Modified average local variance for pixel-level

Modified average local variance for pixel-level scale selection of multiband remote sensing images and its scale effect on image classification accuracy Dongping Ming Jinyang Du Xiyu Zhang Tiantian Liu

Downloaded From: http://remotesensing.spiedigitallibrary.org/ on 09/09/2013 Terms of Use: http://spiedl.org/terms

Modified average local variance for pixel-level scale selection of multiband remote sensing images and its scale effect on image classification accuracy Dongping Ming,a Jinyang Du,b Xiyu Zhang,a and Tiantian Liua a

China University of Geosciences (Beijing), School of Information Engineering, 29 Xueyuan Road, Haidian, Beijing 100083, China [email protected] b Institute of Remote Sensing Applications, The State Key Laboratory of Remote Sensing Science, CAS, Beijing 100101, China

Abstract. The development of remote sensor technology makes it convenient to obtain multiscale satellite data sets, but selecting data with an appropriate scale has become a problem. We propose improvements based on modified average local variance (MALV) for selecting the optimal spatial resolution of multiband images. One improvement is computing the mean MALVs of all bands, and the other is computing the average MALV of the selected bands. We discuss the optimum index factor and principal component analysis (PCA) methods for band selection. Further image classification experiments with different spatial resolutions are employed to verify the proposed methods. The experimental results prove that the MALV method is suitable for images with simplex landscape type. When the spatial extent of the image data is large, the MALV of the subimage whose landscape type is similar to the dominating landscape of the whole image is significantly referential for selecting the optimal spatial resolution. MALV based on PCA is more effective for reflecting the scale effect of spatial resolution and thus is useful for selecting the optimal spatial resolution of a multiband image. The experimental results also prove that very high spatial resolution will lead to high heterogeneity within class, and thus it will lead to low separability and low classification accuracy. Furthermore, the MALV method provides a feasible approach for quantitative research of the modifiable area unit problem. © 2013 Society of Photo-Optical Instrumentation Engineers (SPIE) [DOI: 10 .1117/1.JRS.7.073565]

Keywords: pixel-based scale selection; spatial resolution; multiband remote sensing image; average local variance; band selection; image classification. Paper 12070 received Mar. 20, 2012; revised manuscript received Jan. 24, 2013; accepted for publication Apr. 15, 2013; published online May 9, 2013.

1 Introduction Various satellite images with spatial resolutions ranging from 0.5 to 25,000 m are available for different applications, due to the development of remote sensor techniques. This development offers new and significant changes and challenges for selectively utilizing and analyzing multispectral and multispatial resolution observation data. Selection of the appropriate scale has become an inevitable problem. Spatial resolution is the primary scale of measurement for observations of Earth, so its scale effect has caused continuing interest in remote sensing applications and geographical research.1 The number of mixed pixels will decrease when the spatial resolution of remotely sensed data becomes finer. The decrease in mixed pixels is beneficial for information extraction and image analysis. At the same time, the spectral variation within classes will increase as spatial resolution becomes finer. Increased spectral variation is negative for information extraction and image analysis, so it is necessary to explore the net effects of changes in spatial resolution on image analysis and to explain the modifiable area unit problem2 (MAUP) further. However,

0091-3286/2013/$25.00 © 2013 SPIE

Journal of Applied Remote Sensing

073565-1


Vol. 7, 2013

Ming et al.: Modified average local variance for pixel-level scale selection. . .

selecting an adapted spatial resolution (pixel-based scale selection) to identify geographical elements is still a difficult task for remote sensing-based spatial investigations. There are several commonly used methods to express the relation between the research scale and spatial resolution: geographic variance, average local variance (ALV), texture analysis, and the fractal method. Of these methods, ALV is widely used to characterize the relationship between spatial resolution and object size in a scene,3 and it can be used to select the optimal spatial resolution quantitatively.3–8 There should be an obvious peak in the ALV chart, but the peak is not present in practical calculations. The modified ALV (MALV) method based on variable window sizes and resolutions4 was proposed to resolve this problem. Like traditional ALV, MALV is only adaptive for a single-band image or a pan-chromatic image, which significantly restricts this method’s use. On the other hand, improvements in remote sensor technology and optical compensation techniques have made possible remote sensing imaging with high spatial resolution and high spectral resolution. Selecting the optimal spatial resolution for multispectral and even hyper-spectral images should be considered. This paper proposes improvements based on MALV for spatial resolution selection and provides further validation by analyzing its scale effect on image classification accuracy.

2 ALV and MALV Method In previous research, local variance calculated the mean value of the standard deviation by passing an n × n-pixel moving window for each pixel and then taking the mean of all local variances (ALV) over the entire image to indicate the local variability in an image. The spatial resolution on which the peak of maximal ALV appears is closely related to the dominant size of pattern elements in the image,5–8 and it is the optimal resolution of the image data for the spatial investigation, because it approaches the object size and can reflect the spatial features in the scene.3 Theoretically, there should be an obvious peak in the chart of ALV with the gradual degradation of spatial resolution. However, in practical calculations for images with high spatial resolution, the ALV does not show an evident descending trend as expected; instead, it arises smoothly and then maintains a constant level in much the same way as a semivariogram.4 The reasons can be analyzed from three aspects. First, the computation of ALVs that use different spatial resolutions is somewhat similar to that of semivariances that use different lags on a certain image. The essence of ALV is the synthetic value of semivarinances in different directions.9–12 Second, traditional ALV is computed based on the variable ground area, because it uses the same window size on images with variable spatial resolutions. ALVs based on far different ground areas certainly differ greatly. Third, images with higher spatial resolution tend to show more terrain details (a single building, a single tree, etc.). When the spatial resolution declines, the neighborhood of a n × n window may shift to another object, so the ALV increases. To resolve this problem, the MALV method based on constant ground area (variable window sizes and resolutions) is proposed, and the ALVs of windows in integer size are used to predict those of windows in decimal size by interpolation.4 The reason the MALV method can be used for indicating the optimal spatial resolution is that the MALV based on constant ground area should be a constant value with the change of spatial resolution, without considering the scale effect of spatial resolution. Just for this reason, the actual variable MALV can reflect the scale effect of spatial resolution, and it is especially effective for a single landscape type that has a regular shape or a regular spatial distribution, such as an urban or agriculture landscape.13 Although MALV can actually reflect the scale effect of spatial resolution, there is still a serious limitation for MALV and ALV: They are both dependent on the global variance in the image, so they are only suitable for single-band or panchromatic remote sensing images.

3 Modification of the MALV Method for Pixel-Level Scale Selection of Multiband Remote Sensing Images To break through the limitation that ALV or MALV is suitable only for single-band or panchromatic remote sensing images, this paper proposes two kinds of MALV-based improvements for selecting the optimal spatial resolution of multiband remote sensing images. One is simply to Journal of Applied Remote Sensing

073565-2


Vol. 7, 2013


compute the average MALV of all band images, and another is to compute the average MALV of selected bands.

3.1 Average MALV of All Bands The average MALV is the mean of the MALVs of all band images. For an image with n bands, it can be expressed as MALVAverage ¼

n 1X MALVi ; n i¼1

(1)

where MALVi is the MALV of band i. The calculation formula is described in detail by Ming et al.4

3.2 Average MALV of Selected Bands Some bands in a multiband remote sensing image are often highly correlated, so the information contained in one band (spectral responses or DNs for some objects) is largely a duplication of the information contained in another band. In pixel-based scale selection of a multispectral remote sensing image, the average MALV of all bands does not account for the correlation between different bands. In other words, the weight of every band for selecting the optimal spatial resolution is the same. As a result, the average MALV of all bands cannot precisely reflect the scale effect essence of spatial resolution, because the radiation or reflectance rates for some given object classes differ on different bands. Consequently, it is more rational to select the highly independent bands or a band combination with the most information content for computing the MALV. As statistical indices, a correlation coefficient can effectively represent the degree of similarity between different bands, and eigenvalues of the correlation matrix can be used to decide the principal components of a multiband image. In a similar way, they can be used in selecting the optimal spatial resolution of the multiband remote sensing image based on band selection. The basic process of computing the average MALV of selected bands is shown in Fig. 1, and the details are described in Secs. 3.2.1 and 3.2.2. From the view of concision and facility, optimum index factor (OIF) and principal component analysis (PCA) are two available methods for band selection.

3.2.1 Average MALV based on OIF Chavez et al.14 introduced the OIF to select a three-band combination that displays the greatest details among a maximum of 20 bands. The index is given by OIF ¼

3 X i¼1

Stdi ∕

3 X j¼1

jRij j;

(2)

where Stdi is the standard deviation of band i, and Rij is the correlation coefficient between any two of the possible three pairs. According to Chavez et al.,14 the highest OIF values should be the three bands with the most information content. The measure can be extended to any subset of arbitrary band numbers.15–17 Three bands are usually enough to compute the MALV, because this measure favors the selection of bands with high variances and low pair-wise correlation, which

Fig. 1 Workflow for computing the average MALV of selected bands. Journal of Applied Remote Sensing

073565-3


Vol. 7, 2013


ensures that the proportion of information content contained in the three selected bands is satisfied for the remote sensing applications. Consequently, the average MALV based on the OIF (MALVOIF ) can be described by MALVOIF ¼

3 X

W i MALVi ;

i¼1

(3)

where W i represents the weight of band i and is determined by the standard deviation; that is, W i ¼ Stdi ∕

3 X

Stdi :

i¼1

(4)

The calculation of W i indicates that, the higher the standard deviation is, the larger the weight of this band, because the standard deviation reflects how much variation or dispersion there is from the average. A high standard deviation indicates strong separability between classes within the image.

3.2.2 Average MALV based on PCA As an approach to band selection, the spectral band ranking methods construct and evaluate an objective matrix based on correlation criteria, so PCA is often involved. In PCA-based band selection of a hyper-spectral image (where the dimension of the data is very high), the first step is to reduce dimensionality, which intends to eliminate redundant bands and diminish computational burden. There is no need for dimensionality reduction for PCA-based band selection of a multispectral image (where the dimension of the data is not too high). The cumulative contribution α of all previous principal components can be used as the index of band selection. Commonly, the threshold of α decided by the contribution of the eigenvalues λi of all previous principal components is set between 85% and 95%. We can calculate λi and α by λi ¼ Eigvi ∕

α¼

n X i¼1

j X i¼1

Eigvi

λi ;

(5)

(6)

where Eigvi represents the eigenvalue of band i, and j represents the number of previously principal components with a cumulative contribution α between 85% and 95%. The average MALV based on PCA (MALVPCA ) can be described by MALVPCA ¼

j X i¼1

W i MALVi ;

(7)

where W i represents the weight of band i and can be determined by W i ¼ λi ∕

j X i¼1

λi :

(8)

It is worth noting that there are several other methods of band selection for multispectral or even hyper-spectral images. These methods include information divergence band subset selection,18 an independent component analysis-based method,19 the Kullback-Liebler distance-based method,20 unsupervised and supervised band selection methods,21 linear constrained band selection,22 the Bhattacharyya distance-based method,23 and the weighted independent component analysis-based method.24 The idea of selecting the optimal spatial resolution is similar for all methods. Journal of Applied Remote Sensing

073565-4


Vol. 7, 2013


4 Experimental Verifications and Pixel-Level Scale Effect Analysis by Image Classifications Theoretically, the classification accuracy of the image on selected bands and the optimal spatial resolution should be high. We employed a series of image classification experiments with different spatial resolutions to verify the validity of the two MALV-based improvements (MALVAverage and MALV based on band selection) for selecting the optimal spatial resolution of a multiband remote sensing image. The ideal experimental data should be an image with many spectral bands at a high spatial resolution. However, because of technical constraints, satellite remote sensing systems can offer only the following relationship between spatial and spectral resolutions: A high spatial resolution is associated with a low spectral resolution, and vice versa. Since we are constrained by the accessibility of the remote sensing data, this experiment consists of two parts whose original images correspond to different levels of observation. The first part (experiment 1) uses IKONOS data with high spatial resolution as the original experimental data, and the spatial resolution is degraded from 1 to 15 m. The second part (experiment 2) uses Landsat ETMþ data with moderate or low spatial resolution and a wider spectral range, and the spatial resolution is degraded from 15 to 255 m. There are several reasons the IKONOS data is degraded only to 15 m, not to 250 m. First, the spatial extent of the original IKONOS data that is suitable and available for us is limited. Second, if the size of the original data were big, the experiment would require a huge amount of computing. (As a matter of fact, the posterior experiments show it is not necessary to use original data of excessive size.) Third, if the resolution of the limited-size IKONOS data were degraded to 250 m, the degraded images would be too small to satisfy the needs of our experiment.

4.1 Experimental Data and Preparation Two rural-urban fringe zones north of Beijing, covering a variety of land use types, are selected for experiments 1 and 2 to ensure that the verifications are representative. Experiment 1 uses an original panchromatic (size: 4000 × 4000, spatial resolution: 1 m) and multispectral IKONOS image. The IKONOS image was acquired on August 26, 2002, when the vegetation was flourishing. To maintain experiment consistency and verify the proposed methods at a much wider spatial range, experiment 2 uses an original panchromatic (size: 4000 × 4000, spatial resolution: 15 m) and multispectral Landsat ETMþ image. The Landsat ETMþ image, which contains the area covered by the IKONOS image, was acquired on May 22, 2002, when the vegetation was also flourishing. After image geocorrection and registration, pan-sharpened images were created by principal component transform-based image fusion. Figure 2 shows the two false-color

Fig. 2 Pan-sharpened false-color experimental images: (a) IKONOS (PC432) and (b) Landsat ETM þ ðPC432Þ. Journal of Applied Remote Sensing

073565-5


Vol. 7, 2013


pan-sharpened images (shrinking the display), and the yellow square box in the lower left corner of Fig. 2(b) indicates the spatial extent of Fig. 2(a). Practical computations show that the band statistical features (standard deviations and contribution of the eigenvalues; see Figs. 3 and 4 and Tables 1 and 2) and the band reflectance rate (pixel value) of the two PCA-pan-sharpened images are very similar to those of the original multispectral images. Consequently, the pan-sharpened images used for the experimental data are reasonable and feasible. By nearest neighbor method-based spatial resampling on the IKONOS pan-sharpened image, a series of four-band experimental images with different spatial resolutions (from 1 to 15 m) are prepared. In the same way, a series of seven-band experimental images with different spatial resolutions (from 15 to 255 m) are prepared based on the pan-sharpened Landsat ETMþ image.

4.2 Band Selection and Calculation of MALV According to Figs. 3 and 4, Tables 1 and 2, and Eq. (2), the OIFs of different band combinations of the two experiments are respectively demonstrated in Fig. 5. For the pan-sharpened Landsat ETMþ image, Table 2 shows the correlations between all PCs, and PC4 is the lowest, so it is chosen as one of the three selected bands. Additionally, PC6 keeps the characteristics of the thermal infrared band (the class separability and actual spatial resolution are lower than those of other PCs), so it is excluded from the band selection. Figure 5 also shows that the trend of OIFs of pan-sharpened images is similar to that for the original multispectral images, which proves again that it is reasonable to use the pan-sharpened images as the experimental data. Thus, PC432 and PC743 can be used as the selected bands for experiments 1 and 2, respectively.

Fig. 3 Standard deviations of the pan-sharpened and the multispectral images: (a) IKONOS and (b) Landsat ETMþ.

Fig. 4 Contribution of the eigenvalues of the pan-sharpened and the multispectral images: (a) IKONOS and (b) Landsat ETMþ. Journal of Applied Remote Sensing

073565-6


Vol. 7, 2013


Table 1 Correlation matrix of PCA-based pan-sharpened IKONOS image. PC1

PC2

PC3

PC1

1.0000

PC2

0.9562

1.0000

PC3

0.8983

0.9712

1.0000

PC4

0.3950

0.5065

0.5146

PC4

1.0000

Table 2 Correlation matrix of PCA-based pan-sharpened Landsat ETMþ image. PC1

PC2

PC3

PC4

PC5

PC6

PC1

1.0000

PC2

0.9749

1.0000

PC3

0.9458

0.9793

1.0000

PC4

0.4632

0.5606

0.5062

1.0000

PC5

0.7494

0.8454

0.8589

0.7645

1.0000

PC6

0.6848

0.7343

0.7433

0.4903

0.7609

1.0000

PC7

0.8262

0.8974

0.9371

0.5866

0.9530

0.7603

PC7

1.0000

Fig. 5 OIFs of different band combinations of the pan-sharpened and multispectral images: (a) IKONOS and (b) Landsat ETMþ.

According to Ming et al.4 and Eqs. (1), (3), and (7), Fig. 6 shows the change trends of MALV, MALVAverage , MALVOIF , and MALVPCA of the pan-sharpened images and their degradations with spatial resolution. It must be noted that, to better compare the results obtained from two different sensors, the IKONOS 11-bit data were transformed to an 8-bit format, the same as the Landsat ETMþ data. According to the idea of using MALV to select optimal spatial resolution, there is no explicit indication for the optimal spatial resolution on the MALV curves in Fig. 6(a) and 6(b). Especially when the spatial extent of the study region is large, as in Fig. 2(b), most of the curves show a similar decreasing trend, which would seem to show that none of the approaches (single-band or multiband combination) can offer favorable results for selecting the optimal spatial resolution. However, that is not the case. First, Fig. 6 proves again that the MALV method is not suitable in cases where the study region is large and the landscape structure is complex. Additionally, the Journal of Applied Remote Sensing

073565-7


Vol. 7, 2013


Fig. 6 MALVs of the pan-sharpened images: (a) IKONOS (with constant ground area of 45 × 45 m2 ) and (b) Landsat ETMþ (with constant ground area of 765 × 765 m2 ).

experimental data are based on degraded image fusion results, rather than original satellite images captured by remote sensors, and this inevitably influences the experimental results. A detailed analysis is given in Sec. 4.4.

4.3 Series Image Classifications 4.3.1 Determining the types of land cover Further image classification experiments with different spatial resolutions were employed to verify the validity of the proposed MALV approach for spatial resolution selection and to interpret the relationships among spatial resolution, MALV, and classification accuracy. The pansharpened IKONOS and Landsat ETMþ images show that the study regions are mainly covered with buildings, roads, green land, farmland, bodies of water, and barren land. Considering the separability of a high-spatial-resolution image and the reflectance diversity of building roofs and road surfaces, several main types of land cover are identified as references for classification: artificial terrain (C1), grassland (C2), woodland (C3), water bodies (C4), uncultivated farmland (C5), cultivated farmland (C6), and barren land (C7). The maximum likelihood method is used as the decision rule for supervised classifications.

4.3.2 Selecting training sites For the IKONOS images in experiment 1, to reduce the random effect and uncertainty of classification, two series of classifications (marked with #1 and #2) were employed and were executed based on the selected three components (PC432) with spatial resolutions from 1 to 15 m. Within each series of classifications, taking the IKONOS image and using a land use map (shape file) as an assistant, training sites were visually selected for classification from the same region [as area of interest (AOI), originally created on the high-spatial-resolution image] so that the classification accuracies can be compared and assessed (different training sites are used in the two series of classification). It must be noted that, because training sites selected by AOI will inevitably contain mixed pixels at different spatial resolutions, we manually removed the mixed pixels by visual justification to maintain the homogeneity of the training sites. Additionally, the spectral differences between the same land use types should be taken into account when selecting the training sites, so the training sites should be representative of a certain spectral feature, and there should be enough training sites for each spectral feature to combine into a class. Similarly, for the Landsat ETMþ images of experiment 2, two series of image classifications (marked with #1* and #2*) for Landsat ETMþ images with different spatial resolutions from 15 to 255 m were employed to further verify the validity of the proposed methods. Series #1* is based on the selected three components (PC743), and series #2* is based on the commonly used combination (PC432). Journal of Applied Remote Sensing

073565-8


Vol. 7, 2013


Fig. 7 Average transformed divergences (ATD) of the training sites: (a) Experiment 1 based on IKONOS images, and (b) experiment 2 based on Landsat ETMþ images.

Figure 7 shows the average transformed divergence (ATD) of the training sites of experiments 1 and 2. The ATD values (the minimum value is 1895) show that the separability of the training sites are satisfied, which prevents poor classifications. Figure 7 also shows that higher spatial resolution can not lead to better separability; this is consistent with the research results of Chen and Stow.25 Additionally, when qualitatively evaluating the training sites, a regular trend is found. The heterogeneity within the class increases with a decrease in spatial resolution, and a spatial resolution that is too low will lead to high heterogeneity within the training sites. A similar trend is mentioned by Chen et al.26 Taking the class of cultivated farmland and grassland on the PC743 composite image as an example, as the spatial resolution goes from 15 to 255 m, the tones of the training sites appear to change from light green to green with purple. This shows that the homogeneity within the class decreases, so the training sites can be accepted only when their classification accuracy is higher than 85%.

4.3.3 Classification accuracies To assess the accuracy of every classification, 256 sample points were generated randomly. Figure 8(a) demonstrates the change in overall classification accuracies of classifications #1 and #2 and the terminal average classification accuracies with spatial resolution. Because the two series classifications use different sample regions, the resulting classification accuracies are not the same, but their spatial resolution trends are similar. Figure 8(b) shows the change in overall classification accuracies and the terminal average classification accuracies with spatial resolution. To view the situation as a whole, the classification accuracies of #1* (PC432) are almost higher than those of #2* (PC743). However, the spatial resolution trends of the two series pf classifications are similar. Theoretically, the classification accuracy trend should be consistent with that of MALV, because a high LV indicates strong class separability. As expected, the trends are not perfectly

Fig. 8 Series image classifications accuracies: (a) Experiment 1 based on IKONOS images and (b) experiment 2 based on Landsat ETMþ images. Journal of Applied Remote Sensing

073565-9


Vol. 7, 2013


consistent, because of the disturbance of the random effects of natural landscape and the complexity of a remote sensing image. For example, in experiment 1, as shown in Figs. 6(a) and 8(a), an image with 1-m spatial resolution has a high ALV but a low classification accuracy. There is a similar conflict in experiment 2. One reason for this is that images with very high spatial resolution will lead to high heterogeneity within class and thus to low classification accuracy. To explain the reasons and reveal the intrinsic relation among spatial resolution, MALV, and classification accuracy, each of the two study regions is repartitioned into six subregions, and the validation of the MALV method is given in Sec. 4.4.

4.4 Verification and Analysis 4.4.1 Partitions of the study regions As a matter of fact, just as Ming et al.13 emphasized, the MALV method is suitable for image with a single land use type. To reverify this idea, we partitioned the study regions into six subregions, as shown in Fig. 9. Sub-E, Sub-F, Sub-E* and Sub-F* are mainly covered by building area (the landscape type is simple), and this landscape type is dominant for both experiments 1 and 2. To illustrate the overall spectral response of these subregions, image histograms of the experiments’ subregions are shown in Figs. 10 and 11.

4.4.2 Calculation of MALVs of subimages The MALV, MALVAverage , MALVOIF , and MALVPCA of every subimage at different resolutions are calculated and illustrated in Figs. 12 and 13.

4.4.3 Analysis of the experimental results The following conclusions can be drawn according to the experimental results shown in Figs. 12 and 13. 1. All the data in Figs. 12 and 13 visually demonstrate that there are more obvious peaks and troughs in the curves of MALVPCA and MALVPC1 (the contribution α of PC1 of every subimage is between 70% and 90%), though only very small differences are visible between the results of the presented methods of MALV calculation. It can be concluded that MALVPCA and MALVPC1 (if the contribution α is high enough) are more sensitive to changes in spatial resolution. MALVOIF and MALVAverage are not as effective as MALVPCA and MALVPC1 for indicating the optimal spatial resolution of multispectral images.

Fig. 9 Partitions of the pan-sharpened experimental images: (a) IKONOS and (b) Landsat. ETMþ. Journal of Applied Remote Sensing

073565-10


Vol. 7, 2013


Fig. 10 Image histograms of the six subregions (IKONOS).

2. The experimental results shown in Figs. 12(c), 12(e), 12(f), 13(d), 13(e), and 13(f) prove that the MALV method is suitable for images with simplex landscape type. This agrees with the conclusion of Ming et al.13 These results also illustrate that MALVPCA of the subimage whose landscape type is similar to the dominating landscape of the original image is significantly referential for selecting the optimal spatial resolution. 3. For experiment 1, as shown in Fig. 8(a), the consistency of the changing trends between MALVPCA ∕MALVPC1 of the subimages (especially sub-C, sub-E, and sub-F) and the average classification accuracies is strong, because the peaks all appear at 3 to 5 m and from 7 to 10 m. This shows that the spatial resolutions of 3 to 5 m and 7 to 10 m are optimal for land use research of this region. By measuring the pan-sharpened image of 1-m spatial resolution, it is found that both 3 to 5 m and 7 to 10 m are the usual widths of roads, bungalows, and some buildings. This result is similar with to that found by Ming et al.,13 whose primary experimental image was a panchromatic one with a size of 2000 × 2000 and a spatial resolution of 1 m. 4. For experiment 2, the changing trend consistency between MALVPCAðPC1Þ of the subimages (especially sub-D*, sub-E*, and sub-F*) and average classification accuracies shown in Fig. 8(b) is strong, because the peaks all appear at 45 to 75 m, 105 to 150 m, and 210 m, and the troughs all appear at 90 and 195 m. This shows that the spatial resolutions of 45 to 75 m, 105 to 150 m, and 210 m are optimal for landscape Journal of Applied Remote Sensing

073565-11


Vol. 7, 2013


Fig. 11 Image histograms of the six subregions (Landsat ETMþ).

research of this region. The multipeaks are the direct effect of the MAUP (aggregation and spatial resolution of remote sensing pixels27). The principal pattern elements in the scene used here are buildings, city blocks, agricultural fields, and forested/lake areas. By measuring the image, the sizes of these elements are approximately 15 to 50 m for the houses, 100 to 400 m for the city blocks, and 100 to 250 m for the agricultural fields. The issue of aggregation of measurements must be considered in discussing spatial scale,28 and the MALV method provides a feasible approach for quantitative research of the MAUP. 5. Quantitatively and statistically, to indicate the statistical difference and significance between the presented methods, the correlations between the computation results (MALVs of sub-C, sub-E, sub-F, and sub-D*, sub-E*, sub-F*) and the classification accuracies (the average values of the two series of classifications) are calculated. Figure 14 indicates that there is a positive correlation between the MALVs and the classification accuracies with the change of spatial resolution. For experiment 1, as shown in Fig. 14(a), the correlation coefficients between MALVPCAðPC12Þ and the classification accuracies are greater than 56% (close to strong correlation). For experiment 2, as shown in Fig. 14(b), the correlation coefficients between all MALVs (except PC6) and the classification accuracies are greater than 75% (strong correlation). These results support the idea that MALV based on PCA is effective for reflecting the scale effect of Journal of Applied Remote Sensing

073565-12


Vol. 7, 2013


Fig. 12 MALVs of the subimages (IKONOS).

spatial resolution and thus is useful for selecting the optimal spatial resolution of a multiband image. 6. However, the quantitative correlation analysis shown in Fig. 14(b) also shows that the correlation between MALVPCAðPC1Þ and classification accuracies is not stronger than that of the other proposed method, which seemingly suggests that MALVPCA is not distinctly superior to the other proposed method. In fact, the reasons for this are complex, such as the uncertainty of classification accuracy, high band correlations of multispectral and even hyper-spectral data (as shown in Table 2), and the impact of image resampling in resolution degradation. However, the PCA-based MALV method for pixel-based scale selection is still feasible according to experimental results shown in Fig. 13(d)–13(f). Additionally, some minor inconsistencies in the changing trends between MALVPCA ∕ MALVPC1 and average classification accuracies are analyzed as follows. 1. An important reason that the image with a spatial resolution of 1 m has a high ALV but low classification accuracy is the complexity of the high-spatial-resolution image. First, Journal of Applied Remote Sensing

073565-13


Vol. 7, 2013


Fig. 13 MALVs of the subimages (Landsat ETMþ).

Fig. 14 The correlations between different MALVs and classification accuracies in (a) experiment 1 and (b) experiment 2. Journal of Applied Remote Sensing

073565-14


Vol. 7, 2013


different spectral responses for the same object, and the same spectral response for different objects, will lead to low separability of training sites, especially in the high-spatialresolution image. Markham and Townshend29 and Marceau and Hay30 found that an increase in within-class spectral variability will make per-pixel classifiers confusing. For example, a dark building roof, uncultivated farmland, and barren land are sources of confusion in classification. Second, because of the existence of mixed pixels and shadows, many dark natural objects (especially their borders) and shadows are classified as dark artificial terrain. The results prove again that pixel-based classification is problematic for very-high-resolution image classification, so texture-based or OBIA-based classification is more suitable for this situation. This conclusion is similar to those reached by Chen et al.26 2. There is a large area of water and woodland in the experimental image sub-B, which results in the flatly descending trends in MALV, MALVAverage , MALVOIF , and MALVPCA , as shown in Figs. 2(b) and 9(b). The presence of these features is another reason for some inconsistencies in the trends between MALVPCA ∕MALVPC1 and the average classification accuracies. Ignoring the impact of water bodies and woodlands, the experimental results based on sub-E, sub-F, sub-E*, and sub-F* are beneficial for getting the conclusions about the MALV method. 3. For experiment 2, there are more strong fluctuations on the MALVPC6 curve. However, the correlations between MALVPC6 and classification accuracy are very low. The reason is that the spatial resolution of PC6 is enlarged from 60 to 15 m after image fusion (image resampling), which inevitably impacts the statistical results. Another important reason is the difference between spectral reflectance rates of different objects on PC6 is minor, which means the correlation between MALVPC6 and classification accuracy (based on PC743 and PC432) is lower than others.

5 Conclusions With the progress in remote sensor technology and optics compensation techniques, remote sensing imaging with not only high spatial resolution but also high spectral resolution is possible, so scale selection methods for multispectral and even hyper-spectral images should be considered. This paper has discussed MALV improvements based on band selection for pixel-level scale selection in multiband remote sensing images. Experimental results show that MALV based on PCA is more sensitive to spatial resolution when the difference between band correlations is large. Thus, the PCA-based MALV method is more effective for reflecting the changing trends in local image variances with resolution, and it is supportive for selecting the optimal spatial resolution of multiband or hyper-band images (if the image band number is small or PCA is not necessary, band combinations based on the OIF or with low correlations are also a viable solution). Further classification experiments prove that the trend of classification accuracy plotted against spatial resolution is basically consistent with that of the PCA-based MALV of the subimage whose landscape type is similar to the dominating landscape of the original image. So the MALV method is more suitable for an image with a single landscape type. At the same time, the multipeaks of the MALV calculation results and classification accuracies also reflect the substance of the MAUP, and the MALV method provides a feasible approach for quantitative research of the MAUP. Additionally, the following points should be emphasized: 1. As Hay31 and Hyppanen32 indicated, there is no single absolute optimal scale that can correctly and comprehensively describe the shape and size of an object. Tran et al.8 said that the range of optimal spatial resolution for urban objects or districts is closely related to the urban structure and spectral variability. Therefore, the value of this research is to interpret theoretically the relationships among spatial resolution, local variance, and classification accuracy, but not to calculate the absolute optimal spatial resolution. 2. The improved MALV method for selecting the optimal spatial resolution of a multispectral image is especially suitable for images that contain a simplex landscape type, Journal of Applied Remote Sensing

073565-15


Vol. 7, 2013


because the disturbances caused by landscape complexity in such an image is slight. However, when the spatial extent of the image data is large, the MALV of the subimage whose landscape type is similar to the dominating landscape of the original image is significantly referential for selecting the optimal spatial resolution. 3. The ideal experimental data should be an image with many spectral bands at high spatial resolution. Though the high-spatial-resolution image data source is limiting, the experimental validity employs data from two different images. This influences the continuity of the analysis, because ALV comparison is suitable for only one specific image. 4. A limitation of this research is that the influence of nearest neighbor image resampling in degrading the resolution is quantitatively unknown in our experiments, because the resampling results can not fully substitute for direct data acquisition by remote sensor, and they are only a simulation based on remote sensing data. In other words, the image resampling process can not truly reflect the information aggregation with change of observation scale. Theoretically, it is quite reasonable to use original image data with a different spatial resolution directly captured by different multispectral remote sensors. However, such ideal experimental data are currently unavailable. 5. Similar to the conclusions of Chen et al.,26 Markham and Townshend,29 and Marceau and Hay,30 very high spatial resolution will lead to high heterogeneity within class and thus to low separability and low classification accuracy. The classification results prove again that pixel-based classification is problematic for very-high-resolution image classification, so texture-based or OBIA-based classification is more adaptive for this situation. Additionally, qualitatively analysis shows that too low spatial resolution will lead to high heterogeneity within the training sites based on the same AOI. Therefore, selecting the optimal spatial resolution is significant for remote sensing applications.

Acknowledgments This research was supported by the Fundamental Research Funds for the Central Universities, the National Natural Science Foundation of China (Grant No. 41001259), and the Open Fund of the State Key Laboratory of Remote Sensing Science (Grant No. OFSLRSS201008). The authors especially appreciate the anonymous reviewers for their helpful comments.

References 1. P. Han et al., “Selection of optimal scale in remotely sensed image classification,” J. Rem. Sens. 14(3), 507–512 (2010). 2. S. Openshaw, “The modifiable areal unit problem,” in Concepts, and Techniques in Modern Geography, No. 38, GeoBooks, Norwich, England (1984). 3. C. E. Woodcock and A. H. Strahler, “The factor of scale in remote sensing,” Rem. Sens. Environ. 21(3), 311–332 (1987), http://dx.doi.org/10.1016/0034-4257(87)90015-0. 4. D. Ming et al., “Modified local variance based method for selecting the optimal spatial resolution of remote sensing image,” in Proc. 18th Int. Conf. Geoinformatics, IEEE, Beijing, China (2010). 5. P. K. Bøcher and K. R. McCloy, “The fundamentals of average local variance—part I: detecting regular patterns,” IEEE Trans. Image Proc. 15(2), 300–310 (2006), http:// dx.doi.org/10.1109/TIP.2005.860623. 6. P. K. Bøcher and K. R. McCloy, “The fundamentals of average local variance—part II: sampling simple regular patterns with optical imagery,” IEEE Trans. Image Proc. 15(2), 311–318 (2006), http://dx.doi.org/10.1109/TIP.2005.860621. 7. W. Nijland et al., “Optimizing spatial image support for quantitative mapping of natural vegetation,” Rem. Sens. Environ. 113(4), 771–780 (2009), http://dx.doi.org/10.1016/j.rse .2008.12.002. 8. T. D.-B. Tran et al., “Optimizing spatial resolution of imagery for urban form detection—the cases of France and Vietnam,” Rem. Sens. 3(10), 2128–2147 (2011), http://dx.doi.org/ 10.3390/rs3102128. Journal of Applied Remote Sensing

073565-16


Vol. 7, 2013


9. P. J. Curran, “The semi-variogram in remote sensing: an introduction,” Rem. Sens. Environ. 24(3), 493–507 (1988), http://dx.doi.org/10.1016/0034-4257(88)90021-1. 10. P. M. Atkinson and P. Curran, “Choosing an appropriate spatial resolution for remote sensing investigations,” Photogramm. Eng. Rem. Sens. 63(12), 1345–1351 (1997). 11. P. Curran and P. M. Atkinson, “Issues of scale and optimal pixel size,” in Spatial Statistics for Rem. Sensing, A. Stein, F. van der Meer, and B. Gorte, Eds., pp. 115–133, Kluwer Academic, Dordrecht (1997). 12. P. M. Atkinson and P. J. Curran, “Defining an optimal size of support for remote sensing investigations,” IEEE Trans. Geosci. Rem. Sens. 33(3), 768–776 (1995), http://dx.doi.org/ 10.1109/36.387592. 13. D. Ming et al., “Modified ALV for selecting the optimal spatial resolution and its scale effect on image classification accuracy,” Math. Comput. Model. 54(3–4), 1061–1068 (2011), http://dx.doi.org/10.1016/j.mcm.2010.11.036. 14. P. S. Chavez, G. L. Berlin, and L. B. Sowers, “Statistical method for selecting Landsat MSS ratios,” J. Appl. Photogr. Eng. 8(1), 23–30 (1982). 15. M. Beaudemin and K. B. Fung, “On statistical band selection for image visualization,” Photogramm. Eng. Rem. Sens. 67(5), 571–574 (2001). 16. A. Buhe et al., “Land cover of oases and forest in Xinjiang, China retrieved from ASTER data,” Adv. Space Res. 39(1), 39–45 (2007), http://dx.doi.org/10.1016/j.asr.2006.02.056. 17. A. M. Qaid and H. T. Basavarajappa, “Application of optimum index factor technique to Landsat-7 data for geological mapping of north east of Hajjah, Yemen,” Am. Eurasian J. Sci. Res. 3(1), 84–91 (2008). 18. E. Arzuaga, L. O. Jimenez-Rodriguez, and M. Velez-Reyes, “Unsupervised feature extraction and band subset selection techniques based on relative entropy criteria for hyperspectral data analysis,” Proc. SPIE 5093, 462–473 (2003), http://dx.doi.org/ 10.1117/12.485942. 19. H. Du et al., “Band selection using independent component analysis for hyperspectral image processing,” in Proc. 32nd Applied Imagery Pattern Recognition Workshop, pp. 93–98, IEEE (2003). 20. B. Paskaleva and M. Hayat, “Optimized algorithm for spectral band selection for rocktype classification,” Proc. SPIE 5806, 131–138 (2005), http://dx.doi.org/10.1117/12 .602995. 21. P. Bajcsy and P. Groves, “Methodology for hyperspectral band selection,” Photogramm. Eng. Rem. Sens. 70(7), 793–802 (2004). 22. S. Wang and C. I. Chang, “Linearly constrained band selection for hyperspectral imagery,” Proc. SPIE 6233, 62332B (2006), http://dx.doi.org/10.1117/12.665286. 23. S. Cai et al., “Band selection of hyperspectral images based on bhattacharyya distance,” Wsear Trans. Inf. Sci. Appl. 7(6), 1165–1175 (2009). 24. M. A. Omam and T.-A. Farah, “Band selection of hyperspectral-image based weighted independent component analysis,” Opt. Rev. 17(4), 367–370 (2010), http://dx.doi.org/ 10.1007/s10043-010-0067-7. 25. D. Chen and D. Stow, “The effect of training strategies on supervised classification at different spatial resolutions,” Photogramm. Eng. Rem. Sens. 68(11), 1155–1161 (2002). 26. D. Chen, D. Stow, and P. Gong, “Examining the effect of spatial resolution on classification accuracy: an urban environmental case,” Int. J. Rem. Sens. 25(11), 2177–2192 (2004), http://dx.doi.org/10.1080/01431160310001618464. 27. M. D. Nelson et al., “Effects of satellite image spatial aggregation and resolution on estimates of forest land area,” Int. J. Rem. Sens. 30(8), 1913–1940 (2009), http://dx.doi.org/ 10.1080/01431160802545631. 28. J. Ju, S. Gopal, and E. D. Kolaczyk, “On the choice of spatial and categorical scale in remote sensing land cover classification,” Rem. Sens. Environ. 96(1), 62–77 (2005), http://dx.doi .org/10.1016/j.rse.2005.01.016. 29. B. Markham and J. R. G. Townshend, “Land cover classification accuracy as a function of sensor spatial resolution,” in Proc. 15th Int. Symp. on Remote Sensing of Environment, pp. 1075–1090, Ann Arbor, MI (1981). Journal of Applied Remote Sensing

073565-17


Vol. 7, 2013


30. D. J. Marceau and G. J. Hay, “Remote sensing contributions to the scale issue,” Can. J. Rem. Sens. 25(4), 357–366 (1999). 31. G. J. Hay, “Multiscale object-specific analysis: an integrated hierarchical approach for landscape ecology,” Ph.D. Thesis, Univ. of Montreal (2002). 32. H. Hyppanen, “Spatial autocorrelation and optimal spatial resolution of optical remote sensing data in boreal forest environment,” Int. J. Rem. Sens. 17(17), 3441–3452 (1996), http:// dx.doi.org/10.1080/01431169608949161. Biographies and photographs of the authors not available.

Journal of Applied Remote Sensing

073565-18


Vol. 7, 2013

Modified average local variance for pixel-level

Modified average local variance for pixel-level

Suggest Documents

modified minimax quadratic estimation of variance ...

Intensity-based modified Doppler variance algorithm dedicated for ...

Modified exponentially weighted moving average (EWMA) control ...

A RED MODIFIED WEIGHTED MOVING AVERAGE

Estimating Average and Local Average Treatment Effects ... - CiteSeerX

Modified Minimum Variance Approach for State and ...

Non-local bispectra from super cosmic variance

Phenotypic variance explained by local ancestry in

Minimal Weighted Local Variance as Edge Detector for Active Contour

Minimizing the Variance of a Weighted Average - Scientific Research ...

Detrending Moving Average variance: a derivation of the scaling law

A Local Average Consensus Algorithm for Wireless ... - CiteSeerX

Local bond average for the size and temperature dependence of ...

Generalization of the Total Variance Approach to the Modified Allan ...

A modified two-factor multivariate analysis of variance ... - Springer Link

Intensity-based modified Doppler variance algorithm ... - OSA Publishing

Enhanced modified moving average analysis of T-wave alternans ...

Adaptive Substring Extraction and Modified Local NBNN Scoring for ...

Modified Differential Evolution with Local Search Algorithm for Real ...

Combination of Morphological, Local Binary Pattern Variance and ...

Local Variance-Controlled Forward-and-Backward ... - IEEE Xplore

Phenotypic variance explained by local ancestry in ... - Frontiers

Minimum Local Emissivity Variance Retrieval of Cloud ... - AMS Journals

Average local ionization potential within the framework of the electron ...