Multivariate Image Analysis in Mineral Processing - Advanced Control and Supervision of Mineral Processing Plants - page 106

D j ||

2
F

E jq = || . (3.13)

Several other features have also been proposed and used for representing multi-
scale image texture, such as wavelet histogram signatures or simply wavelet signa-
tures ( i.e. , first order statistics of the sub-image histograms) [53], and higher-order
statistics of the co-occurrence matrix of the detail sub-images called wavelet co-
occurrence signatures ( e.g. , contrast, correlation, entropy, angular second moment,
etc. ) [54]. Some guidelines as to which features to use can be found in [13, 53, 54].
However, the main objective is to use those which provide the desired degree of
texture discrimination between images.
Finally, other textural methods are also available for extracting the spatial organi-
zation of pixels intensities from images, such as statistical methods ( e.g. ,gray-level
co-occurrence matrices or GLCM [54], the angle measurement technique [55]),
structural based methods, model based methods and filter-based methods ( e.g. ,
Fourier and wavelet transforms) [13]. A comparison between some of these im-
age texture extraction methods was performed by [51] using images of steel sheets.
Wavelet texture analysis was shown to be one of the most powerful technique for
image texture analysis.

3.4.1.3 Multiresolution Multivariate Image Analysis (MR-MIA)

The complexity of the information to be obtained from multivariate process images
often requires extraction of both spectral ( e.g. color) and textural features. These can
be computed separately, using MIA and textural methods, and later combined by
concatenation of color and textural feature vectors. However, more efficient meth-
ods for combining them in a unified framework have been developed, such as mul-
tiresolution multivariate image analysis (MR-MIA) [56]. Two MR-MIA algorithms
have been proposed ( i.e. , MR-MIA I and II), depending on the degree of interaction
between the spectral and textural (spatial) information. Both algorithms use MIA
( i.e. PCA on images) to extract spectral features and multiresolution analysis ( i.e. ,
wavelets) for texture, but in a different order.
MR-MIA I . When spatial and spectral features are interacting, for example when
some textures are observable only at specific wavelengths within a multivariate im-
age, and not in other regions of the spectra, then MR-MIA I should be used [56].
It consists of applying 2-D DWT to a given decomposition level j = 1 , 2 ,..., J ( i.e. ,

scale) and orientations q = h , v , d separately, on each spectral channel l of a multi-

variate image, l λ. Since the detail images obtained for each wavelength

at the same scale j and orientation q , are congruent, these can be combined into a
new multivariate image. Considering all scales and orientations, applying 2-D DWT
to each spectral channel results in 3 J new, congruent multivariate detail images D j ,
j

= 1 , 2 ,...,

= , ,..., = , ,

d , plus a multivariate approximation image A J .Theseim-
ages are then analyzed using MIA to extract textural-spectral (or spatial-spectral)
features.

1 2 J and q h v