Image Processing Reference
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sense inputs from sensory units in the retina of the eye to cortex cells of the brain stimulated by sense
inputs. A sense input can be represented by a number representing the intensity of the light from the
visual field ( i.e. , everything in the physical world that causes light to fall on the retina.) impacting
on the retina. The intensity of light from the visual field will determine the level of stimulation of a
cortex cell from retina sensory input. Over time, varying cortex cell stimulation has the appearance
of an electrical signal. The magnitude of cortex cell stimulation is a real-value. The combination
of an activated sensory cell in the retina and resulting retina-originated impulses sent to cortex cells
(visual stimulation) is likened to what Poincare calls a sensation in his essay on separate sets of
similar sensations leading to a perception of a physical continuum (Poincare, 1902). This model for
a sensation underlies what is known as a probe function in near set theory (Peters, 2007b; Peters
and Wasilewski, 2009).
Visual Probe Function
Let O =
perceptual objects
. A perceptual object is something in the visual field that is a source
of reflected light. Let
denote the set of reals. Then a probe
is a mapping
: X
, φ
( x ) denotes an amplitude in a visual perception (see, e.g. , Fig. 1.2) .
( x ) measures the strength of a feature value extracted from
each sensation. In Poincare, sets of sensations are grouped together because they are, in some sense,
similar within a specified distance, i.e. , tolerance. Implicit in this idea in Poincare is the perceived
feature value of a particular sensation that makes it possible for us to measure the closeness of an
individual senation to other sensations.
A human sensation modelled as a probe measures observable physical characteristics of objects in
our environment. The sensed physical characteristics of an object are identified with object features.
In Merleau-Ponty's view, an object is perceived to the extent that it can be described (Merleau-Ponty,
1945, 1965). 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 evaluation.
In effect, a probe function value
Axiom 2 Formulate object description to achieve object perception.
In a more recent interpretation of the notion of a near set, the nearness of sets is considered in
the context of perceptual systems (Peters and Wasilewski, 2009). Poincare's idea of perception of
objects such as digital images in a physical continuum can be represented by means of perceptual
systems , which is akin to but not the same as what has been called a perceptual information sys-
tem (Peters and Wasilewski, 2009; Peters, 2010). A perceptual system is a pair
, F
where O is
a non-empty set of perceptual objects and
is a non-empty, countable set of probe functions (see
Def. 1).
Definition 1 Perceptual System (Peters, 2010)
A perceptual system
consists of a sample space O containing a finite, non-empty set of
sensed sample objects and a non-empty, countable set
, F
containing probe functions representing
object features.
The perception of physical objects and their description within a perceptual system facilitates pattern
recognition and the discovery of sets of similar objects. In the near set approach to image analysis,
one starts by identifying a perceptual system and the defining a cover on the sample space with an
appropriate perceptual tolerance relation.
Method 1 Perceptual Tolerance
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