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Digital Puglia (SARA)

Digital Sky

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Interferometric
Synthetic Aperture
Radar

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Globally Interconnected Object Databases

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Laser Interferometer Gravitational-Wave Observatory)

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Extensible Scientific Interchange Language

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Visualization and Processing of Multichannel Images

Channels

This image, taken from the Synthetic Aperture Radar Atlas, shows part of the delta of the river Volga, as it flows into the environmentally-sensitive Caspian Sea in Russia, as shown in the summary map. For all the thumbnail images on this page, you can click on thumbnail to see the full-size image.

The area covered by this image shows estuarial and littoral features, such as salt marsh, as well as man-made features such as canals, agricultural fields, and houses. However, many of these features are not easily visible, because much of the information in the original radar data is not accessible. In this article, we summarize ways to make more of the data available.

The data that makes up the image is taken from a Synthetic Aperture Radar instrument mounted on the US Space Shuttle. A radar beam illuminates the ground surface below, and the reflected signal is measured. For this image of the Volga delta, two wavelengths were used, and for each wavelength four polarization channels were measured. Thus we can think of the dataset as an eight channel image.

Shown at the right are the channels, labelled by wavelength (L is 23cm, C is 12cm) , by the outgoing polarization (H or V for horizontal or vertical), and by the returned polarization (H or V).

In constructing the color image above, the first three of these channels were used for the three color components: red is LHH, green is LHV, blue is LVH. The reason why this image does not show all the information in the dataset is that only three of eight channels are shown. The rest of this article discusses two ways in which an image can be made that shows a much larger quantity of this latent information. Unsupervised classification can be done by computer with no human help, synthesizing three maximum contrast channels from the eight; whereas supervised classification methods, such as the one discussed below, require selection of supposedly uniform regions from the image, and contrast between these is maximized.

Unsupervised Classification:

Example: Principle Component Analysis

Principle component analysis (PCA) can be used to reduce the dimensionality of a color space. As a concrete example, let us think of printing a color image when we only have a monochrome (black-and-white) printer. A simple algorithm might turn any color into black so that red and green are printed the same. But PCA considers the actual colors that are used in the image to provide maximum contrast in the resulting image. If, for example, the image consists mostly of bright red and bright green, with little blue or black, then PCA would print the green as white and the red as black, and yellow (which is a combination of red and green) would be printed as mid-gray.

PCA works in 'color space'. With a three-channel (red, green, blue) image, color space is three-dimensional, with axes labelled by red, green and blue; for a monochrome image has a one-dimensional color space whose axis ranges from black to white. Each pixel of the image corresponds to a point in the space, and thus a complete image corresponds to a collection of points in color space. PCA approximates the collection of points by an ellipsoid, and considers the axes of the ellipsoid as the axes of a new, transformed, color space. Mathematically, this process is a principle-components analysis, or equivalently diagonalizing the moment-of-inertia tensor of the collection of points. In the example above, the red pixels form a cluster, and the green pixels another cluster. The approximating ellipsoid has a long axis stretching from one cluster to the other: it is this line that defines the new, monochrome, color space. For the SAR image of the Volga delta shown above, there are eight, not three, channels; thus the color space is eight dimensional. Doing the PCA results in a new set of channels, of which the first three are shown here. Each channel is uncorrelated with any of the others, revealing a different kind of detail. Composing the principle components into a color image (first - red, second - green, and third - blue) provides the image shown in the color image.

Much more of the information in the original eight-channel image is visible in this three-channel image than in the unclassified version at the top of this document. The missing information, in the remaining five principle components is to a large extent noise.

Supervised Classification

Example: Minimum distance from Means

We can use the ideas of color space again to think about supervised classification. Here, the assumption is that some `field-truth' is known, for example in the image to the left it may be known that there is open water, land that has been reclaimed from the delta, or land that was laid down as alluvial deposits in the past. By selecting a region representative of such classifiers, we can use the computer to classify all the rest of the pixels in the image as well.

In color space, we take all the pixels from a selected, labelled area, such as one of the green rectangles at the left. If indeed this region represents a homogeneous land cover, then those pixels will be closely clustered in color space. We can take the average position of those pixels to represent that type of land cover. Proceeding in this way with all the selected regions, we can assign each land cover type to a point in color space.

Now we can go through the complete image, assigning each pixel to be one or another of the land cover types, depending on which is closest (in color space). Hence this algorithm is called `minimum distance to means': the means refer to the averaging of the pixels from each selected region to form a representative point; the minimum distance represents the classification of the image pixels according to which land cover type it is closest to.

Classification is done in order to make quantitative measurements of images. If, for example, we believe that the quantity of salt-marsh is decreasing for some reason, then a set of images from different times gives a qualitative idea that is open to interpretation. However, if we can reliably classifiy the pixel of each image as salt-marsh/not-salt-marsh, then we can count (or the computer can count) the number of salt marsh pixels, and we can make quantitative statements that get the attention of policy-makers.