Journal of Signal and Information Processing, 20 11 , 2, 59 - 71
doi:10.4236/jsip.2011.22009 Published Online May 2011 (
Copyright © 2011 SciRes. JSIP
Improved 3-D Particle Tracking Velocimetry with
Colored Particles
Christian Bendicks1, Dominique Tarlet2,3, Christoph Roloff2, Robert Bordás2, Bernd Wunderlich2,
Bernd Michaelis1, Dominique Thévenin2
1Institute of Electronics, Signal Processing and Communication Engineering, University Magdeburg, Magdeburg, Germany;
2Institute of Fluid Dynamics and Thermodynamics, University Magdeburg, Magdeburg, Germany; 3Laboratoire de Thermocinétique,
Université de Nantes, Nantes, France.
Received January 13th, 2011; revised February 25th, 2011; accepted March 2nd, 2011.
The present work introduces an extension to three-dimensional Particle Tracking Velocimetry (3-D PTV) in order to
investigate small-scale flow patterns. Instead of using monochrome particles the novelty over the prior state of the art is
the use of differently dyed tracer particles and the identification of particle color classes directly on Bayer raw images.
Especially in the case of a three camera setup it will be shown that the number of ambiguities is dramatically decreased
when searching for homologous points in different images. This refers particularly to the determination of spatial parti-
cle positions and possibly to the linking of positions into trajectories. The approach allows the handling of tracer parti-
cles in high numbers and is therefore perfectly suited for gas flow investigations. Although the idea is simple, difficult-
ties may arise particularly in determining the color class of individual particle when its projection on a Bayer sensor is
too small. Hence, it is not recommended to extract features from RGB images for color class recognition due to infor-
mation loss during the Bayer demosaicing process. This article demonstrates how to classify the color of small sized
tracers directly on Bayer raw images.
Keywords: Particle Tracking Velocimetry, Color Recognition, Artificial Neural Network, Photogrammetry
1. Introduction
Over the last 20 years Particle Tracking Velocimetry
(PTV) has been established as an interesting tool for 3-D
flow measurements, cf. [1,2] and references within. PTV
relies on the stereoscopic recognition and subsequent
tracking in time of small particles in an illuminated vol-
ume using a multi-camera system. In this way, the flow
information is contained in reconstructed particle trajec-
tories. Typical applications cover pure liquid flows, pure
gas flows and multiphase configurations. Concerning
gas-eous flows PTV measurements are still considered a
major challenge. First, as a consequence of the high
temporal and spatial resolution required by measure-
ments in gas flows [3,4], it is necessary to employ a suf-
ficiently high particle number density. Additionally, the
trajectories have to be long enough for a Lagrangian flow
analysis: interesting physical results can only be deter-
mined if long correlation lengths have been recorded
A flow chart for a typical procedure of the measure-
ment process is shown in Figure 1. Assuming the cam-
eras are properly calibrated and corrected for lens distor-
tion, the algorithm consists of five major modules that
process the tasks:
1) Image pre-processing: Correction of inhomogene-
ous illumination and noise reduction.
2) Segmentation: Making a decision for each pixel
whether it belongs to a particle or to the background.
3) Locating particle centers: Computing particle cen-
ters from results of segmentation.
4) Determination of 3-D coordinates and intrinsic pro-
perties: Determining spatial particle locations for each
frame from corresponding locations in camera images
and calibration data; detecting also properties like color
in the present case.
5) Use of the obtained information in a post-treatment
specific to Fluid Dynamics, for instance for Particle
Ambiguities constitute the major problem. They occur
first when trying to reconstruct the 3-D coordinates of par-
ticles out of different camera perspectives; ambiguities
Improved 3-D Particle Tracking Velocimetry with Colored Particles
Figure 1. Usual design of a measurement system to perform
particle tracking veloc i metry.
are found again when assigning successive particle posi-
tions in time using the tracking algorithm (cf. Maas et al.
in [8]). To reduce the number of ambiguities the simplest
approach would be to use a low seeding density, but this
would also reduce the spatial resolution of the system
and the basis for an accurate analysis. A more sophisti-
cated way of reducing ambiguities is to build classes of
particles with distinctive properties, such as size [9],
shape [10] or color (Figure 2). The first two criteria are
not useful because proper particles for seed- ing in gases
have to be very small to follow the flow. Using color as a
distinctive criterion has already been proposed and in-
vestigated in detail by the research group of Prof. Brod-
key [11,12]. Colored particles of a diameter of 38-44 µm
were recorded on a 16 mm film and the pictures were
digitized with considerable effort in several steps. To
identify the color of a particle, particle pixels were aver-
aged to create an RGB intensity vector which was com-
pared to signature RGB vectors corresponding to one of
the applied colors. Because of associated problems the
use of color information has been found to be very diffi-
cult, if not impossible, using this post-processing strategy
Instead of digitizing analog film material, today, digi-
tal high-speed cameras based on one CMOS or CCD
sensor are commonly used to image the flow of particles.
But since such type of sensor responds to all frequencies
in the visible spectrum, it is unable to produce color im-
ages. Therefore, a color filter array is placed in front of
the sensor of single chip color cameras, which allows
only the light of a specific range of wavelengths to pass
through each photodetector. The most commonly used
color filter array is the Bayer filter array which is based
on the human visual system. It consists of three kinds of
filters, one for each primary color (red, green and blue).
Green is sampled as twice the frequency of the other col-
ors since the human visual system is most sensitive to the
Figure 2. Reducing the apparent particle number density
with the help of color classes.
green range of the spectrum. In addition, to ensure full
image resolution, missing samples must be reconstructed
through a process called demosaicing. This leads to sig-
nificant color artifacts especially in high spatial fre-
quency and/or small image structures. As a consequence,
the assignment of a particle to its color class simply
based on reconstructed RGB images is not reliable, when
a particle projection covers only a few pixels.
In the following, the practical application of colored
particles for digital PTV is demonstrated using classify-
cation of color classes prior to 3-D localization by the
method of epipolar lines based on a three-camera setup.
Note, in general the idea shown in Figure 2 is applicable
for PTV experiments with two or more than three cam-
eras. First, the experimental setup is described, including
the choice of appropriate tracers and their coloring. An
important step consists of image pre-processing and lo-
calization of particle centers on camera images. This in-
formation will subsequently be used for color classifica-
tion, and will feed the correspondence solver to obtain
3-D localizations. The classification of small-sized col-
ored particles (Ø 20 µm) is obtained by means of Arti-
ficial Neural Networks (ANNs). For the investigation of
larger particles (Ø 70 µm), successful application of
ANNs has been reported in [1]. The use of other classify-
ers like Support Vector Machines (SVM) is also possible
and has been investigated by Bendicks et al. [13]. Here,
ANNs have been retained because of the considerable
experience of our group with this technique and of the
huge amount of collected data for training and tests [14].
ANNs are highly flexible and are robust against slight
variations in feature space. After the description of parti-
cle assignment to color classes, camera calibration is
presented for the experimental setup. Then, the advan-
tage of using color classes is shown in combination with
the epipolar constraint for particle assignment among
camera views. This is used as a basis for computing 3-D
particle locations in each time frame. Quantitative meas-
urement results (for example, proportion of successful
correspondences with the same color) are finally dis-
cussed for three cases involving 3-D PTV.
2. Experimental Setup: Particles and
Imaging Method
2.1. Choosing and Dyeing Tracer Particles
The material of the tracer particles is important since it
Copyright © 2011 SciRes. JSIP
Improved 3-D Particle Tracking Velocimetry with Colored Particles 61
determines their density ρp and their agglomeration
property. Ideally, a tracer particle of neutrally buoyant
density is preferred. This is relatively easily realized in
liquids [5,6,15]. In gas, smaller particle diameters are
needed to keep the ability to follow the flow. However,
the minimum diameter of the particles is limited by the
production process and by optical considerations. A
minimum number of pixels is needed on the camera sen-
sor for each tracer particle to allow proper localization.
In the present situation involving color recognition, the
minimum number of pixels is about nine. Thus, a diame-
ter of 20 µm is at least required for the particles with the
present setup. The physical properties of the tracer parti-
cles finally retained for the present study are reported in
Table 1. The choice of suitable tracers is discussed in
detail in other publications (see [1,16]).
Expanded Micro Spheres (EMS) have been finally
identified as being the most suitable material due to ap-
propriate size, low density, acceptable price, and good
dyeing properties with low electrostatic loading. Dyeing
of the particles is realized according to a standard, man-
ual protocol. A small quantity (70 mg) of EMS particles
with a diameter of 20 µm is introduced into a polyethyl-
ene container that has a volume of 4 cm³. Then, 250 mg
of a mix of 50% dye mass (in the present case Edding
T25 liquid ink of color red, green or blue), and 50%
ethanol is added to the particles. This ethanol mix is re-
alized in order to obtain a brighter color for the particles,
in comparison with a non-diluted dye. Five minutes of
careful mixing by means of a laboratory spatule ensures a
homogeneous repartition of the dye through transport and
diffusion within this porous medium. The dyed particles
are then spread onto a cardboard layer for a day, during
which they are turned three times. After drying the ob-
tained colored particles are sieved through a metal filter
of 25 µm in size in order to remove possibly agglomer-
ated particles. A microscopic check confirms that the
particles have kept their original structure and that the
increase in diameter is at most equal to 3 µm. This dye-
ing process results finally in a density of 320 kg/m³ for
the colored EMS particles with diameter of 23 µm. Only
the three primary colors (red, green and blue) are used
for the present study, allowing an easier recognition
through a Bayer-Pattern sensor, composed of pixels of
these 3 primary colors. The same method is nevertheless
applicable to other colors as well as shown by further
2.2. Imaging of Particles in the Flow
For suitable test measurements some small-sized (typical
scale: mm) flow patterns seeded with colored tracer par-
ticles have to be generated within the focal depth of the
cameras. Figure 3 shows a drawing of the employed
Table 1. Properties of employed tracer particles.
Density (kg/m³) Mean diameter (µm)
availableused here availableused here
Expancel® (EMS) 24 - 70 70 20 - 12020
Colored EMS 320 23
Figure 3. Pe rspective view of the eiffe l wind tunnel used for
all measurements.
wind tunnel and the arrangement of cameras and lighting
in front of the observation window (an anti-reflective
glass). The depth of the wind tunnel is 8 mm and is tai-
lored to match the possible measurement depth (z coor-
dinate). The air flow is seeded with the tracer particles at
its open extremity on the left (air intake). Beyond the
right extremity (outflow), an electric fan entrains the air
flow through a filter tissue with a pore size of 11 µm.
This filter tissue captures the tracer particles and regular-
izes the flow induced by the fan in the wind tunnel. The
optical setup is discussed in detail in the next section.
Lamps and cameras are typically placed 20 to 30 cm
away from the window giving optical access to the mea-
surement section.
On top of the mainstream velocity, suitably tailored
bluff bodies are placed in the measurement section to
create a variety of flow properties. In Case 1 a set of
three polyethylene winglets (length: 17 mm, see Figure 4)
simultaneously induce in the measurement volume large
streamline curvature, continuous flow acceleration and
small-scale recirculations. In Case 2, a transverse hori-
zontal cylinder with a diameter of 6 mm creates a large
recirculation zone downstream. These two flow patterns
are mostly two-dimensional. To complete this experi-
mental campaign of 3-D PTV, Case 3 relies on a rotating
asymmetric device (width: 5 mm, 10 rotations per second)
leading to spiraling flow structures in the measurement
section. In what follows, all aspects pertaining to color
recognition and 3-D localization of the tracer particles
are discussed.
To acquire the images three cameras (CMOS sensor
with 1280 × 1024 pixels) are focused on the measure-
ment section by means of a LINOS Apo-Rodagon D-2x
Copyright © 2011 SciRes. JSIP
Improved 3-D Particle Tracking Velocimetry with Colored Particles
Figure 4. Set of three winglets (Case 1).
object lens with a focal length of 75 mm used at an
f-number of 11 and located at a distance between 20 and
23 cm from the measurement section. For later calcula-
tions of 3-D coordinates, synchronization of the camera
images - always acquired at 500 fps during this project -
is of high importance. This synchronization is checked
by simultaneously imaging a blinking light diode and
verifying that illuminated states appear on the same
frame. The cameras are designed to obtain a close-up
image of the employed tracer particles with a diameter of
23 µm. Recording in monochrome mode enables to cap-
ture raw information from the CMOS sensor (Bayer Pat-
tern of type G-R/B-G) that has a resolution of 1.3 mega-
pixels (1280 × 1024). As later discussed, color recogni-
tion will be based on these Bayer raw data. Table 2 sums
up the properties of the employed optical systems. It is
important to note that the measurement section is of a
size 25 × 25 × 8 mm, which is less than the field of view
of a 2-D image since all the areas of the 2-D images (es-
pecially the edges) have to intersect for 3-D localiza-
For illumination four light heads are employed, based
on halogen lamps emitting a light of color temperature
between 3000 and 3400 K. They are located at a distance
of about 30 cm from the measurement section. Addition-
ally, the light heads are equipped with hot mirrors and
daylight filters, which are actively air-cooled to prevent
loss of filtering properties resulting from excessive heat.
In this way, the daylight filters and the measuring vol-
Table 2. Properties of the DEDOCOOL lamps and the
BASLER A504kc cameras.
Color temperature (K): 5300 (Halogen + Daylight filter)
Distance (cm): 20 30 40
Light intensity (lux):24 × 106 1.1 × 106 0.58 × 106
Footcandle: 222 000 105 000 54 000
Illum. area ø (cm): 6.5 7 9
3 synchronized BASLER 504kc cameras
Size of a pixel (µm):12 × 12 Bayer Pattern: G-R/B-G
Sensor size (mm): 15.36 × 12.29 Resolution: 1280 × 1024
f-Number: 11 Object dist.(cm): 20 - 23
Focal length (mm):75 Depth of field (mm): 6
Recording rate (fps):500 Exposure time (ms): 0.8 - 1.0
ume are protected against heat produced by the illumine-
tion. Furthermore, the resulting illumination spectrum is
similar to a light source with a color temperature of 5300 K
(daylight). Therefore, Bayer sensor elements are not af-
fected by near-infrared or reddish light, which would
hinder color recognition. Properties of the lamps for dif-
ferent working distances are given in Table 2. Using
three light heads placed between the cameras would lead
to a more homogeneous illumination. However, tests
revealed that the particle and color class recognition rate
is higher with four light heads arranged as in Figure 3.
3. Image Pre-Processing and Locating 2-D
Particle Centers on an Image
3.1. Image Pre-Processing
For each camera channel, an averaged image is first cre-
ated over 20 consecutive images of the measurement
section without seeding, which is later used to perform
background subtraction on the entire Bayer image se-
quence. This ensures the removal of irrelevant structures
like the winglets or dust deposition on the window. Since
the algorithm employed to detect particle center consid-
ers grayscale images as input, Bayer images need to be
converted in an intermediate step to RGB color images
using a bilinear interpolation. This is performed with a
demosaicing algorithm [17]. After that the images are
converted to grayscaled ones using equal weights for red,
green, and blue components to compute the intensity
The following pre-processing stage on grayscale im-
ages (introduced by Crocker and Grier [18]) deals with
two problems complicating particle detection: 1) long
Copyright © 2011 SciRes. JSIP
Improved 3-D Particle Tracking Velocimetry with Colored Particles 63
wavelength modulations of the background intensity due
to non-uniform sensitivity of the camera pixels or uneven
illumination and 2) unavoidable digitization noise in the
camera. To solve the first problem the background is
removed by a boxcar average (ba) over a square region
with a side length of (2w + 1) pixels:
Ixy Ixiyj
w 
 .
The user-defined parameter w denotes a number of
pixels larger than the apparent particle radius but smaller
than the smallest interparticle separation. Digitization
noise is modeled as uniformly Gaussian with a correla-
tion length of λ = 1 pixel. Thus, the convolution of image
I with a Gaussian surface results in the suppression of
such noise without excessively blurring the image:
 
IxyI xiyj
 
 (2)
with normalization
exp .
The application of Equations (1) and (2) to image I can
be combined into one single convolution with the kernel
 
11 1
, exp.
Kij Kb w
The normalisation constant
1exp 221
can be used to compare filtered images with different
values of w. The improved image is given by:
 
 
 (6)
3.2. Locating 2-D Particle Centers
To estimate particle center positions in a filtered image If
a connectivity analysis is performed as described by
Maas [19]. This method can also handle overlapping par-
ticles. The goal is to find local maxima and assign sur-
rounding pixels over a defined threshold to one maxi-
mum. Assigning a pixel to a maximum means assigning
a pixel to an individual particle. The algorithm starts the
search in the image pixel by pixel. When the pixel value
is greater than a given threshold the pixel is tested to
check if it is a local maximum. There is a local maximum
when the pixel value is greater than or equal to the values
of the eight neighboring pixels. If this is not the case, the
search is continued. The local maximum is used as a
seeding point for a region-growing operation in order to
associate and label all pixels belonging to the particle.
For this purpose, a so-called discontinuity threshold D is
introduced to decide if a pixel is assigned to a maximum
or not. Suppose a pixel at location p0 with intensity I(p0)
is already assigned to a maximum and the exploration is
continued at one of the unlabeled neighbors, called p1
with intensity I(p1). Then, pixel p1 is assigned to the cur-
rent maximum if the following two conditions are true: 1)
I(p1) I(p0) + D and (2) there are one or more pn1 which
satisfy I(p0) I(pn1) – D, where pn1 identifies one of the
other seven neighbors of p1.
The operator described above considers the following
1) All pixels belonging to a particle have values great-
er than the threshold.
2) A particle has exactly one local maximum.
3) The grayscale gradient within a particle projection
is continuous.
4) A pixel, which represents a local minimum and
could be assigned to several neighboring pixels, is as-
signed to the neighbor pixel with the largest value.
The second and the third rule can be weakened or
strengthened by changing the discontinuity threshold D.
Discontinuities up to D grayscale values are tolerated
within a single particle.
During the region-growing search process, the n pixels
belonging to the current local maximum are stored in a
pixel list. Finally, particle coordinates are computed by
the center of mass method:
iii iii
ii ii
x Ixyy Ixy
Ixy Ixy
4. Color Classification by an Artificial
Neural Network (ANN)
In the present application color classification is needed.
Directly using RGB images created by a Bayer conver-
sion algorithm and working with thresholds is not possi-
ble since this conversion leads to artifacts (see Figure 5).
For our purpose, when attributing for instance the color
“blue”, the exact shade or brightness of the observed
colored particle should not be taken into account since
those will vary in time and space and differ slightly from
particle to particle. As a consequence, the use of an Arti-
ficial Neural Network (ANN) is an appropriate solution
for attributing particle color class [14]. ANNs are robust
and able to learn and adapt according to training data
associated with a given context. Other adequate classify-
ers like Support Vector Machines have been tested as
well [13] but could not beat ANNs for the present appli-
Copyright © 2011 SciRes. JSIP
Improved 3-D Particle Tracking Velocimetry with Colored Particles
The proposed network design is a fully connected
back-propagation network illustrated in Figure 6. It con-
sists of
an input layer with 10 neurons;
a first hidden layer with 8 neurons;
a second hidden layer with 8 neurons;
an output layer with 3 neurons (corresponding to
the number of applied color classes).
The number of output neurons is determined by the
number of color classes used in the measurement ex-
periment. Hence, the network has to be adapted when
more or less colors are employed. All neurons in hidden
layers and the output layer use sigmoid activation func-
tions. In this way the network is able to make a predict-
tion based on fuzzy logic about the color class of a parti-
cle. The output neuron with the largest response value is
considered as indicator of the particle color. In Figure 6
the outputs are denoted with C1, C2 and C3 corresponding
respectively to blue, green and red color classes. This
notation is introduced to remind the reader that these are
only color classes that have been determined without
considering the exact shade and brightness. In the present
work all experiments are performed only with blue, green
and red particles. Nevertheless, other tracer colors like
cyan, magenta or yellow have been tested as well and are
in principle suitable for further measurements.
The features used for network input are obtained di-
rectly from Bayer raw images (“input data”, see Figure
6). Once a particle is localized on the grayscale image (as
described in section 3.2) the values of the red, green and
blue pixels (integer values of brightness between 0 and
255 - 8 bit) of the Bayer Pattern around its center are
used to build the feature vector. The location of the cen-
ter of the tracer particle given in integer coordinates (x0,
y0) is taken into account as being located either on a red,
a blue or a green pixel of the Bayer Pattern. Green pixels
are subdivided into two categories of green, due to their
different localizations between red or blue pixels on the
Bayer Pattern (cf. Figure 5). Finally, the feature vector
includes ten components, the first one being a function Φ
of the color associated with the center of the particle (x0,
0, if , is Green 1
1, if , is Red
Φ,2, if , is Blue
3, if , is Green 2
xy xy
The nine others are the intensity values I(x,y) at the
particle center pixel and at the eight neighboring pixels,
in a clockwise scheme reported in Table 3. As explained
previously, the image of the tracer particle must cover a
Figure 5. Appearance of different colored tracer particles
(23 µm) in Bayer images (upper row) and in resulting RGB
images created by bilinear demosaicing (lower row). On the
right there is the arrangement of color filters (Bayer pat-
tern) on the CMOS-Chip. Color distortions appear on the
RGB images as a consequence of demosaicing. Therefore,
the RGB color space cannot be used for color classification.
Figure 6. Principle of color classification with an Artificial
Neural Network based on particle center position and sur-
rounding Bayer data. Here, the network is designed for the
use of three particle colors (therefore 3 output neurons).
Table 3. Feature vector definition.
Feature vector component value
f1 Φ(x0, y0)
f2 I(x0, y0)
f3 I(x0 + 1, y0)
f4 I(x0 + 1, y0 – 1)
f5 I(x0, y0 – 1)
f6 I(x0 – 1, y0 – 1)
f7 I(x0 – 1, y0)
f8 I(x0 – 1, y0 + 1)
f9 I(x0, y0 + 1)
f10 I(x0 + 1, y0 + 1)
minimum area of 3 × 3 pixels in a Bayer Pattern in order
to recognize particle color classes.
The training procedure consists in arranging the weights
among the neural network (connections between neurons
of adjacent layers, cf. Figure 6) in such a way that the
Copyright © 2011 SciRes. JSIP
Improved 3-D Particle Tracking Velocimetry with Colored Particles 65
color class resulting from the neural network is uniquely
related to the actual color class of the particle. This color
class is known in the case of training data, since three
separate measurement passages are made in the wind
tunnel, each with exclusively red, green, or blue particles.
When acquiring training data, the measurement section
has been fully equipped with the flow pattern device (i.e.
winglets, cylinder or swirl generator). This ensures that
the ANN is trained under the same flow and optical con-
ditions as found during the later, actual measurements
with a mix of colors.
After seeding the wind tunnel exclusively with red,
green or blue EMS-particles of 23 µm diameter, the im-
age processing as well as localization of the tracer parti-
cles is realized as explained previously. At the end, the
collected feature vectors constitute a training file com-
posed (in each camera channel A, B and C) of 15 000
feature vectors for each primary color class; this means
45 000 feature vectors in a single training file for each
camera channel. The training algorithm is based on the
principle of Back Propagation [20] during 30 000 train-
ing steps, so that a global squared error below 10% is
finally attained.
The resulting ANN is then tested upon another set of
45 000 feature vectors of each color, collected separately
from the data used for training. For each color class, the
percentage of correctly recognized vectors is called the
recognition rate. Good results are obtained, with a typical
recognition rate between 80 and 90%, as detailed respect-
tively in Table 4 (Case 1: winglets), Table 5 (Case 2:
cylinder), and Table 6 (Case 3: swirl generator). The
recognition rate is only slightly lower than in experi-
ments performed with larger particles (Ø 70 µm) as
reported in [1] with a typical recognition rate of 85% -
Considering these results, a preference for some colors
seems apparent among the mistakes. For example, green
particles are mistaken with blue 5 or 10 times more often
than with red. This point requires further investigations.
The highest recognition rate is always for the red color.
This could be attributed to the halogen lamps, emitting a
color being slightly reddish in spite of the heat mirror.
This would lead to a shift in the spectrum of light re-
flected by particle surface. Hence, the influence of blue
and green Bayer pixel types in the feature vector would
be reduced. Consequently the classification would main-
ly be based on intensity values of red pixel types, only.
Also, in feature space the distance between green and
blue color classes would be too small to separate these
classes clearly by the neural network. To avoid this
problem an ideal light source is needed, which emits all
wavelengths of the visible spectrum in the same amount:
white light. In respect of coloring particles it is important
Table 4. Performance of color recognition for each camera
(Case 1: winglets).
Color classCameraP(C1) P(C2) P(C3)
A 82.21% 14.98% 2.81%
B 73.3% 23.94% 2.76%
C 76.33% 22.07% 1.6%
A 23.48%
72.1% 4.42%
B 10.66%
84.0% 5.34%
C 11.5%
80.82% 7.68%
A 5.54% 6.39%
B 1.38% 5.53%
C 0.8% 7.77%
Table 5. Performance of color recognition for each camera
(Case 2: cylinder).
Color classCameraP(C1) P(C2) P(C3)
A 73.22% 24.84% 1.94%
B 68.69% 28.81% 2.5%
C 83.05% 15.43% 1.52%
A 15.1%
82.76% 2.14%
B 12.08%
84.68% 3.24%
C 27.06%
69.98% 2.96%
A 2.44% 4.93%
B 1.89% 6.42%
C 6.59% 7.48%
Table 6. Performance of color recognition for each camera
(Case 3: swirl generator).
Color classCameraP(C1) P(C2) P(C3)
A 84.74% 14.59% 0.67%
B 90.18% 9.18% 0.64%
C 79.93% 19.05% 1.02%
A 5.97%
93.05% 0.98%
B 20.03%
78.66% 1.31%
C 7.92%
90.47% 1.61%
A 0.54% 1.58%
B 1.39% 2.32%
C 0.83% 2.54%
Copyright © 2011 SciRes. JSIP
Improved 3-D Particle Tracking Velocimetry with Colored Particles
to choose ink that can be distinguished well under the
prevailing light conditions. This is all the more difficult
the more color classes to be used.
5. Locating Particle Centers in 3-D
5.1. Camera Calibration
The purpose of calibration is the determination of all
extrinsic (6 unknowns: location and orientation of the
camera) and intrinsic (5 unknowns: principal point, cali-
brated focal length, lens distortion parameters) parame-
ters of the used camera model. The mathematical formu-
lation of the camera model is expressed by the collinear-
ity equations which describe the transformation of 3-D
world coordinates to 2-D image coordinates [21]. To
compute all unknowns a set of well-known 3-D coordi-
nates is needed (reference points), which can be mapped
to their corresponding positions in camera images. For
each reference point two equations are set up (one for
each image coordinate). This leads to an overdetermined
system of equations, solved by the least squares method.
For calibration a two-level calibration target (shown in
Figure 7) with 25 reference points is used. In contrast to
a plane target field, reference points are spatially distrib-
uted in all three dimensions and the calibration becomes
more reliable [22]. First, the target is imaged in eight
different orientations to determine the intrinsic parame-
ters of each camera precisely. Then the target is placed in
the center of the observation volume so that it faces the
observation window. One snapshot is taken by each
camera and is used to calibrate extrinsic parameters
while keeping the intrinsic parameters fixed. This posi-
tion of the calibration target determines the origin of the
world coordinate system.
5.2. Particle Assignment among Camera Views
Figure 8 illustrates the whole process of solving the spa-
tial correspondence problem for a single particle. The
particle of interest is marked by a surrounding red square
in Camera A - hence classified as a red one. Now, one
Figure 7. Two-level calibration target (dimensions: 20 mm ×
20 mm × 5 mm; level height: 2 mm) with 25 reference
points of known coordinates (Ø = 0.5 mm).
Figure 8. Reducing the number of ambiguities using epipo-
lar geometry and color information.
corresponding partner should be found in Camera B and
Camera C. There are eight possible candidates near the
epipolar line (red, from Camera A) which is constructed
in Camera B, which means that their distance to the line
is smaller than the tolerance value ε. Because the obser-
Copyright © 2011 SciRes. JSIP
Improved 3-D Particle Tracking Velocimetry with Colored Particles 67
vation volume is limited in depth (8 mm), only a small
segment of the epipolar line is considered. This leads to a
further restriction of the search space, shown as a red box.
Only four candidates are located in this red box and only
two of them are classified to be red. In Camera C an ep-
ipolar box is constructed from the chosen particle in
Camera A, and two additional boxes are constructed
from the red candidates in Camera B. When looking at
the two intersection areas of the epipolar boxes, it is ap-
parent that only one red particle can serve as a corre-
spondence partner. If there is more than one candidate,
the one with the smallest distance to one of the epipolar
line intersections is chosen. The approach works very
well as long as the tracer particles can be clearly assigned
to their real color class.
The advantage of the proposed method is quantified in
Table 7. The search for corresponding particles was per-
formed as described above for four sample frames with
different particle number densities obtained from the real,
full-scale experiments. Here, n denotes the number of
particles in Camera A to which one or more possible
correspondences have been finally found in Camera B
and C. The columns Na and Nac contain the average
number of ambiguities for each particle association when
assuming all particles as monochrome (i.e., without con-
sidering color: Na), respectively taking into account the
color information (Nac). These real measurements differ a
little bit from the theoretical calculations presented in the
appendix (see later Figure 10) but the trend is very simi-
lar. Using the color information it is possible to reduce
considerably the number of ambiguities, which is of the
utmost importance for successful PTV measurements.
5.3. Reliability of Color Class Recognition in
Full-Scale Experiments
The process employed to recognize a tracer particle is
closely linked to the recognition of color classes. Indeed,
the candidates should belong to the same color class
when searching for correspondences in camera images B
and C to a selected particle in A. Nevertheless, in con-
flicting situations where only two of the three corre-
sponding particles in the camera images are of the same
color, the particle position in 3-D is assigned to this color
class. If all three color classes are different, no 3-D posi-
tion is assigned.
In Table 8, statistics resulting from three full-scale
experiments associated with Case 1, 2 and 3 are pre-
sented. The number of possible matches in all three cam-
era views, denoted here by n, is limited by the camera
image containing the smallest number of detected parti-
cle centers for the selected frame. This number is further
separated into the numbers of successful matches, where
three (n3/3) or two (n2/3) of the three correspondences be-
Table 7. Measured number of ambiguities without ( Na) and
with (Nac) considering color classes.
n Na N
572 2.59 1.24
756 3.34 1.28
952 4.66 1.44
1535 9.27 2.02
Table 8. Matching particle color statistics in three camera
views for the different configurations. The number of possi-
ble matches is denoted by n. The notation ni/3 is used for the
number of matches where i of 3 correspondences belong to
the same color class. The number of lost matches is denoted
by nlost.
Case 1: WingletsCase 2: Cylinder Case 3: Swirl
N 1020 1478 929
n3/3 460 675 224
n2/3 455 694 554
n1/3 27 21 33
nlost 78 88 118
long to the same color class. In this table the correspond-
dences associated with three different colors (n1/3) and
therefore not considered further, and the number of lost
matches, which cannot be determined at all by epipolar
geometry (nlost) are also listed. In Cases 1 and 2, n2/3 is
similiar to n3/3 due to the occurrence of overlapping par-
ticles on the different camera images. Case 3 (highly
three-dimensional flow in the transverse direction) leads
of course to a particularly challenging situation. Tracers
in the foreground move transversally in the opposite di-
rection compared with particles in the background. The
probability of overlapping particle images rises and color
classification becomes more difficult because of un-
known/untrained particle patterns. One may notice in
Table 8 that in all three Cases, epipolar associations with
three different colors (n1/3) are very rare; about 2 to 4%
only. This is one more indication of the reliability of the
developed algorithm for color class recognition. Indeed,
a failure of the algorithm is much more often the result of
an impossible epipolar association (nlost) and not of a
failed color association.
5.4. Calculation of Spatial Tracer Coordinates
The spatial location of a tracer p can be computed if ho-
mologous points are found in at least two different cam-
era views. In this subsection the index i = 13 is used
to indicate the three different camera views. Note that be-
cause of small imprecisions due to the calculated coordi-
Copyright © 2011 SciRes. JSIP
Improved 3-D Particle Tracking Velocimetry with Colored Particles
nates of homologous points si and camera parameters the
viewing rays do not necessarily intersect exactly in 3-D
space. Accuracy and reliability increase when corre-
spondences are found in all three camera views. The
viewing rays from the homologous points si given in
world coordinates on the sensor plane of camera i in di-
rection di = oi si to the projection center oi should al-
most intersect at the spatial point p searched for, where
si + tidi = p, i.e.:
si di
sii di
si di
yty y
 
 
 
 
 
Since there are three equations and one unknown, one
still gets an overdetermined system of equations when
performing a triangulation between two cameras only (6
equations 3 unknowns x, y, z + 2 unknowns t1 and t2).
If the solution is computed by adjustment of direct ob-
servations [23], this approach can easily be extended to
three or more cameras. When rearranging (9) to
di si
idi si
di si
yty y
 
 
 
 
 
the unknowns can be separated and (10) can be expressed
in matrix form
010 .
di si
di si
di si
Combining all viewing rays results in an overdeter-
mined equation system of the form:
.Axy (12)
The design matrix is denoted by A, vector x contains
all unknowns x, y, z and the negative scaling parameters
ti, and vector y contains all observations of xsi, ysi and zsi.
If there are three corresponding points the system of equ-
ations results in
1000 0
0100 0
0010 0
010 00.
001 00
010 00
001 00
Finally, the calculation of the unknowns in x can be
performed using the least squares method:
5.5. Experimental Determination of the
Localization Uncertainty
To get a reliable order of magnitude for the measuring
error, a reference plate with circular 49 marks was fixed
on a translation stage with manual adjustment of mi-
crometer accuracy. It was placed inside the observation
volume, so that all marks can be imaged from each cam-
era. The 3-D coordinates of the marks were calculated as
described above. The new 3-D positions of the marks
were determined when the plate was moved 5.98 mm
towards the cameras using the translation stage. Ideally,
the shift should be the same for all 49 marks. In fact the
measurement of 49 shifted marks resulted in a mean shift
value of 5.98 mm and a standard deviation of 0.0069 mm.
The maximum measured shift within the set of marks
was 5.9953 mm and the minimum was 5.9677 mm. This
results in a difference of 0.0276 mm. This tiny value in-
dicates that the uncertainty is below 0.5% in terms of
distance between actual and measured localization.
To track the particles in time a 3-frame algorithm
based on Minimum Acceleration algorithm is employed
[2,24]. The computation of trajectories is described in
detail in a separate publication [25]. Figure 9 demon-
strates the ability to obtain PTV data within the whole
three-dimensional volume of observation around three
winglets (Case 1). There is a factor 20 between the high-
est and the lowest measured velocity, which already
represents a challenge for 3-D PTV [2].
6. Conclusions and Perspectives
Dense trajectory bundles have to be reconstructed to re-
solve small flow patterns in PTV experiments. Therefore,
a high number of tracer particles is necessary. But this
will increase the occurrence of ambiguities leading to
problems when searching for corresponding particle lo-
cations in different camera views. The relative number of
the particles can be reduced if particles can be distin-
guished e.g., by color. An original procedure has been
developed to dye, localize in 3-D, and identify the color
class of small tracer particles on Bayer raw images, used
to investigate three different flow patterns by Particle
Tracking Velocimetry. A post-processing strategy using
Artificial Neural Networks combined with a standardized
procedure for particle dyeing results in high color recog-
nition rates, typically between 80 and 90%. Furthermore,
based on the huge amount of available training data Arti-
ficial Neural Networks are robust enough so that the de-
veloped procedure can be rapidly adapted to different
conditions. The described method for classifying particle
color is recommended when particle projections cover
Copyright © 2011 SciRes. JSIP
Improved 3-D Particle Tracking Velocimetry with Colored Particles 69
Figure 9. Visualization of trajectories in gas flow for case 1
only a few pixels. Then, classifying the color in RGB or
HSI color space is erroneous, because of artifacts due to
the demosaicing process. Finally, the feasibility of the
particle recognition in 3-D gas flows has been demon-
strated. Typically, 90% of all tracer particles can be fi-
nally localized with high precision (spatial uncertainty
about 0.5%) using 3-D photogrammetry. When using
color information, more tracers can be applied for seed-
ing the flow, as required for PTV to resolve small-scale
flow patterns.
In future measurements, further color classes (starting
with yellow) will be added for seeding. Also, first tests
involving smaller fluorescent tracer particles appear to be
even more interesting, but also challenging. While the
employed EMS particles are suitable for present condi-
tions and slow gas flows with low Reynolds number,
smaller particles are needed to investigate real turbulent
flows with higher velocities. Furthermore, using fluores-
cence will eliminate the effect of specular reflection on
the particle surface, which could be a reason for deterio-
rated color classification.
7. Acknowledgements
The authors would like to thank the DFG (Deutsche For-
schungsgemeinschaft, Schwerpunktprogramm 1147) for
the financial support of this project. Interesting discus-
sions with R.V. Ayyagari, and T. Ruskowski are grate-
fully acknowledged.
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Improved 3-D Particle Tracking Velocimetry with Colored Particles 71
Appendix: Theoretical Prevision of
A significant problem when using imaging measurement
methods in 3-D flows is the occurrence of ambiguities
during the spatial correspondence analysis. This is par-
ticularly true when a high number density of tracer parti-
cles is required i.e., when resolving small-scale flow
structures. The correlation of particles between different
images at a given time is mainly based on geometrical
conditions such as the epipolar geometry. The intersect-
tion between the image plane and a plane formed by the
object point and the perspective centers of the cameras
should form a line. A corresponding tracer can only be
found along this line. This decreases the search area from
2-D (the whole image) to 1-D (a line in the image). Using
more than two cameras, the search space becomes small-
er and smaller. Nevertheless, the ambiguities cannot be
completely avoided in practice.
The same problem arises when correspondence analy-
sis is performed in time to deduce information concern-
ing the Lagrangian description of the flow field. Trajec-
tories should be as long as possible without any interrupt-
tion [2]. A restriction of the search space when consider-
ing successive time steps can be derived from physical
considerations, taking only into account acceptable varia-
tions of velocity and acceleration and the local correla-
tions between velocity vectors.
In what follows, the spatial correspondence problem is
analyzed in greater detail. The formula to calculate the
total number of expected ambiguities Na in a three-cam-
era arrangement is given by (15) [4] and is also illustrated
in Figure 10.
12 12
23 13
nn bb
n total number of tracers in image
F image size
α intersecting angle between epipolar lines in the third
ε tolerance of the epipolar band
bxy distance between camera x and camera y
The number of ambiguities becomes minimal when the
cameras are arranged in an equilateral triangle so that
b12 = b13 = b23, and α = 60˚. Under this condition, used in
the present experimental setup, the term in brackets is
simply replaced by the factor 3. Note that the number of
ambiguities grows with the square of the number of trac-
ers. An introduction of color classes for tracers acts like a
reduction of the tracer particle number density. This re-
duces the number of ambiguities when the set of particles
s separated by color into individual subsets. Assuming i
n = 1000
n = 1500
n = 500
n = 572
n = 992
n = 1535
Figure 10. Theoretical reduction of the number of ambigui-
ties when using up to six color classes (cf. Table 9). For
comparison, the actual measured number of ambiguities for
different numbers of particles (n = 572, 952, 1535) when
using three color classes is also plotted (cf. Table 7).
Table 9. Number of ambiguities predicted by (16), see also
Figure 11.
c 1 2 3 4 5 6
Nac(c, n = 500) 2.640.66 0.29 0.16 0.10 0.07
Nac(c, n = 1000) 10.562.64 1.17 0.66 0.42 0.29
Nac(c, n = 1500) 23.775.94 2.64 1.48 0.95 0.66
that the colored particles are uniformly distributed in
camera images, the number of tracers nc of a particular
color in each subset is n/c, where c is the number of used
colors. Since the correspondence problem is solved for
each subset, the number of ambiguities Nac decreases as
the square of the number of color classes (replacing n by
nc = n/c in (15)):
12 .
Results obtained from this equation are listed in Table
9 and plotted in Figure 10 using the parameters used in
the present experiments: F = 1280 × 1024 pixels, α = 60˚
and ε = 1 pixel considering up to six color classes c and
three different values for the number of tracers n (500,
1000 and 1500). It can be seen in Figure 10 that the
number of ambiguities is theoretically reduced by typi-
cally 80% when 3 color classes are taken into account.
Copyright © 2011 SciRes. JSIP