Cantor, Fuzzy, Near, and Rough Sets in Image Analysis - Rough Fuzzy Image Analysis: Foundations and Methodologies - page 5

Near sets offer an ideal framework for solving problems based on human perception that arise in
areas such as image processing, computer vision as well as engineering and science problems. In
near set theory, perception is a combination of the view of perception in psychophysics (Hoogs,
Collins, Kaucic, and Mundy, 2003; Bourbakis, 2002) with a view of perception found in Merleau-
Ponty's work (Merleau-Ponty, 1945, 1965). In the context of psychophysics, perception of an object
(i.e., in effect, our knowledge about an object) depends on sense inputs that are the source of signal
values (stimularions) in the cortex of the brain. In this view of perception, the transmissions of
sensory inputs to cortex cells senses are likened to probe functions defined in terms of mappings
of sets of sensed objects to sets of real-values representing signal values (the magnitude of each
cortex signal value represents a sensation) that are a source of object feature values assimilated by
the mind.
Perception in animals is modelled as a mapping from sensory cells to brain cells. For example,
visual perception is modelled as a mapping from stimulated retina sensory cells to visual cortex cells
(see Fig. 1.2) . Such mappings are called probe functions. A probe measures observable physical
characteristics of objects in our environment. In other words, a probe function provides a basis
for what is commonly called feature extraction (Guyon, Gunn, Nikravesh, and Zadeh, 2006). The
sensed physical characteristics of an object are identified with object features. The term feature
is used in S. Watanabe's sense of the word (Watanabe, 1985), i.e. , a feature corresponds to an
observable property of physical objects. Each feature has a 1-to-many relationship to real-valued
functions called probe functions representing the feature. For each feature (such as colour) one or
more probe functions can be introduced to represent the feature (such as grayscale, or RGB values).
Objects and sets of probe functions form the basis of near set theory and are sometimes referred to
as perceptual objects due to the focus on assigning values to perceived object features.
Axiom 1 An object is perceivable if, and only if the object is describable.
In Merleau-Ponty's view (Merleau-Ponty, 1945, 1965), an object is perceived to the extent that it
can be described. In other words, object description goes hand-in-hand with object perception. It
is our mind that identifies relationships between object descriptions to form perceptions of sensed
objects. It is also the case that near set theory has been proven to be quite successful in finding
solutions to perceptual problems such as measuring image correspondence and segmentation eval-
uation. The notion of a sensation in Poincare (Poincare, 1902) and a physical model for a probe
FIGURE 1.2: Sample Visual Perception
function from near set theory (Peters and Wasilewski, 2009; Peters, 2010) is implicitly explained by
Zeeman (Zeeman, 1962) in terms of visual perception. That is, 'seeing' consists of mappings from