INTRODUCTION
In the following project two dimensional signals which represent
images obtained from an electronic microscope are analyzed. These
images are obtained from different types of metallic materials formed
by diverse alloys. The metals contain degradation levels in the
surface which have been exposed to corrosive environment
conditions, in which different type of pittings are produced . These
pittings are related to the material type and the corrosive media.
The
microscope images provide a great visual approach and allow the
researcher to inspect the texture and the tonality of the surface.
In
other words the corrosion morphology and the pittings. The
electronic microscope provides other characteristics in the pictures
besides the approach. These characteristics are treated with signal
processing techniques and models to extract the information that
is
not evident for the human eye and which accelerates the research
procedures in the corrosion area.
DEVELOPMENT
The project started initially from pictures obtained
by an electronic
microscope, which included different quantities of textures, colors
and forms of the corrosive damages in metals. The original idea
was
to extract most information as possible for being able to classify
the
pittings in an automatic way through a personal computer. Initially
we
had certain interpretations of the pictures generated by the electronic
microscope. Most of these interpretations were based in the visual
experience of the researchers regarding the corrosive processes.
These parameters were based in the tonalities and the morphology
of
the damage caused by the corrosion in the metal.
If we represent mathematically a signal then we have the following
expression:
Figure 1 represents an example of these
images. The pictures relate
to the ddxsdxonment with high content of salts (right). Corrosion
in
high temperatures in alloys FeCr (middle), and NiCr (left) of
approximately 50 microns wide. The analysis in another material
type
with alloy NiCr in another corrosive environment generated by high
temperatures (1200º C). We can visualize different color and texture
zones. The histograms (below) show basically the tonality distribution
where the darker colors represent the zones with more degradation.
Figure 2 is an image from which the image
(right) of carbon steel in
figure 1 was extracted. In this image we can see low damaged areas
(left side), damaged zones with mixed textures (middle regions)
and
high damaged areas (right side). As an initial objective we separated
the colores in order to visualize the gray tones that were not visible
for the human eye and we obtained the first results. In area 1 we
obtained depth relationships related to the gray tone which show
us
the real appearance of the effects of corrosion.
What apparently looked as a non degradated
part of the material as
shown in the left side of figure 2 (area 1), show us that it really
had a
low level of decomposition, non visible for the human eye.
Analysis of Corrosion in the Pictures
We classified the types of composite and characterize the
morphology that looked random in form and size. We obtained the
negative of the regions with the lighter pittings and the visual
tool
clarified the topographies.
Figures 3 and 4 show the original and the
negative respectedly. In
this imageswe can visualize how the darker areas are not composite
spots but the depth of the pittings.
Figure 4 shows clearly the depht of the pittings. The normal picture
(Figure 3) shows dark tones, difficult to be seen, with the appearance
of being diffuse and dark spots but not showing the depth.
We took advantage of the electronic microscope which can obtain
pictures not only with each pixel position but also the depth related
directly with the gray tones using electron retroprojection to acquire
the image with a Sweep Electronic Microscope (MEB).
The black color represents the maximum depth and the lighter or
white color the surface, the highest point of the image plane. To
be
able to analyze and visualize this results in the computer, the
images
were reduced to 256 gray tones which didn’t affect our methodology
to find new results. The original images were treated in 3D, which
wouldn’t be able to be visualized and observed directly with
the
electronic microscope. Figures 5 and 6 show the depth levels and
the
3D model respectedly.
We applied to the images a spatial filter to soften the peaks and
for
the texture in the model to be visualized in an easier way. The
filter
was applied in windows of 3X3 pixels and is defined in the following
equation.
The filter was used to soften the image and model it in 3 dimensions
as showed in figure 6.
Also, Figure 6 shows the colors that relate with the different
heights
of the surface.
Signal Processing
With the new perspective of the images, we proceed to interpret
the
cross sections in the surface as two dimensional signals. One cross
section in the surface is considered a one dimensional signal, i.e.
a
vector. In Figure 7, a region of the image is displayed and the
horizontal line represents a cross section which crosses a more
deep
pittting than the others in the image.
Figure 7 shows the cross sections and the
type of pitting is
interpreted as a discrete signal. The high frequencies show that
the
pittings are new, i.e. with not a high degree of decomposition in
a
corrosive environment. We get to the conclusion that the components
with the lowest frequencies show the presence of pittings that are
geometrically wider.
The NiCr alloy shows the upper cut, which
cuts a cloud of white
tones, i.e. a white region with dark colors in the center. This
image
was obtained by the microscope and is for the researcher a possible
pitting but in the graph of the cut we can visualize the altitudes
of the
region which allows us to analyze the form of the signal. The second
cut crosses through a dark circle. The microscope visualizes
perfectly that figure. We can observe the morphology of the pitting,
which is more profound and better outlined. Also the general cut
of
the region shows a soft signal with low frequency. This image
provides us with the ideal characterisitics to separate its contours
through a Laplace Operator.
This operator helps us to detect edges, specially the ones which
are
well defined like the ones marked by the NiCR alloy. In the graphs
we
obtain a interesting form of the topography of the surface which
is
normally not seen by the researcher.
The lower part of figure 7 shows the FeCr
alloy with the same
temperature conditions of the NiCr alloy which produced a different
damage. This type of pitting presented differences from the previous
analysis like the frequencies which were higher than the NiCR alloy,
in which the walls of the valleys in the signal are not triangular.
There
are high frequency components in the low frequency signal, which
components have a greater amplitude.
Other Results
When considering this images as two dimensional signals and the
cross sections as one dimensional signals, it was easy to make
certain considerations for the processing of the signals to obtain
more information. We considered that the wider pittings
corresponded to low frequency signals and the narrower pittings
corresponded to high frequency signals. When we apply the Discrete
Fourier Transform we know that the graph that shows the spectral
of
the frequencies has something to tell us regarding the textures,
that
we define as follows:
Figure 8 shows the frequencies corresponding
to the image with a
low temperature (lower). The spectrum of the frequencies indicates
a
regularity of frequencies in all the regions, it mantains a uniformity
in
the magnitudes of the frequencies. At the same time when we apply
the Discrete Fourier Transform in One Dimension to one of the cuts
we obtain the same uniformity of the spectrum. When we visualize
the spectrum we can determine if we have a region with regular pittings,
with few pittings or maybe none and we are talking about longitudes
and diameters and not about depth. In the upper part of Figure 8
we have the Fourier spectrum of the graph. It is a region composed
by wide pittings and textures with more frequency changes. The cut
indicates a signal formed by low frequencies and the spectrum indicated
a higher concentraion of low frequencies at the middle of the mirror
in the graph.
Figure 9 shows the frequencies without the
mirror of the spectrum and it is practically the same than the one
obtained by Fourier.
Extraction and Characteristics of the
Pittings
With the results that were obtained we can deduct that in a
microscopic image the deepest pittings have an important function
in
the characterization of the pittings themselves. That is why to
characterize the pittings is an important and useful process for
the
researcher in the solution of corrosion problems. When applying
certain filters to the images, good results were obtained.
In a Frequency Domain a Low Pass Filter
is equal to a Gaussian
Function, which mathematically is defined in the following way:
We obtain a similar equation in the Time Domain.
The Final Result was the splitting of the important pittings in
the
image removing what was considered noise in the frequencies as
shown in Figure 12.
The textures that have changes in the frequency
are the higher
components in the image. This way only the most important pittings
will remain, the ones that are characterized by their morphology
and
the environment from which they were produced. We can apply
statistical methods to the pittings to calculate the density in
different
regions. The depth is data we already know and that was extracted
from the transversal cuts in different regions of the image. With
this
filtering techniques, the small pittings almost dissappeared
compared with the important pittings as shown in Figure 13.
With the images from Figure 13 we obtained the damaged regions
with respect to time as shown in Figure 14. The NiCr was damaged
in 23.83% and the speed of corrosion by area of 893.62m 2 /hr was
0.158%/hr. The FeCr was damaged in 6.52% and we calculated
244.5m 2 /hr per 0.043%/hr. The comparison is valid because we
exposed the two alloys to equal conditions.
CONCLUSION
This information has given us a new vision in the
materials analysis
area with the objective of understanding the evolution processes
of
corrosion and simulate and approximate to real life a initial corrosive
process.
We obtained the following benefits:
• Fast processing of the visual characteristics of the corrosive
state.
• Classification of statistical properties like: damage regions,
the
perimeters of the pittings, number and form, density damage by
area, pattern characterization.
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Industry
Manufacturing
Application
Materials Corrosion
Product
IMSL
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