Multivariate Image Analysis in Mineral Processing - Advanced Control and Supervision of Mineral Processing Plants - page 108

PLS / PLS-DA

K K+L A M

PCA

X F T F Y

N

Image
features

Process data
(instrumentation)

Latent variables
(score vectors)

Classes /
key process variable

Figure 3.11 Typical applications of machine vision in the process industries can be formulated into
either a classification or a regression problem

MIA, see Figure 3.7), or pixel densities obtained from a rectangular grid ap-
plied to the score histogram ( i.e. , discretized 2-D density histogram, see Section
3.4.1.1); (2) textural features only, such as the wavelet signatures ( e.g. , energy)
and/or the co-occurrence signatures obtained from detail images; and (3) both
spectral and textural features, either obtained separately and subsequently con-
catenated, or computed jointly using one of the MR-MIA algorithms. When use-
ful for classification or prediction purposes, X F may be augmented with a set of
L measurements obtained from current process instrumentation, after appropriate
synchronization with the images.

• Y This second block is a matrix of responses that may, or may not be available

depending on the machine vision objective and the application per se . Typical
responses may be key process variables which we would like to predict using
the images, such as froth grade in flotation, or categorical response ( i.e. , dummy
or binary variables) used to associate each image with some pre-defined classes,
such as process states, type of raw materials, etc. This information may be useful
in supervised classification problems.

.

• T F The third block consists of the lower dimensional latent variable space which

will be used for classifying the images, establishing multivariate statistical pro-
cess control schemes for process monitoring and fault detection, or for predicting
response variables of interest. These score vectors are obtained using the latent
variable method, such as PCA or PLS, which is the most appropriate for the
problem at hand. Note that to simplify the discussion, Figure 3.11 focuses on the
score vectors since they represent the projection of the multivariate features onto
the latent variable space. However, one should also consider the square prediction
errors (or DMODX, see Section 3.2) to diagnose observations that are at a signif-

.