Multivariate Image Analysis in Mineral Processing - Advanced Control and Supervision of Mineral Processing Plants - page 130

2. Feature extraction. Both color and textural features were extracted from each
subimage as described below. These will later be used to classify subimages into
one of the three rock classes (see Table 3.2). The classification results will, in
turn, allow estimation of the proportions of the various rock types within a mix-
ture.

• Color features. As discussed previously, pixel-by-pixel color signatures ( i.e. ,

MIA color distribution features) are not efficient for discriminating rock types
due to the overlap between some classes. Instead, the p 1 p 2 loading vectors

are used as representative average color features of the subimages. These are
obtained by applying PCA to each individual subimage. Such a way of rep-
resenting average image color is further discussed and compared with other
methods in Yu and MacGregor [32]. The vector of color features for each
subimage

−

p 1 p 2 [ ] is therefore (1 × 6)-D.

• Textural features. Two sets of textural features were computed for each

subimage. The first set consists of energy features ( i.e. Equation 3.13) ob-
tained after applying DWT on the subimages at two levels of decomposition.
This yields six energy features since all three detail images ( h

, ,

d )wereused
at both levels. To generate even more informations about the images, second
order statistics obtained from the six detail images were also computed as
proposed in [36, 91]. These are the energy, entropy, contrast and correlation
features obtained from the GLCM [54] of the six details images. This provides
24 additional texture descriptors for each subimage, resulting in a (1

v

× 30) tex-

ture vector after combining the two sets of textural features.

3. Feature reduction and analysis. After extracting and combining the color and
textural features for all subimages, the following matrices are obtained for one
full size rock mixture image: X F 3). The latter corre-

sponds to binary numbers ( i.e. , 0-1) assigning each subimage to a rock class. If
the i th subimage belongs to class 1, then Y

( 512 × 36) and Y ( 512 ×

( i , : )=[ 100 ] , if it rather belongs

to class 2, Y , and so on. This correspondence between subim-

ages and rock classes is obviously only known apriori for the training dataset.

( i , : )=[ 010 ]

• Discriminant PLS. To reduce the 36-D feature space and to enhance class

separation, made necessary due to overlap, a supervised latent variable clas-
sification technique ( i.e. , PLS-DA) was then applied to ( X F , Y ). The PLS-DA
model extracts those linear combinations in X F that are the most highly corre-
lated with the classes or, alternatively, the information that maximizes class
discrimination. This operation also partially removes the systematic color
variations caused by surface moisture. Indeed, moisture will be made inde-
pendent of class information by design since all three rock classes will contain
dry and wet rocks. Hence, the PLS-DA model will not capture the effect of
moisture. This should increase the robustness of the rock classification model
to weather conditions.