International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
Regarding these assumptions, spectral bands for the various
case studies presented in this paper were generated. Algorithm
firstly considers the class number of the pixels gathered from
the ground truth map. Then it searches the mean and variance
matrices and selects the corresponding values for mean and
variance vectors considering the class number. After that using
these signatures the pixel value per band is generated using a
function that returns a vector of random numbers having the
normal distribution, this algorithm repeats for each pixel until
all of the pixels have their appropriate values in the 3 bands.
Figure 2 shows a sample ground truth map and generated color
composite image.
3.2 Investigating Relationship between Accuracy and
Uncertainty
The mentioned algorithm (Section 3.1) was used to produce the
desired images to perform the experiments on them. Some
constraints and conditions were applied on the all of the
experiments. Size all of the images is 512 x 512 pixels and have
been generated using the algorithm explained at section 3.1. For
the classification of the images it was decided to use maximum
likelihood classification because of the relative powerful ability
to classify images, also this method is available at the most
image processing softwares. Additionally the results of this
method are per pixel probabilities and labels which permit us to
evaluate and calculate pixel by pixel quadratic score and
accuracy values. All of the cases were done based on the equal
prior probability assumption of the classes.
Figure 2. The generated ground truth map (A)
and the corresponding sample synthetic image (B).
As Masseli and et.al (1994) have noted and the authors have
investigated the mean of entropy values has not à
straightforward and certain relationship with accuracy
measures. Therefore we choose the mean quadratic score
(MQS) which shows a strong linear regression between the
overall accuracy (OA) and kappa coefficient (K) (as the
accuracy measures) and this uncertainty measure.
In order to show the strong (inverse) relationship between
classification uncertainty related measure and accuracy of the
classification some images were generated by changing the
radiometric overlap between the various classes. This was done
simply by altering the mean and variance values. When two
classes have more similar values then radiometric overlap
between them also increased aecordingly. The closer mean
vectors the higher radiometric overlap. Also using the large
values for the variances can lead to the more radiometric
overlap.
Regarding this logical assumption the mean and variance values
of the classes were changed 11 times and then 11 data sets were
obtained. Having applied the maximum likelihood classification
on the data sets; 11 overall accuracies and corresponding mean
quadratic scores and kappa coefficients were calculated. Figure
3 shows the approximately linear relationship between overall
accuracies and kappa coefficient and corresponding mean
quadratic scores.
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Figure 3. Relationship between MQS and OA (A) and
relationship between QMS and K(B). See the strong linear
relationship between accuracy and uncertainty parameters.
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