Multivariate Image Analysis in Mineral Processing - Advanced Control and Supervision of Mineral Processing Plants - page 107

This algorithm is especially useful for hyperspectral images, where spectral res-
olution is often very high and features of interest ( e.g. , some chemical groups in
the NIR region) absorb light in a narrow wavelength band. For RGB images, how-
ever, the spectral sensitivity of the red, green and blue detectors of the camera CCD
matrix ( i.e. , detectors in the Bayer pattern) are strongly overlapping. Therefore, tex-
tures often appear similarly in each channel ( i.e. , there is little interaction between
spatial and spectral features). In this case, MR-MIA I and II algorithms will yield
similar results, and since MR-MIA II is less computationally intensive, it will be the
most efficient algorithm for RGB images [56].
MR-MIA II . In this algorithm, MIA is performed first and the score images
( e.g. , T 1 and T 2 ) are obtained. The first score image is very close to a gray-scale
version of the image, whereas subsequent components extract color informations
that are independent of the intensity component [56]. These score images capture
the dominant color features of the RGB image. Texture methods ( e.g. ,2-DDWT)
are then applied to the score images. If A score images are extracted using MIA, and
texture analysis is performed to the J th level of decomposition, and along all three
orientations ( q

a
j are obtained plus A
approximation images A J . Therefore, textural features are obtained for each color
contrast captured by each principal component. One then computes wavelet signa-
tures ( e.g. , energy, Equation 3.13) on each of the 3 AJ detail images, and combines
them into a single spectral-spatial feature vector. This approach will be illustrated
in one of the case studies (Section 3.5.2). For a more detailed analysis of the MR-
MIA algorithms, the reader is referred to the work of Liu and Liu and MacGregor
[13, 56].

d ), then 3 AJ univariate detail images D q

,

= h , v ,

3.4.2 Feature Reduction and Analysis

Most applications of machine vision in the process industries can be formulated
as either a classification problem or a regression problem, aimed at classifying the
state of the process or at predicting some key process variables based on a set of
images and, perhaps, on some data obtained from process instrumentation. Images
are typically collected under various process conditions selected so as to capture
the effect of disturbances or manipulated variables, using designed experiments or
simply during normal or abnormal production situations. After extracting spectral
and/or textural features from each image of the set, and synchronizing these with
process data obtained from data historians, one obtains the dataset shown in Figure
3.11, which is composed of three blocks or data matrices: X F , Y ,and T F . The nature
of the data included within each of these blocks is discussed below.
• X F K computed

for each of the N images of the set. These image features could represent: (1)
color (or spectral) feature only, such as the loading vectors of PCA applied on
each image separately, or counts of pixels falling under one or a few masks seg-
menting a particular region of the score space (density histogram obtained by

. This block contains a collection of feature vectors of size 1 ×