Background:
Malaspina Glacier is in  southern Alaska and the given image is oriented N-S and is 35.4 km in height and 50..4 km in width. The data are from a 30x30 gridded elevation model; The topography in the image was created by the Shuttle Radar Topographic Mapping project of NASA.
The image of the Malaspina Glacier in Alaska is digital elevation Model (DEM), that shows the topography of the glacier surface.

Goal:
The objective is to find evidence in the long wavelength surface topography that may reflect the presence of large sub-glacieal rivers that drain the glacier.
 

Procedure and Result:
The image shown in Fig. 1a contains high frequency structures associated with crevasses and low frequency structures. Those low frequency structures are assumed to represent the subsidence of the ice above the channels. Also of higher frequency are moraines and eskers below the glacier.

The flow of procedures used is:
0. Original image (Fig. 1a)
1. Histogram equalization (Fig. 1b)
2. Low Pass filtering (Fig. 1c and Fig. 3 and Fig.4)
3. High Pass filtering (Fig. 1d)
4. Subtraction LP-image from HP-image (Fig. 2a)
5. Histogram equalization of this image (Fig. 2b)
6. Low Pass filtering  = final image (Fig. 2c)
7. Comparison to original image (Fig. 2d)

1. The first job is to histogram equalize the original image to enhance the contrast. See Fig. 1b)
2. To emphasise the long wavelength features, the short wavelength structures (from now on called crevasses) can be filtered by a low pass filter. Fig. 1a) shows that the orientation of  the crevasses changes within the picture, but one can divide the picture in 4 parts, where the crevasses have mainly one orientation. Fig. 3a) shows, how the parts are defined. The overlap of the filters is 50 pixels to each side. The filter for part I is shown in Fig.3b) and the result in Fig. 3c). As you can see, the crevasses oriented NE-SW are removed. Fig. 4 images the filters and results of part II and IV. Part III is not filtered, since there are no short wavelenght structures visible. (We also tried a low pass filter on part III, which did not improve the picture significantly.) Before patching in the filtered parts, they had to be darkened respectively lightened. The factors are 1/14.5 for part I and II. The other 2 images have the same range of gray. The final low pass filtered image is shown by Fig. 1c)
3. The high pass filter used is a 100x100 filter (ones(100,100)/10000) shown by Fig. 1d)
4. Subtracting the high pass image from the low pass image produces a low contrast image (Fig. 2a)
5. Histogram equalization enhances the contrast of the subtracted image, but there are some arteficial high frequency structures in the upper part of the image.
6. A 17x17 lowpass filter decreases those structures. Fig. 2c) is our final image.
7. A comparison of Fig. 2c) and Fig. 2d), which is the original image, points out, that unobtrusive structures in the original image are enhanced in the processed image, that now also shows a lot more structures, that were not visible in the original. The lower parts of the smaller structures in the processed image merge with the larger structures, that flow off the glacier in the south.

Figure 1. First processing steps

 

Figure 2. Last processing steps.

 

Figure 3. Low pass filters and results.

Figure 4. Low pass filters and results.

Conclusion:
In order to find the sub-glacial rivers, the contrast of the original image had to be enhanced and the high frequency noise associated with crevasses had to be reduced. This was done by subtracting a low pass filtered image from a high pass filtered image. The low contrast of this image was enhanced by histogram equalization and high frequency artifacts were reduced by a low pass filter. The result showes a lot more detail on low frequency structures than the original image. The patterns of the structures are characteristic for a river system with confluences.
Therefore, we believe, that the low frequency structures of the topography map represent the subsidence of ice above the sub-glacial channels.

In order to get a better resolution some other filters like Prewitt, Roberts and Laplacian and filter sizes were applied, but none of those produces satisfying results. The Kirsch and Robinson filters produces some interesting images (see http://webserver-12.inscc.utah.edu/~zijang ). A better resolution of the structures might be producable by applying other methods, like slant stack and median filter and many, many others.
 

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