Euclidean Distance Fraction™ Analysis

Another powerful technique for conducting land use studies is PANCROMA™ Euclidean Distance Fraction™ analysis. Euclidean distance analysis considers the target spectrum as a multi dimensional vector. It also considers each pixel in the data set as a similar vector. It then computes the distance between each pixel and the target, in the vector sense. Rather than display the entire Euclidean distance plot, Distance Fraction™ analysis allows you to select all pixels within a selected fraction of the difference between the maximum and minimum Euclidean distance in the data set. This can result in very selective classifications of land features based on spectral signature matching.

Implementing this technique proceeds in a similar fashion to the Euclidean Distance method described in the previous section. For example, to conduct the analysis using Landsat data, start by opening your multispectral data files. Then select 'Spectral Analysis' | 'Landsat Spectral Analyzer' | 'Six/Seven DN Bands' | 'Euclidean Distance'. When the Spectral Criteria form appears, enter your target spectrum using the slider bars as before. If you have run Spectral Analyzer™, your values will of course already be entered. Check the 'Distance Fraction' check box at the lower right side of the form. This will enable the nine radio buttons on the Euclidean Distance Fraction panel as shown below.

Euclidean Distance Fraction Panel

Now select one of the radio buttons. Choosing the top button will display only those pixels having the closest Euclidean distance (best match) with the target spectrum. These will be all pixels within 11% of the total span between the maximum and minimum Euclidean distance. For example, if the maximum distance is 0.947 and the minimum distance is 0.155, checking the first button will display all pixels within a Euclidean distance D:

D = 0.11*(0.155 + (0.947 - 0.155)).

from the target spectrum. Checking the second button will display pixels with a distance D of

D = 0.22*(0.155 + (0.947 - 0.155)).

and so on. These pixels will be overlayed onto the image. By moving the selection down the scale, more and more pixels are added to the overlay display. An example image from the snow pack example is shown below.

Euclidean Distance Fraction Plot

In this image, all pixels that are less than 0.5165 (dark green on the scale) from the target spectrum are overlayed onto the image. When the analysis is run, the area coverage as a percentage of the total image is displayed on the Main Window dialog box.

The idea is to adjust the included pixels to entirely cover ground features that are known by ground truthing or other means. When the match is close, it is likely that all other instances of that feature in the image will be closely identified. In the case of the snow pack example, the snow is easily identified visually. By adjusting the Distance Fraction™, an accurate snow pack coverage measurement can be taken.

One of the main benefits of this technique is that it allows for accurate classification of ground features without any foreknowledge of the feature spectrum. To illustrate this point, consider the image shown below of an area of the Midwestern United States. Let's assume that we are interested in the plot of vegetation ground cover shown inside the red circle in the image shown below.

Vegetation Feature Target

We first start by running the PANCROMA™ Point Spectrum Generator™. I selected ten random points, all within the confines of the small plot. The computed spectrum is shown in the image below

Point Spectrum Generator™ Target Spectrum

The next step is to run Spectral Analyzer™ Euclidean Distance analysis. (Note that the spectrum will be automatically inserted into the Spectral Analysis form). Check the Distance Fraction check box and select the default radio button. The form configuration is shown below.

Spectral Criteria Form Image 1

The corresponding image is shown below. Note that the target plot is identified, along with a few other areas in the image with very close overall matches to the target spectrum.

Image 1 Distance Fraction™ Plot

If we believe that our match criteria were too exacting, we can expand the search by conducting another run, this time including another level of match pixels. We will include all pixels that are 22% of the difference between the maximum and minimum Euclidean distance by selecting the next radio button. This is shown in the form below.

Spectral Criteria Form Image 2

This results in a broader selection of targets as shown in the image below.

Image 1 Distance Fraction™ Plot

We can continue expanding the match criteria until we are satisfied that we have all of the targets included. Of course there is no way to determine if we are under selected or over selected a-priori. It would be necessary to have some ground truthing knowledge of two or more plots that we have positively identified as belonging to the target set. The addition of this information would greatly increase the probability of including all of the target plots without the plot spilling over into non-target features as a result of relaxing the comparison criteria too much. Note that we could have conducted two separate classification analyses in one run by checking the 'Input Two Spectra' check box on the Spectral Criteria form. In that case the drop down selection menu becomes activated so that we can switch among Image 1, Image2, and the base image.

Distance Fraction™ analysis provides an interesting and powerful method for classification of surface features. It requires no library spectra and works best with some ground truthing information. The technique differs from statistical-based methods such as K-Means classification in that it is not able to simultaneously handle large numbers of targets. However, when combined with suitable ground truthing information it can provide exceptionally reliable classifications.