Image Processing Reference

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structuring element with the image underneath. On the other hand in rough set theory, the

universe is partitioned or covered by some classes(indiscernibility, tolerance or arbitrary)

and the objects in the universe are perceived based on the knowledge available in these

classes. The interaction of the structuring element with the image underneath is localized

in space; In other words, the underneath image is being seen(characterized) through the

small window opened by the structuring element. In rough set theory a set is approximated

by the knowledge gathered in equivalence classes from the whole universe. This is the main

difference in mathematical morphology and rough sets.

In mathematical morphology, especially when the concept of lattice is introduced in this

field, the universe consists of all the possible images. But when we are applying morpho-

logical operators on images, there is only one image and a set of structuring elements. The

result is a new image belonging to the universe. In the application of rough set theory,

the available data in databases forms the universe and all the approximations are based on

the available data. To have almost the same milieu, we also consider a set of finite images

to be our universe (this is possible, if we view the universe X as a set of points and each

image A in the universe to be a subset of the universe, i.e., particular set of points A⊂X).

Ten sets of images in different categories are considered. Each set consists of 100 images.

Figure 4.4 shows samples of some of the categories. A category of images is defined as a

collection of images with visual/semantic similarities. For instance, the category of seaside

images, mountain images, dinosaurs or elephants can be derived from images in the Sim-

plicity image archive (Group, 2009). The categorization is done by an individual and it is

not unique. Each image may belong to different categories. For instance, in figure 4.5a

the elephant pictures are categorized into elephant category; but in figure 4.5b, they are

in animal and/or nature categories. Therefore the categorization is completely application

dependent and subjective.

FIGURE 4.4: Some image samples from different categories

The aim is to approximate a query image, I∈X, based on one and/or several of these

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