Jökull - 01.12.1994, Side 50

The maximum grey value for pixels defined as parti-
cles is e.g. 75, thus the background covers the grey
value interval 76-255. A matrix of the size 255x255
(sufficiently larger than the expected largest tephra
grain) is applied to every pixel and whenever the cen-
tral pixel of the matrix belongs to a grain its grey value
is substituted with that of the pixel in the upper right
comer of the matrix. This operation is succeded by a
100x1 average (lowpass) filter to balance out possible
discontinuities. Dividing the original image by the the
background reference image and multiplying with a
fixed value (200) results in grey values in the vicinity
of 200 for all background pixels and consequently in
corrected tephra grain grey values. Thus, besides the
shade correction the method provides a grey value cal-
ibrated image, and, therefore, minor fluctuations in the
light intensity are of no consequence.
The next step is to define a suitable grey value range
which includes all the darkest particles. The interval 0-
100 omits none of the tephra particles. The segmenta-
tion converts the background grey values to black (0)
and the particle grey values to white (255). This binary
image is the basis for the measurement, however, each
particle must be defined as an entity. This involves the
use of a connectivity mle which states that all image
object pixels are connected in eight directions whereas
the background pixels are connected in four directions
only. In this way the individual grains are identified and
in practice given separate grey values.
The final steps of the image analysis sequence are
definition of the measuring parameters (three shape in-
dices, the minimum and maximum diameters and the
surface area), the actual measurement and the data
storage.
MEASURING PARAMETERS
Textural characteristics are three-dimensional.
When using image analysis, however, the tephra
grains are only represented by projections of their
outlines and the sizes and shapes are thus dependant
on the actual spatial orientation of the grains. In dis-
persed preparations the short diameter will most like-
ly be perpendicular to the horizontal plane. This
means that the projected outlines most likely are max-
imum projections. All image analysis measurements
refer to the projections and hence are subject to cer-
tain limitations (Russ, 1986), especially conceming
concavities on particle surfaces. The sizes of the
tephra grain area and diameter projections are mea-
sured in millimetres.
The basic parameters measured on the tephra
grain projections are the minimum diameter (DMIN),
the maximum diameter (DMAX), the area (AREA),
the perimeter (PERIM) and the convex perimeter
(CPERIM). DMIN and DMAX are defined as the
shortest respectively the longest of the Feret diame-
ters measured in 32 directions. AREA is defined as
the total number of pixels representing the particle.
PERIM is calculated as the sum of the number of pix-
els in the 0 degree direction, the number af pixels in
the 90 degrees direction and the number of pixels in
the 45 degrees and 135 degrees directions multiplied
by V2. CPERIM is defined as the mean particle diam-
eter (sum of 32 Feret diameters divided by 32) multi-
plied by p.
The shape indices measured are mathematical
combinations of the basic parameters. They are ex-
pressions of ruggedness, circularity and elongation.
Ruggedness 0,94 0,94 0,93 0,92 0,92 0,84 0,80 0,74 0,73
Circularity 0,90 0,82 0,70 0,52 0,31 0,70 0,41 0,47 0,27
Elongation 0,98 0,65 0,46 0,26 0,17 0,98 0,36 0,45 0,41
Fig. 9 Particle shapes and their corresponding indices Ruggedness = Ratio of convex to total perimeter (CPERIM/PERIM),
Circularity = 4pAREA)/(PE)2, Elongation = Ratio of minimum diameter to maximum diameter (DMIN/DMAX).
9. mynd. Dœmi um niðurstöður myndgreiningar á þáttunum hrjúfleiki, hringlögun og ílengd.
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JÖKULL, No. 44