=Paper=
{{Paper
|id=Vol-3766/CVCS2024_4_Paper_Filip_etal
|storemode=property
|title=Angle-dependent analysis and modeling of absorption and structural colors in feathers
|pdfUrl=https://ceur-ws.org/Vol-3766/CVCS2024_4_Paper_Filip_etal.pdf
|volume=Vol-3766
|authors=Jiři Filip,Frank J. Maile,Radomír Vávra
|dblpUrl=https://dblp.org/rec/conf/cvcs/FilipMV24
}}
==Angle-dependent analysis and modeling of absorption and structural colors in feathers==
https://ceur-ws.org/Vol-3766/CVCS2024_4_Paper_Filip_etal.pdf
Angle-dependent analysis and modeling of absorption
and structural colors in feathers
Jiří Filip1,* , Frank J. Maile2 and Radomír Vávra1
1
The Czech Academy of Sciences, Institute of Information Theory and Automation, Prague, Czech Republic
2
Schlenk Metallic Pigments GmbH, Roth-Barnsdorf, Germany
Abstract
Bird feathers represent one of the most challenging examples of material appearance, driven by a
combination of structural properties at different scales. At the microscopic scale, feather appearance is
dictated by the anisotropic behavior of directional feather parts. At the nanoscale, some species exhibit
structural color due to light diffraction on structures comparable in size to the wavelength of light. In
this paper, we capture feathers from four different species, analyze various aspects of their appearance,
and suggest its efficient modeling approach.
Keywords
Feather, Appearance, Structural color, BTF, BRDF, angle dependency
1. Introduction
The specific appearance of feathers allows for the introduction of glossy, metallic, or iridescent
effects [1], which are related to specific pigments or structures within the feather parts. A
typical feather consists of a central shaft (rachis), with serial paired branches (barbs) forming a
flattened, usually curved surface called the vane (see Fig. 1). The barbs possess further branches
called barbules. The barbules of adjacent barbs are attached to one another by hooks, stiffening
the vane. In many birds, some or all of the feathers lack barbules or hooks, resulting in plumage
with a loose, hairlike appearance [2].
Feather parts are made from keratin, and color effects in feathers arise from absorption colors
produced by carotenoid, melanin, and porphyrin pigments, or from structural colors. Structural
colors can lead to iridescent effects, such as those seen in hummingbirds, or to blue colors
specifically observed in the serially paired branches called barbs. This is due to a unique porous
structure with dimensions smaller than the wavelength of light.
Feathers are known for their intricate angle-dependent appearance, as demonstrated in
Fig. 2. Although the composition of feathers and their relationship with color appearance
have been deeply studied in recent years, the angle-dependent interaction of complex feather
structures with lighting or observation from varying directions, and its simulation for appearance
characterization and visualization purposes, remains an open research task.
CVCS2024: the 12th Colour and Visual Computing Symposium, September 5–6, 2024, Gjøvik, Norway
*
Corresponding author.
$ filipj@utia.cas.cz (J. Filip)
https://staff.utia.cas.cz/filip (J. Filip)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
Figure 1: A scheme of typical feather structure.
Figure 2: Pictures depicting the angle-dependent appearance of feather (maned or Australian wood
duck, chenonetta jubata) by courtesy of Heidi & Hans-Jürgen Koch [3]).
In this paper, we examine the intricate details, including blue structural coloration, in bird
feathers. We performed an angle-dependent analysis of feathers of four avian species. The
main contributions of this work are the characterization of the angle-dependent appearance of
feathers, specifically:
• Capturing high-resolution angle-dependent photographs of four feather samples.
• Explaining the details of the angular behavior including structural colors and their rela-
tionship to local aspects of the feather texture.
• Proposing a novel analytical reflectance model of major features of the feather textureless
appearance.
2. Related Work
The principles of color in feathers were discussed as early as Newton [4], who suggested that
peacock feathers "appear of several colors in several positions of the Eye" and that their color
"arises from the thinness of the transparent parts of the Feathers." The physical principle of
structural colors in feathers was first explained by Bancroft [5].
More recently, general principles of angle-dependent optical effects deriving from sub-micron
structures of films and pigments were surveyed Pfaff and Reynders [6]. Srinivasarao [7] provides
a comprehensive survey of nano-optics related color principles in the biological world, including
beetles, butterflies, birds, and moths. Gruson et al. [8] suggested a straightforward method
to characterize the angle-dependent effects of structural colors using spectrometry with an
optimized set of geometries and five parameters: hue, angle dependence of hue, maximum
brightness, tilting, and angle dependence of brightness. Maia et al. [9] have shown that
feather gloss depends on the shape and structure of the keratin cortex of the barbules, and
that glossy feathers are morphologically intermediate between matte black and iridescent
feathers. Saranathan et al. [10] used synchrotron small-angle X-ray scattering and optical
spectrophotometry to characterize the nanostructure and optical function of 297 distinctly
colored feathers from 230 species, confirming the presence of a predominant, isotropic length
scale of variation in refractive index that produces strong reinforcement of a narrow band
of scattered wavelengths. Parnell et al. [11] studied Eurasian Jay feathers and explained the
reasons for periodic variations in the reflected color of a single barb, ranging from white
through light blue, dark blue, and black. Imafuku [12] characterized the angle-dependent
behavior of butterfly wings. Structural colors have been thoroughly studied, and there are even
attempts to mimic their appearance in practical industrial applications [13]. Magkiriadou et al.
[14] introduced angle-independent structural colors by packing core-shell colloidal particles
consisting of high-refractive-index cores and soft, transparent shells.
While the majority of the studies focused on the spectral behavior of feather parts under fixed
viewing and illumination condition, we focus on the detailed characterization and modelling of
feather appearance as a function of illumination and viewing angle.
Figure 3: An example of angle-dependent effect of a macaw parrot feather.
3. Feather samples
We selected feathers from four distinct bird species covering different types of color formation
principles (structural, absorption, and a combination) and an achromatic one. Therefore, our
sample set contains macaw parrot (parrot), Cochin cock (rooster), greater flamingo (flamingo),
and white stork (stork), as shown in the first row of Fig. 4.
parrot rooster flamingo stork
Figure 4: Four feather samples were analyzed in our study. Detailed structural images of these samples
were obtained using light microscopy (second row) and scanning electron microscopy SME (third row).
All feathers have distinctly different colors and structures, as shown in the light and scanning
electron microscopy (SME) images in the second and third rows of Fig. 4. These images clearly
display the varying topology and shape of barbules. While the flamingo and stork have their
coloration based on absorption pigments [1], the parrot and rooster also include structural
coloration.
In natural feathers, blue coloration, such as that in macaw parrot feathers Fig. 3, is structural,
resulting from a unique porous structure in the barbs with dimensions smaller than the wave-
length of light. The smaller barbules branching from these barbs retain their dark coloration
because they lack this particular structure. Some species combine both absorption and structural
colors, such as creating green by combining yellow absorption pigment with structural blue.
The Cochin cock features a green absorption pigment, a mixture of black and yellow com-
pounds, giving it an olive green color. Green or possibly violet reflections result from structural
variations in the keratinized surface of the feathers and are not due to a pigment different from
the usual present pigments. The high glossiness of these feathers is due to melanin, which
has a very high index of refraction [15], greater than that of the surrounding keratin. Single
structures of eumelanin are iridescent, endowed with metallic-like colors that change according
to the angle of illumination.
4. Appearance Capture
To gain insight into the angle-dependent behavior of our feather specimens, we captured
the specimen surfaces using the SIGHTTEX Q goniometric device. This device is based on a
goniometric setup utilizing two arms outfitted with five RGB cameras and 28 non-polarized LED
lights, both positioned approximately 300 mm from the measured area, which has a maximum
size of 40 × 40 mm. The device allows for capturing arbitrary azimuthal angles, while polar
angles are fixed at 15-degree intervals up to 75 degrees. The captured high dynamic range
images of a 3×3 mm feather patch, with a resolution of 1500 DPI, have a size of 237 × 237 pixels.
We captured several types of data. First, we used in-plane analysis, a standard method for
characterizing the scattering of isotropic materials. During this measurement, the view was
fixed at 45 degrees, and the light varied between -81 and 81 degrees at 3-degree intervals,
resulting in 55 captured images. Next, we captured the full view- and illumination-dependent
texture of the samples using the bidirectional texture function (BTF) [16]. Both illumination
and viewing directions were sampled in 15-degree steps in polar angle and 30-degree steps in
azimuths, resulting in 3660 captured images. The capturing time was approximately 30 minutes.
We also captured different patches of feathers, resulting in very similar appearance data when
the alignment of the barbules was constant.
5. Angle-Dependent Analysis
5.1. Inplane Analysis
As feathers are highly anisotropic due to their structure, the in-plane analysis of feather samples
is highly dependent on the orientation of the captured plane relative to the sample. We used
a similar orientation of the plane to the barbs (the plane perpendicular horizontally to the
captured barb structure), as shown in Fig. 5.
parrot rooster flamingo stork
Figure 5: Samples luminance for a diffuse illumination obtained from the measurements (captured area
3×3 mm).
The results of our analysis in CIE L*a*b* are shown in Fig. 6. Fig. 6-a presents luminance
as a function of illumination angle, highlighting the retro-reflection and specular reflection
directions. We do not observe any sharp peaks at the specular reflection direction due to the
overall diffuse nature of the samples. Only the parrot and flamingo samples exhibit a stronger
increase in luminance in this direction. In the flamingo feather, we observe a relatively wide
peak, while the parrot shows a narrower peak slightly offset from the ideal specular direction.
This is likely due to the fact that the specularity arises from the protruding cylindrical structure
of barbs with a porous structure that induces blue structural color in the retro-reflective region
but exhibits bright highlights at specular directions. In the retro-reflective direction, peaks can
only be observed for samples that include some structural colors, i.e., parrot and rooster. In the
case of the parrot, such peak is actually of higher intensity than the specular one.
We also compared color changes due to the change of in-plane illumination direction. Fig. 6-b
shows an a*-b* chart including all the samples, and it is evident that the only sample exhibiting
significant color changes is the parrot, moving from dark achromatic hues to strong structural
blue.
(a) (b)
Figure 6: In plane CIE (a) luminance and (b) color a*b* chart of the tested feathers.
5.2. Uniform angle-dependent measurements
Angle-dependent appearance measurements sampled uniformly over the hemisphere of in-
coming and outgoing directions provide ample information useful for appearance analysis and
visualization in virtual environments. Fig. 7 provides an overview of the geometries captured. It
represents each of the 3660 captured images by their average color as a single pixel, forming an
image where rows correspond to 61 illumination directions and columns to 60 viewing directions.
This image displays values of the bidirectional reflectance distribution function (BRDF) [17]
and demonstrates the material’s reflectance distribution as a function of illumination (rows)
and viewing (columns) directions, moving circularly from the pole of the hemisphere above
the material to its bottom. Polar angles are sampled in 15° steps (for light 0∘ , 15∘ , 30∘ , 45∘ , 60∘ ,
75∘ ; for view 15∘ , 30∘ , 45∘ , 60∘ , 75∘ ). Within each polar angle, 12 azimuthal angles are sampled.
This BRDF image provides a fingerprint of the material’s angle-dependent behavior and reveals
specific characteristics such as color intensity, presence and strength of anisotropy, and strength
of specular reflection. A comparison of the BRDFs of our feather samples is shown in the first
row of Fig. 8. When we compare these BRDF images with similar images obtained for a single
Figure 7: An overview of captured angle-dependent data, where each pixel represent average color of
one captured image, visualizing four-dimensional BRDF function in a two-dimensional image.
image pixel in the second row, we can see clear differences due to local view occlusion and
masking effects, exhibited by vertical stripes. This occurs when a part of the feather, such as
a barb, is higher than its surroundings, as is clearly visible in the image of the parrot sample,
which has barbs slightly protruding from the feather plane. Due to these effects, the data do
not fulfill BRDF assumptions and are often referred to as apparent BRDFs (ABRDF). The last
two rows show the minimal and maximal values in the captured images. Again, the strongest
difference is observed in the parrot, showing a contrast between pixels representing structural
blue barbs and darker areas between barbules. This difference is also visible for the rooster but
is less prominent for the flamingo and stork.
When examining detailed surface behavior at specific geometries, we can analyze individual
images. For our analysis, we selected low polar angles 30∘ to avoid large perspective foreshort-
ening of the feather samples’ structure and analyzed the samples’ behavior for a fixed viewpoint
and varying illumination azimuths at the same polar angle. These twelve geometries are illus-
trated by the red rectangle in the BRDF image in Fig.7. Fig.9 shows the corresponding twelve
captured images arranged azimuthally around an image showing feather structure obtained by
SME. The azimuthal arrangement corresponds to the azimuthal direction of illumination and
provides an intuitive explanation of light interaction with the feather structure.
Let’s observe the texture of the samples in more detail. The parrot sample, at retro-reflective
directions (where the light and camera are close enough), exhibits strong structural blue at the
barbs, while the barbules become very dark. At near-specular directions, we observe specular
highlights from the barbs, indicating they likely have a smooth, glossy surface. Additionally,
the barbules become brighter, with a clear boundary between two touching rows of structures.
This behavior is supported by the sample’s BRDF in Fig. 8, showing structural blue and gray
Figure 8: A comparison of BRDFs obtained as by images averaging (the first row), as a value of a single
pixel (the second row), as minimal and maximal image values (the third and fourth row).
anisotropic reflection as the main visual features.
The rooster’s sample BRDF shows strong anisotropic behavior as the main visual feature,
driven by the orientation of the barbules. The rooster’s barbules have a larger area, making
them more effective reflectors of incoming light. Consequently, this sample is not the brightest
at specular directions but at directions where the barbules are properly oriented relative to the
light and camera.
Similarly to the rooster, the flamingo sample does not show barbs but has two layers of
barbules, one slightly above the other. The main visual feature is the increased contrast between
these two layers at specular directions, where only the upper layer participates in light trans-
mission. A very similar effect is observed in the stork sample, which has a similar structure
topology to the parrot; however, as it lacks structural color, the main visual effect is the increased
contrast between differently oriented regions of barbules. The BRDFs in Fig. 8 for all the last
three samples show anisotropic reflection from oriented barbules as the major visual behavior.
As the captured illumination and viewing angle-dependent data represent a bidirectional
texture function (BTF), they can be readily used for sample visualization. Fig. 10 shows a
visualization of the captured physical area (3×3 mm) on a blob-like object. The first row shows
parrot rooster
flamingo stork
Figure 9: Feather local structure change as a function of illumination azimuthal direction for view and
illumination polar angles fixed to 30∘ . Yellow and white dots denote illumination and viewing azimuths.
The inset image shows a structure details obtained using SME.
frontal (retro-reflective) illumination, while the second row shows the object illuminated from
the left. These two lighting conditions clearly demonstrate the retro-reflective properties of the
parrot sample’s structural blue, as well as the anisotropic highlights of the rooster and flamingo
samples.
parrot rooster flamingo stork
Figure 10: Feather samples were visualized using BTF on a 3D object under both frontal and side
illumination. This visualization effectively demonstrates the angle-dependent properties, showcasing
retro-reflective properties and anisotropic highlights.
6. Angular behavior modelling
As shown in Fig. 8, the main visual features of captured BRDFs include anisotropic, retro-
reflective, and specular highlights. While the locations of the latter two are clearly defined by
the mutual azimuthal positions of light and camera, the locations of anisotropic highlights are
quite non-intuitive, forming an intricate pattern in the BRDF angular space.
However, the locations of anisotropic in angular domain can be reliably predicted on di-
rectional surface elements, laying in planes orthogonal to the bisector (often denoted as the
half-way direction H = ||𝜔𝜔𝑖𝑖 +𝜔
+𝜔𝑣 || ) of directions of the incidence 𝜔𝑖 = [𝜃𝑖 , 𝜙𝑖 ] and reflectance
𝑣
𝜔𝑣 = [𝜃𝑣 , 𝜙𝑣 ] directions, as proposed in [18]. Therefore, the anisotropic highlights can be
predicted [19] at directions of the bisector that are orthogonal to the anisotropic angle 𝜙𝑎 of
the material U = [sin 𝜙𝑎 , cos 𝜙𝑎 , 0]. Thus, the angular locations of anisotropic highlights can
be expressed as
𝐹 (𝜙𝑎 ) = 1 − |H · U(𝜙𝑎 )| (1)
U(𝜙𝑎 ) = [sin 𝜙𝑎 , cos 𝜙𝑎 , 0]
To account for areas of anisotropic highlights, we generate a support mask 𝑀 around the
highlights as shown in Fig. 11-2. The support mask 𝑀 with a smooth boundary can be expressed
as a function of anisotropic angle 𝜙𝑎 , width of anisotropic highlight 𝑤, and width of its smooth
edge 𝑑𝑤 as follows ⎧
⎨1
⎪ 𝑥 ≤ 𝑤 − 𝑑𝑤
𝑀 (𝜙𝑎 , 𝑤) = 0 𝑥 ≥ 𝑤 + 𝑑𝑤
⎪
𝑓 (𝑥) 𝑤 − 𝑑𝑤 < 𝑥 < 𝑤 + 𝑑𝑤
⎩
BRDF model 1: background 2: anisotropy
3: near-spec. 4: retro 5: specular
Figure 11: Illustrative decomposition of the proposed BRDF model (parrot) into its five additive
factors: (1) constant background, (2) anisotropic highlight, (3) near-specular highlight, (4) retro-reflective
highlight, and (5) specular highlight.
where 𝑥 = 1 − |H · U(𝜙a )|, and 𝑓 (𝑥) is a smoothstep function 𝑓 (𝑥) = 𝑦 2 (3 − 2𝑦) where
2𝑑𝑤 .
𝑦 = 𝑥−𝑤+𝑑 𝑤
Our BRDF model is composed of five additive factors each accounting for (1) constant
background, (2) anisotropic highlight, (3) near-specular highlight, (4) retro-reflective highlight,
and (5) specular highlight, as shown in Fig. 11. Therefore, the model can be expressed using five
additive terms constrained by support areas defined by mask 𝑀 or out of it using its complement
(1 − 𝑀 )
𝑓 (𝜔𝑖 , 𝜔𝑣 , 𝑗) = (1 − 𝑀 ) · C𝑏 (𝑗) + (2)
+ 𝑀 · C𝑎 (𝑗) +
+ (1 − 𝑀 ) · C𝑠 (𝑗) · 𝐸 · 𝐷(0) · 𝐹 +
+ (1 − 𝑀 ) · C𝑟 (𝑗) · 𝐸 · 𝐷(𝜋)𝛾 · 𝐹 +
+ 𝑀 · 𝛼𝐸 𝛽 · 𝐷(0) ,
(3)
where 𝑗 is the RGB channel index, 𝐶𝑏 , 𝐶𝑎 , 𝐶𝑠 , and 𝐶𝑟 denote background, anisotropic highlight,
near specular, and retro-reflective RGB color. The parameters 𝛼 and 𝛽 perform elevation-
dependent scaling of the cosine factor defined as
𝐸 = 1.1 − cos 𝜃𝑖 cos 𝜃𝑣 . (4)
A normalized difference of azimuthal angles represents the shape of the azimuthally dependent
lobe specified by angle 𝛿 (0 for specular lobe, 𝜋 for retro-reflective lobe):
|𝜙𝑖 − 𝜙𝑣 − 𝛿|
𝐷(𝛿) = . (5)
2𝜋
Finally, the width of the retro-reflective lobe is specified by parameter 𝛾, and factor 𝐹 accounts
for the decrease of retro-reflective intensity for different elevations of light and camera as
follows:
|𝜃𝑖 − 𝜃𝑣 |
𝐹 =1− , (6)
𝜃𝑚𝑎𝑥
where 𝜃𝑚𝑎𝑥 specifies the maximum elevation angle captured in the data, in our case 75∘ .
We fitted our model to the captured BRDFs of individual feather samples and obtained the
parameters outlined in Tab. 1. A comparison of the captured and fitted BRDFs is given in the
first two rows of Fig. 12. Rendering of the respective variants on a bird shape model illuminated
from the frontal direction is shown in the third and fourth row of the same figure, while the
fifth row shows the difference. From the rendering it is clear that model well preserves the
main visual the tested features and represents satisfactory simulation of their angle-dependent
appearance.
The meaning of the model’s parameters is quite intuitive. They define the direction of
anisotropy 𝜙𝑎 , and the colors of the background 𝐶𝑏 , anisotropic highlights 𝐶𝑎 , near-specular
highlights 𝐶𝑠 , and retro-reflective highlights 𝐶𝑟 . The remaining parameters 𝛼, 𝛽, 𝛾, 𝑤, 𝑑𝑤 shape
the width and intensity of individual highlights. For the purpose of this paper, the parameters
were tuned manually. However, due to the model’s close-form definition, they can be easily
fitted using a non-linear fitting method, such as the steepest descend. The analytical definition
of the model also allows for its fast evaluation, enabling the OpenGL rendering in Fig. 12 to run
at speed of 20 FPS on a PC with an Intel Core i7.
7. Conclusions
This paper analyzed the angle-dependent optical properties of four feather samples, one of which
included structural color. By analyzing in-plane behavior, BRDF, and BTF data, we highlighted
the differences between optical properties of the samples and suggested the reasons for this
behavior. Finally, we proposed an analytical BRDF model that reproduces feather sample’s
reflectance behavior based on a few intuitive parameters. A shader function of the model is
publicly available at the project website https://staff.utia.cas.cz/filip/pub.html.
8. Acknowledgements
This research has been supported by the Czech Science Foundation grant GA22-17529S. We thank
Heidi & Hans-Jürgen Koch for providing pictures depicting the angle-dependent appearance of
feathers in Fig.2.
parrot rooster flamingo stork
captured BRDF
BRDF model
captured BRDF
BRDF model
difference
Figure 12: A comparison of the captured BRDF and its fit using the proposed BRDF model. The
quality of the fit is illustrated by rendering a bird shape illuminated from a frontal direction, visualizing
angle-dependent effects of feather samples on a complex geometry.
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Table 1
Parameters of the fitted BRDFs.
par. parrot rooster flamingo stork
𝜙𝑎 [∘ ] 90.0 -20.0 -80.0 -20.0
C𝑏 R 0.155 0.089 0.701 0.792
G 0.214 0.198 0.607 0.809
B 0.290 0.194 0.535 0.812
C𝑎 R 0.390 0.344 0.891 0.874
G 0.384 0.413 0.819 0.888
B 0.416 0.415 0.768 0.888
C𝑠 R 0.206 0.104 0.961 0.422
G 0.285 0.190 0.851 0.429
B 0.387 0.187 0.771 0.429
C𝑟 R 0.107 0.089 0.779 0.792
G 0.277 0.198 0.674 0.809
B 0.446 0.194 0.595 0.812
𝛼 3.0 5.0 5.0 5.0
𝛽 12.0 12.0 5.0 5.0
𝛾 4.0 0.0 0.0 0.0
𝑤 0.95 0.85 0.80 0.80
𝑑𝑤 0.40 0.20 0.40 0.60
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