Image texture is an important visual cue in image processing and analysis. Texture feature expression is an important task of geo-objects expression by using a high spatial resolution remote sensing image. Texture features based on gray level co-occurrence matrix (GLCM) are widely used in image spatial analysis where the spatial scale is especially of great significance. Based on the Fourier frequency-spectral analysis, this paper proposes an optimal scale selection method for GLCM. Different subset textures are firstly upscaled by GLCM with different window sizes. Then the multiscale texture feature images are converted into the frequency domain by Fourier transform. Consequently, the radial distribution and angular distribution curves changing with different window sizes from spectrum energy can be achieved, by which the texture window size can be selected. In order to verify the validity of this proposed texture scale selection method, this paper uses high-resolution fusion images to classify land cover based on multiscale texture expression. The results show that the proposed method combining frequency-spectral analysis-based texture scale selection can guarantee the quality and accuracy of the classification, which further proves the effectiveness of optimal texture window size selection method bases on frequency spectrum analysis. Other than scale selection in spatial domain, this paper casts a novel idea for texture scale selection in the frequency domain, which is meant for scale processing of remote sensing image.
High spatial resolution remote sensing images contain rich texture information, and accurate description of texture features can effectively distinguish complex land-cover category [
A GLCM is a symmetric matrix with each value representing the probability value of the nearest-neighbor gray tone at a given distance and orientation [
Empirical and enumeration methods were frequently used in the determination of a scale parameter for GLCM texture feature. However, an empirical method is easily influenced by subjective mind, and an enumeration method requires mass of redundant computation when selecting the appropriate scale [
High-resolution imagery has abundant meaningful information integrating spectral features with shape and texture, and the periodicity and direction of image texture in the frequency domain can more easily reflect its subtle differences than in the spatial domain [
Since a statistical analysis of the Fourier spectrum can reflect the scale effect of texture expression, this paper explores the optimal scale selection method for GLCM texture feature by using the Fourier spectrum analysis. Considering the performance and popularity of GLCM, based on the CLCM texture feature images at different scales, contrast was selected and used to analyze a set of frequency spectrum energy statistical curves to determine the optimal scale parameter for GLCM.
Firstly, four typical objects with different texture features in high-resolution imagery are chosen, and then their CLCM texture features with different moving window sizes are extracted and calculated. Next, GLCM texture feature images are converted into the frequency domain and then the multiscale change trend in spectrum energy distribution curves are analyzed at 18 scales. Finally, according to the change in trend, the optimal scale parameter of GLCM could be selected. In addition, this paper uses the local variance method to select the optimal window size and finally compares the effectiveness of the two methods through experimental verification.
Set
Polar coordinates can be used to measure the Fourier energy spectrum [
Spectrum energy statistical schematic diagram: (a) radial spectrum energy and (b) angular spectrum energy.
Frequency spectrum energy statistics have the following two properties [
To be more specific,
Figure
Four subset textures and their spectrum. (a) Houses. (b) Farmland_1. (c) Farmland_2. (d) Image covered with mixed features. (e)–(f) are the related spectrum feature images of (a)–(d).
(a) Radial spectrum curve and (b) angular spectrum curve of four different subset textures.
Figure
The texture of house is coarse, which determine that spectrum energy is concentrated in low frequency; single house arranged repeatedly leads to more than one peak (
As shown in Figure
In the same way, Farmland_2 is of monotonous texture which is vertically distributed as shown in Figure
As shown in Figure
As stated above, scale parameter greatly influences GLCM-based texture feature expression. Generally, if the moving window size is set small, the texture feature image is clear and informative while the edge of geo-object is obscure. As the moving window size increases, the texture feature image becomes coarser with sharpness reduced.
Actually, what changes along with the window size is the direction and period of the texture; that is to say, the orientation and periodicity of the texture feature correspondingly change with the varying window size. As analyzed in Section
To improve the performance of texture features to distinguish geo-objects categories based on GLCM, this paper combines frequency spectrum knowledge into calculating multiscale texture features based on the Fourier transformation and proposes an optimal textural window size selection method by analyzing the relationship between texture data in spatial and frequency domains. The idea of this paper is based on theoretical framework of frequency statistics and aims at deducing the spatial geometry features of objects.
Steps for selecting the optimal texture window size are as follows: Extraction of the multiscale texture images based on GLCM Plotting the frequency spectrum energy curves of various subset textures on multiscale images Analysis of radial and angular energy curves of different textures with the change of scale Selection of the optimal texture scale (or the optimal window size)
The experimental image used in this paper is downloaded from Google Maps in the year of 2018. The study area is located in Liujiabao Township, Taiyuan City, Shanxi Province. The size of the study area is 688 × 737 pixels (Figure
Experimental image. (a) House. (b) Farmland_1. (c) Farmland_2. (d) Mixed object.
Haralick proposed 14 kinds of statistical texture features for GLCM. The eight frequently used statistics are the angular second moment, contrast, correlation, mean, entropy, homogeneity, variance, and dissimilarity. Among them, contrast is the moment of inertia near the principal diagonal line of the GLCM which measures the distribution of matrix values and local variations in image and reflects the clarity of the image and the depth of the texture grooves. After trial and comparison, the contrast feature was chosen for analyzing the optimal texture scale.
The first step of the experiment was to calculate contrast feature with window size ranged from 3 × 3 to 35 × 35 and then contrast feature images with different window sizes are shown as Figure
Contrast images at series scale: (a) original image, (b) 3 × 3, (c) 5 × 5, (d) 7 × 7, (e) 9 × 9, (f) 11 × 11, (g) 13 × 13, (h) 15 × 15, (i) 17 × 17, (j) 19 × 19, (k) 21 × 21, (l) 23 × 23, (m) 25 × 25, (n) 27 × 27, (o) 29 × 29, (p) 31 × 31, (q) 33 × 33, and (r) 35 × 35.
Figures
Radius distribution and angular distribution curves of four subset textures at different scales. Angular and radial spectrum curves of (a) houses, (b) farmland_1, (c) farmland_2, and (d) mixed objects.
As illustrated in Figure
As illustrated in Figure
As shown in Figure
As shown in Figure
Further analysis also shows that (1) with the increase of scale, change of the radial curve is sensitive and significant which is represented in decrease in the spectrum energy or the transfer of the peak value; (2) the change of the angular curve is reflected in increase or decrease of peak value; however, tendencies of the curves are relatively steady. (3) When the texture of geo-objects is not obvious, the radial and angular spectrum energies reduce greatly, even disappear with the increase of scale.
According to the analysis results in Section Change of peak value in radial and angular curves can show the variations of frequency spectrum energy with the increase of scale, both of which can be used as the basis of choosing the best scale. Choosing the radial curve for selecting the optimal scale should take the subpeak as the standard because the subpeak can reflect the period of texture. If there are no double or multiple peaks in the radial curve, the angular spectrum peak can be taken as the criterion. Compare the frequency spectrum curve on the initial scale with a certain scale, if the peak energy changes dramatically (the peak obviously transfer or shrinks), it indicates that the textural information of original geo-objects cannot be reflected at this scale. However, if the peak value on a scale is consistent with the initial scale, it means that the scale retains the texture information and it can be selected as the optimal texture scale. For a texture with single and fine characteristics, the larger the window size is, the more texture information is lost, which is because texture feature values calculated by one pixel are closer to its adjacent ones, and they cannot maintain the original neighborhood state of the feature pixel with a large window size. In this case, optimal scale selection can rely on the result of the mixed ground objects.
As shown in Figure
The peak value change of curves of four subset textures: (a) house radial curve, (b) house angular curve, (c) farmland_1 radial curve, (d) farmland_1 angular curve, (e) farmland_2 radial curve, (f) farmland_2 angular curve, and (g) mixed ground objects angular curve.
For houses, both of the radial and angular spectrum curves can be used as the basis of choosing the best scale. As shown in Figure
For farmland_1 and farmland_2, as shown in Figures
For mixed objects, there is no subpeak on the radial curve, so the changes of the angular curve peak (
According to the analysis presented above, the best classification results can be obtained by using a window size of 13 × 13, 15 × 15, 19 × 19, or 21 × 21.
Theoretically, the land cover classification result should have higher accuracy with the optimal texture scale selected by the method presented in this paper. To verify the validity of the method, this paper carried out a series of land cover classification experiments based on GLCM features with different moving window sizes from 3 × 3 pixels to 35 × 35 pixels. Since SVM (support vector machine) is an effective machine-learning algorithm for high-dimensional data and it could achieve high accuracy even with a small sample amount [
Table
Number of samples for different geo-objects.
Geo-objects | Training samples | Test samples |
---|---|---|
Farmland_1 | 6230 | 775 |
Farmland_2 | 1097 | 168 |
House | 1284 | 386 |
Road | 592 | 63 |
Bare land | 1832 | 150 |
Tree | 152 | 28 |
Waterbody | 173 | 30 |
Total | 11360 | 1600 |
Classification experiment consists of 18 groups: the first is to directly classify the original image only based on spectral features; other 17 groups involve texture features into the classification in which the feature vector is composed of 24 features (HOM, CON, DIS, ENT, VAR, ASM, COR, and MEAN of the three original bands) calculated by using different moving window sizes. The classification results are shown in Figure
Series of classification results. (a) Only based on spectral features, (b) 3 × 3, (c) 5 × 5, (d) 7 × 7, (e) 9 × 9, (f) 11 × 11, (g) 13 × 13, (h) 15 × 15, (i) 17 × 17, (j) 19 × 19, (k) 21 × 21, (l) 23 × 23, (m) 25 × 25, (n) 27 × 27, (o) 29 × 29, (p) 31 × 31, (q) 33 × 33, and (r) 35 × 35.
As can be seen from Figure
To assess the accuracies of classification results, this paper employs a confusion matrix [
Overall accuracy and kappa coefficient on different scales.
Figure
Figure Since the texture of farmland_1 is not obvious, the change of the moving window size has little effect on farmland_1, which results in the accuracy being maintained at a relatively high level. With the increase in the moving window size, the texture details inside farmland_2 are ignored. The larger the window size used, the lesser the texture detail. Therefore, classification accuracy is mainly determined by spectral features and thus gets higher because crop is sensitive to spectrum. When the window size approaches to 17 × 17, the accuracy is maintained at a high level. The Prod. Acc. curves of bare land, road, and tree have the same change tendency (increasing first and then decreasing). It can be deduced that it is effective to improve classification accuracy by setting large moving window size for these kinds of categories. However, it is not true that “the bigger the scale, the higher the accuracy” because when large scale is used, more information will be ignored, which results in misclassification or unclassification. From the analysis of Section
Producer accuracy curves of objects in different scales.
However, the overall accuracy is affected by the six kinds of geo-objects, and high precision of the house does not represent global accuracy. In contrast, the optimal scale of mixed objects are 13 × 13 and 15 × 15, and the highest accuracy is achieved on scale 15 × 15 in experimental result, and the higher accuracies are achieved on scale 13 × 13 and 17 × 17.
Generally, these three sizes are consistent with the determined optimal window sizes by using the proposed method. The experimental results show that the optimal scale selection method based on frequency spectrum texture analysis can effectively ensure the classification accuracy.
Local variance is a scene texture statistic that has been used to characterize the relationship between spatial scale and object size in the scene. Woodcock and Strahler originally used a 3 × 3 window and degraded images to coarser levels to examine the change in local variance as pixel size [
Local variance curve of four different subset textures.
Figure
Table
Optimal scale selected by different methods.
Subset textures | Frequency spectrum method | Local variance method | Best scale in experiment |
---|---|---|---|
House | 13 × 13, 19 × 19, 21 × 21 | 17 × 17 | 21 × 21 |
Farmland_1 | None | 7 × 7 | None |
Farmland_2 | None | 9 × 9 | 17 × 17 |
Mixed-objects | 13 × 13, 15 × 15 | 13 × 13 | 15 × 15 |
Global optimal scale | 13 × 13, 15 × 15 | 15 × 15 |
Firstly, the frequency spectrum method is more accurate than the local variance method for subset textures with significant texture, such as house and mixed-objects. Secondly, when choosing the global optimal texture scale, the frequency spectrum method performs better than the local variance method. According to the spectrum analysis of house and mixed-objects, it can be quickly determined that the global optimal texture scale is 13, 15, or 17; however, it is somewhat difficult to use the local variance method to determine an appropriate global optimal window size because the optimal scale span of the four objects is relatively large; if the local variance results of the house and mixed objects are used to select the optimal scale, 13 and 17 would be the selected scales, but the two scales did not result the best classification accuracies.
On the other hand, the frequency spectrum method performs better than the local variance in determining the optimal scale of different subset textures. Comparing Figure
Scale selection for textural feature expression is always troublesome in information extraction from remote sensing images. Based on the texture frequency spectrum analysis of four subset textures and peak variation with different window sizes, this paper presents a method based on texture spectrum statistics to determine optimal GLCM scale parameter for high spatial resolution image analysis. According to experimental results, the conclusions are as follows: It is a feasible way to use the frequency spectrum energy curve of GLCM contrast feature image to effectively reflect the periodic pattern and direction of texture. It casts a novel approach for scale selection of remote sensing image analysis from the frequency domain, which is the main contribution of this work. The change of the GLCM scale parameter leads to the change of the spectrum energy peak of the subset textures, and the change of peak values can be used as the basis for the optimal scale selection. In practice, the texture of the remote sensing image is complex and aperiodic, but the direction of texture generally exists, so it is easier to obtain the angular peak value than the radial peak value. Therefore, angular peak variation can be preferentially considered in application. The optimal scale of feature extraction needs to be determined by subset textures on remote sensing imagery. In comparison with single subset textures, peak variation on the spectrum curve of mixed objects performs better in determining the global optimal scale. The combination of texture features based on GLCM can be directly used in a high-resolution remote sensing image classification. Also, the proposed method is the image feature statistics in the frequency domain. Theoretically, it can be used in the selection of segmentation scale parameters. Although how to assess accuracies in object-based image classifications is still an open question, some currently used quantitative segmentation evaluation indexes [ The scale factor is dependent on the correspondence between spatial scale and object features itself, so it is less realistic to obtain an absolutely optimal scale suitable for all features on the image; however, it is a compromise to get a relatively optimal scale by using the proposed frequency spectrum statistics method. When the images are mosaics of different classes or features because of the scale dependence of geo-object, stratified scale processing [
The high-resolution remote sensing imagery used to support our work were supplied by Arceyes Softwere Maps Downloader under license and so cannot be made freely available. These data are available to access via the website
The authors declare no conflicts of interest.
Cao Min conceived, designed, and performed the experiments and wrote the paper. Ming Dongping proposed the research idea and supervised the research and revised the manuscript. Lu Xu, Ju Fang, Lin Liu, and Xiao Ling helped to perform the experiments. Weizhi Ma provided significant comments and suggestions.
This research was supported by the National Natural Science Foundation of China (41671369), the National Key Research and Development Program (2017YFB0503600), and “The Fundamental Research Funds for the Central Universities.”