EFFECT OF SPATIAL AND GRAY SCALE RESOLUTIONS ON SATELLITE IMAGERY OF URBAN AREAS

Transcription

1 EFFECT OF SPATIAL AND GRAY SCALE RESOLUTIONS ON SATELLITE IMAGERY OF URBAN AREAS Ram M. Narayanan Center for Electro-Optics Department of Electrical Engineering University of Nebraska Lincoln, NE Tel: (402) Fax: (402) Abstract Satellite imagery is well-suited for monitoring the growth and development of urban areas in a synoptic manner. However, for meaningful interpretation of urban features such as roads and buildings, adequate spatial as well as the gray-scale resolutions are required of the imagery. Poor spatial resolution tends to merge smaller features into larger features, while poor gray-scale resolution causes merging of neighboring features having low radiometric contrast. On the other hand, excessively good resolutions in an image, while preserving detail and providing high information content, may not always be necessary for analysis. There exist, therefore, optimum spatial and gray-scale resolutions, depending upon the nature of the task, that allow the analyst to utilize the image data without adding unnecessary information and resources. Our approach to quantifying image information content is based upon classification accuracy. Pixels get misclassified upon degrading the spatial or the gray-scale resolution, thereby reducing the image information content. We have developed negative exponential models for characterizing the image information content as a function of spatial and gray-scale resolution that is applicable for SPOT imagery of urban areas. Based upon the model formulation, optimum resolutions can be deduced. Keywords: gray-scale resolution, spatial resolution, urban remote sensing 1. Introduction Remote sensing images are formed by recording the reflected energy or radiance from a target scene. In remote sensing terminology, an image refers to a two dimensional representation of the energy reflected from or emitted by the scene. Modern remote sensing sensors use digital systems to store and process the image data. A typical digital image shown in Figure 1 consists of a two dimensional array of pixels, each with a gray level. The pixel coordinates are labeled (,) on the image for the coordinates (x,y) on the ground cell. If n b represents the number of bits to represent the digital image, then n may take an integer value between 0 and (2 n b-1).

2 Figure 1: Scene to image transformation. Each pixel in the image represents the average reflectance or emittance of the target on the ground: darker areas representing lower values, while brighter areas represent higher values. The brightness of each pixel depends on the size of the scatterers within the pixel, properties of targets contained within the pixel, the wave polarization, and the viewing angle, and the target's chemical composition. Brightness also depends on surface roughness relative to wavelength. Remote sensing images acquired in various spectral bands are used to estimate certain geophysical parameters or detect the presence or extent of geophysical phenomena. Examples include the estimation of soil moisture or delineation of the ice-water boundary in polar regions using synthetic aperture radar imagery. In a majority of cases, the raw image acquired by the sensor is processed using various operations such as filtering, compression, enhancement, and others. In all of these cases, the analyst is attempting to maximize the information content in the image to fulfill the end objective. While this appears deceptively simple, there are a variety of issues that need to be addressed in order that available information content is maximized for a particular application. Remotely sensed images have information of varying value. Different methods of sensing and processing the data are needed to extract the maximum amount of information from the image effectively. Since information of high value is not always the easiest or most effectively obtained, an analyst needs to identify categories of high information value against the kind of information sensed and identified. The information content needs to be quantified before one attempts to perform operations to increase its value for a particular application. However, information content is not easily quantifiable. Various methodologies have been proposed to characterize the information content of remotely sensed data (Dowman and Peacegood, 1989; Kalmykov, Sinitsyn, Sytnik, and Tsymbal, 1989; Oliver, 1991; Blacknell and Oliver, 1993), and relate it to several variables such as resolution (both radiometric as well as spatial), scale of variability of the geophysical parameter of interest, image statistics, etc. It is also important to recognize that the same image

3 may contain different amount of information depending on the application. To illustrate this point, consider a digital image of a scene containing targets and features of different sizes and extents. Although the spatial resolution of the system may be poor, it may still be useful in identifying those targets and features of interest as long as their sizes are much larger than the sensor spatial resolution. We can then say that the information content of the image for identifying targets and features is high. On the other hand, it may be impossible to identify targets and features of sizes much smaller than the sensor spatial resolution using the same image. In this case, we say that the information content of the image for identifying targets and features of interest is low. Thus, the same image contains high information content for delineating large sized targets, but low information content for identifying small sized targets. Choosing an appropriate and meaningful spatial resolution for a particular application is therefore an important task for the remote sensing analyst (Atkinson and Curran, 1997). In addition, consider a photogrammetric image of a scene containing different types of terrain. Despite the poor gray-scale resolution of the image, it may still be useful in classifying different terrain types, as long as the radiometric differences between the means of the individual terrain types are larger than the gray-scale resolution. We can then say that the information content of the image for classifying terrain types is high. On the other hand, if it is desired to estimate the amount of soil moisture in a bare soil area with a high degree of accuracy, the poor gray-scale resolution may be unable to yield the accuracy required for this purpose. In this case, we say that the information content of the image for soil moisture estimation is low. However, in a typical application, the information content of the same image may lie somewhere between the above two extremes. The number of gray levels needed to properly digitize an image for visual quality depends upon the characteristics of the human eye. It has been determined that the eye can typically resolve between gray levels without succumbing to false contour detection (Weeks, 1996). In general remote sensing applications, 256 gray levels (or 8-bits) are used to represent an image. However, if only 16 levels (or 4-bits) are adequate without sacrificing quality, two images can be stored in place of one, thereby doubling the storage capacity. Thus, an understanding of the effects of gray-scale resolution on image quality and interpretability is important from the standpoint of resource allocation. Table 1 shows typical generic applications that make use of remote sensing imagery, and lists specific examples in each generic category. One logical approach for quantification of information content may be based on classification accuracy, as classification procedures are used to extract information about the scene from the remotely sensed data. In this paper, we propose simple mathematical models to relate information content in urban images based on classification accuracy to the spatial resolution as well as gray-scale resolution. The models were tested on SPOT images of two urban areas chosen for analysis: Washington and Moscow. 2. Proposed information content model based on scene classification Classification of images is performed to delineate areas in the image possessing common features. This operation gives information about the scene in the image, rather than just the numerical data. Image classification produces a thematic map of the region where the themes include vegetation, soil, water bodies, urban features, etc. A classified image consists of labels of

4 Table 1: Typical applications using remote sensing imagery. Generic Application Edge Detection Specific Examples Ice-water edge in polar regions Water-vegetation edge in wetlands Classification Vegetation types in mixed forest Soil types in desert regions Feature Detection Landmines in inhomogeneous soil Targets in cluttered background Parameter Estimation Soil moisture patterns Vegetation biomass variability a particular landcover or type of soil present in the image. By labeling, the data has more informational value than just a set of digital numbers. Multispectral images, which may contain spectral characteristics from several bands with at least 8 bits/pixel/band, are reduced to a single band informational image with less than 8 bits/pixel. Spatial resolution of the image and scale of the target of interest are very important parameters in classification of images (Cao and Lam, 1997). The spatial resolution determines the degree and type of information that can be extracted from an image. For example, TM imagery, which has a spatial resolution of 30 m can be used to extract the types of crops, trees, urban areas in Nebraska, whereas the AVHRR imagery, which has a resolution of 1 km cannot be used for this purpose, but in turn can be used to provide global land cover. Numerous textural measures are used to characterize the local and global variability in a remotely sensed image. These measures include the mean, the standard deviation with respect to windows of various sizes, gradients in different directions and, correlations between textural parameters at different locations (Haralick, Shanmugam and Dinstein, 1973; Tamura, Mori and Yamawaki, 1978, Tomita and Tsuji, 1990; Potopav, Galkina, Orleva, and Khlyavich, 1991; Shen and Srivastava, 1996). Radar image simulations were performed at C-Band frequency at an incidence angle of 30( in order to understand the effect of spatial resolution and spatial extent of the object on the image information content (Narayanan, Desetty, and Reichenbach, 1997), and the salient results are briefly described. The local statistics of the image was used to identify targets of various spatial extents in a cluttered background. The local mean (Lee, 1980) was used in classifying a pixel as belonging to either the target or the background using a distance measure based on mean radar reflectances. The targets were chosen to represent both small as well as large differences between their mean radar reflectances and that of the clutter. Spatial resolution was degraded by convolving a local mean filter with equal weights of different window sizes for the images, and the average value of local mean for each target was computed using the averaging aggregation method (Bian and Butler, 1999). As the size of the window increased, more of the background pixels were mixed with the target pixels and the mean reflectance of the

5 target approached the background. The rate of advance depended on the size of the target under consideration: the target mean attained the background mean faster for the small sized targets than for the large sized targets. Typical images were generated using the above guidelines to provide a clear understanding of the effect of spatial resolution. As the spatial resolution improves and the pixel size, R, reduces, the amount information to delineate the spatial features of targets increases. We obtain high information when the pixel size approaches zero, while the information content reduces to zero at pixel size of, i.e., no information. The information content data from the simulated images was plotted versus the pixel size. It was found that it followed an exponential decline. Hence, we model the information content, I, as a function of pixel size, R, as Iexp{ kr n } (1) where k and n are the best-fit parameters related to the interpretability of the image, as well as the contrast between the target and the background (Narayanan, Desetty, and Reichenbach, 2001). The above formulation is intuitively satisfying, since the information content is unity for R=0, and is zero for R =. Using simulations to provide data points, various best fit values can be computed from the above equations. Rearranging and taking natural logarithm on both sides, we get ln(1/i)kr n (2) Again, taking the natural logarithm, we have ln(ln(1/i))lnknlnr (3) Equation (3) is in the form a linear equation Y=mX+C, where Y=ln(ln(1/I) ) and X=lnR. The slope and intercept from Equation (3) can be used to find the values of k and n for each case. The slope m is equal to the parameter n, while the intercept C is equal to ln k, from which k=exp(c). Before proposing a model for the information content as a function of gray-scale resolution, various simulation experiments were performed on Landsat TM and SIR-C SAR images. For the SAR images, speckle was also included. Contrast-enhanced 8-bit images were generated using a total of 5, 10, and 15 classes of terrain types, for various spatial arrangements. For each image, the gray-scale resolution was degraded, and the image reclassified. The classification accuracy, used as a measure of information content, was plotted as a function of the number of gray-levels. It was observed in all of the images that the rate of fall of the information content appeared to be negative exponential in nature, although with different shape factors. Based upon the results of our simulation experiments, the following model for information content I is proposed (Narayanan, Sankaravadivelu, and Reichenbach, 2000). Iexp k L l n (4) l 2 In Equation (4), L is the number of gray-levels in the original image, or its gray-scale resolution, while l is the gray-scale resolution of the degraded image. Thus, 0 l L. Also k and n are best-fit sensor specific constants.

6 While developing the above model, we assumed that a bi-level (l=2) image does not convey any information about the textural features of the scene. In other words, the information content of such an image is zero. It is important to note that our formulation is intuitively appealing, since for l=l, I=1, i.e., all the information is preserved, while for l=2, I=0, which indicates that the degraded image does not furnish any information about the textural aspects of the scene. From our model described by Eq. (4), we obtain the relation, ln(ln(1/i m )) = ln(k) + nln(g), where L 1 G =. This is the equation of a line of the form Y = mx + c, where m and c are the slope l 2 and y-intercept of the line respectively. For the above relation, ln(ln(1/i m )) and ln(g) correspond to Y and X. Hence we can estimate k=exp(c) and n=m from the best-fit line. Later, k and n are substituted back into the model to obtain the information I at any given gray-scale resolution l. 3. Image Analysis and Results 3.1 Site description SPOT images of urban areas were downloaded from the web for analysis. These 8-bit images had a resolution of 20 m. The total image size selected for analysis was 300 pixels 300 pixels; thus, the image was 6 km 6 km in extent. All three bands, viz., Band 1 ( µm), Band 2 ( µm), and Band 3 ( µm), were used to generate the reference or "ground truth" image. The spatially and gray-scale degraded Band 1 image was compared against this reference image. The color composite RGB images using all three bands are shown in Figure 2, and represent (a) vicinity of Washington, DC, in October 1990; and (b) vicinity of Moscow, Russia, in May The strong heterogeneity in the images is clearly seen, especially the wider roads that demarcate specific area The color composite image of Washington, located at 38( 9' N latitude and 77( 1' W longitude, is shown in Figure 2(a). The network of overpasses and roads is clearly seen in the image. Also seen are both the urban features, such as buildings (seen in blue), and vegetation (seen in red). The color composite image of Moscow, located at 55( 33' N latitide and 37( 22' E longitude, is shown in Figure 2(b). The city is intersected by the Moscow River, clearly seen meandering through the image. As before, both urban features and vegetative regions can be seen. 3.2 Procedure for inducing spatial and gray-scale resolution degradation The spatial resolution in the original Band 1 image selected for analysis for both cities was equal to 20 m. In order to induce spatial resolution degradation, a convolution filter with equal weights with varying sizes was used on the original image in order to obtain spatially degraded images. These filters were of sizes 3 3, 4 4, 5 5, 7 7, 9 9, 11 11, 15 15, 16 16, 17 17, and Details of the procedure are fully described in Narayanan, Desetty, and Reichenbach (2001).

7 Proc. Computers in Urban Planning and Urban Management (CUPUM) Conference (a) (b) Figure 2: Color composite SPOT images of (a) Washington, DC, and (b) Moscow, Russia. The original image was an 8-bit image, with the number of gray-levels L being equal to 256. Gray-scale degraded images with l =128, 64, 32, 16, 8, 4, and 2, were generated by performing an integer division of the value of each pixel in the original image by corresponding powers of 2, followed by rescaling to l =256. Details of the procedure are described in detail in Narayanan, Sankaravadivelu, and Reichenbach (2000). In a few cases, both spatial and gray-scale resolutions were simultaneously degraded to study the combined effect. The spatial resolution was degraded first, and then the gray-scale resolution was degraded. 3.3 Analysis of results The analysis of information content was carried out on the basis of the classification accuracy. The classification accuracy was considered to be a reasonable parameter to characterize the information content in an image, because a thematic map contains information about the different classes in a scene. Misclassification of pixels tells us that we are losing information about the scene. An unsupervised classification was performed for each Band 1 image (at every spatially and/or gray-scale degraded resolution) using the K-means approach for three number of classes, Nc, equal to 5, 10, and 15. The reference classified image for each city was obtained using all three bands, and it was with this classified image that comparisons were made for computing the classification accuracy. Since we are investigating the interpretability of classified remote sensing images, we need to compare the reference image with the classified degraded image to ascertain the latter's information content. A loss in information would occur whenever a pixel in the classified degraded image is misclassified in comparison to the same pixel in the ground-truth image. Hence classification accuracy would be a good measure of information.

8 In order to measure classification accuracy, we define a quantity called the modified mean absolute difference, E, as given below. E 1 N O 1 i0 (5) N l N N Z 1 j0 / ij w In Equation (5), N l and N w are the length and width of the image in pixels, while / ij takes a value of 0 if the pixel at the (i,j)th location in the degraded image is correctly classified in comparison to the reference ground-truth image. If not, / ij takes a value of 1, which means that the pixel at the (i,j)th position in the degraded image has been incorrectly classified. Therefore, the mean of all /s over the area of the image yields E, the modified mean absolute difference. The information content I, is computed using, I1 E (6) It is clear from the above equations that both E and I will be real numbers in the range A value of I=1 indicates that the classified degraded image is identical in interpretability to the reference image, while I=0 indicates that the classified degraded image has no interpretability value for the scene that it represents. Spatial resolution degradation: Figure 3 shows the effect of spatial resolution degradation on the classification of the Washington image when the number of classes equals 5. 8-bit images are shown for pixel size R = 1, 4, and 16, where R = 1 represents the original resolution of 20 m. From the figure, we note that spatial resolution degradation has a very strong influence on classification accuracy, and pixels get increasingly misclassified as R increases. (a) (b) (c) Figure 3: Classified Washington image for N c = 5, l = 8, and (a) R = 1, (b) R = 4, (c) R = 16. Figure 4 shows the actual and modeled information content as a function of pixel size for number of classes equaling 5 for (a) Washington, and (b) Moscow. The value of the best-fit model constants k and n for the spatial model, as described by Equation (1), are shown in Table 2 for the number of classes 5, 10, and 15.

9 (a) (b) Figure 4: Plot of information content I as a function of pixel size R for (a) Washington, and (b) Moscow. The number of classes, N c is 5. The line shows the model, while the asterisks are the true values. The interesting thing to note from Table 2 is that the k and n values for both cities are nearly the same for all three values of N c. This can be seen more clearly on comparing the effect of pixel size on information content for both cities on the same plot, as shown in Figure 5 for (a) N c = 5, (b) N c = 10, and (c) N c = 15. Figure 5 also reveals that on using Band 1 alone, the information content at the best spatial resolution (20 m) is approximately 0.68 for N c = 5, 0.44 for N c = 10, and 0.35 for N c = 15. Table 2: Model constants k and n for spatial resolution model. N c = 5 N c = 10 N c = 15 Image k n k n k n Washington Moscow Figure 6 shows more clearly that the information content falls with increasing number of classes, since with a larger number of classes there is a greater chance that a pixel may get misclassified. The plots are shown for (a) Washington, and (b) Moscow.

10 (a) (b) (c) Figure 5: Plot of modeled information content I as a function of pixel size R for Washington and Moscow for (a) N c = 5, (b) N c = 10, and (c) N c = 15. Gray-scale resolution degradation: Figure 7 shows the effect of gray-scale resolution degradation on the classification of the Washington image when the number of classes equals 5. Images are shown for bit lengths l = 8, 6, and 4, where l = 8 represents the original 8-bit resolution. From the figure, it is noted that the gray-scale resolution has a weaker influence on classification accuracy, with almost no perceptible difference between l = 8 and l = 6.

11 (a) (b) Figure 6: Plot of modeled information content I as a function of pixel size R for (a) Washington, and (b) Moscow. (a) (b) (c) Figure 7: Classified Washington image for N c = 5, R = 1, and (a) l = 8, (b) l = 6, (c) l = 4. Figure 8 shows the actual and modeled information content as a function of number of bits for number of classes equalling 5 for (a) Washington, and (b) Moscow. The value of the best-fit model constants n and k for the spatial model, as described by Equation (4), are shown in Table 3 for the number of classes 5, 10, and 15. We note that there is essentially no difference in the information content between an 8-bit image and a 4-bit image, and this is confirmed by comparing the images in Figure 7(a) and Figure 7(b).

12 (a) (b) Figure 8: Plot of information content I as a function of bits/pixel for (a) Washington, and (b) Moscow. The number of classes N c is 5. The line shows the model, while the asterisks are the true values. We note from Table 3 is that the k and n values for both cities are quite different for all three values of N c. This can be seen more clearly on comparing the effect of number of bits on information content for both cities on the same plot, as shown in Figure 9 for (a) N c = 5, (b) N c = 10, and (c) N c = 15. Table 3: Model constants k and n for gray-scale resolution model. N c = 5 N c = 10 N c = 15 Image k n k n k n Washington Moscow Figure 10 shows more clearly that the information content falls with increasing number of classes, since with a larger number of classes there is a greater chance that a pixel may get misclassified. The plots are shown for (a) Washington, and (b) Moscow.

13 (a) (b) Figure 9: Plot of modeled information content I as a function of pixel size R for Washington and Moscow for (a) N c = 5, (b) N c = 10, and (c) N c = 15. (c) Combined resolution degradation: In Figure 11 is shown the combined effect of spatial and gray-scale resolution degradations for the Washington image for N c = 5. The image on the top left is the original image (R = 1, l = 8), while the image on the bottom right is the image with both the spatial and gray-scale resolution degradations induced (R = 4, l = 6). Other images show the effect of either the spatial (bottom left) or the gray-scale (top right) resolution degradation. This figure clearly indicates that spatial resolution degradation has a more detrimental effect in loss of information compared to gray-scale resolution degradation, for the same advantage in memory resources. Note that the memory requirements are reduced by the same factor of 2 2 = 4 either by degrading the spatial resolution from R = 1 to R = 4, or by degrading the gray-scale resolution from l = 8 to l = 6.

14 (a) (b) Figure 10: Plot of modeled information content I as a function of bits/pixel for (a) Washington and (b) Moscow. (a) (b) (c) (d) Figure 11: Classified Washington image for N c = 5, and (a) R = 1, l = 8, (b) R = 1, l = 6, (c) R = 4, L = 8, (d) R = 4, l = 6.

15 4. Conclusions In this paper, we have studied the effect of degrading the spatial and gray-scale resolutions on the information content of images of urban areas. Empirical negative exponential models have been tested and found to be valid for both cases for both regions. It turns out that for the same savings in memory requirements, it is more advantageous to degrade the gray-scale resolution than the spatial resolution. This is attributed to the fact that urban areas have features that are of the order of m, and degradation of spatial resolution to achieve pixel sizes of 50 m or greater causes regions to merge and blur. 5. Acknowledgments This work was supported by a grant from NASA under the EPSCoR program, awarded through the Nebraska Space Grant Consortium. Technical assistance by S. Ponnappan is appreciated. References Atkinson, P.M. and Curran, P.J. (1997). Choosing an appropriate spatial resolution for remote sensing investigations. Photogrammetric Engineering and Remote Sensing, 63, Bian, I. and Butler, R. (1999). Comparing effects of aggregation methods on statistical and spatial properties of simulated spatial data. Photogrammetric Engineering and Remote Sensing, 65, Blacknell, D. and Oliver, C.J. (1993). Information content of coherent images. Journal of Physics, 26, Cao, C. and Lam, N.S.N. (1997). Understanding the scale and resolution effects in remote sensing and GIS. In Scale in Remote Sensing and GIS, edited by D.A. Quattrochi and M.F. Goodchild (pp ). Boca Raton, Florida: Lewis Publishers. Dowman, I.J. and Peacegood, G. (1989). Information content of high resolution satellite imagery. Photogrammetria, 43, Haralick, R.M., Shanmugam, K.S., and Dinstein, I. (1973). Textural features for image classification. I.E.E.E. Transactions on Systems, Man, and Cybernetics, 3, Kalmykov, A.I., Sinitsyn, Y.I., Sytnik, O.V., and Tsymbal, V.N. (1989). Information content of radar remote sensing systems from space. Radiophysics and Quantum Electronics, 32, Lee, J.S. (1980). Digital image enhancement and noise filtering by use of local statistics. I.E.E.E. Transactions on Pattern Analysis and Machine Intelligence, 2, Narayanan, R.M., Desetty, M.K. and Reichenbach, S.E. (1997). Textural characterisation of imagery in terms of information content. In Proceedings of Ground Target Modeling and Validation Conference (pp ), Houghton, MI, August 1997.

16 Narayanan, R.M., Desetty, M.K. and Reichenbach, S.E. (2001). Effect of spatial resolution on information content characterization in remote sensing imagery based on classification accuracy. International Journal of Remote Sensing, to appear. Narayanan, R.M., Sankaravadivelu, T.S., and Reichenbach, S.E. (2000). Dependence of image information content on gray-scale resolution. Geocarto International, 15, Oliver, C.J. (1991). Information from SAR images. Journal of Physics D: Applied Physics, 24, Popatov, A.A., Galkina, T.V., Orlova, T.I., and Khlyavich, Y.L. (1991). A dispersion method for observing deterministic objects on textured optical and radar images of the earth's surface. Soviet Journal of Communications Technology and Electronics, 36, 1-7. Shen, H.C. and Srivastava, D. (1996). Texture representation and classification: The feature frequency approach. In Advances in Imaging and Electron Physics, Vol. 95, edited by P.W. Hawkes (pp ). San Diego, California: Academic Press. Tamura, H., Mori, S., and Yamawaki, T. (1978). Textural features corresponding to visual properties. I.E.E.E. Transactions on Systems, Man, and Cybernetics, 8, Tomita, F. and Tsuji, S. (1990). Computer Analysis of Visual Textures. Boston, Massachusetts: Kluwer. Weeks, A.R. (1996). Fundamentals of Electronic Image Processing. SPIE Press: Bellingham, Washington, U.S.A.