Multivariate Image Analysis in Mineral Processing - Advanced Control and Supervision of Mineral Processing Plants - page 93

Here, λ 3 since the froth image was captured using a three-color RGB camera

collecting light intensities in the red (R), the green (G), and the blue (B) colors.

=

3

Multivariate RGB image

346

346

516

Spatial axis x

516

346

3

516

Figure 3.3 A multivariate image is a stack of congruent images collected at various wavelengths.
An example of a three-channel RGB image of a froth flotation process is shown. Adapted from
Bharati and MacGregor [25]

The camera CCD is responsible for this three-way array structure. It basically
consists of a matrix of photo-sensitive detectors each giving rise to a pixel within
the image. The number of detectors in both spatial directions define the spatial res-
olution of the image. Each detector is sensitive to a certain spectral range within
the electromagnetic spectrum. If all detectors of the CCD have a similar spectral
sensitivity, then a monochrome or gray-level image of dimensions ( x 1) is ob-

tained. When the CCD consists of a mosaic of detectors having different spectral
sensitivities or when a spectroscope is mounted in front of a monochrome camera
(in this case λ can be in the order of a few hundred), then a full three-way array
structure ( x

× y ×

× ×

λ) is generated. The images used in this chapter were all collected
using 1-CCD RGB cameras, that is a single CCD made of a mosaic of three types
of detectors, some sensitive to the red, the green, and the blue colors, and spatially
distributed across the CCD matrix according to the the well known Bayer pattern.
To fill the empty pixels within the three-way array X ( e.g. , a red-sensitive detector
is less sensitive to green and blue colors) interpolation using appropriate neighbor-
ing detectors is usually performed (within the camera electronics, transparent to the
user). Cameras having three different CCDs, each specialized in one spectral range
( i.e. , each pixel has a true reading in each of the RGB channel), are also available
on the market but are much more expansive.
The readings provided by each detector of the CCD is proportional to the num-
ber of photons accumulated by the detector during the user-defined exposure time,
which are then converted into numbers ( i.e. , integers) using an analog-digital con-
verter. The resolution of this AD converter defines the number of gray levels with
which light intensities will be quantified. For example, a typical 8-bit camera will
result in light intensities described by integers varying from 0-255 gray levels, 0
corresponding to black and 255 to white. In Figure 3.3, each univariate image or

y