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ogy. Additionally, by incorporating automation and
tackling limitations of conventional strategies, isolat-
ing sub-micron bio-particles can potentially acceler-
ate the development of Point-of-Care devices.
In this work, we use an acoustofluidic 3D printed
device (fluid chamber) to measure the density of
polystyrene beads. The device is initially filled with
a fluid in which the analytes are embedded. Trans-
ducers are then excited to generate an acoustic field
responsible for “trapping” the particle in a given po-
sition. A microscope is used to acquire images of the
cells as exemplified in Fig. 1, where the “trapped” par-
ticle is represented by the first image (top-left). After
the acoustic field is disabled, the particle falls along
time, causing a strong blur as shown in the middle and
final images in Fig. 1, since the particle is no longer
within the microscope focus plane. By observing the
fall velocity (depth per moment in time) and using a
calibration curve obtained in beforehand that relates
the particle’s diameter to depth, one can compute a
good estimate of the cell’s density (cf., Section 2).
Unfortunately, annotating cell’s diameters on dif-
ferent images is a manual process due to a very low
Signal-to-Noise Ratio (SNR) inherent to the blurring
process caused by the particle fall and short Depth-of-
Field of the microscope optical apparatus. Therefore,
one must manually annotate each image in both stages
of calibration and dynamic measurement. Manually
annotating images is a time-consuming and cumber-
some process due to many characteristics. It is prone
to human error and fatigue, rendering automation and
development of Point-of-Care devices unfeasible.
The bead’s diameter is related to the depth, which
can provide information regarding the velocity of the
fall (depth per time). It can be shown that the velocity
with which the particle falls into the medium, along
with other quantities can provide the particle’s den-
sity value (cf. Section 2). Therefore, we propose a
method capable of measuring the particle’s diameters
during its fall. Due to the amount of noise, we found
that fitting a 2D Gaussian in a Gradient Descent fash-
ion can provide reasonable performance in the final
densisty measurement.
Fitting a Gaussian onto a signal (image) is a
method that can be applied on different scenarios for
different purposes. For instance, Ananthanarasimhan
et al., used the technique to estimate the diame-
ter of discharges viewed by High Speed Cameras
(HSC) to characterize a rotating gliding arc (RGA)
reactor (Ananthanarasimhan et al., 2022). Kizel et
al. proposed a method for fully constrained spa-
tially adaptive spectral unmixing for the localiza-
tion of endmembers (Kizel et al., 2015). Lei et
al., used a 2D Gaussian fitting procedure to lo-
cate motion-blurred, weak celestial objects in im-
ages (Lei et al., 2016) for the purpose of orbital de-
bris monitoring. Dai et al., used the method to es-
timate the Point Spread Functions of different opti-
cal apparatus and ultimately increase the resolution of
Single-Photon Emission Computerized Tomography
(SPECT) to sub-millimeter range (Dai et al., 2010).
Anniballe and Bonafoni proposed a Gaussian fitting
procedure aimed at analyzing remotely sensed ther-
mal multi-resolution images to monitor variations in
urban occupancy throughout area and time (Anniballe
and Bonafoni, 2015). Bui et al., proposed the segmen-
tation of murine tumor from noisy ultrasound clinical
images using Gaussian distribution to model local in-
tensities (Bui et al., 2015).
In this context, we propose a Computer Vision
strategy capable of automatically measuring cell di-
ameter on noisy images using a simple, yet effective,
method based on 2D Gaussian fitting using Genetic
Algorithm (GA) and a subsequent refinement with
Gradient Descent (GD) method. Experiments showed
that the methodology provides a satisfactory perfor-
mance and can eventually contribute to the develop-
ment of fully automated devices.
2 EXPERIMENTAL
METHODOLOGY
The density of a particle embedded in a liquid affects
the rate in which it falls (in distance per time). The
relation between fall rate and density can be found by
analyzing the problem’s dynamics, which, for a parti-
cle embedded in a fluidic medium, is ruled by a spe-
cific set of forces. As explained by (Zhao et al., 2014),
forces caused by particle-to-particle interaction, ther-
mal effects and Brownian motion can be disregarded
due to their low order of magnitude when compared
with other forces that act on the system. Thus, the
resulting force that pulls the particle down along the
vertical axis can be expressed as a combination of
gravitational, viscosity and buoyancy forces:
∑
−→
F =
−→
F
gravitational
+
−→
F
viscosity
+
−→
F
buoyancy
(1)
Considering that the vertical axis is pointed down-
ward and approximating the particle as a perfect
sphere, one can express the forces mentioned above
as
−→
F
gravitational
=
4
3
πgr
3
ρ
particle
ˆ
k (2)
−→
F
buoyancy
=
−
4
3
πgr
3
ρ
f luid
ˆ
k (3)
−→
F
viscosity
= (6πrµv)
ˆ
k, (4)
Model Fitting on Noisy Images from an Acoustofluidic Micro-Cavity for Particle Density Measurement
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