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Classification of peacock feather reflectance using principal component analysis similarity factors from multispectral imaging data

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Iridescent structural colors in biology exhibit sophisticated spatially-varying reflectance properties that depend on both the illumination and viewing angles. The classification of such spectral and spatial information in iridescent structurally colored surfaces is important to elucidate the functional role of irregularity and to improve understanding of color pattern formation at different length scales. In this study, we propose a non-invasive method for the spectral classification of spatial reflectance patterns at the micron scale based on the multispectral imaging technique and the principal component analysis similarity factor (PCASF). We demonstrate the effectiveness of this approach and its component methods by detailing its use in the study of the angle-dependent reflectance properties of Pavo cristatus (the common peacock) feathers, a species of peafowl very well known to exhibit bright and saturated iridescent colors. We show that multispectral reflectance imaging and PCASF approaches can be used as effective tools for spectral recognition of iridescent patterns in the visible spectrum and provide meaningful information for spectral classification of the irregularity of the microstructure in iridescent plumage.
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Classification of peacock feather reflectance
using principal component analysis similarity
factors from multispectral imaging data
José M. Medina,1,* José A. Díaz,1 and Pete Vukusic2
1Universidad de Granada, Facultad de Ciencias, Departamento de Óptica, Edificio Mecenas, Granada 18071, Spain
2School of Physics, University of Exeter, EX4 4QL, UK
*jmedinaru@cofis.es
Abstract: Iridescent structural colors in biology exhibit sophisticated
spatially-varying reflectance properties that depend on both the illumination
and viewing angles. The classification of such spectral and spatial
information in iridescent structurally colored surfaces is important to
elucidate the functional role of irregularity and to improve understanding of
color pattern formation at different length scales. In this study, we propose a
non-invasive method for the spectral classification of spatial reflectance
patterns at the micron scale based on the multispectral imaging technique
and the principal component analysis similarity factor (PCASF). We
demonstrate the effectiveness of this approach and its component methods
by detailing its use in the study of the angle-dependent reflectance
properties of Pavo cristatus (the common peacock) feathers, a species of
peafowl very well known to exhibit bright and saturated iridescent colors.
We show that multispectral reflectance imaging and PCASF approaches can
be used as effective tools for spectral recognition of iridescent patterns in
the visible spectrum and provide meaningful information for spectral
classification of the irregularity of the microstructure in iridescent plumage.
©2015 Optical Society of America
OCIS codes: (170.1420) Biology; (330.1690) Color; (350.4238) Nanophotonics and photonic
crystals; (310.6188) Spectral properties; (110.4234) Multispectral and hyperspectral imaging;
(100.5010) Pattern recognition.
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1. Introduction
The brilliant iridescent color appearances of many avian feathers are produced by complex
optical phenomena. They principally arise from coherent light scattering from self-assembled
quasi-ordered structures that have a spatially periodic variation in refractive index. This can
lead to iridescent colors [1–4]. A canonical example is the well-known iridescent effects of
male peacock tail feathers [Fig. 1(a)] [5, 6].Within the cortex of these feathers’ barbules,
melanin rods are arranged to create two-dimensional (2D) photonic crystal-like structures at
the sub-micron scale [Fig. 1(b)] [7–9]. Polarization effects from the photonic structure are not
discernable and do not strongly influence the structural color appearance of feather barbules
[7, 8]. The spatial organization of barbules is complex: it produces the intricate iridescent
patterns of reflectance at the macro-scale which ultimately give rise to the visual effects that
contribute to the bird’s appearance [1, 6, 9, 10]. A certain extent of spatial disorder is crucial
for achieving this appearance. An irregular spatial arrangement of barbules appears to smooth
the angle-dependence of reflectance giving rise to the feather’s diffuse reflection over a wide
angular range [1, 9, 11]. The colorful eyespots of peacock feathers are also considered a
classical example in research on intra-specific animal communication (i.e. relating to female
mate choice) and do not exhibit reflectance maxima in the ultraviolet (UV) spectrum [12].
The measurement of the bi-directional reflectance distribution function (BRDF) in
iridescent feathers is often simplified by fixing certain angles of illumination and detection
[13]. Although several spectrophotometric methods have been implemented to examine the
angular dependence of reflectance spectra over small feather patches [7–9, 12, 14–20], those
studies that collect both spatial and spectral information simultaneously are rare. Stavenga et
al. [18] have investigated light scattered patterns from a single boomerang-like barbule of the
Lawes’ parotia (Parotia Lawesii) using an imaging scatterometer based on an ellipsoidal
mirror [13, 18, 21]. Kim et al. have used a snapshot-based hyperspectral acquisition system to
compute three-dimensional (3D) spatial patterns and hyperspectral reflectance
simultaneously, that extends from the near UV to the near infrared (IR) of the entire plumage
of the Papuan Lorikeet (Charmosyna papou goliathina) and the Northern Rosella
(Platycercus venustus) [22]. Harvey et al. have investigated the dependence between scattered
light and orientation of feather barbs of the Purple Glossy Starling (Lamprotornis purpureus)
and the African Emerald Cuckoo (Chrysococcyx cupreus) using a imaging scatterometer
based on a spherical gantry configuration and an RGB camera [23, 24]. Brydegaard et al.
have investigated the existence of iridescent effects in the mid-IR region of many avian
species for remote classification at long distances [25]. They have concluded that these IR
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(C) 2015 OSA
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010198 | OPTICS EXPRESS 10200
iridescent features have a structural origin at the micrometer level. These authors have
performed hyperspectral reflectance polarization imaging [26–28] of the Mallard (Anas
platyrhynchos) demonstrating that IR iridescence persists in the entire bird [25].
In this study, we present details of a spectral classification method of reflectance patterns
in the visible spectrum comprising the collection of series of multispectral images of peacock
feathers, using a spatial resolution of a few microns, as a function of the illumination angle.
Investigation of these reflectance patterns at the micrometer level has a direct link with the
roughness of the microstructure and the spatial configuration of barbs and barbules [1, 9]. The
peacock plumage is chosen to investigate if the emerging reflection patterns from quasi-
periodic arrangement of structurally colored barbules can be classified among different
categories of interest from the spectral perspective. For this purpose we have performed
multispectral reflectance imaging on three representative peacock feather samples that exhibit
different stages of feather development. This is also important in animal biometrics to
examine the effects of weak microstructural disorder on iridescent colors across members of
the same species. Multispectral imaging methods result from the combination of digital image
analysis of an imaged scene and subsequent spectroscopic analysis pixel-by-pixel [29–31].
Multispectral imaging offers an important advantage for analysis of the micro-appearance of
feathers by providing spectral data with high spatial resolution. Standard single-point
spectrophotometric methods are limited because spatial details are often diluted within the
illuminated area [13]. Multispectral imaging methods, however, enable the extraction of the
spectral reflectance function at each pixel of the imaged scene [29, 30].
Fig. 1. Structural characterization of peacock tail feathers. Color photographs. Panels (a-c-e)
show the eye region of an adult peacock feather (P. cristatus), a young peacock feather (P.
cristatus), and a white peacock feather (P. cristatus mut. alba), respectively. Transmission
electron micrographs (TEM). Panels (b-d-f) show TEM images of the transverse cross section
of a brown barbule (adult P. cristatus), a brown barbule (young P. cristatus), and a white
barbule (P. cristatus mut. alba) in the eyespot, respectively. Scale bars (b-d-f) 1 µm.
The principal components analysis similarity factor (PCASF) has previously been used for
approach methodologies serving pattern recognition [32–34]. It is a PCA-based approach that
is a useful technique for pattern matching which quantifies the similarity between two data
sets in many industrial applications [32, 33, 35]. Principal component analysis (PCA) itself is
an effective statistical method that has been widely used in multivariate image analysis for
dimensionality reduction, data compression, classification, visualization, noise reduction, etc
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(C) 2015 OSA
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010198 | OPTICS EXPRESS 10201
[30, 32, 36–39]. In color science, PCA is also widely applied to uncover the spectral bands of
colorants. PCA decomposes reflectance spectra into a linear combination of few uncorrelated
basis functions or eigenvectors over a large number of reflectance data sets [32, 36, 37, 40,
41]. The first eigenvectors explain most of the variance within the data set [30, 37, 40, 42].
PCASF quantifies the similarity between the principal component subspaces that contain the
most significant eigenvectors by using a single number. PCASF ranges from zero (no
similarity) to one (similar samples) [32–35]. PCASF thereby enables comparison of the
reflectance patterns created by arrays of feather barbs at different spatial locations, feather
orientation, and illumination angles. Two different metrics were examined: the standard
PCASF and a weighted PCASF (WPCASF). In the standard PCASF the eigenvectors are
equally weighted, while in the WPCASF each eigenvector is weighted by the square root of
its associated eigenvalue. WPCAF provides a measure of similarity using feature eigenvectors
that explain a significant amount of variance [32, 35].
Classification of the reflectance properties of iridescent plumage overcomes current
limitations of colorimetric methods [12, 17, 20, 43]. For example, classification of reflectance
spectra does not depend on the illuminant spectra and receptor spectral sensitivities.
Additionally, it avoids potentially misleading results from metamerism of pairs of color
patterns [44]. In this study we illustrate PCASF by analyzing reflectance spectra collected
from male peacock feathers (Pavo cristatus). We first describe PCASF between an iridescent
peacock feather [Fig. 1(a)] and a white peacock feather (Pavo cristatus mut. alba) [Fig. 1(e)].
The white peacock belongs to the same species and displays non-iridescent effects. Its
constituent feather barbules lack melanin rods [Fig. 1(f)] and its white color appearance is
principally produced by broadband scattering in its keratin matrix [45–47]. We follow this by
applying PCASF to the comparison of spatial reflectance patterns produced by feathers from
an adult and a young peacock [Figs. 1(a) and 1(c)], where the young peacock feather is
deemed to be in an intermediate state of growth [48]. In this sample the development of blue,
green, brown and yellow barbules, as well as the spatial formation of the feather’s eyespot
region, are incomplete [Fig. 1(c)]. For instance, the brown barbules in the young peacock are
thinner and the 2D photonic crystal structures in the cortex surface also reveal differences in
the lattice structure [Fig. 1(d)]. The young and adult brown barbules have the same number of
melanin layers (4 to 5). The lattice constant (rod spacing) along the direction parallel to the
cortex, a, is shorter in the young peacock. However, that in the perpendicular direction, a,
is very similar to the adult peacock. The separation of the two melanin arrays nearest to the
cortex, d, is slightly shorter in the young peacock [Figs. 1(b) and 1(d)]. These lattice values
are similar to those previously reported for the Pavo muticus, a different species of peafowl
[7, 8]. Table 1 summarizes the lattice constants of brown barbules in the young and adult
peacock.
Table 1. Mean lattice constants a, aand the inter-distance between the two melanin
arrays nearest to the cortex, d, of the 2D photonic structure of brown barbules in the
young and adult peacock derived from TEM images [Figs. 1(d) and 1(b)]. The standard
error of the mean ( ± 1SEM) is also shown.
Young brown barbule Adult brown barbule
Lattice constan
t
Mean ( ± 1 nm)
a 150 (2) n
m
187 (3) n
m
a 194 (3) n
m
198 (4) n
m
d 218 (4) n
m
231 (5) n
m
Further differences between TEM images in Figs. 1(d) and 1(b) can be found beneath the
lattice structure at the center of brown barbules. There are more melanin rods in the young
peacock that are randomly distributed. It has been suggested that these melanin granules offer
increased absorption of transmitted light, reduce the extent of diffuse scattering, thereby
making iridescent effects in these feathers more vivid [9].
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(C) 2015 OSA
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010198 | OPTICS EXPRESS 10202
2. Materials and methods
2.1 Structural analysis
Male peacock tail feathers were obtained from a farm in Málaga, Spain. Peacock feathers
were characterized in Fig. 1 by using a digital color camera Canon PowerShot SD1000 and a
transmission electron microscope (TEM) Carl Zeiss Libra 120 Plus EDX. TEM samples were
prepared by fixing feather barbules in 2.5% glutaraldehyde in 0.1 M cacodylate buffer, pH 7.2
at 4 °C for 24 h, followed by rinsing in buffer for 1 h and 30 min at 4 °C. Barbules were then
post-fixed in 1% aqueous OsO4 in buffer at room temperature for 1 h followed by block
staining in 2% aqueous uranyl acetate at room temperature for 2 h. Dehydratation was
performed through a graded series of acetone ending with 100% acetone. Then, barbules were
embedded in an epoxy resin (EMbed 812, EMS). Ultrathin microtome sample sections were
stained with lead citrate.
2.2 Multispectral imaging acquisition system
Many theoretical and experimental approaches have been proposed for the calculation and
measurement of the BRDF of anisotropic surface materials [9, 12–20, 22, 41, 49–57]. In
computer graphics and rendering, the microscopic description of rough surfaces in structural
colors is often modeled by using a collection of tiny facets or microfacets and physical-based
models [49, 51–53, 56, 57]. Here we have used an experimental approach that comprises the
measurement of components of the multispectral BRDF of a feather’s surface microstructure
using a calibrated multispectral camera in a simple goniometric stage. The multispectral
imaging set up, procedure and spectral calibration are described in detail elsewhere [58], and
it has been adapted to the study of peacock tail feathers. Figure 2 shows a schematic
representation of the multispectral imaging acquisition system. Spectral reflectance
information of peacock feathers varies with the illumination angle θ. Three different angular
positions were established at the illumination angle θ of 15 °, 45 ° and 75 °. Collection of
multispectral images was performed by tuning a liquid crystal tunable filter LCTF (Varispec
VS-VIS2-10HC-35-SQ) from 410 nm to 700 nm in steps of 10 nm. The LCTF was attached
in front of a lens (Navitar Zoom 7000 18: 108 mm) of a monochrome charge-couple device
(CCD) camera (Retiga QImaging SVR1394). The illumination system uses a Hamamatsu
L9588-04 150 W highly stable mercury xenon (Hg-Xe) lamp. Light is collected by an
elliptical cold mirror and a Hamamatsu A10014-50-010 light guide with a condenser lens
Hamamatsu E5147-06. At the distance of 20 cm perpendicular to the imaged surface, the lens
uniformly irradiates an area of 40 mm diameter with a relative intensity 100%. This is equal
to the intensity at 10 mm away from the output end of the light guide without the condenser
lens. The condenser lens was mounted in a rotation stage Thorlabs RBB12. Peacock feather
samples were mounted directly beneath a 50 mm diameter aperture [58]. The spectral
reflectance factor at each pixel of the imaged surface was calculated by taking white- and
dark-field measurements [29, 30, 36, 58]. The white-field correction indicates the intensity
values of a calibration sample and was obtained by defocusing a white reflectance standard
(Spectralon 99% Labsphere) [29, 30, 6, 58]. The dark-field correction denotes the intensity
values of the dark current from the CCD sensor [29, 30, 36, 58] and was obtained with the
light source off, without the sample holder, and preventing any residual light entering in the
CCD camera [58]. The multispectral imaging system has a spatial resolution of 14.4 µm per
pixel. Spectral calibration was done by using the Macbeth color checker chart [30, 37, 58].
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(C) 2015 OSA
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010198 | OPTICS EXPRESS 10203
Fig. 2. Schematic representation of the multispectral imaging system. A liquid crystal tunable
filter (LCTF) was placed in front of a zoom lens and attached to a monochrome charge-couple
camera (CCD). The LCTF, zoom lens and CCD camera were in a fixed position and they were
exactly aligned perpendicular to the sample. A light source module was connected to a light
guide fiber. The fiber was mounted in a goniometric stage and was rotated at the illumination
angle θ of 15 °, 45 ° and 75 °.
2.3 Principal component analysis of reflectance spectra
Reflectance spectra of each selected area were treated as a data matrix Rof n rows of
samples by 30 columns of wavelength intervals (at 10 nm resolution). Rwas centred around
the corresponding mean reflectance factor R, RR. PCA decomposes Rin the following
matrix equation [30, 42]:
30
1
ii
i=
=+
RR αS (1)
Where i
αand i
S are the scores and the eigenvectors or loading vectors, respectively. Each
eigenvector indicates the i-th principal component direction which reflectance spectra are
distributed. Eigenvectors are often ranked in decreasing order of their associate eigenvalues
i
β
which correlates with decreasing order of variance accounted. In general, only the first k
eigenvectors are taken in Eq. (1) using a stopping rule [30, 37, 42] that reduces the
dimensionality of the original reflectance data set from 30 (as much dimensions as
wavelength intervals) to k
()
30k<.
2.4 Principal component analysis similarity factors for reflectance spectra
The standard PCASF compares the relative angle ,ij
φ
between the eigenvectors of the two
samples. The eigenvectors of the reference and test sample are arranged in the loading
matrices L and M, respectively, both with k principal components [32–34]:
()
TT
2
,
11
cos
kk
ij
ij
trace
PCASF k
φ
==
==
 MLLM (2)
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20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010198 | OPTICS EXPRESS 10204
The superscript T denotes the matrix transpose. A weighted PCASF or WPCASF weights
each eigenvector by their associated eigenvalue to take into account the amount of variance
explained by each principal component [32, 35]:
()
LM 2 TT
,WWW W
11
LM LM
11
cos
kk
ij ij
ij
kk
ii ii
ii
trace
WPCASF
ββ φ
ββ ββ
==
==
==


MLLM (3)
WL
=LLΛ and WM
=MΜΛ denote the weighted loading matrices. Subscripts and
superscripts L and M denote the reference and test, respectively. In each case L
Λand M
Λ are
diagonal matrices that contain the square roots of the first k eigenvalues [32]. Therefore, each
principal component direction is distinguished by its explained variance. This is relevant to
the classification of spatial reflectance patterns because those principal components having
low variance are of little importance in Eq. (3) and they are often associated with spatial and
temporal noise from the multispectral imaging system [37–39, 58]. The number k of principal
components is an important parameter in Eqs. (2) and (3). A widespread and accepted
stopping rule in color science as well as in process monitoring comprises first selecting those
eigenvectors that account for a certain percentage of total variance [32, 33, 35–37, 40, 41].
This stopping rule is adequate when the total spectral variability in the imaged scene is not
very large [32, 36, 37, 58]. The number k was selected as the maximum value between the
number of principal components of the reference and test sample that describe at least 95% of
the total variance.
3. Results and discussion
3.1 Reconstruction in the sRGB color space
Figure 3 represents the entire selected imaging areas of size 841 x 841 pixels (146.6 mm2) in
the sRGB color space [8, 49, 58, 59]. The sRGB color space is intended for visualization in
conventional color displays and the Internet [59]. Figures 3(a)-3(c) (left column), Figs. 3(d)-
3(f) (central column) and Figs. 3(g)-3(i) (right column) correspond to the white, adult
iridescent and young iridescent peacock feathers at the illumination angle θ of 15 °, 45 ° and
75 °, respectively. This gives a total of 9 different spatial color maps grouped in a matrix
arrangement of 3 rows by 3 columns. Color images capture different parts of the central
eyespot and the peripheral region containing feather barbs. White feather barbs [Figs. 3(a)-
3(c)] have a similar orientation to the adult iridescent peacock [Figs. 3(d)-3(f)]. Feather barbs
in the young iridescent peacock have a different orientation [Figs. 3(g)-3(i)]. Different user-
defined regions of interest of size 101 x 101 pixels (2.11 mm2) were selected for further
analysis. These are feather barb segments covered with many barbules.
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20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010198 | OPTICS EXPRESS 10205
Fig. 3. Spatial color maps of peacock tail feathers. The entire selected imaging areas (size 841
x 841 pixels) as a function of the illumination angle θ. For each color image, at each pixel
position the spectral reflectance function was mapped to CIE XYZ tristimulus values and then
converted to the sRGB color space for visualization. Panels (a), (b), and (c) (left column), (d),
(e), and (f) (central column) and (g), (h) and (i) correspond to the white peacock (P. cristatus
mut. alba), the adult iridescent peacock (P. cristatus) and the young iridescent peacock (P.
cristatus) at the illumination angle θ of 15 °, 45 ° and 75 °, respectively. Open squares (size
101 x 101 pixels) labeled from “1” to “24” indicate different user-defined regions of interest.
Squares in the left column labeled as “1”, “2”, “3” and “4”, “5” and “6” indicate a non-
iridescent white area in the central eyespot and in the periphery of the eye region, respectively.
Squares in the central column labeled as “7”, “8”, “9” and “10”, “11”, “12” and “13”, “14”,
“15” indicate a blue iridescent area of the central eyespot and a green and a brown iridescent
area in the periphery of the adult peacock feather, respectively. In the right column, squares
labeled as “16”, “17”, “18” and “19”, “20”, “21” and “22”, “23”, “24” indicate a blue
iridescent area of the central eyespot and a green and a brown iridescent area in the periphery
of the young peacock feather, respectively.
3.2 Global spectral analysis
Figure 4 shows the mean spectral reflectance factor [44] of each selected area in Fig. 3. Each
mean reflectance factor was obtained from the average of 101 x 101 = 10201 reflectances (i.e.
the reflectance of each pixel). Reflectance values are grouped in 8 different panels in a matrix
arrangement of 3 rows by 3 columns. The magnitude of the reflectance factor changes from
place to place due in part to the spatial configuration and orientation of feather barbs.
Reflectance spectra in the white peacock have never been analyzed before. White barbs
exhibit non-iridescent effects [Figs. 1(e) and 1(f)] and mainly shift the reflectance factor in the
vertical axis as a function of the illumination angle [Figs. 4(a) and 4(b)]. The results in the
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white peacock indicate that shape of reflectance curves is very similar to that of the Platalea
regia white feathers as measured with conventional spectrometers [60].
Fig. 4 . Mean reflectance factor of peacock tail feathers. Mean spectral reflectance factor as a
function of the illumination angle. Panels (a) and (b), (left column), (c), (d) and (e) (central
column) and (f), (g) and (h) correspond to a white peacock (P. cristatus mut. alba), an adult
iridescent peacock (P. cristatus) and a young iridescent peacock (P. cristatus), respectively.
Numbers in each curve labeled from “1” to “24” indicate the mean spectral reflectance factor
of each selected region in Fig. 3. Each mean reflectance factor was obtained from the average
of 10201 reflectances.
In general, the shape of the reflectance factor in iridescent feather barbs is similar to that
measured with standard spectrometers [7–9]. The reflectance factor shifts to shorter
wavelengths as the illumination angle θ changes from 15 ° to 75 °. Blue iridescent effects in
the adult peacock are weak [Fig. 4(c)]. The spectral peaks from 460 nm to 410 nm are very
similar to the value at 700 nm. This gives rise to the visual perception of magenta, due to the
additive combination of blue and red reflected wavelengths. This red component of this effect
may originate from melanin pigment [9]. In contrast in the young peacock feathers the
spectral peaks from 440 nm to 410 nm are more intense than that at 700 nm [Fig. 4(f)]. In
green iridescent feather barbs, the wavelengths at which each reflectance factor is a maximum
were similar between the adult and the young peacock. The spectral reflectance maxima range
from 490 nm to 450 nm in the adult and from 500 nm to 470 nm in the young peacock [Figs.
4(d) and 4(g)]. However, this is not the case in brown feather barbs and differences are higher
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20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010198 | OPTICS EXPRESS 10207
[Figs. 4(e) and 4(h)]. In the red part of the spectrum, the spectral maxima range from 600 nm
to 570 nm in the adult and from 630 nm to 600 nm in the young peacock. In the blue part of
the spectrum, the spectral maxima range from 500 nm to 460 nm in the adult and from 520
nm to 490 nm in the young peacock. These differences can be attributed to the existence of
different sub-micron 2D photonic structures within the cortex of barbules [Figs. 1(b) and 1(d)
and Table 1] [7, 8]. This issue will be discussed further later.
3.3 Analysis of eigenimages
PCA for the 10201 reflectances in each selected imaged surface of peacock feathers were
performed (Fig. 3). Then, we examine the spectral variability within each imaged surface
across each principal component direction separately. For each principal component, the
scores i
α in Eq. (1) provide the spatial distribution of pixels in the imaged surface and
preserve the spectral information of the eigenvectors i
S. Reconstruction of reflectance spectra
along each principal component direction k
R was performed by taking the mean reflectance
factor R and the corresponding eigenvector, kkk
=+RRαS [58]. Then, the resulting
reflectance spectra can be displayed in sRGB color space producing characteristic spatial
color patterns associated with each principal component direction or “eigenimages” [38, 39,
58]. For instance, Figs. 5(a) and 5(b) exemplify the original and the first three eingenimages
of the green and brown iridescent feather barbules of the adult peacock at the illumination
angle θ of 15° and 75°, respectively.
Fig. 5 . Example of eigenimages in the sRGB color space. The first row indicates the original
imaged surface. Numbers in orange indicate the selected region annotated in Fig. 3. The
subsequent rows indicate the reconstruction of reflectance spectra that result by the linear
combination of the mean reflectance factor (Fig. 4) and the first three eigenvectors separately.
Panels (a) and (b) show green and brown iridescent feather barbs of the adult peacock (P.
cristatus) at the illumination angle θ of 15° and 75°, respectively. For each eigenimage,
numbers in white indicate the percentage of variance explained by each associated eigenvector.
In general, the total spectral variability within each imaged surface is not very large. This
is because each feather barb contains many identical barbules placed in a quasi-periodic
spatial organization and each individual barbule has the same sub-micron 2D photonic
structure inside [1, 9]. In each imaged surface the first eigenimage contains most of the spatial
details and the corresponding eigenvector points to the weighted average direction (Eq. (1)
[40]. In the examples provided in Figs. 5(a) and 5(b), the eigenvector indicates an overall
cyan and yellow, respectively with spectral maxima located at 490 nm in green barbules and
at 570 nm and 460 nm in brown barbules, respectively. The subsequent eigenimages represent
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different corrections that are related to the random spatial displacements of barbules and their
orientations. The first few eigenimages retain most of the total percentage of explained
variability. In Figs. 5(a) and 5(b), 3 and 5 eigenvectors respectively, were necessary to
account for more than 95% of total variance. The PCA data from these peacock feathers
corroborate the existence of a few principal component directions that explain a large amount
of variance and many principal component directions with negligible variance in a large
number of reflectance data sets [32, 36–40, 58].
3.4 Principal component analysis similarity factors
PCASF values were calculated and contrasted. For instance, Fig. 6(a) shows the PCASF
between brown and white feather barbs as reference. The standard PCASF and the WPCASF
were calculated. The number of principal components k in Eqs. (2) and (3) was varied to
account for at least 90%, 95% and 99% of total variance. At 90% of total variance, the
number k was equal to 4, 5 and 3 at θ = 15°, 45° and 75°, respectively. At 95% it was equal to
9, 11 and 6 at θ = 15°, 45° and 75°, respectively and at 99%, k was equal to 24, 25 and 16 at θ
= 15°, 45° and 75°, respectively. The results conclude that the PCASF depends on the number
k and increases as the total percentage of explained variance increases. However, WPCASF is
nearly independent of the total variance explained by the principal components. The standard
PCASF approach weights all the principal components equally (Eq. (2) and the number of
loading vectors with low variance is inappropriately high at 95% and 99% of total variance.
These loading vectors are usually associated with different sources of noise from the
multispectral imaging acquisition system [37–39, 58] and mask the comparison between the
spatial reflectance patterns from feather barbs. Therefore, the WPCASF was chosen in
subsequent analyses and it was calculated to account for at least 95% of total variance.
Fig. 6. PCA-based similarity factor in adult peacock feather barbs. (a) Example of PCASF
between brown (P. cristatus) and white feather barbs as reference (P. cristatus mut. alba). The
number of principal components varied to account at least 90%, 95% and 99% of total variance
of reflectance spectra. Diamonds, down and left triangles indicate the PCASF at the
illumination angle θ of 15 °, 45 ° and 75 °, respectively. Open symbols connected by dashed
lines correspond to the standard PCASF. Solid symbols connected by solid lines correspond to
the WPCASF. (b) WPCASF plots (95% of total variance) with the white and green iridescent
feather barbs as reference. Grey, blue and orange symbols indicate the WPCASF of white non-
iridescent, blue and brown iridescent feather barbs, respectively. Hexagons, diamonds and
circles correspond with θ = 15 °; pentagons, down triangles and squares with θ = 45 ° and
starts, up and right triangles with θ = 75 °. Dashed lines indicate the tolerance limit at 0.9.
Figure 6(b) represents the WPCASF using two different spectral categories: white feather
barbs at the centre of the white eyespot [Figs. 3(a)-3(c), squares “1”, “2” and “3”] (labeled
“WPCASF white”) and green iridescent barbs [Figs. 3(d)-3(f) squares “10”, “11” and “12”]
(labeled “WPCASF green”). As a control condition, white feather barbs were compared
between the centre of the eyespot and the peripheral part of the eye region [Figs. 3(a)-3(c),
squares “4”, “5” and “6”]. It was concluded that the WPCASF white was always higher than
0.9 at all illumination angles. We establish 0.9 as a tolerance limit in subsequent analyses.
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Figure 6(b) clearly shows that iridescent brown and blue feather barbs are more similar to
white barbs (WPCASF white > 0.7) than to iridescent green barbs (WPCASF green < 0.5).
Further, blue iridescent barbs are spectrally similar to the white peacock (WPCASF white >
0.9). This is due to the location of the selected area in the adult peacock in the peripheral part
of the eyespot where blue iridescence is weak [see Figs. 3(d)-3(f) squares “7”, “8” and “9”
and Fig. 4(c)]. Previous studies have established the chemical, structural and mechanical
similarities between blue iridescent and white peacock tail feathers [45, 46]. Here we report
their similarity from the spectral point of view. Figure 7 represents in a 3D space the
WPCASF between the adult and young peacock feathers. Three different spectral categories
were established: blue, green and brown taking the adult peacock as the reference sample
[Figs. 3(d)-3(f)].
Fig. 7. PCA-based similarity factors in young peacock feather barbs. WPCASF (95% of total
variance) with the blue, green and brown iridescent feather barbs from the adult peacock as
reference. Spheres represent the WPCASF at different illuminant angles. Blue, green and
brown spheres indicate the WPCASF of the blue, green and brown young iridescent feather
barbs. Solid circles indicate the projection in the plane that corresponds with the blue and green
WPCASF.
Blue and green iridescent barbs in the young peacock are similar to the blue and green
counterparts in the adult at all illumination angles (WPCASF > 0.9). Comparisons between
different iridescent feather barbs (e.g. adult blue versus young green etc.) always exhibit
lower spectral similarity (WPCASF < 0.9). The spectral similarity was also lower than 0.9 in
brown feather barbs (0.7 < WPCASF < 0.8). The influence of the area selected in the young
peacock was also established by using a search procedure that maximizes the WPCASF
within the brown region [Figs. 3(g)-3(i)]; in this instance WPCASF was always below 0.8.
4. Conclusion
Micro-scale structures of peacock feathers comprise complex branching patterns of barbs and
barbules that depend on their surface curvature, twist, orientation distributions, etc., and
change during feather growth [1, 6, 9, 10, 47, 48]. The spatial average over many barbules
smoothes the reflectance spectra created by sub-micron 2D photonic crystal structures within
the cortex surface of each single barbule and spread reflected light over a wide angular range
[1, 9, 11]. Optical methods for investigating peacock feathers often provide single-point
spectral data using conventional spectrometers that average over small feather patches with
typical size of a few millimeters [1, 7–9, 12, 13]. This makes the research on the micro
appearance of peacock tail feathers and texture analysis very difficult. Multispectral and
hyperspectral imaging methods can offer advantages for characterization of surface materials
by collecting both spectral and spatial information simultaneously [22, 58]. In this work we
propose a multispectral imaging arrangement that has an excellent spatial and spectral
performance in the visible part of the spectrum using commercially available optical
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components. We measured components of the multispectral BRDF of feather barbs containing
many barbules as a function of the illumination angle. We applied PCASF to classify their
spatially-varying reflectance patterns. Spectral pattern matching was investigated in user-
defined regions of interest within the eyespot region of the common peacock (P. cristatus) as
well as in the white peacock (P. cristatus mut. alba). Each user-defined region of interest
consisted of a small area of 2.11 mm2 containing 10201 reflectances, i.e., one at each pixel of
the imaged surface with a spatial resolution of 14.4 µm per pixel [58]. We demonstrate that
the multispectral classification methodology based on PCA is an effective and useful non-
destructive tool for spectral pattern recognition of iridescent feather barbs over spatially
extended areas. WPCASF has successfully evaluated reflectance patterns by weighting a few
key principal components that explain at least 95% of the total variance [32, 33, 35].
When iridescent effects are visually discernable in the feather samples used, we found a
high degree of similarity within blue and within green iridescent barbules at different stages
of feather development (Fig. 7, WPCASF> 0.9) [Figs. 1(a) and 1(c)]. Therefore, we conclude
that these reflected light patterns are a good match across members of the same species. This
also suggests that the different quasi-ordered organization of barbules can lead to the same
smooth angle-dependent color variations during feather growth (Fig. 3). In addition, we found
a spectral mismatch between the adult and young brown barbules (Fig. 7, WPCASF< 0.8).
This is mainly due to the different sub-micron 2D photonic structures within the cortex
surface of the young and adult feather barbules [Figs. 1(b) and 1(d), Table 1]. These spectral
differences persist in the mean reflectance factor averaged over many barbules at different
angular positions [Figs. 4(e) and 4(h)] and are comparable with the degree of similarity
between feather barbules containing different photonic crystals (e.g. adult green versus young
blue, etc.) (Fig. 7). Conversely, when iridescent effects are weak, we found a high degree of
similarity between non-iridescent white and blue iridescence barbules [Fig. 6(b), WPCASF>
0.9]. This suggests that the 2D photonic structures inside each barbule in the adult peacock
have a residual contribution to the peripheral region of the blue part of the eyespot (Fig. 3).
Classification of these spatial reflectance patterns could be correlated with an effective color
signaling process in peacocks [12].
The measurement of the multispectral BRDF in peacock feathers assumes that scattering
occurs at each point source of the imaged surface separately and strong subsurface scattering
from one spatial position to a different distant position is considered negligible [13]. It is also
assumed that PCA operates in a static state and employs a linear transformation between the
original reflectance spectra and a new set of uncorrelated loading vectors [30, 32, 35, 42]. Our
findings conclude that the static linear assumption is entirely appropriate: PCA was performed
in user-defined regions of interest under controlled conditions in the laboratory and is a
successful linear model of reflectance spectra in peacock feathers. Our results also confirm
that PCA provides a good description of a large number of surface reflectance data sets [36,
37, 40, 41, 58]. The WPCASF could be less efficient for the classification of spatial
reflectance patterns in external dynamic situations under the influence of temporal
disturbances such as in remote classification and bird migration for which other multivariate
statistical classification methods [30, 37] might be more efficient. This issue deserves further
investigation.
We have focused our analysis on the common peacock (P. cristatus) the feathers of which
neither exhibit strong polarization effects in their reflectance spectra [7, 8] nor any UV
reflectance maxima [12]. Classification of spatial reflectance patterns using PCA-based
similarity factors can be applied to similar animal species when the effects of disorder and
spatial averaging over repeated nanostructures contribute to smooth angular color variations
[1, 9, 11]. However, there are iridescent birds and other animal species that have
tetrachromatic vision, from the UV to the visible region, and show polarization effects and
reflection maxima in the UV [1, 14–17, 19, 20, 43] and in the IR spectra [15, 22, 25]. This
issue remains open and requires multispectral or hyperspectral polarization imaging methods
in those spectral ranges [22, 25]. Here, combining a multispectral method in the visible
spectrum and the WPCASF we describe an efficient classification method for the reflectance
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20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010198 | OPTICS EXPRESS 10211
properties of barbules that avoids current limitations associated with colorimetric analyses of
bird colors [12, 17, 20, 43]. We suggest this multispectral classification method could be used
effectively to elucidate novel perspectives in animal biometrics and the diagnosis of local
spatial defects such as partial leucism.
Acknowledgments
This research was developed during a visiting research stay of Dr. José M. Medina in the
Departamento de Óptica, Universidad de Granada, Spain. We thank to José Medina and
Rosalía Ruiz who provided the peacock samples, to David Porcel and Juan de Dios Bueno
from the Servicio de Microscopía, (Centro de Instrumentación Científica, Universidad de
Granada) for technical assessment, and to the Color Imaging Group (Universidad de Granada)
for their hardware partial support. JMM and JAD acknowledge the Departmento de Óptica,
Universidad de Granada, Spain. PV acknowledges USAF funding (FA9550-10-1-0020).
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... The iridescent structural color was derived from the specular reflection from the cortical thin films of feathers such as rock dove and mallard. The tail feathers of male peacocks have a distinctive iridescent eyespot pattern composed of several different colors, which are thought to be derived from photonic crystals consisting of a lattice structure of rod-shaped melanin granules in the barbules (Yoshioka and Kinoshita, 2002;Zi et al., 2003;Dakin and Montgomerie, 2013;Medina et al., 2015). In recent years, studies on structural color expression by three-dimensional colloidal photonic crystals composed of artificial melanin granules (polystyrene granules are coated with polydopamine) have been conducted (Kawamura et al., 2016;Xiao et al., 2017). ...
... The source of the beautiful, brilliant colors of bird feathers can be pigmented or structural. Pigment colors; include melanin (D'Alba et al., 2014;Galván and Solano, 2016), carotenoids Thomas et al., 2014;Thomas and James, 2005;Shawkey and Hill, 2005;McGraw and Toomey, 2010;Yim et al., 2015), porphyrins (With, 1978), psittacofarvin (Tin-bergen et al., 2013), and spheniscin (Thomas et al., 2012), and structural colors; include thin-film interference of cortical β-keratin (Nakamura et al., 2008;Eliason and Shawkey, 2010;Stavenga, 2014;Okazaki, 2019), a spongy layer bellow the cortex (Shawkey et al., 2009;Yin et al., 2012;Saranathan et al., 2012;Prum et al., 2009;Okazaki, 2020a;Stavenga et al., 2011), and the lattice structure of melanin granules (Yoshioka and Kinoshita, 2002;Zi et al., 2003;Dakin and Montgomerie, 2013;Medina et al., 2015). When either the left-or right-handed CPL was irradiated on the surface of dove and mallard feathers, the structural color reflected the left-or right-handed CPL opposite to the direction of irradiated light. ...
... The structural color of peacock tail feathers has been thought to be derived from photonic crystals consisting of the lattice structure of rod-shaped melanin granules (Yoshioka and Kinoshita, 2002;Zi et al., 2003;Dakin and Montgomerie, 2013;Medina et al., 2015). However, from the results of the specular reflection experiment and TEM observation, it was assumed that the color of peacock feathers might be derived from thin-film interference from the cortex (Fig. 4). ...
Article
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In order to clarify the relationship between the structural color and the nanolevel structure of bird feathers, the cortical thin-film structure, the shape of melanin granules, and their arrangement were observed using transmission electron microscopy. The reflection spectra were calculated based on the electron microscopic image data using Fresnel's equation to simulate a thin-film interference and Bragg's law to simulate a photonic crystal, then were compared with the actual reflection spectra. The simulation spectra calculated using Fresnel's equation were very similar to the reflection spectra from dove and mallard feathers. The reflection spectra from each part of the eye-spot pattern of peacock feathers were very similar to both simulation spectra using Fresnel's and Bragg's equations. In the peacock feathers, the structural color from the cortex and the three-dimensional photonic crystal consisting of the lattice structure of rod-shaped melanin granules were fused to further enhance the selectivity.
... F) Adapted with permission. [31] Copyright 2015, The Optical Society. G) Adapted with permission. ...
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... This shows that the choice of specimens for more detailed investigation was completely justified. The analysis of spectral data using PCA may be useful for the extraction and representation of small multivariate differences in color, e.g., for processing a large number of similar colors Knüttel and Fiedler, 2000;Medina et al., 2015) or color changes occurring upon vapor exposition of photonic crystal structures (Kittle et al., 2017;Piszter et al., 2014). ...
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