International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
densities differ in shape but exhibit a high degree of
overlap. Classifying objects instead of pixels also allows the
measurement and use of spatial characteristics such as size,
shape and texture, which have been found to be useful in
classification.
2- An object representation is often more compact than a pixel
description. This savings in storage space or transmission
speed occurs if objects contain enough points so that
specifying the locations and essential properties of the
objects takes fewer bits than specifying the collection of
individual pixel properties.
In the analysis and processing of multispectral images one
encounters a large amount of data. To enable efficient
processing of this data, it would be preferable to have an
underlying model that explains the dominant characteristics of
the given image data. Subsequent processing of the images can
be efficiently accomplished by using the models fitted to the
data. With the above scheme, a scene is segmented into
spatially disjoint objects (Ghassemian & Landgrebe, 1987).
Objects in imaged scenes are describable by sets of relevant
attributes or features (Ghassemian & Landgrebe, 1988). These
features represent distinct measurements or observable
properties. The object's initial measurements, which are
encoded as pixel-features, are subsequently subjected to art
object-feature transformation. Each of the objects contains a
union of similar pixels, and the union of the simple objects
represents the whole scene. All pixels of an object, whose
pixels satisfy the unity relation, can be represented by an
object-feature set (Ghassemian, 1990).
The accuracy of this system (the information content in the
object-feature-set) is dependent on the parametric primitives
who are used in object- feature construction; however, this
accuracy has an upper bound which is controlled by the level of
noise which exists in the acquired data. In the analysis of a set
of data points in multidimensional space, the need to choose the
most relevant features frequently arises. Feature selection
techniques are used to find properties of objects in the scene
which can serve as the strongest clues to their identification.
One way to characterize this dependency, among the
neighbouring pixels, is to represent it by a unity relation. The
unity relation among the pixels of an object means that an
object consists of contiguous pixels from a common class where
their features are statistically similar. The keys to the unity
relation among the pixels of an object are the adjacency relation
and the similarity criterion. Mathematically it can then be said
that the unity relation exists between two pixels if they satisfy
two criteria simultaneously (Ghassemian & Landgrebe, 2001):
l- They have an adjacency relation with each other, in the
sense that they are spatially contiguous or their spatial
distance is filled by a sequence of contiguous pixels from the
same class. The subset of L (spatial-feature) whom their
corresponding pixels having an adjacency relation with the
pixel X, is represented by the set Ay, called neighbourhood
set.
They have the same attributes, or they carry equivalent
useful information about the scene, in the sense that their
features are similar to each other. This means that the
distance between these attributes, in an appropriate metric-
space, is less than unit, d,(X,, X,)«1.
N
1
Let R (.) be a relation on pixel-feature-set P. When the relation
exists it is represented by R(.)=1, otherwise by R(.)-0. Then
R(.) is a unity relation provided that it satisfies the following
properties for all X,, X,, X, belonging to pixel-feature-set P:
I- Similarity and Adjacency Properties:
R(X,, Xy)- Fl if and only if d(X,, Xy)<l andr € A,
[I- Reflexive Property: R(X, Xi) = 1
I1I- Symmetric Property: R(X, X4) = R(X, X,)
IV- Transitive Property:
Xo Xy) = | and R(X, Xn) =1 = R(X, Xy) =
The unity relation is defined by a property between two
individual pixels in an object, can be extended to the property
between a pixel and an object. We had pointed out that, the
unity relation in the observation space is defined by an
adjacency relationship together with a similarity criterion
among the pixels’ attributes. The similarity between the pixels’
attributes is of basic importance in attempting to test the
existence of the unity relation. This is evident since the
existence of two adjacent objects, is a consequence of the
dissimilarity of features from neighbouring pixels where two
adjacent objects differ in at least one of the spectral or
contextual features.
The accuracy of the similarity measure is dependent on the
selected metric space used for functional construction and has
an upper bound which is controlled by the amount of noise in
the system. The uncertainty in the similarity measure is
significantly reduced using the within object regularities. This
property is used in the path-hypothesis for unity relation
construction. The path of sequential association, which pixels
follow in the spectral space, from a continually evolving
hypothesis regarding the object definition. Elements in this path
are determined on a spectral basis relative to the current status
of all other adjacent objects by the spectral variation between
two consecutive points in the path, using a specific metric to be
defined presently. Elements in the path are also determined
based upon the spectral separation between the current and the
most recently preceding pixel of that object in spatial space,
thus incorporating both spectral and spatial information in that
association of pixels with objects.
It should be realized that the path-object P; is defined in the
spectral space and it is different from a spatial path in the scene.
A path-object P; is represented by its spectral- feature S; ,
spectral variation regularity V; , and the path end point Xxi+1-
The path hypothesis thus determines a possible sequence of
points in the observation space for each object, which implies
that each object forms a well-defined sequence in observation
space, called the path-object. The succession of consecutive
observations describes a particular trajectory in the observation
space. Any change in the behaviour of two consecutive points
(the end point of the path-object X,;., and the current pixel X; )
in this trajectory can define a start point of a new object.
3. FEATURE EXTRACTION
In theory, decision about class membership for a noisy object
should be based upon as many observations of the object as
possible and preliminary decisions concerning subsets of
object-features can provide less than maximally reliability
recognition. Thus theoretically, the most reliable decision
should be based upon all the pixels in the object. Also in theory,
every result achievable with d variables can also be achieved
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