Multivariate Image Analysis in Mineral Processing - Advanced Control and Supervision of Mineral Processing Plants - page 131

• Establishing class boundaries. The final step involves establishing class

boundaries of each rock type within the latent variable space of the PLS-DA
model ( i.e. , in the score space of that model). A wide range of techniques are
available for this purpose, from Fisher's linear discriminant analysis [77] to
nonlinear classification algorithms such as self-organizing maps [92], based
on artificial neural networks, or support vector machines [40, 93, 94]. The lat-
ter will be used in this case study since it is efficient with overlapping classes.

3.5.3.4 Training and Validation of the Mineral Type Classification Model

A database of rock images was first collected for training and validation of the rock
type classification model. The available rock loads for each type were sequentially
spread on a conveyor belt. Then, between 50 and 60 images were captured for each
rock type in order to cover the variability of appearance of each type. After collect-
ing a dry rock image, and before moving the conveyor, the rocks contained within
the field of view were watered and a second image was captured ( i.e. , the wet rock
image). Therefore, a wet rock image corresponds to each dry rock image. Repeating
this procedure for each rock type led to a set of about 500 images with almost half
of them showing wet rocks.
The training dataset was made of 10 composite images representing the variabil-
ity of each rock type in dry or wet conditions. Each composite image of a particular
rock type was formed with 10 smaller images randomly selected from the larger
database discussed above. The size of the smaller images was selected such that the
composite images have the same size as the original images in the large database
( i.e. , 1024 1376 pixels). Furthermore, once a smaller image was selected for one

of the five dry composite images, its wet counterpart was also selected for the cor-
responding wet composite image. These training images are available in [78].
The procedure described in Section 3.5.3.3 was then applied to the 10 composite
images of the training set, one for each rock type in dry and wet condition. That is,
each image was further divided into 512 subimages after which color and textural
features were extracted for each. The resulting feature and class matrices, X F and Y ,
were (4316

×

3)-D, respectively, after removing some outlier images
showing the conveyor belt only. The soft/high grade rocks (MS) were assigned to
class 1, the medium hardness/grade rocks (DS and NT) were assigned to class 2 and,
finally, the hard/waste rocks (G and P) were assigned to class 3. These components
PLS-DA model was built on the training dataset, together explaining 44% of the
variance of X F . That is, about half of the information contained in the feature matrix
is correlated with the classes and is used for class discrimination. The t 1

× 36) and (4316 ×

t 2 score
scatter plot of the PLS-DA model showing the clusters corresponding to each class
are shown in Figure 3.24. Note that in these score plots, each dot corresponds to a
multivariate summary of the visual features of one subimage.
If the ROM ore consists of only soft/high grade and hard/waste rocks ( i.e. ,class1
and 3), then the classification problem would be easier as shown in Figure 3.24(a). A
simple linear classification problem aiming at finding the location of a straight line

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