u 5000p
5000p
| device. Both well
e seen. The bright
cused bubbles arises
.1%) which passes
sd by the telecen-
can be completely
tric stop CCD
centric path of rays:
optical axis causes
dard optics, but not
HNIQUE
e the size distrib-
tation and depth-
med, a brightness
eliminate inhomo-
lumination.
ation process and
is independent of
es is an essential
hnique. The nor-
lumination model
3) are further pro-
(2)
à obtained by tak-
96
ing a background image gs (Z) with illumination switched off
(I(@) = 0) and a zero image gz(Z) in which no bubbles are
present (I(Z) — Io(x)).
If we describe the objects by their light absorbing coefficient
r(X) in the object plane (capitals denote object plane co-
ordinates and small letters denote image plane coordinates)
their image is given by :
-—
xr
with v(Z) describing vignetting and Vz being the magnifica-
tion.
Then, the linear inhomogeneous point operation
A EDS
n) — 0D = 9) ; Io(z) (7) en
4
results in a normalized gray value n in the range of 0 to 1.
4.2 Segmentation
The image processing step of the segmentation distinguishes
objects from the background and calculates their apparent
(blurred) size. After the depth-from-focus calculation has
been performed, the apparent size is corrected to the true
particle size. Because blur causes the originally step edges of
the objects to become flat, the boundary of a blurred object
is not a priori well defined. Therefore we define the boundary
to be at these locations where the gray value has decreased to
the 1/g-th of the maximum gray value (Fig. 6). The method
used to segment the bubbles is a two-step approach which
combines a pre-segmentation step with a fast region growing
algorithm. Bubbles within the largest possible size of the
measuring volume show a plateau with a gray value of 1 in
the normalized image. At the very border of that volume,
the plateau shrinks to a single point. Beyond this maximum
distance from the focal plane, the width of the PSF exceeds
the size of the (well-focused) image of the bubble. For that
reason it is no longer possible to calculate size and depth from
the blurred image and therefore it is not necessary for the pre-
segmentation to detect those bubbles. Because all bubbles
which may be within the measuring volume have to show a
0.84
0.64
044
0.24
= We
04 TN = fp A
NAN
Figure 6: Definition of the 1/q-area as the size of blurred objects.
As an example, the image shows a blurred object and it’s boundary
given by the intersection with the 1/q = 0.4 plane.
maximum gray value of about 1 and the background has been
made uniform by the normalization, pre-segmentation can be
carried out by a global thresholding. It is important to note
that the value of the threshold does not affect the result of the
segmentation, since it is guaranteed that all bubbles within
the measuring volume are found as long as the threshold is
within a sensible range, e.g. 0.2 to 0.8.
The exact boundary of a bubble is found by the sec-
ond step, the region-growing algorithm. This algorithm is
a modification of a region growing method developed by
[Hering et. al, 95] and shall be briefly described here. The ini-
tial step of a region growing segmentation is the detection of
seeding points as starting locations for the growing. With our
algorithm, seeding points are defined as the location of the
gray value maximum of each object. The image is smoothed
by a small binomial filter to reduce noise and therefore avoid
mislocating the maximum due to random noise peaks. The
region growing phase starts with each seed defining different
objects, which consists of this single pixel each. Pixels are
than added to the objects if their gray value is larger as 1/q
times the gray value of the initial seeding point and if they are
8-neighbors of the current boundary line of the object. The
growing phase stops if no new object pixels can be found.
The region growing procedure causes the objects to be con-
nected and to have the correct size regardless of their size in
the starting image provided by the thresholding. Fig.7 shows
the final result of the segmentation for several bubbles.
Figure 7: Final segmentation result of two images. The gray lines
indicate the boundary of the particles (obtained with 1/q — 1/e).
4.3 Depth-from-Focus
A usual approach for depth-from-focus is to calculate a mea-
sure of blur at each image point. Thus a depth-map of the
image can be calculated which contains the distance from fo-
cal plane for each pixel. This is only possible if more than one
image of the same scene is available, due to the impossibility
to distinguish between PSF and object function from the gray
value image. À modification of this approach for one-image
depth-from-focus has been given by [Lai et al.,92] who uses
the assumption of a Gaussian shaped PSF. At step edges the
standard deviation of the Gaussian is estimated and at these
points a depth map is calculated. Different from calculating a
depth-map, our approach performs the object detection first
and then does an object-oriented depth-from-focus, measur-
ing the amount of blur of complete objects. This allows for a
fast depth determination, suitable for the evaluation of long
image sequences.
A good integral measure of the blur of a particle is the mean
gray value gm on the segmented area. With increasing blur-
ring, the edges of the particles become less steep and there-
fore the mean gray value decreases (Fig.8 and 11).
197
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
