Aerospace images with a spatial resolution of less than 1 m are actively used by regional services to obtain and update information about various environmental objects. Considerable eforts are being devoted to the development of remote sensing methods for forest areas. The structure of the forest canopy depends on various parameters, most of which are determined by ground-based methods during forest management works. Remote sensing methods for assessing the structural parameters of forest stands are based on texture analysis of panchromatic and multispectral images. A statistical approach is often used to extract texture features. The basis of this approach is the description of the distributions characterizing the mutual arrangement of image pixels in grayscale. This paper compares the efectiveness of matrix based statistical methods for extracting textural features for solving the problem of classifying various natural and manmade objects, as well as structures of the forest canopy. We consider statistics of various orders based on estimates of the distributions of gray levels, as well as the mutual occurrence, frequency, diference and structuring of gray levels. The results of assessing the informativeness of statistical textural characteristics in determining various structures of the forest canopy are presented. Dependences of the classification results on the choice of distribution parameters are determined. For the quantitative validation of the results obtained, data from ground surveys and expert visual classification of very high resolution WorldView-2 images of the territories of Savvatyevkoe and Bronnitskoe forestries are used.
In recent years, machine learning methods have been widely used for various tasks of automation
and increasing the information content of procedures for thematic processing and analysis of
aerospace images in the visible and near infrared spectral ranges. Multispectral satellite images
of low and medium spatial resolution are traditionally used for survey of the soil and vegetation
cover and the construction of large-scale thematic maps [
High (1–4 m) and very high (< 1 m) spatial resolution of panchromatic satellite images,
forms the basis of methods for solving new tasks of monitoring land, forest and water resources,
searching for mineral deposits and assessing ecological situation, which are more complex
from the point of view of increased consumer requirements. There is a need to develop special
approaches for analyzing large amounts of information and obtaining remote estimates of
the characteristics of the examined objects with a given accuracy. Improving the eficiency
of thematic processing of aerospace images of high spatial and spectral resolution is in high
demand in many applications in the fields of natural resource management, agriculture, forestry
and environmental monitoring [
The current trend in the development of methods for thematic processing of high resolution
images is the combined use of spectral and texture features. So for example, a method of
spectral-texture processing of aerial hyperspectral images of a forest canopy was presented
in [
The presented results on improving the accuracy due to the use of texture features are
also confirmed by the comparison with the previously obtained results of thematic processing
of hyperspectral images of nearby territories presented in [
The work [
The accuracy of texture analysis depends on the chosen feature extraction method [
The panchromatic satellite images presented in grayscale are considered as an object of texture analysis since they have the highest spatial resolution. The texture is formed by the spatial arrangement and the mutual combination of structural elements. Natural objects are characterized by a random arrangement of structural elements and significant variations in their parameters, for example, tone and size. Thus, the task of constructing parameters characterizing a particular texture is associated with obtaining statistical estimates.
Statistical methods of texture analysis are based on assessing the spatial distribution of local characteristics of structural elements for all possible locations in the image and extracting statistical parameters from the obtained distributions of local characteristics. Matrix methods assume that the desired distribution is discrete and has a finite number of elements. An image for which a texture extraction is made must contain a suficiently large number of structural elements to obtain reliable estimate of probability mass function. Texture features obtained on the basis of matrix methods are subdivided into characteristics of the 1st and 2nd orders.
The construction of first order texture characteristics implies that the structural elements are
individual pixels of the original image [
GLM() = # {(, )| (, ) = , (, ) ∈ × } where # means the number of elements in the set, = 1, . . . , , and is the number of gray scales.
For building the Gray Level Diference Matrix (GLDM), the original image is converted into a diference image :
Δ,Δ = | (, ) − ( + Δ, + Δ)| where parameters Δ and Δ are displacements along the horizontal and vertical directions, respectively. GLDM is a vector of frequencies of occurrence of absolute values of diferences in gray levels at the given displacement: GLDM() = # {(, )| (, ) = , (, ) ∈ ( − Δ)× ( − Δ)} , = 0, . . . , − 1.
An example of constructing GLM and GLDM matrices is shown in Figure 1.
For calculating extract texture features, GLM and GLDM are converted into corresponding probability mass function estimates
GLM() GLM() = ∑︀ GLM() =1 , GLDM() =
GLDM() − 1 ∑︀ =0
GLDM() .
The corresponding 1st order texture characteristics are presented in Table 1.
The extraction of second order texture characteristics is primarily associated with the
construction of two-dimensional distributions. Structural elements in this case consist of two pixels
or two groups of pixels, for each of which a corresponding characteristic is determined. The best
known is the method proposed in [
The original image (, ) is a function of two spatial coordinates, so for each pixel we can calculate the diferential estimate of the gradient function. The magnitude of the gradient (, ) = √︃︂( )︂ 2 (︂ )︂ 2
+ characterizes the rate of changing tone of the image in reference pixels. To obtain a diference estimate, we use the Sobel operator:
(, ) = √︁2(, ) + 2 (, ) ≃ (, ) where (, ) = [( + 1, − 1) + 2( + 1, ) + ( + 1, + 1)] − (, ) = [( − 1, + 1) + 2(, + 1) + ( + 1, + 1)] − − [( − 1, − 1) + 2( − 1, ) + ( − 1, + 1)] , − [( − 1, − 1) + 2(, − 1) + ( + 1, − 1)] .
Thus, by specifying the number of gradient gradations to be equal , we can build an image
of modules of brightness gradients
(, ) = int
︂[ (, ) − min ]︂
max − min
·
in pixels of the original image. Gray Gradient Co-occurrence Matrix (GGCM) [
The estimate of the probability mass function of the co-occurrence of a given number of gray levels can be obtained as the normalized GLCM (, ) =
GCLM(, ) ∑︀ GCLM(, ) ,=1 where , are indices GLCM elements. For GGCM, this estimate is calculated in a similar way.
Based on the values (, ), statistics known as Haralick texture features are calculated.
Initially, 14 diferent texture features (Haralick features) were proposed in the original paper [
Texture segmentation of panchromatic satellite images is based on the moving window method. The moving window is a rectangular contour selecting the analyzed part of the image under processing. The size of the window is determined by the characteristic scale of recognized textures. If the window size is chosen too small, the result of the texture classification will represent the high frequency noise. On the other hand, too large size of the window leads to excessive smoothing of the contours of recognized objects. The center of the window runs through all the points of the panchromatic image. To reduce the amount of computation in practical tasks, it is suficient to run only pixels whose coordinates correspond to the pixel centers of the joint multispectral image, when processing panchromatic and multispectral images together.
To carry out the supervised classification texture features we employed an ensemble algorithm known as Error Correcting Output Codes (ECOC). The algorithm is designed to formalize the responses of binary learners as the multiclass classifier based on some results of the theory of information and coding. Le the algorithm of binary classification is the Support Vector Machine (SVM) with the Gaussian kernel. The response of the SVM algorithm is the classification score which means the normalized distance from the classified sample to the discriminant surface in the area of the relevant class. The coding stage of the ECOC algorithm consists of calculating classification scores or each of SVM binary learners defined by one-versus-one coding design matrix and corresponded Hinge binary losses for each of the considered classes. The decoding stage consists of the selection of the class corresponding to the minimum average loss. For optimizing the feature space arises, the regularized forward selection method is used. The method has better stability in comparison with the standard greedy selection algorithm sufering from the high sensitivity of the selected optimal sequence of features to small changes in the training set. On the other hand, the regularized algorithm requires more computational costs.
The classification quality was assessed by confusion matrix (CM) and the related parameters, such as total error (TE), total omission error (TOE) and total commission errors (TCE). CM is the basic classification quality characteristic allowing a comprehensive visual analysis of diferent aspects of the classification method used. Rows of CM represent reference classes and columns represent predicted classes. TE is defined as the amount of incorrectly classified samples over the total number of samples. TOE is the mean omission error over all classes considered, where the omission error is the amount of false classified samples of the selected class over all samples of this class. TCE is the mean commission error over all possible responses of the classifier used, where the commission error is defined as the probability of false classification for each possible classification result.
During the joint spectral-texture processing of satellite images, texture features are usually employed for solving the following two tasks: segmentation of the contours of natural and manmade objects (including the selection of building zones and forest areas), and classification of structural parameters of the forest canopy. Thus, for carrying out numerical experiments using the above methods, we selected two relevant test plots in WorldView-2 panchromatic images with the spatial resolution ∼ 0.5 m. The first test plot, which hereinafter referred to as Konstantinovsky, is located on the territory of the Savvatyevskoe forestry (Tver region) near the Domnikovo village. The plot contains several large zones corresponding to 5 types of objects of varying complexity having well difering texture: water surface (Konstantinovsky sand quarry), pine forest, building zone, field and peat swamp forest. The RGB image of the test plot, the corresponding expert map of objects and the results of texture analysis are shown in Figure 3.
The classifier used is sensitive to the diference in the number of training samples for the considered classes. Increasing the number of training samples for one of the classes leads to increasing the prior probability of its classification. Thus, in order to avoid this problem, we used a balanced training set containing 500 samples for each class. Remaining data (testing set) were used for independent validation. Also, since the accuracy of texture classification essentially depends on the size of the moving window, we carried out a series of calculations, which allowed us to determine the range of acceptable size values. Thus, we used the moving window with the size of 109 pixels in horizontal and vertical directions. The original image has been reduced to 64 gray levels. The described above feature optimization was used for the GLCM and GGCM methods to avoid the curse of dimensionality problem. For the classification of texture features obtained by the GLM and GLDM methods, we used a full set of features.
Estimates of total characteristics of classification quality obtained from training (resubstitution method) and testing sets (independent validation) are represented in the Table 3. We can see that the GLCM method provides the most accurate results. The total error is about 1%. At that the total omission and commission errors are very close. It should be noted that diference between dependent and independent estimates of the error is insignificant, which indicates a good generalization ability of the trained ECOC SVM classifier. The total errors of the GGCM and GLM methods are significantly higher, but remain at an acceptable level. It should be noted that a visual comparison of the classification results presented in Figure 3 shows that GLM
TE TOE TCE TE TOE TCE TE TOE TCE 0.10 0.10 0.10 0.25 0.25 0.25 0.01 0.01 0.01 0.068 0.068 0.066 0.22 0.22 0.218 0.234 0.234 0.239 0.015 0.015 0.015 0.023 0.023 0.023 0.247 0.243 0.315 0.319 0.250 0.365 0.033 0.026 0.115 0.043 0.033 0.115 0.12 0.11 0.12 0.268 0.253 0.261 0.012 0.012 0.011 0.083 0.079 0.098 GGCM reproduces the expert map of objects much better and contains significantly less noise in comparison with GLM.
Table 4 contains class-wise omission and commission classification errors for Konstantinovsky test plot. The best classification result corresponds to water surface. We can see that all the methods reveal a high accuracy. The building zone and field are classified with acceptable level of errors. The worst accuracies correspond to conifer and peat swamp forest stands, however it low enough for GLCM and GGCM methods. GLDM demonstrates worst results and it cannot be used texture segmentation of forest areas.
The second test plot, hereinafter referred to as GFP Dementyev, is located on the territory of the Bronnitskoe forestry near the Lubninka village. The plot is part of the territory of the geographical forest plantations (GFP) of the forester P.I. Dementyev. The RGB image of GFP Dementyev and the corresponding expert classification map are shown in Figure 4. The choice of this site is due to the large variety of plantations with diferent structures. By the variety
natural confer forest peat swamp forest GLM
CE OE CE OE CE buildings 0.15 0.09 0.332 0.329 of species, the stands of the Bronnitskoe forestry cover the main forest-forming species of Russia. From the 1950s to the present, various species and ecotypes of larch, which are grown here outside the natural habitat, have been tested in this area. The forest canopy of the test site contains 7 visually noticeable texture classes: 1 — mixed conifer stand (larch, pine and spruce) with a dense canopy and high values of density; 2 and 3 — agricultural areas of diferent structure; 4 — deciduous stand with a predominance of birch, dense canopy and the relative stocking of 0.9; 5 — mixed birch stand with the relative stocking of 0.8; 6 — mixed birch stand with a pronounced cluster structure of the canopy; 7 — cultivated plantations of larch with a regular structure.
In this case GLCM and GGCM methods show similar results. Total classification error is about 4%. Accuracy of GLCM seems to be a little higher compare to GGCM, however we can see for this method that diference between resubstitution and independent estimates is also more significant than for GGCM. GLM and GLDM method demonstrate weak classification results. Analyzing class-wise errors presented in Table 5, we can see that the regular structure of larch stands corresponds to minimum errors, about 2% for GLCM and GGCM methods. This result is confirmed also by Figure 4. The highest errors correspond to the dense deciduous stand, however it is explained by small number of pixels corresponding to this object.
The reported study was funded by RFBR, projects No. 20-07-00370 “Fundamental problems of increasing the informativeness of processing data from optoelectronic aerospace devices of high spatial and spectral resolution” and No. 19-01-00215 “Investigation of operative opportunities of hyper-spectral technologies of remote sensing of the Earth to solve regional problems using updated hyper-spectral cameras from space”.