A method of classification of hyperspectral images of terrain is described. It includes preprocessing of the spectral data in the form of conversion to the principal components, spatial processing consisting of finding the empirical mode of the principal components (Hilbert-Huang transform), and classification itself using RBF neural networks. Experiments are conducted on a large-format (580x580) hyperspectral image, and difficult-to-distinguish classes are not united. .
Classification method As is known from the pattern recognition theory, object preprocessing is an extremely important stage of the classification procedure. Here we consider a spectral-spatial object; hence, preprocessing is performed in the spectral-spatial domain. As it was already mentioned, each pixel is characterized by 200 spectral features. The analysis shows that they are mutually correlated to a large extent; therefore, it is logical to pass to non-correlated features. This can be done by several methods, but the most effective option is to perform transformation to the principal components (PCs). An important issue is the number of components to be left in order to lose the minimum possible amount of information. Kaiser and scree tests are applied for this purpose. After the transformation to the principal components is performed, a spatial transformation is applied. It was shown in many publications [5, 6, 7] that the use of these tests ensures significant enhancement of the overall accuracy, which is the percentage of the ratio of the number of correctly classified pixels to the total number of pixels in the sample. In these publications, similar to many others, however, the spatial transformation is reduced to changing the pixel value depending on its neighborhood. The structure of the classified fragment regions is absolutely ignored, and large errors of classification are observed in the case of difficult-todistinguish regions. Because of that, in particular, in [6, 7, 8] all soya regions with different methods of soil treatment were united into one class. The same refers to corn. Our method is based on another procedure. Each principal component is expanded into the so-called empirical functions (or intrinsic mode functions, IMFs). In contrast to the Fourier transform or wavelet transform, IMFs are not defined analytically and are determined exclusively by the analyzed sequence itself. The basis functions of the transform are formed adaptively, directly from the input data.
The algorithm of expansion into IMFs is based on constructing smooth envelopes on the basis of the extreme (maximum and minimum) points of the sequence and subsequent subtraction of the mean value of the envelopes from the initial sequence. For this purpose, the maximum and minimum points are found and approximated by splines. These splines are the upper and lower envelopes. The process of envelope construction is illustrated in Fig. 2.
The analyzed sequence is presented in Fig. 2 by the thin blue curve. The maximum and minimum points of this sequence are marked by the red and blue colors, respectively. The envelopes are shown by the green curve. The mean value is calculated on the basis of two envelopes (shown by the dashed curve in Fig. 2). The thus-found mean value is further subtracted from the initial sequence.
These steps are performed to find the first approximation of the sought IMF. For definite
identification of the IMF, it is necessary to find the maximum and minimum points of this IMF
estimate and repeat these steps again. This process (called sieving) is continued until a threshold
condition is satisfied. If the sieving process is successfully finalized, we obtain the first IMF. To
find the next IMF, it is necessary to subtract the found IMF from the initial signal and repeat the
procedure again. The procedure is repeated until all IMFs are found. The algorithm of expansion of
the two-dimensional signal into IMFs formally does not differ from expansion of the
onedimensional signal, thought there are certainly some specific features associated with the search for
extreme points and interpolation [
Experimental results The HSI shown in Fig. 1a was expanded into the principal components from which four components were chosen on the basis of the scree test (which include 99.42% of data dispersion). Then each of the PCs was expanded into five IMFs. The first PC and its five IMFs are shown in Fig.3.
Thus, after all these transformations, the HSI is described by a 580х580х20 array divided into 33 classes. The number of pixels in each class is divided in the ratio LS:CS:TS= 50%:25%:25%. Learning is performed in the RBF neural network. The learning time is several hours. Let us consider the results of classification after the learning process. Let us first give the list of all classes with numeration that will be used in the tables.
The classification results are summarized in Table 2. The network architecture in the left box of the table means 20 input features (number of neurons in the first layer), 851 neurons (RBF functions) in the hidden layer, and 33 neurons in the output layer (number of classes). The classification accuracy (CA) is not that high as in experiments performed with smaller fragments and a smaller number of classes [2, 3], but it should be again recalled that the present study involves difficult-to-distinguish classes of corn and soya, which are not united into two classes.
RBF 20-851-33
class 33” Classification accuracy Control sample 87.36
Test sample 87.31 Let us consider the results of TS classification in more detail with indication of CA percentage (Table 3).
It is seen that the CA percentage varies from 42% (class 3 “Buildings”) to 99.3% (class 58 “Forest”). It should be noted that higher CA values are normally provided by classes with a large number of pixels: the mean percentage of correct classification is 83.63% based on classes and 87.31% based on pixels.
Let us consider Table 4, which is the error matrix showing the classes to which erroneously classified data are referred to. Each row of the matrix is normalized to the number of correctly classified pixels in the corresponding classes.
The gray regions are the classes of one plant type: all classes of corn (left) and all classes of soya (right). It can be concluded from the comparison of these regions with others that the total cross error in the soya region is several times smaller than that in other regions. It fact testifies that soya regions with different types of soil processing and other characteristics are indeed hard to distinguish. This phenomenon for the corn regions is observed to a smaller extent. Probably, this difference is caused by specific aspects of processing of corn and soya regions.
Conclusions Thus, the experiments aimed at classification of a large-format hyperspectral image confirmed the high efficiency of the method including preprocessing in the form of the transformation to the principal components of the spectral components, spatial transformation in the form of expansion of the principal components into intrinsic mode functions, and classification in the neural network. The method ensures a high probability of correct classification of hyperspectral images having similar spectral compositions and effectively operates in situations with terrain areas that can be hardly distinguished by conventional methods.
This work was supported by the Presidium of the Russian Academy of Sciences within the framework of the Complex Program of Basic Research of the Siberian Branch of the Russian Academy of Sciences (Project No. II.1.37).