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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
with d+1 variable, but the converse is not true. Thus one might
expect that by increasing the number of features the object
recognition error rate should decrease or at least stay the same,
but in practice quite often the performance of the features will
improve up to a point , then begin to deteriorate as further
attributes are added. This is referred to as the Hughes’
phenomenon (Hughes, 1968). The existence of an optimal set of
features is indicated for the representation of the objects,
relative to feature selection and feature reliability problem. An
object can be described by a set of parametric primitives. Such
primitives may be based on observation as well as knowledge
about the object. Typically in remote sensing the important
primitives, for recognition of an object, are spectral feature and
/ or contextual features. But since it is usually presumed that the
shape and the size of natural objects in a scene (ground cover
types) are random and unrelated to the ground cover classes,
these features are often ignored in feature extraction and pattern
recognition of the ground cover types. However in this work,
the objects’ geographical features are preserver in the spatial-
feature-map L, and can be used by an appropriate pattern
recognition system, if it be necessary. It is assumed that two
adjacent objects differ in a measurable way relative to the
spectral or contextual features. In this system, a set of points
representing similar patterns are represented with the same
features. Thus the attributes of P can be refined by observation
which is given by a set of three parametric primitives:
Vz Sr Kind) (1)
Where S is estimated within-object spectral feature
representation, V is the estimated contextual feature, and L is
the spatial-feature-map or the object geographical shape and
location in the scene. Let n be the number of pixels in the object
P, and L be the corresponding spatial-feature- map, then the
object spectral feature S is estimated by averaging the spectral
response of pixels within the object P. Then the contextual
feature, V, is estimated by averaging the spectral variation of
pixels within the object P.
]
s,=—> x, (2)
n kel,
Notice that the spatial variation can be horizontal, vertical,
diagonal, and any other possible spatial direction. The objects
with small area, whose number of pixels within the object is not
sufficient for contextual feature estimation, will be represented
only by the spectral feature. This is done by adjusting the
degree of uncertainty in the feature extraction process: the
uncertainty about the feature is inversely dependent on the
number of pixels that are contained within the object P.
Although the contextual feature is dependent on the sensor
resolution as well as the sensor altitude from the scene, the
intra- object spatial variation between adjacent pixels can be a
significant factor for on-line object extraction. A metric for
testing the unity relationship between the pixel-feature X, and
object-feature Y; is introduced. This metric normalizes the
spectral distance by their spectral gradient vector:
dX, ,Y,) - (S, - X, (aV, € BV.) G)
where a=(wn;/n;+w) and B=(w"/n+w), n; is the number of
pixels in the current object, w is the size of observation
window, and S, V;, X and Y are the same vectors as defined
before.
4. FEATURE EVALUATION
The performance of a feature extraction process is measured in
terms of the information-bearing quality of the features versus
the size of the data set. Classification accuracy is an important
quantitative measure of feature quality in applications where the
data is automatically interpreted. The comparative performance
results for the various feature configurations between the
original pixel-features X and compacted object-features Y. The
features’ reliability and quality are measured in terms of overall
misplacement error in the scene (OME), feature classification
performance (FCP), and subjects' appearance (SOA).
The first evaluation is a simple quantitative criterion which has
a conventional mathematical form to measure the number of
pixels assigned to an incorrect neighbouring object based on the
object classification, relative to the total number of pixels in the
scene (overall misplacement error) Let GTM represent the
ground-truth-map of original data, and let CPM represents the
classification-pixel-map result of feature classification. Then
the overall misplacement error can be computed by comparison
of the CMP and the GTM. The feature classification
performance (FCP) measures the number of pixels classified
into the correct class relative to the total number of pixels in
that particular class. This criterion is used to evaluate the
object-feature performance when the effects of classifier
decision rule and training samples on the class feature
performance should be considered. Good ground truth
information is a very important parameter in feature evaluation
to minimize the unrelated error in the feature extraction.
However, obtaining a valid ground-truth-map (GTM) and
registering the multispectral image data with this map is often
costly and very time consuming. Thus among the available real
data those subsets which have a relatively reliable ground-truth-
map should be selected and used for the OME and FCP feature
evaluations.
The subjective appearance is an appropriate criterion when the
ground-truth-map is not accurate enough to be used by other
feature evaluators, or when some objects in the scene are more
important than the others regardless of the size of the objects. In
such cases it is often too difficult to define a mathematical
expression for a feature quality adequate for quantitative
evaluation. In this case visual assessment will be used for this
kind of qualification. This criterion is used to evaluate the
spatial quality of the spatial-feature-map, for prediction of more
information about the scene, by using more complex features,
which should be extracted from the training samples. In other
words, by incorporating the object appearance in the spatial-
feature-map into the feature selection strategy, more complex
objects in the scene can be detected. For example some
significant within-class variation shows that more information
about the complex objects (perhaps soil type covered by
vegetation) in the scene might be extracted by using even more
complex features.
The proposed feature extraction technique is applied to several
set of image data. As previously stated, the objective of this
experiment is to demonstrate the validity of the unity
relationship and the path-hypothesis, and to show that the
performance of object-feature is better than the performance of
pixel-feature regardless of the choice of classification decision
rule and the training set. To establish the unity relation, the
system learns about the functional coefficients simultaneously
with the data acquisition process by measuring the object
spectral gradient which, is then, normalized within a window.
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