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)