Image Processing Reference
In-Depth Information
function representing a feature of the physical object
. A set of probe functions
F = 1 2 , ..., φ l } can be defined to extract all the feature-values for each object
x
x
. However, not all the probe functions (features) may be used all the time. The
set
B⊆ F
represents the probe functions in use. This approach to representation
and comparison of feature values by probe functions started with the introduction
of near sets (See (Peters, 2007a) and (Peters, 2008a)). Probe functions provide a
basis for describing and discerning anities between sample objects in the context
of what is known as a perceptual system. This represents a departure from partial-
functions known attributes define in terms of a column of values in an information
system table in rough set theory.
Example 8.1
An image can be partitioned into
subimages viewed as perceptual objects. Each subimage has feature values that are
the result of visual perception, i.e. , how we visualize a subimage ( e.g. , its colour,
texture, spatial orientation). Figure 8.1 for example shows an image of size 255 × 255
pixels divided into pixel windows (subimages) of size 85
Perceptual Subimages (pixel windows).
85 pixels. For simplicity,
the size of the subimages are very large here. In practice, the size of subimages
are much smaller, resulting in a higher number of subimages. (see figure 8.2 for
example). Therefore, the image can be represented with a set (
×
O
) of 9 perceptual
objects as follows:
O
=
{x
,x
, ...x
}
(8.1)
1
2
9
Different probe functions can be defined to extract feature values of an image
or subimage. Average gray, image entropy, texture and color information in each
subimage are some examples. For practical use, several feature values are needed to
represent an image. However, in some examples of this chapter, only average gray
value and sometimes entropy have been used. Moreover, feature values have been
normalized between 0 and 1 in cases where more than one probe function is used.
Figure 8.1 shows the image as well as all the subimages, where all of the pixels in
each subimage the gray level of a pixel is replaced with the average gray level of
the subimage containing the pixel. By way of illustration, average gray levels are
shown in each subimage in Fig. 8.1.
8.2.2
Perceptual Indiscernibility and Tolerance Relations
Indiscernibility and tolerance relations are defined in order to establish and measure
anities between pairs of perceptual objects in a perceptual system
O, F
.These
relations are a subset of
. Indiscernibility relation is a key concept in approx-
imation spaces in rough set theory. A perceptual indiscernibility relation is defined
as follows.
O × O

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