Environmental Engineering Reference
In-Depth Information
in the
t
1
t
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latent variable space that minimizes classification errors could be used
for automatic identification of soft and hard rocks (
i.e.
green and red dots, respec-
tively). However, when the medium hardness/grade rocks (class 2) are introduced
the classification problem becomes more difficult as shown in Figure 3.24(b). The
medium rock class (
i.e.
, blue dots) significantly overlap with the other two classes,
and the contribution of the third component (not shown) to class discrimination is
marginal. This justifies the need for more sophisticated methods for establishing
class boundaries in the presence of significant class overlap. Support vector ma-
chines, a statistical learning technique [40, 93, 94], was used in this study for seg-
menting class boundaries. It essentially projects the data into a higher dimensional
space where simple linear classification is possible. This is particularly useful when
clusters overlap. A complete description of SVM is outside the scope of this chap-
ter. However, the reader is referred to the following publications for more details
[40, 93, 94]. A total of three 3-class SVM models were trained for establishing class
boundaries in the latent variable space of the PLS-DA model (
i.e.
Figure 3.24(b)).
The parameters of these models as well as their performance in training are de-
scribed in [26, 78]. The performance of the complete machine vision approach will
be discuss later in this section.
The last score plot in Figure 3.24(c) shows the clustering pattern of the subim-
ages from all three rock classes, but dry and wet images were identified using red
and blue dots, respectively. Both clusters overlap almost completely, which supports
the assumption that PLS-DA does not treat dry and wet images differently, but fo-
cuses only on rock class discrimination based on rock hardness/grade. This should
improve the robustness of the classification model to systematic variations in rock
visual appearance introduced by surface moisture condition, which is irrelevant for
classifying rocks in hardness/grade categories.
To validate the rock type classification model a second series of 10 composite
images was created, five for dry and five for wet rocks. One composite image of
dry rocks is shown in Figure 3.25(a). These composite images again consist of 10
smaller images but, instead of showing different pictures of a single rock type as for
the training phase, they include smaller images belonging to all three rock classes.
The advantages of this approach, compared with using pre-defined rock mixtures
on the conveyor belt (
i.e.
, Figure 3.25 (b)), is that the location of each rock type
within the composite image is perfectly known, and it is also easier to control the
composition of the rock mixture. For example, if two smaller images of MS rocks
appear in a composite image, then MS proportion in the mixture is 20%. For the dry
rock composite images, five different proportions of the three rock types were sim-
ulated by deciding upon the number of smaller images of each rock type to include
in the composite image. Then, the required number of smaller images of each rock
type were randomly selected from the large image database discussed earlier in this
section. The five wet composite images were made of the wet couterpart of the dry
images. Again, a correspondence between wet and dry images was maintained for
easier comparison. It is also important to mention that none of the smaller images
selected in the validation step were used in the training dataset.
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