Image Processing Reference
In-Depth Information
This concept has been described in (Peters, 2008c) as follows: “
Our mind identifies
relationships between object features to form perceptions of sensed objects. Our
senses gather the information from the objects we perceive and map sensations to
values assimilated by the mind. Thus, our senses can be likened to perceptual probe
functions in the form of a mapping of stimuli from objects in our environment to
sensations (values used by the mind to perceive objects)
”.
8.2
Perceptual Systems, Feature Based Relations and Near
Sets
In this section, formal definitions of perceptual systems, tolerance and nearness
relations are provided.
TABLE 8.1
Perceptual System Symbols
Symbol Interpretation
Symbol Interpretation
O
X
X ⊆ O
Set of perceptual objects,
Sample
,
F
B
B⊆
F
Set of probe functions,
Sample
,
Set of real numbers,
φ ∈B
Probe
φ
:
O −→
,
∼
B
Indiscernibility relation,
∼
B
Weak indiscernibility relation,
=
B,ε
A ⊂
=
B,ε
∀x, y ∈ A, x
=
B,ε
y
Tolerance relation,
(preclass)
x
/∼
B
=
{y ∈ X | y ∼
B
x}
,
x
/
=
B,ε
x
in maximal preclass (tolerance class),
O
/∼
B
=
{x
/∼
B
| x ∈ O}
,
X
/∼
B
=
{x
/∼
B
| x ∈ X}
, quotient set,
B
Nearness relation,
B,ε
Tolerance nearness relation,
B
Weak nearness relation,
B,ε
Weak tolerance nearness relation.
8.2.1
Perceptual Systems
DEFINITION 8.1
Perceptual System
A
perceptual system
O,
F
is a real-
valued, total
∗
, deterministic information system where
O
is a non-empty set of
perceptual objects
, while
F
is a countable set of
probe functions
.
) represents something in the physical world that can
be perceived with our senses (for example a pixel in an image, or an image in a set
of images). Usually, we are dealing with a set of objects
A perceptual object (
x ∈ O
(for example an
image that consists of pixels or subimages). A
probe function
φ
(
x
) is a real-valued
X ⊆ O
∗
A perceptual system is total inasmuch as each probe function
φ
maps
O
to a single real-value.
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