Dependence of Image Information Content on Gray-scale Resolution Ram M. Narayanan Department of Electrical Engineering Center for Electro-Optics University of Nebraska Lincoln, NE 68588-0511, U.S.A.
T.S. Sankaravadivelu Department of Computer Science & Engineering University of Nebraska Lincoln, NE 68588-0115, U.S.A.
Stephen E. Reichenbach Department of Computer Science & Engineering University of Nebraska Lincoln, NE 68588-0115, U.S.A.
Abstract Remote sensing images acquired in various spectral bands are used to estimate certain geophysical parameters or detect the presence or extent of geophysical phenomena. In a majority of cases, the raw image acquired by the sensor is processed using various operations such as filtering, compression, enhancement, etc. In performing these operations, the analyst is attempting to maximise the information content in the image to fulfill the end objective. The information content in a remote sensing image for a specific application is greatly dependent on the gray-scale resolution of the image. One of the measures to quantify information content is classification accuracy. In such applications, the loss in information content as a result of degraded gray-scale resolution may not be significant. This is because, although the value of a pixel may change as a result of the decrease in the resolution, the same pixel may, in most cases, be correctly classified. Our research reveals that the loss in information is exponential with respect to the number of gray levels. The model is seen to be applicable for Landsat TM and SIR-C images. Using our mathematical model for the information content of images as a function of gray-scale resolution, one can specify an “optimal” gray-scale resolution for an image.
Introduction and Background Digital images acquired by various sensors in remote sensing applications are used to estimate certain parameters or detect the presence or extent of specific phenomena. Examples in the geophysical domain include the estimation of soil moisture or the 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, etc. In all of these cases, the analyst is attempting to assess and maximise 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 the available information content in imagery is enhanced for a specific purpose. One needs to quantify the information content of an image before
one attempts to perform operations to increase this parameter. In general, image information content is a function of several variables, including resolution (both gray-scale as well as spatial), scale of variability of the physical parameter of interest, image statistics, etc. (Dowman and Peacegood, 1989; Kalmykov et al., 1989; Blacknell and Oliver, 1993). It is important to recognize that the same image may contain different information content values depending on the objective. For example, consider an optical image of a scene containing different types of terrain. Despite the poor grayscale 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
Geocarto International, Vol. 15, No. 4, December 2000 Published by Geocarto International Centre, G.P.O. Box 4122, Hong Kong.
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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. Spatial resolution is also an important parameter, and it has been deduced that imagery from different sensors provide varying amounts of information depending upon the physical scale of the features being investigated (Desetty, 1998). The number of gray levels needed to properly digitise an image for visual quality depends upon the characteristics of the human eye. It has been determined that the eye can typically resolve between 40-60 gray levels without succumbing to false contour detection (Weeks, 1996). In general remote sensing applications, 256 gray levels (or 8bits) are used to represent an image. However, if only 16 levels (or 4-bits) are adequate without sacrificing quality, two images can be 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, and is the subject of our research presented in this paper. This work was carried out with the following objectives. 1. To obtain a mathematical model for the information content of remote sensing imagery based on the grayscale resolution. 2. To illustrate the differences between SIR-C and TM images based on the model developed. 3. To arrive at the optimal gray-scale resolution for these two types of remote sensing imagery. Before proposing a model for the information content as a function of gray-scale resolution, various simulation experiments were performed at Landsat TM and SIR-C SAR wavelengths. For the SAR images, speckle was also included. Contrast-enhanced 8-bit images were generated using a total of 5 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 Im is proposed: Im =exp -k L-1 –––– l-2
{ (
n
)}
(1)
In Eq. (1), 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. 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 18
information content of such an image is zero. It is important to note that our formulation is intuitively appealing, since for l = L, Im = 1, i.e., all the information is preserved, while for l = 2, Im = 0, which indicates that the degraded image does not furnish any information about the textural aspects of the scene.
Procedure for Analysis of Data Both TM and SIR-C imagery were analysed. The method of analysis was very similar and consisted of the following steps. Detailed explanations of the methods used in some of these steps are provided in succeeding sections of the paper. (1) Choose the bands in the original image to be used for generating the classified image. (2) Perform an unsupervised classification of the chosen bands of the original image, by using the K-means approach for a number of classes (Nc = 5, 10, 15). (3) Obtain the reference image using classification of the original bands, with a pixel size (R) equal to l, for each value of Nc. (4) Degrade the gray-scale resolution for l = {128, 64, 32,16, 8, 4, 2} for each band and reclassify the image. (5) Compare the degraded image of step (4) with the reference image of step (3) to obtain the information content I. (6) Plot I obtained from step (5) against bits/pixel ranging from 1 to 8. (7) Determine the best-fit constants k and n. (8) Substitute the values of k and n in the model to generate a plot of Im against bits/pixel for values of l ranging from 0 to 255. (9) Compare the plots from steps (6) and (7) to determine the accuracy of the model. Later, the same procedure from step (2) was repeated for spatially degraded original bands at other values of spatial resolution, i.e., for R = 5,11. Spatial degradation was induced using an appropriate equally weighted local mean filter (Lee, 1980). It is imperative to mention that the impact of increasing or decreasing Nc is to divide or aggregate the existing classes into subclasses or superclasses respectively. Hence, when subtle details within existing classes need to be studied, a higher Nc is chosen. The following subsections illustrate the methods used for degrading gray-scale resolution, for measuring I, and for computing the constants k and n.
Degradation of Gray-scale Resolution The original bands had a gray-scale range of L = 256. Gray-scale degraded images with l = {128, 64, 32, 16, 8, 4,2} were generated by performing an integer division of the value of each pixel in the image by powers of 2 corresponding to the seven values of l, followed by rescaling to an l = 256. The rescaling process is effected by the use of the following formula:
P-Pmin S = ––––––––– 255 Pmax-Pmin
(
)
(2)
In Eq. (2), S is the value of the pixel after gray-scale degradation and rescaling, and P is the pixel value before the resealing process and after integer division. Pmax and Pmin are the largest and smallest pixel values present in the image after integer division. Since we performed a contrast-stretch operation on the images before analysis, its minimum and maximum gray levels were always 0 and 255 respectively. Thus, the image resulting after the integer division operation will always have a minimum gray level of 0. Hence in our case, Pmin = 0 and Pmax = l-1. Thus our rescaling formula reduces to: P 255 S = –––– l-L
(
)
(3)
Measurement of information using modified mean absolute difference Since we are not defining or measuring information content of remote sensing images according to Shannon’s information theory (Price, 1984), we use a measure other than those derived from mutual information or entropy based models. These traditional entropy based methods are more suited for quantifying the information content of unclassified images (Frost and Shanmugam, 1983). This is because the probability density functions of unclassified images can be much more accurately determined than those of the classified images, which have a much smaller range of pixel values. 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 groundtruth image. Hence classification accuracy would be a good measure of information. In order to measure classification accuracy, we define a quantity called the modified mean absolute difference, E, as given below. N l -1 N w-1
Σ
j=0
δij
I= 1-E
(5)
It is clear from the above equations that both E and I will be real numbers in the range 0.0-1.0. 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. We also define the Maximum Achievable Information, Imax as that value of I at 8 bits/pixel for each combination of Nc and R.
Determining k and n
Although the degraded images have a dynamic range of L = 256, they have at the most only l different gray-levels. This results in rounding of the pixel values to the largest integer multiple of (25l 6) smaller than itself. However, those pixel values that are multiples of (25l 6), remain unchanged.
1 E =–––––––– Σ Nl Nw i=0
in the degraded image has been incorrectly classified. Therefore, the mean of all δs over the area of the image yields E, the modified mean absolute difference. The information content I, is computed using,
(4)
In Eq. (4), Nl and Nw are the length and width of the image in pixels, while δij 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 ground-truth image. If not, δij takes a value of 1, which means that the pixel at the (i, j)th position
From our model described by Eq. (1), we obtain the relation, ln(ln(1/Im)) = ln(k) + nln(G), where G = (Ll -- 2l ). This is the equation of a line of the form Y = mX + c, where m and c are the slope and y-intercept of the line respectively. For the above relation, In(ln(1/Im)) and ln(G) correspond to Y and X. Hence we can estimate k = exp(c) and n = m from the best-fit line, obtained by substituting the values of I for lm in the above relation. Later, k and n are substituted back into the model to obtain the information Im at any given gray-scale resolution l.
Landsat TM Imagery The information content formulation and its dependence on gray-scale resolution was investigated for Landsat Thematic Mapper (TM) imagery. Two sites depicting completely different features were studied in order to check the performance of the K-means classifier in resolving the various classes distinctly. Site A represented Morro Bay, California, which was predominantly homogeneous within classes with separable classes such as, soil, water, lowlands, rock, and trees. On the other hand site B depicting Moscow in summer was generally heterogeneous with distinct classes such as, a river, trees, soil, and numerous roads and buildings. Since TM imagery is not contaminated with speckle as in radar images, it was felt that it would be ideal for verifying the accuracy of our image information model. Each TM band was contrast stretched so that the minimum and maximum gray-level values present in the band were 0 and 255 respectively.
Site Description Site A: The chosen scene, shown in Figure 1(a), lies along the central California coast about half way between San Francisco and Los Angeles, in the county of San Luis Obispo. This sub-scene was extracted from Landsat 5 Thematic Mapper scene 5026-31810 (Path 043; Row 035) acquired 19
(a) Figure 1
The colour composite images using TM bands 2, 3 and 4, of (a) Morro Bay, California and (b) Moscow, Russia, in summer.
on November 19, 1984 with center latitude and longitude as 35°21’N and 120°49’W respectively. Each pixel has a size of 30 m, and the entire image is about 16 km (10 miles) in length. The largest town in the image is Morro Bay, a resort community of about 10,000 permanent residents, some of whom are still actively involved in commercial fishing. The town is located about 21 km (14 miles) NW of the city of San Luis Obispo. The coastal Highway 1, which rambles along much of the California coastline, extends inland to the east in this scene. The second major road, California Highway 41, is visible as it passes through a valley between hills enroute to Atascadero 27.5 km (17 miles) to the NE. Cayucos is a small residential town along the coast just north of Morro Bay. Near the bottom of the image is another large settlement, the town of Los Osos (and adjacent to its north, Baywood Park). Morro Rock, a great erosional monolith made of granite that reaches a height of 175 m above the Pacific is also visible. Dense forestation extends from the higher elevations into the lowlands along the streams. Site B: The scene shown in Figure 1(b) is that of Moscow, Russia, in summer. Moscow is located at 55°33’N latitude and 37°22’E longitude off the Greenwich meridian. It is in the centre of the East-European plain in the zone of mixed forests. The city is intersected by the Moscow river, which takes a number of tributaries between the Oka and the Volga rivers. Moscow covers an area of about 878.7 square kilometers (386 square miles), its outer limit being roughly delineated by the Moscow Ring Road. Most of the area beyond this highway has been designated as a Forest-Park Zone, or greenbelt. The pattern of rings and radials that marked the historical stages of Moscow’s growth remains evident in its modern layout. The center of all rings is Moscow Kremlin and the famous Red Square. Successive epochs of development are traced by the Boulevard Ring and the Garden Ring, the Moscow Little Ring Railway, and 20
(b)
the Moscow Ring Road. The large Central Airfield is distinctly visible in the NW of the image. Dynamo Stadium, which is oval in shape lies to the east of the Central Airfield. Moscow also has numerous railroads that radiate from central Moscow, near which the Kazan train station is located.
Information analysis & model efficiency Six TM bands (Bands 1-5 and 7) were used to obtain the K-means classified images for the eight different values of l. Band 6, the thermal IR band was not used, since it has a different spatial resolution of 120 m compared to 30 m for the other bands. For each value of l, I was calculated using the modified Mean-Absolute Difference formula using Eqs. (4) and (5), following which the best-fit values of k and n were obtained. Then, an equally weighted local mean filter was used to spatially degrade the original image to obtain images with R = 5 and R = 11, after which the same procedure was repeated for calculating the information content at different l values. Figures 2 and 3 illustrate the visual effects of degrading the gray-scale resolution for the case when Nc = 5. It can be easily deduced that the classified images for values of l = {256, 128, 64, 32} shown in Figure 2 are practically indistinguishable from one another. Similarly, the images with l = {16, 8} from Figure 3 are equally indistinguishable from the reference image, i.e the classified image with l = 256. However, the images with I values lower than 8 are clearly different, and show increasing misclassification in comparison to the reference image. This implies that the interpretability (information content) of the image with l = 8 is practically the same as the interpretability of the reference image. Hence, we may as well use the image with l = 8 instead of the reference with l = 256 for characterising the scene (when Nc = 5), and in the process save 5 bits/pixel. To check whether this observation was mathematically consistent, the plots between the calculated information
content, I, and bits/pixel, log2l, were studied. Figure 4 shows the plots for the three pixel sizes, for Morro Bay, when the K-Means classifier was used with Nc = 5, 10 and 15 classes for site A. On studying the plots of I for R = 1, it can be seen that for number of classes, Nc, equal to 5 the measured information content of the image is greater than 0.9 for bits/pixel of 3 and higher. For bits/pixel less than 3, there is a sudden drop in the value of I. This supports our observations made from Figures 2 and 3, which show visual image degradation for I values less than 8, corresponding to 3 bits/pixel. Thus we can define the grayscale resolution (in bits/pixel), at I = 0.9, R = 1 and Nc equal to the probable number of classes present in the scene, as the optimal gray-scale resolution. Since this particular TM imagery has an optimal gray-scale resolution of 3 bits/pixel, we can save 5 bits/pixel on storage or transmission of this imagery, even without applying any kind of compression. From Figure 5, we can see that the plots for R = 1 show similar patterns to the corresponding plots for site A, except that the optimal gray-scale resolution is slightly higher for site B. This was confirmed through visual analysis of the
Figure 2
classified Moscow images at various values of l. Figure 5 also shows that for grayscale resolutions less than 4 bits/ pixel, the information loss is more erratic in nature for site B. This is attributed to the heterogeneity of this scene. As the number of classes increase, we can notice that the rate of fall of information also increases. This results from the creation of subclasses within the existing classes. This increases the probability of misclassification of a pixel, since each pixel now has a greater range of classes into which it can be classified. We can see that the model very accurately follows the observed values of I for all the cases. For the image with a R = 5, the maximum achievable information, Imax is about 0.64 for site A and only 0.29 for site B. This disparity in the value of Imax is again due to the increased heterogeneous nature of site B. More precisely, site B is dominated by a large number of buildings and roads that typically have dimensions less than 100 meters. Hence, when R = 5, the effective spatial resolution of the data set degrades to 30 x 5 = 150 meters. This implies that features, such as buildings, that are smaller than 150 meters would get merged with other buildings, or even with other
(a)
(b)
(c)
(d)
Classified Morro Bay TM images with R = 1, Nc = 5, and (a) l = 256, (b) l = 128, (c) l = 64, (d) l = 32. 21
Figure 3
(a)
(b)
(c)
(d)
Classified Morro Bay TM image with R = 1, Nc = 5, and (a) l = 16, (b) l = 8, (c) l = 4, (d) l = 2.
classes. Thus, this process would make the classified images corresponding to R > 1 greatly different from their reference image. This misclassification is also the reason for the more erratic behaviour of I compared to the I of Morro Bay imagery. Similarly for higher pixel sizes, Imax is even lower than site A. This clearly indicates the effect of the degraded spatial resolution. However, we could not analyse the images of site B for R = 11 since, at this low spatial resolution all the buildings, roads and trees merge into an unresolvable blur. The problem of classes merging does exists for site A also. However, due to the homogeneous nature of the image, this phenomena is not as detrimental to the information content, as it is for site B images. Interestingly, it can be observed from the plots for R = 5 and R = 11 that, the rate of information loss decreases with increasing R. As pixel size increases larger localized regions, i.e., regions in the image with very small variance in the pixel values, are formed. When these images are gray-scale degraded and rescaled, almost all the pixels existing within a local region tend to get rescaled to the same value and 22
classified into the same class, irrespective of the gray-scale resolution. Thus, the information content of the degraded images is expected to be very similar over a larger range of gray-scale resolutions compared to images with better spatial resolutions. Furthermore, for higher values of Nc, the reduction in the maximum information is greater as Nc increases, but I is approximately maintained at a constant value as shown by the plots for both site A and B. Once again, the model plots show good correlation with the observed results. As expected, at R = 11 for the site A images, the plots illustrate a trend similar to that shown in the case of R = 5. Finally, from the analysis of site A and site B images, which are at the two extremities in terms of homogeneity, we can see that the general shape of the information plots is similar for TM imagery. However, the behaviour and rate of information loss at gray-scale resolutions lower than the optimal gray-scale resolution, is more unpredictable and rapid for TM imagery that exhibit high levels of heterogeneity.
bay. The scene has a central latitude and longitude of 34°41’N and 120°27’W respectively. It is therefore inferred that this site is slightly SE of the Morro bay scene. Although we expect the physical features of this area to be similar to the area represented by the TM image, differences do exist in the cultural vegetation in both areas. The scene shows a small town called Lompoc, through which Highway 1 also runs. The Mission hills are to the north-east of Lompoc and stretch up to a small village by the name of Vandenberg. The Pacific coast line is to the west. The region has a number of small rivers flowing through the valleys, formed by small mountain ranges, that ultimately flow into the ocean; one of the rivers being the Sisquoc river, along whose banks are seen cultivated and grass lands. The cultivated fields appear as distinct squares in different shades of gray - probably indicating that different crops are being actively grown in the region. Both Gavito and Refugio beaches are also close by. Figure 6 shows the SIR-C image.
Information analysis & model robustness
Figure 4
Graphs of the Morro Bay images for R = {1, 5,11} and Nc = {5, 10, 15} are shown. The measured information, I, is shown as points at different values of l, while the modeled information, Im, is shown as a line.
SIR-C imagery The results obtained from the experiments with the TM images showed us that that our information content model was valid. However, we also wanted to investigate the robustness of the model. Hence we experimented with SIR-C radar images, which have a great deal of speckle. Apart from determining the robustness, this analysis also threw some light on the sensor specific behaviour of the model. Both the single-look complex (SLC) SIR-C and the multi-look complex (MLC) imagery were analysed. The MLC was extracted by using a filter with a window of 10 x 4 (40 looks). Similar to the TM imagery, a contrast stretching operation was performed on all the bands to ensure a gray-level range of 256.
Site description We could not obtain the SIR-C data of Morro Bay for exact comparison with the TM data sets. However we obtained the data set of Santa Barbara channel which lies geographically close to Morro
The data set acquired was by default singlelook complex containing both HH and HV polarisations at L and C band frequencies. Hence, we had four images for generating the classified images. The size of the multi-look image was exceedingly large (881 x 958 pixels), and that of the single-look was even larger (3524 x 9584 pixels). For appropriate comparison, it was decided to keep the dimensions of the multi-look images, the same as that of the TM Morro bay images. Hence, a 256 x 256 portion in the south-west region of the multi-look data was extracted from all the four bands. The corresponding single-look data was also extracted from the four single-look complex bands. It is to be noted that the MLC image variability falls between the TM image, which has no speckle, and the SLC image, which has substantially higher speckle. This difference in speckle content is visually evident in Figure 6.
Multi-look complex imagery: analysis The HV and HH polarisations of both the L and C bands were used to generate all the classified images. We used the original images of these bands with the K-Means classifier program to generate the classified reference image for each Nc = {5,10,15}. Then, as in the case of the TM imagery, 23
Figure 5
Graphs of the Moscow TM images for R = {1,5} and NC = {5, 10, 15} are shown. The measured information, I, is shown as points at different values of l, while the modeled information, Im, is shown as a line.
(a) Figure 6 24
(b)
L-Band HH polarised SIR-C images of Santa Barbara channel: (a) Multi-look complex, (b) Single-look complex.
classified images for l = {128, 64, 32, 16, 8, 4, 2} were obtained. These images were then compared with the appropriate reference image, using the modified Mean-Absolute-Difference method to obtain the information content. Following this, the parameters k and n were obtained by the same method used in the case of TM imagery. Next, spatially degraded images (pixel sizes 5 and 11) of the original four images were obtained as in the TM case. Following this, the information content of the gray-scale degraded images, at each spatial resolution, was measured. Figure 7 shows the plots of the information I for Nc = {5, 10, 15} for each R = {1, 5, 11}. For R = 1 and Nc = 5 we can see that I remains between 0.9 and 1.0 up to 3 bits/pixel. After that it rapidly drops to less than 0.25. For higher values of Nc, Imax is lower, and later on, there is an almost linear fall in I with decreasing number of bits/pixel. The increased rate of information loss with increasing values of Nc is due to reasons identical to that described in the case of TM imagery. In general, we can observe that the modeled information Im accurately mimics I. It is interesting to compare the plots in Figure 7 with the corresponding plots for the TM imagery (Figure 4). From this comparison, we note that between 3 and 8 bits/pixel for Nc = 5, and for all the three values of R, the corresponding sensor images show identical
behaviour with respect to I. However the rate of decrease in I from 3 bits/pixel to 1 bit/pixel is much higher in the case of the multi-look complex SIR-C images. An overall increased rate of information loss can also be observed for multilook complex images corresponding to Nc = {10, 15} and R = {1, 5, 11} compared to the TM images. This is attributed to the effect of speckle present in the multi-look complex images, which greatly increases the chances for the misclassification of a pixel. Recall that TM imagery are devoid of any speckle. It can be observed that for R = 5 and Nc = 5, Imax is not 1.0, but only 0.55. Again, from 3 bits/pixel to 8 bits/pixel I remains within a narrow range (0.5-0.6). Furthermore, as in the case of R = 1, I starts decreasing at an increased rate from 3 bits/ pixel to 1 bit/pixel. Similarly, for higher values of Nc, Imax is lower, and for hits/pixel lesser than 8, I falls almost linearly. We can see that the model once again worked well as shown by the model plots. The graphs for R = 11 indicate that the behaviour of I was very similar to the case of R = 5, except that Imax is much lower in all the cases of Nc. We can see that the model worked well for all the cases of Nc, except when Nc = 5 and l = 2. This anomalous behaviour is due to the fact that, at such a highly degraded spatial and gray-scale resolution, the behaviour of I cannot be predicted accurately.
Single-look complex imagery: analysis
Figure 7
Graphs of the SIR-C multi-look images for R = {1, 5, 11} and NC = {5, 10, 15} are shown. The measured information, I, is shown as points at different values of l, while the modeled information, Im, is shown as a line.
Although the model worked well with the multi-look complex imagery, the most severe test of robustness would be with the single-look complex imagery, since it has significantly more speckle. The entire process of gray-scale and spatial resolutions degradation, information measurement, generation of plots from the information measurements and model, is identical to the process used for the multi-look complex imagery. After information analysis, we generated the plots shown in Figure 8. These plots show patterns similar to those observed in Figure 7. The plots also illustrate the similarity in shape and orientation to the plots generated from the study of the multi-look complex SIR-C imagery. However, there do exist a few striking differences illustrated as follows. The rate of information loss is even higher than that observed for the MLC image in Figure 7. This is definitely due to the much greater speckle content present throughout the single25
look complex SIR-C data. This phenomena is evident from the SIR-C scene in Figure 6. The intersection of these two plots, which is even very accurately followed by the model, at around 2 bits/ pixel is not significant, since at a gray-scale resolution this low, the value of I cannot be predicted accurately. Another significant observation we can make is that, the Imax value for every case of R > 1 is always less than the corresponding ones observed in Figure 7. This is once again the influence of the additional speckle present in the single-look complex imagery. Yet, the optimal gray-scale resolution remains the same as that of the multi-look imagery, at 3 bits/pixel. Finally, we note that the model worked accurately for all the cases of R and Nc in the presence of speckle, confirming the robustness of the model.
Study of the model parameters model parameters vs model behavior
Figure 8
Graphs of the SIR-C single-look images for R = {1, 5, 11} and NC = {5, 10, 15} are shown. The measured information, I, is shown as points at different values of l, while the modeled information, Im, is shown as a line.
Figure 9
Plots generated by the model for k = 0.003 and n = (0.01, 0.02, 0.03, 0.04, 0.05, 0.35, 0.45, 0.65, 0.85, 1.05, 1.25).
26
All observations made with TM and SIR-C imagery was based on just Nc, R and l. Since the model does not include Nc and R in its formulation, the effects of changes to these parameters must be reflected on some other parameters that are present in the formulation. Since k and n are the only other parameters in the formulation, apart from l, the behaviour of information, with respect to Nc and R could also be correlated to the values of k and n. Table 1 shows the values of k and n obtained for the three cases of R and Nc, with both the TM and SIR-C imagery. Although the table presents the k and n values obtained for all the TM and SIR-C imagery we had analysed, it would be most interesting to study TM and single-look complex SIR-C imagery since they are at the extremities regarding speckle content, and are also characteristic of their respective sensors. We infer from Table 1 that for a constant R, k increases with an increase in Nc, whereas, n decreases in almost all the cases. If we keep Nc a constant, it is evident that k once again increases with increasing values of R, while n mostly decreases. Before embarking on a comparative study of the various images based on their k and n values, it is to be noted that, for the case of R = 1, the images with different Nc values cannot be compared based on k. This is because, images with R = 1 form the reference image for each value of Nc, hence their Imax would always be unity. Here we assume that k is related to Imax, which is shown in the following section. From Table 1, it is evident that all the values of k and n are greater for the TM Moscow image compared to the Morro Bay image, for constant R and Nc. This is due to greater heterogeneity of the Moscow imagery. Similarly, the single-look SIR-C
information
constant n = 0.03
Figure 10
Plots generated by the model for n = 0.03 and k = (0.0025, 0.0075, 0.0150, 0.0500, 0.2250, 0.3750, 0.6050, 1.0000, 1.6500, 2.5000 ).
imagery have higher k and n values than the multi-look imagery. This is phenomena can be attributed to the higher speckle content of the SLC imagery. Since TM imagery are not contaminated with speckle, we can expect their k and n values to be mostly less than those of the SLC and MLC imagery of a similar scene. This is clearly evident from the values of k and n for the Morro Bay and Santa Barbara channel imagery.
The role of k and n In our quest for understanding how k and n independently influence the rate of information loss and Imax, we designed the following experiment. We chose the value of k and n to lie in the ranges (0.00252.5000) and (0.01 - 1.25) respectively, which span their ranges in Table 1. Then, for a fixed value of k, n was varied with its range, and plots of information (Im) versus bits/pixel were generated. Similarly
plots with a fixed value of n for varying values of k were also generated. From Figure 9, we observe that as n increases, the rate of information loss also increases, but the maximum achievable information is the same. This is not surprising, since for R = 1, at a fixed value of Nc, Imax can be written as exp{-k}, which is independent of n. Imax will still depend on n only for R values that are non-unitary (Desetty, 1998). Interestingly, Figure 10 illustrates that, by keeping n a constant and varying k, the rate of information loss remains almost the same for all values of k, but Imax decreases with larger values of k. We observed almost similar patterns in the graphs with other combinations of k and n. Thus, this experiment showed us that although the rate of information loss and Imax are functions of both k and n, the parameter k has much greater influence on Imax than n. On the other hand, the parameter n has a greater influence on the rate of information loss than k. In all our experiments with remote sensing images, we obtained k and n from the information measured using the modified Mean Absolute Difference method. The best way to obtain the value of these parameters for a given data set is, to substitute the input parameters, namely R and Nc, into functions that return the values of k and n. Once we obtain k and n, we can directly substitute them into the model and obtain the information content at any desired gray-scale resolution. To check whether such a function exists, we performed the following experiment on the TM Morro Bay imagery. The number of classes Nc, was varied from 4 to 20. For each value of Nc, a pair of k and n values was found. The same procedure was then repeated after increasing the pixel size of the data set to 5. These values were then plotted against Nc as shown in Figure 11. Figures 11(a) and 11(b) correspond to the plots for R = 1 and R = 5 respectively. The patterns exhibited by the plots in Figure 11
Table 1 k and n values for R = {1, 5, 11} and Nc = {5, 10, 15} for TM and SIR-C imagery
SIR-C
TM Nc 5 10 15
Morro Bay n k 0.8743 0.0032 0.6191 0.0247 0.3938 0.1443
k 0.0095 0.0684 0.2422
n 0.9787 0.7252 0.4860
S. Barbara - MLC n k 0.8413 0.0058 0.5841 0.0636 0.5272 0.1418
5
5 10 15
0.4229 0.7087 0.9287
0.0310 0.0217 0.0103
1.1806 1.4863 1.8239
0.0394 0.0455 0.0446
0.5593 0.8602 1.2000
0.0287 0.0921 0.0532
0.5984 1.2739 1.7156
0.0499 0.0322 0.0330
11
5 10 15
0.5730 0.9008 1.2203
0.0188 0.0202 0.0152
-
-
0.7659 1.1691 1.3752
-0.0026 0.0215 0.0433
0.7354 1.3270 1.7688
0.0236 0.0253 0.0248
R 1
Moscow
S. Barbara - SLC n k 0.9649 0.0045 1.1183 0.0162 0.6820 0.1055
27
Figure 11
Plots of k (top) and n (bottom) for Nc varying from 4 to 20 for (a) R = 1, and (b) R = 5
are consistent with those observed in Table 1 to some extent. That is, for a constant R, k increases with an increase in Nc, whereas n decreases. Similarly for a constant Nc, k once again increases with an increase in R, and n mostly decreases. Although this correlation can be observed from the plots, a distinct relationship between k and Nc or n and Nc is not present. This is true because the points in the plots show high scatter, and thus cannot be described mathematically. This implies that expressing k and n as functions of Nc and R may not be possible with high accuracy. However, one way of obtaining these parameter values is through a lookup table, after creating a table of average k and n values found through analysis of a large number of data sets for different values of Nc and R. Note that similar tables need to be generated for different sensors.
Discussion and conclusions This paper presents the effects of gray-scale resolution on the information content of remote sensing imagery. Our formulation relates information content to accuracy of pixel classification. This approach showed that even though the unclassified bands may be greatly degraded in gray-scale 28
resolution, they may yield a classified image very similar to the reference or the ground-truth image. We have also presented the empirical model that was developed for information content of remote sensing imagery, which is a measure of the interpretability of the classified image in comparison to a reference or ground-truth image. We model information as a utility value which lies between 0 and 1, which should not be confused with the definition of information as in Shannon’s information theory. Our study of real imagery indicates that the information content of both the TM and SIR-C imagery, which have Nc (number of classes) equal to the number of distinctly recognisable classes in the scene, is comparable between 3 and 8 bits/pixel, and also lies over 0.9. However, the heterogeneity of the imagery, has an inverse relation to the rate of information loss and Imax. Also, the information diminishes at a much higher rate for the SIR-C imagery in comparison to the TM imagery, for gray-scale resolutions lower than 3 bits/pixel. This is due to the presence of speckle in the SIR-C imagery which greatly increases the possibility of misclassification of a pixel. Hence we can conclude that, the optimal gray-scale resolution for both the TM and SIRC imagery is between 3 and 4 bits/pixel (8 and 16 graylevels). This is also consistent with the visual inspection of these imagery. Practically, this property implies that a great deal (at least 4 bits/pixel) of memory overhead can be reduced even before applying any compression on the data set. More importantly, this reduction in the overhead is independent of the speckle content of the imagery. This would prove extremely valuable during transmission or archiving of remote sensing imagery, after which the user only needs to scale up the imagery to a gray-scale resolution of 8 bits/ pixel or 256 gray-levels to perform the classification. We surmise that a lossless compression algorithm such as the JPEG-LS would provide greater compression if it handles pixel values at word lengths equal to the optimal gray-scale resolution instead of 8 bits/pixel. Our studies also show that for a constant k and n, Imax (Maximum Achievable Information) of the TM imagery is always greater than that of the multi-look complex (MLC) SIR-C imagery, which in turn is greater than that of the single-look complex (SLC) SIR-C imagery. This is attributable to speckle in the SIR-C images. Since k and n vary with Nc and R, we attempted to express them as functions of Nc and R. However, we concluded that such a function, if it does exist, is highly complex. Yet, these experiments clearly illustrate that k has a greater influence on Imax (directly proportional), while n has a greater influence on the information rate. Finally, through our study of real data we conclude that our model was indeed very accurate, and also robust, since it remained valid even in the presence of speckle. This research work is being continued with the ultimate goal of determining the functions for k and n. More TM and SIR-C data sets need to be studied for this purpose. To determine a sensor independent formulation for k and n, a measure such as autocorrelation may be incorporated into
the model, which may serve to distinguish between various sensor images to some extent and also characterise the heterogeneity of the imagery. Also, improvement in information content by combining optical and microwave data sets need to be investigated. The results of a recent study that merged Landsat TM and JERS-1 SAR data showed improved detection of soil erosion features than using Landsat TM data alone (Metternicht and Zinck, 1998).
Acknowledgments This work was supported by a NASA EPSCoR grant through the Nebraska Space Grant Consortium.
References Blacknell, D., and C.J. Oliver, 1993. Information Content of coherent images. Journal of Physics D: Applied Physics. 26(9):1364-1370. Desetty, M.K., 1998. Characterization of Information Content in Remote Sensing Images. Master’s Thesis, University of NebraskaLincoln, Lincoln, NE, U.S.A.
Dowman, I.J., and G. Peacegood, 1989. Information content of high resolution satellite imagery. Photogrammetria. 43(6):295310. Frost, V.S., and K.S. Shanmugam, 1983. The information content of synthetic aperture radar images of terrain. IEEE Transactions on Aerospace and Electronic Systems. 19(5):768-774. Kalmykov, A.I., Y.I. Sinitsyn, O.V. Sytnik, and V.N. Tsymbal, 1989. Information content of radar remote sensing systems from space. Radiophysics and Quantum Electronics. 32(9):779-785. Lee, J.S., 1980. Digital image enhancement and noise filtering by the use of local statistics. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2(2):165-168. Metternicht, G.I., and J.A. Zinck, 1998. Evaluating the information content of JERS-1 SAR and Landsat TM data for discrimination of soil erosion features, ISPRS Journal of Photogrammetry & Remote Sensing. 53(3):143-153. Price, J.C., 1984. Comparision of the information content of data from the Landsat TM and Multispectral Scanner. IEEE Transactions on Geoscience and Remote Sensing. 22(3):272-281. Weeks, A.R., 1996. Fundamentals of Electronic Image Processing. SPIE Press: Bellingham, Washington, U.S.A.
29
GLOBAL ENVIRONMENTAL DATABASES —Present Situation; Future DirectionsEdited by R. Tateishi and D. Hastings Research, education, and policy making of/for global environmental change need global databases of environmental parameters. There are many independent projects to develop global datasets to meet this need. However, there has been no integrated review for these datasets/databases. This book was written, as the first attempt, by internationally reputed scientists to review the present situation of existing global datasets, to identify obstacles in global datasets/ databases development and their usage, and to find the better directions to remove these obstacles. The book consists of two parts- Thematic domains and Cross-cutting issues. The Part 1, Thematic domains, deals with a reference framework for global environmental data, topographic data, oceanographic data, land cover data, biodiversity data, soil data, and hydrological data. The part 2, Cross-cutting issues, deals with common subjects among various environmental parameters such as geometric registration and meta-data. This book is useful for environmental scientists, remote sensing scientists, spatial information scientists, and graduate students of these fields. Why don’t we cooperate with each other to develop integrated global environmental databases for our planet?
Convenors/Authors Karent D. Kline Timothy W. Foresman K. Eric Anderson David A. Hastings Ben Searle Tom Loveland
Chandra Prasad Giri Freddy Nachtergaele Iyyanki V. Murali Krishna Ian Dowman Lola M. Olsen
Published in 2000 17.5 cm x 24.5 cm, 256 pages ISBN: 962-8226-02-9
Authors John E. Estes Paula K. Dunbar Harry Dooley Bob Keeley Joseph Scepan
Jeff Hemphill Surendra Shrestha Ashbindu Singh Jonathan Iliffe
US$30.00 (postpaid surface mail)
Distributed by Geocarto International Centre G.P.O. Box 4122, Hong Kong Tel: (852) 2546-4262 Fax: (852) 2559-3419 E-mail:
[email protected] Website: http://www.gecoarto.cm 30
