the texture, improving the

realism. In the case of feathers, the interconnection

between barbs-barbules plays a very important role in

the ﬁnal appearance of a feather. In order to repre-

sent these details in our model, we based our solution

in an approach proposed in (Chen et al., 2002). We

built the geometric structure of the interconnection

between barbs-barbules, an rendered it from several

different combinations of viewing and lighting condi-

tions, using POV-Ray. As a result, we have an image

of the structure for each different combination sam-

pled. Since this is an off-line step, we can use com-

plex geometries and sophisticated lighting models.

During rendering, we map the BTF texture to sim-

ulate the barb-barbules interconnections. Each barb B

is described as a polyline L

with vertices x

, ..., x

When the barb is rendered, instead of rendering only

a B´ezier curve, a quadrilateral is built for each seg-

ment of the polyline L

. For each of these segments,

we obtain lighting and viewing directions. With these

directions, we can extract the 1D texture of the image

built off-line, map it onto the quadrilateral represent-

ing the segment, and merge it with the RGBA color

that was obtained from the texture of the MCLONE

pattern, resulting in the ﬁnal pixel’s color. In order to

reduce aliasing and the size of the texture, we apply

supersampling when generating the BTF, ﬁltering it

with a gaussian kernel.

5 RESULTS

In this section, we show three results of our approach.

All results are realtime, considering that the compu-

tation of the MCLONE pattern and BTF are done of-

ﬂine. A detailed explanation about the MCLONE pa-

rameters can be found in (Walter et al., 1998). We list

the parameters used for these results in Tables 1 and 2.

In Figure 6, we can see that our approach simu-

lates in a realistic way the eyespots found in peacock

feathers. In addition, using BTF improves the overall

visual appearance of the result, when compared with

the rendering using only curves. In other approaches

that use Reaction-Diffusion (Prum and Williamson,

2002) such results could not be achieved. We can no-

tice also that for these results we have two set of val-

ues for the MCLONE parameters. This is because in

order to synthesize the eyespot, we used MCLONE

cascade simulations, where the result of one simula-

tion is used as input for the second.

Figure 6: Central Spot (Pavo cristatus, Phasianidae). a)

Image of real feather. b) Feather rendered with B´ezier.

c)B´ezier curves’s details. d) Polyline rendering. e) Ren-

dering with polylines and BTF.

With the MCLONE we are able to generate sev-

eral different visual feather patterns. Together with

the set of parameters proposed to model the structure

of feathers, we have a robust model that allows us to

generate procedurally all types of feather structures

and many of the visual patterns as well. One of the

main advantages of using a procedural mechanism for

pattern generation is the ﬂexibility. If we have a tex-

ture sample extracted from a picture, for instance, all

the models where we map it would have exactly the

same appearance, that came from the picture. If us-

ing a procedural mechanism, on the other hand, we

can generate many slightly different patterns, which

is much more similar to the way Nature works. As

examples we show Figures 7 and 8. Both illustrate

typical spots and stripes found in many feathers. For

Figure 8, we can see that we have two different values

for each parameter for modelling the structure, and

the parameter I

is set. This means that we divided

the feather into two different segments, each one us-

ing a set of parameters.

Figure 7: Stripes (Phloeceastes guatemalensis). First pic-

ture is from a real feather, second result generated only with

B´ezier curves, third with polylines. and last with polylines

and BTF.

Although not very extensive, these results conﬁrm

the potential of an integrated approach for modelling

feathers as a whole, shape and visual together. More

DIRECT TEXTURE SYNTHESIS OF FEATHER PIGMENTATION PATTERNS

281

Table 1: Values of the parameters for the peacock feather (ﬁg. 6). ρ = 18, w

= 3.0 e time = 40, same in both simulations.

Model N

MCLONE w

mit F mit B mit M mit I αFF αBB αMM αII mut FM no. cells

Figure 6 180 0.045 0.2 T T F - 1.0/0.25 - - -

0.15 5 150 7 0 0.6 0.4 0.95 0.0 0.3 45/5000/82/0

0.1 160 160 160 5 0.2 0.2 0.3 0.95 - 45/5000/81/821

Table 2: Values of the parameters for results shown in Figures 7 and 8.

Model N

MCLONE ρ w

time w

mit F mit B αFF αBB no. cells

Figure 7 250 0.135 0.2 T T F - 2.5/0.1 -

18 2.4 30 0.1 10 150 0.9 0.6 2029/4664

Figure 8 10 0.200 0.35 T T F 0.2 2.0/0.1 -

60 0.035 0.2 T T F - - -

18 3.0 55 0.1 6 150 0.9 0.6 506/4999

Figure 8: Central and circular Spots (Chrysocolaptes lu-

cidus). First picture is from a real feather, second result

generated only with B´ezier curves, third with polylines. and

last with polylines and BTF.

sophisticated visual patterns could be achieved with

elaborated MCLONE simulations.

6 CONCLUSIONS

This work introduced an approach to compute inte-

grated generation of shape and visual pattern in feath-

ers. The approach presented here includes both the

geometric model of a single feather and the visual pat-

tern of the same. We have also extended the Clonal

Mosaic Model, applying it for procedural genera-

tion of feather visual patterns. In comparison with

other approaches (Dai et al., 1995), the set of para-

meters that deﬁnes the model showed greater ﬂexibil-

ity, where we can simulate several different types of

feathers. Besides that, our approach includes a model

to generate the patterns procedurally, in opposition

to other approaches where the textures are extracted

from pictures of real feathers (Chen et al., 2002; Streit

and Heidrich, 2002). The use of a procedural model

brings ﬂexibility as needed to generate several similar

textures, with only small variations.

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