XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 1105
The Discriminant Functions applied to calculated image
features enabled us to classify a given image to a training
group of images that represented the froth images of similar
value of a Pb content in the froth. The Pb content in the
froth was measured in the chemical way
The calibration procedure of the system requires a
parallel sampling of flotation froth for XRF and chemical
analysis for determination of the useful mineral content in
the froth. Once the image of the individual picture is linked
to technological results (i.e., content of useful minerals in
the froth) the training process of the system can be carried
out. Training of recognition and classification algorithms
requires application of linear discriminant analysis (LDA)
and an artificial neural network (ANN). In these systems, a
single image is described by a set of parameters or by its pix-
els. It is based on a set of M-groups of training images that
characterize various types of flotation froth, which can be
associated with different course of technological process of
beneficiation. The scheme of LDA is presented in Figure 2.
This procedure treats a single image as a point in
k-dimensional decision space. Images are categorized into
several groups according to the useful mineral or metal con-
tent. The group centroid, understood as its gravity center,
is determined for each group. A specific image is classified
into an individual group according to the classification (or
recognition) rule, which takes into consideration the dis-
tance to the group centroids. The image is classified to the
group for which a distance to the gravity center (a group
centroid) is minimal among all the groups in question. The
procedure for ANN algorithm is similar, but a Decision
Vector (instead of Decision Space) is obtained as a result of
recognition. Each coordinate of this vector indicates a spe-
cific group, to which image is assigned. The image is classi-
fied into a specific group when the coordinate of the vector
equals 1. Then we obtain a vector of m-length (where m
denotes a number of groups), with one value of 1 and the
remaining values of 0.
Testing of the system was carried out in a lead ore pro-
cessing plant. Three single tests were performed, each for
various settings of operational conditions. Ten measure-
ments in total were taken during each test.
RESULTS OF INVESTIGATIONS
Figure 3 summarizes the results of each test. It can be seen
that for test 1 rather lower values of Pb content in the froth
were registered. Variation of these results seems the lowest,
as well. Test 2 presents average Pb contents, while the high-
est values of the useful mineral were registered during test
no. 3. Table 1 characterizes average Pb values for each test,
along with determination of standard deviations and ranges
of variability.
On the basis of the presented results it can be seen that
various average contents of Pb were obtained for each test.
If, additionally, we take into account that each test was car-
ried out for different operational conditions, we can see,
that the setting of these conditions can be associated with
Figure 1. Placement of the vision system
=
Image
=
Vector
of Parameters Algorithm Decision Space
Figure 2. Scheme of vision system
The Discriminant Functions applied to calculated image
features enabled us to classify a given image to a training
group of images that represented the froth images of similar
value of a Pb content in the froth. The Pb content in the
froth was measured in the chemical way
The calibration procedure of the system requires a
parallel sampling of flotation froth for XRF and chemical
analysis for determination of the useful mineral content in
the froth. Once the image of the individual picture is linked
to technological results (i.e., content of useful minerals in
the froth) the training process of the system can be carried
out. Training of recognition and classification algorithms
requires application of linear discriminant analysis (LDA)
and an artificial neural network (ANN). In these systems, a
single image is described by a set of parameters or by its pix-
els. It is based on a set of M-groups of training images that
characterize various types of flotation froth, which can be
associated with different course of technological process of
beneficiation. The scheme of LDA is presented in Figure 2.
This procedure treats a single image as a point in
k-dimensional decision space. Images are categorized into
several groups according to the useful mineral or metal con-
tent. The group centroid, understood as its gravity center,
is determined for each group. A specific image is classified
into an individual group according to the classification (or
recognition) rule, which takes into consideration the dis-
tance to the group centroids. The image is classified to the
group for which a distance to the gravity center (a group
centroid) is minimal among all the groups in question. The
procedure for ANN algorithm is similar, but a Decision
Vector (instead of Decision Space) is obtained as a result of
recognition. Each coordinate of this vector indicates a spe-
cific group, to which image is assigned. The image is classi-
fied into a specific group when the coordinate of the vector
equals 1. Then we obtain a vector of m-length (where m
denotes a number of groups), with one value of 1 and the
remaining values of 0.
Testing of the system was carried out in a lead ore pro-
cessing plant. Three single tests were performed, each for
various settings of operational conditions. Ten measure-
ments in total were taken during each test.
RESULTS OF INVESTIGATIONS
Figure 3 summarizes the results of each test. It can be seen
that for test 1 rather lower values of Pb content in the froth
were registered. Variation of these results seems the lowest,
as well. Test 2 presents average Pb contents, while the high-
est values of the useful mineral were registered during test
no. 3. Table 1 characterizes average Pb values for each test,
along with determination of standard deviations and ranges
of variability.
On the basis of the presented results it can be seen that
various average contents of Pb were obtained for each test.
If, additionally, we take into account that each test was car-
ried out for different operational conditions, we can see,
that the setting of these conditions can be associated with
Figure 1. Placement of the vision system
=
Image
=
Vector
of Parameters Algorithm Decision Space
Figure 2. Scheme of vision system