SEQUENCES
ohy
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The particles are
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3ASED
REMENT
onal scene onto a
causes the loss of
ry needs additional
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from two images.
| images for depth
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96
Defocused imaging can be described by the convolution of
the well focused image (as it would be with a pinhole lens)
with the point-spread-function (PSF). The PSF is the image
of a point object and describes the properties of the optics.
Thus
spatial domain G(£) PSF(Z) & O()
i à 9 11)
Fourier domain G(k) = PSF(k) . Ó(K)
with O(Z) being the object function and G(z) the result-
ing image. In Fourier space, defocusing is a multiplication
with the Fourier transform of the PSF, the optical transfer
function. Because multiplication is a commutative opera-
tion, it is not possible to distinguish between properties of
the object and of the PSF from the gray values in the image.
The same amount of blur in the image may arise from steep
edges and a wide PSF or from smooth edges and a narrow
PSF. But measuring depth from blur requires estimating the
width of the PSF from blurring, and thus to avoid inclusion
of apparent blur caused by object properties. Many depth-
from-focus approaches use additional information provided
by several images taken from the same scene to solve this
problem. As an example depth series and multi-aperture se-
quences ([Ens and Lawrence,93], [Pentland,87]) may be men-
tioned here. Taking several images of the same scene with dif-
ferent parameters of the optics allows to determine the width
of the PSF independly of object properties. A very simple
setup would consist of a pinhole lens and a second lens with
finite aperture. The image given by the pinhole lens does not
contain blur caused by a PSF and holds all information about
the object properties. With that information, depth can be
reconstructed from the second image. For partical purpose,
systems with several lenses of different aperture are used.
For the investigation of fast moving objects, this approach
results in significant experimental effort and can hardly be
used. For such applications depth-from-focus techniques
which need only a single image are of great advantage. This
is only possible if additional information either about the PSF
or the objects is introduced. In this application, like in many
other technical applications, the shape of the objects is a pri-
ori known. The depth-from-focus technique described here
uses the knowledge about the shape of the object to com-
pute an object-global measure of blur from a single image.
2.2 Concentration Measurement
The calculation of size distributions from image sequences
of particles requires knowledge of number and size of the
observed particles as well as knowledge about the measur-
ing volume. Usually, the measuring volume is determined by
means of mechanical delimiters. This gives a fixed and easy
to handle volume, but also causes flow disturbances which
cannot be neglected. To overcome this problem, we use the
following approach:
The basic idea of depth-from-focus based concentration mea-
surements is the use of a virtual measuring volume. The cam-
era looks freely into the medium, so that the volume defined
by its depth of field is much smaller than the volume observed.
Both particles inside the measuring volume as well as parti-
cles located far outside are imaged. The small depth of field
then results in defocused imaging for most particles. The 3D-
positions of all observed particles are now determined: The
position perpendicular to the optical axis is directly given by
the gray value center of the image of the particle, multiplied
E ii
| / =
light source lens CCD
Figure 2: Principle of depth-from-focus based concentration
measurement. The three-dimensional position of each particle is
determined from the amount of blur in the image.
by the magnification of the optics, while the position along
the optical axis (subsequently denoted by 'z-coordinate’) can
be inferred from the defocus (Fig. 2).
If the 3D-positions are known for a suitable long image se-
quence, the boundaries of the measuring volume can be de-
termined from these data. If a particle is located too far
away from the focal plane, the width of the PSF becomes
larger than the particle itself. The image is than better de-
scribed as a 'blurred image of the PSF’ than a blurred image
of the particle. Therefore no accurate measurement can be
done and these particles have to be excluded from the mea-
suring volume. This is done by specifying a minimum value
for a measure of the amount of blur. Mechanical delimiters
become obsolete to define the measuring volume and are re-
placed by a virtual measuring volume whose boundaries are
controlled by the minimum sharpness criterion.
To obtain the distribution of particle sizes, in addition to the
three-dimensional position the size of each particle has to be
measured. The size of blurred particles is not a priori given
and has to be defined in a suitable manner. This by some
means arbitrary measure of size is then combined with the
position to correct for the true size of the particle.
It is important to note that the use of depth-from-focus
to measure concentrations requires an adequate visualization
method to image the particles in a way suitable for the depth-
from-focus technique.
3 THE SENSOR
3.1 Sensor setup
The bubble concentration sensor (imaging bubble gauge,
IBG) has been used for measurements in the large wind wave
tank at Delft Hydraulics (The Netherlands). The device con-
sists of two water tight housings, mounted at the bottom of
the flume in a distance of 40 cm (Fig. 3). The measuring vol-
ume has a length of several cm in z-direction and is therefore
located far away from the device body. The vertical position
of the device can be changed, thus allowing the measurement
of bubble size distribution at various depths to the mean wa-
ter surface. One of the housings contains the illumination
system, while the optical receiver is located in the other one.
The air bubbles are imaged using a CCD camera looking di-
rectly into the light source. Light hitting an air bubble in the
measuring volume is scattered so that it does not reach the
camera lens. Therefore, a dark image of the bubble is ob-
tained on the image plane, allowing the determination of the
shape of each individual bubble. Bubbles with a diameter of
195
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
