2. Experimental Setup
5. Results
4. Simultaneous Registration andVolumetric Reconstruction
LayersDownwardtranslations
Pixel
[Image Interpolation]
Imag
e #0
(stil
l pat
tern
)
Imag
e #2
0
Imag
e #4
0
363
pixe
ls (5
2.2
mm
)
72 pixels (10.4 mm)
Video sequence #2
1 5 10 15 201 5 10 15 200
10
20
30
40
Tran
slat
ions
(pix
els)
z-axis (# layer) z-axis (# layer)
Image #5 Image #37
1 10 20 30 401 10 20 30 400
0.5
1
1.5
2
Velo
citie
s(p
ixel
s / i
mag
e)
z-axis (# layer) z-axis (# layer)
Image #5 Image #37
1. Context and Objective
Camera
t0 ti
Patterninitiallytagged
Deformedpattern
Motion torecover
Stillwater
Drainingoff water
~1mm
Sever
al cen
timetr
es
Observedimage
Observedimage
Time Time
- Computer vision applied to experiments in fluid mechanics-
Densely measure the Laminar Poiseuille Flow in an Hele-Shaw cell-
Pattern printed in the liquid using molecular tagging- Tracking and
volume reconstruction by combining: - direct image registration - a
volumetric image formation model- Use as few physical assumptions
as possible
CameraLaser 488 nm
Mask
Hele-Shawcell Spherical
lens
Laser527 nmx
y z
Drain valve
Left
view
Camera
Laser 488 nm
Laser527 nm
Mirrors
Mask
Hele-Shawcell
Automatedarm
Sphericallens
Cylindrical lens
xyz
Top
view
Molecular tagging based on photobleaching- Truly non-invasive- A
molecular tracer (fluorescein) is uniformly mixed to the water-
When excited with a `green laser', the tracer becomes fluorescent-
The fluorescence can be inhibited using a powerfull `blue
laser'
3. Direct Image Registration
Reference image What we would observewith a uniform motion
along
the z-direction of the cell
What is actually observedDepth of
the cell
Sensor
Principalaxis
Pixel
Hele-Shaw cellVolume of the cellcorresponding tothe pixel
When the brightness constancy assumption is satisfied then
direct image registration consists in minimizing the intensity
difference between the input image ( ) and the reference image (
):
In our case, the brightness constancy assumption is not
satisfied due to the image formation model and the nature of the
observed flow:
- Bilinear and bicubic interpolation introduce a systematic
bias- Problem solved by fitting a regularized B-spline to the image
(the images are thus considered as continuous functions)
Bibliography
R. Szeliski. Image alignment and stitching: A tutorial.
Foundations and Trends in Computer Graphics and Vision, 2:1–104,
2006.
C. Garbe et al. An optical flow MTV based technique for
measuring microfluidic flow in the presence of diffusion and Taylor
dispersion. Experiments in Fluids, 44:439–450, 2008.S. Hosokawa and
A. Tomiyama. Molecular tagging velocimetry based on photobleaching
reaction and its application to flows around single fluid
particles. Multiphase Science and Technology, 16:335–353, 2004.I.
Ihrke et al. State of the art in transparent and specular object
reconstruction. STAR Proceedings of Eurographics, pages 87–108,
2008.
Simultaneous Image Registration andMonocular Volumetric
Reconstruction of a Fluid Flow
Florent Brunet1,2,3,4, Emmanuel Cid1,2,3, Adrien Bartoli4INPT,
UPS, IMFT (Institut de Mécanique des Fluides de Toulouse)F-31400
Toulouse, France
1
CNRS, IMFT, F-31400 Toulouse, France2
Fédération de recherche Fermat FR 3089, Toulouse, France3
Clermont Université, ISIT (Image Science for Interventional
Techniques)F-63000 Clermont-Ferrand, France
4ermat
ToulouseMidi-Pyrénées
The 22nd British Machine
Vision ConferenceUniversity of Dundee
September 2011
Motion model and image formation modelKey idea: consider that
the volume ismade of layers moving independentlyfrom each
other.
Additional hypotheses
Final optimization problem
Symmetry. The flow is symmetric with respect to the centre of
thecell in the z-direction.Positivity. All the translations are
downward translations.Temporal consistency. A layer never goes
upward.Spatial consistency. The inner layers are faster than the
layersclose to the walls of the cell.
Image #0 Image #60 Image #120
171
pixe
ls(2
4.6
mm
)
192 pixels (27.6 mm)
Video sequence #1
(still pattern)
Tran
slat
ions
(pix
els)
Velo
citie
s(p
ixel
s / i
mag
e)
0
20
40
60
80
100
1 5 10 15 20
Image #8
z-axis (# layer)1 5 10 15 20
Image #115
z-axis (# layer)
0
0.5
1
1.5Image #8
1 10 20 30 40z-axis (# layer)
1 10 20 30 40
Image #115
z-axis (# layer)
Theoretical Poiseuille flow model
[http://www.columbia.edu/cu/gsapp/BT/RESEARCH/Arch-atmos]
1 5 10 15 20
Image #44
z-axis (# layer)1 5 10 15 20
Image #80
z-axis (# layer)
Image #44
1 10 20 30 40z-axis (# layer)
Image #80
1 10 20 30 40z-axis (# layer)
image #0 image #30 image #60 image #90 image #120
3D view of the computed flow (front: acquired images, side:
computed deformations)
20 40 60 80 1000
0.2
0.4
0.6
0.8
Image number
Velo
city
(pix
els
/ im
age)
Period when the steady laminarPoiseuille flow is established
Velocities computed with our approach
Average of the computedvelocities(0.6054 pixels / image)
Average velocity computed from the water/air interface(0.5774
pixels / image)
Comparison between thecomputed velocities and the
ground truth velocities(determined from the water/air
interface)
+ computed deformation(and image formation
model)
Deformed pattern Corresponding true imagePattern Comparison of
the initial pattern
warped using the translationscomputed with our approach
and of the corresponding imageof the video
-2 -1.5 -1 -0.5 0 0.5 1 1.5 20.5
1
1.5
2
2.5
3 BicubicB-spline
Bilinear
Exp
ecte
dm
inim
um
×10-3
Val
ue o
f the
imag
e di
ffere
nce
(app
rox.
cos
t val
ue o
f di
rect
imag
e re
gist
ratio
n)
