The method of multispectral aerospace image decoding based on a nonparametric approach is considered. It is offered to apply a cumulative distribution function and a probability density function constructed from source images and transformed one by means of various algorithms for the analysis of objects demanded for recognition. The way for increasing image decoding reliability by means of sequential algorithm application of their transformation and use of a large number of test samples is discussed.
where: ( ) – empirical distribution function of the sample { } ; ( , ) – function of the normal distribution with parameters and 2[ ] – weight function.
Non-parametric models are appropriate to use if distribution differs from normal one.
Reference functions are also various for various surveying systems. For this reason when using non-parametric approach it is necessary to create database of both the probability density and cumulative distribution functions for each surveying system and all classes required for recognition. Reference function database is received with the help of cartographic materials. Reference functions are created for image sites corresponding to a certain class on a map. Then having carried out image decoding for any other area with a segmentation method the probability density and cumulative distribution functions are created for each image site. Created functions are compared with reference ones based on a given decision rule.
As the result of the study carried out earlier the value of Pearson’s correlation coefficient calculated between two functions of images was chosen as the decision rule at assessment of probability density functions. The special case of Kolmogorov’s criterion offered by authors was chosen as the decision rule at assessment of cumulative distribution functions.
At the beginning for comparing cumulative distribution functions using the special case of Kolmogorov’s criterion
the greatest value of brightness Bmax among all compared image sites in each spectral band is defined. Some of these
image sites are decoded, the others – reference. The cumulative distribution function is calculated in the range [0,
Bmax] for a corresponding site in each band. Then brightness values B of a site under test are defined for cumulative
distribution function values multiple 0.1 in the range [
Distances between cumulative distribution functions calculated for bands of each reference site and decoded one are compared together. The decoded site will belong to that reference one to which the distance calculated by definition 1 will be lowest. The total distance among the functions of all image bands can be also calculated.
The results of such analysis can have various degree of reliability for certain object types in various spectral
bands. For example water area can be correctly recognized using various spectral bands based on comparing both
cumulative distribution functions and probability density functions while recognition reliability of forest species will
be significantly lower. It can occur that the certain forest species will be correctly recognized based on one of the
function type calculated for the certain spectral band [
Recognition of forest species is the most difficult task. It can occur that forest species are not recognized is any
band. In this case as the source feature space an image transformed in accordance with a priori specified probability
model of multispectral measurements using one of the algorithm such as principal component analysis, independent
component analysis, Tasseled Cap, vegetation indices can be used instead of a multispectral source image. It is
possible to increase final reliability of various object class recognition significantly having carried out calculating the
considered functions on the basis of transformed images and having consistently analyzed the results of their
calculation by means of their similarity comparison by one of the offered decision rules [
As a method of the consecutive analysis the most appropriate algorithm is the decision tree. The decision tree is a multi-step algorithm. Decision trees represent various methods of rule description for data division in the form of consecutive and hierarchical structure where the only node giving the decision corresponds to each object. 3
For the analysis of natural object decoding results based on application of structural-statistical approach and algorithms of source multispectral image transformation a four-band space image Ikonos for an area close to Akademgorodok of Novosibirsk was chosen. The resolution of each band is 3.2 m. Creation of samples was carried out according to this image and on the basis of thematic map for species composition of forest (Fig. 1). Sites with the largest area were chosen as reference samples.
In Figure 2 an example of a reference sample limited to a contour of red color and corresponding to pine forest is shown. In total next object classes were chosen as samples: birch forest, pine forest, aspen forest, ground, water. The area of reference samples was at least 3 ha. For estimation of decoding reliability with applying the probability density and the cumulative distribution functions test sites were also chosen according to the thematic map.
Probability density and cumulative distribution functions were calculated for each multispectral image band, images transformed with vegetation index and for each component obtained as the result of image transformation with principal component analysis. Figure 3 shows an example of cumulative distribution function calculation for a red band of a source image for reference samples and one of the decoded samples. Birch forest site was chosen as the decoded sample. In this figure the distance from a test sample to each of reference samples calculated by definition (1) is also shown. The minimum distance was received between cumulative distribution functions of birch forest and the reference sample of this forest type. This means that decoding of the sample was correctly done.
Correlation coefficients shown in figure 4 were calculated between the probability density function of a test sample and these functions of reference samples. The highest value of a correlation coefficient was obtained between the probability density function of a test sample for birch forest and a reference one for this type of forest.
Thus, the test sample was correctly decoded for a red band using both the cumulative distribution function and the probability density one.
As it was noted above calculation of described functions can be carried out not only for source multispectral images but also for images transformed with a certain algorithm. Transformed images can increase reliability of a certain test sample decoding. The results of comparing the considered test sample with the reference ones for all spectral bands separately, for four-dimensional space of the image, for all components of the image transformed with principal component analysis algorithm and for the indexed image obtained using definition of calculating the normalized difference vegetation index (NDVI) are given in Table 1. These results demonstrate that the reliability of decoding significantly differs depending on the data that were used for calculating the cumulative distribution function and the probability density one.
To estimate objectively what algorithms of image transformation provide the greatest reliability of the certain object class decoding it is necessary to calculate functions using larger number of test samples and to compare them with reference ones. That algorithm and that function providing the greatest distinction of classes have to be chosen for a basis. To achieve a larger proportion of reliability it is also possible to apply several algorithms of transformation consistently by means of the decision tree. 4
Application of the non-parametric approach when decoding aerospace images is capable to significantly increase the results of various object class recognition. The offered decision rules allow estimating differences between cumulative distribution functions and the probability density ones calculated for source images and images transformed with various algorithms. Carried out comparing these functions calculated for a large number of samples of various types it is possible to choose that function and to select those bands of source and transformed images allowing reaching a larger proportion of reliability. Moreover consecutive combining several algorithms for transformation is capable to provide achievement of the reliability largest proportion.
Further study will be directed to collecting a larger number of statistical information for the purpose of searching steady statistical characteristics of various object class brightness distribution in source and transformed multispectral images as well as to determining the sequence of applying algorithms of transformation and to the choice of the typical function site defining the greatest distinction of classes.
Test sample class
Four-dimensional space