Landsat Euclidean Distance Analysis

The previous methods discriminate targets by manually setting the spectral selection criteria levels and the "greater than" or "less than" slider settings. This essentially allows the identification of a single class of terrain objects based on the reflectance characteristics of the objects. An alternative way to match spectral signatures is distance minimization. In this technique, the multispectral band data is considered to be an n-dimensional vector, with 'n' being the number of spectral bands available for the analysis. This is the so-called hypercube approach, i.e. three orthogonal vectors defining the edge of a standard cube and additional orthogonal vectors defining a hypercube.

Distance methods compute the distance between each multispectral reflectance vector and the target vector defined by spectral signature you are trying to match. At this time, the target vector must either be formulated manually, i.e. from spectral plots or numerical spectral data. Alternatively, the target can be formulated using the Point Spectrum Generator, by clicking on selected pixels in one of the band files or a RGB true or false color composite image. The target vector is then input using the band sliders on the Spectral Criteria form. PANCROMA then computes the Euclidean distance between each vector and the target. The distance array is displayed as an RGB color contour plot and a grayscale image. The closer the distance, the better the overall match between a given vector (i.e. pixel location) and the target.

This exercise will repeat the analysis presented in a previous White Paper for using the Point Spectrum Generator and Spectral Analyzer to measure snow pack. The first step is to generate the Point Spectrum. This is done exactly as presented in the previous White Paper entitled Landsat Point Spectrum Generator. After you acquire your spectrum, the average reflectance values for each band are automatically entered into the Spectral Criteria form. After you generate your spectrum, select 'Close Graphics Files and Reset'

To conduct a distance match, re-open your six Landsat or ASTER DN band files. Then select 'Spectral Analysis' | 'Landsat Spectral Analyzer' | 'Six DN Bands' | 'Euclidean Distance'. The Spectral Criteria Form will become visible. The average reflectance values should already be entered into the band sliders.

Alternatively, you can use the band sliders for bands 1,2,3,4,5 and 7 (Landsat) or bands 4,5,6,7,8 and 9 (ASTER), to input or adjust the reflectance values for the target vector taken. Click 'OK'. The TOA Reflectance Data Form will become visible. Enter the Solar Elevation Angle and the Acquisition Date and click 'OK'. After a bit of computation, two images will become visible, a grayscale image and an RGB contour image. The grayscale image displays the Euclidean Distances, scaled to fall between 0 and 255. The RGB contour plot plots the actual Euclidean Distances with red being the shortest distance and violet being the greatest. Note that in the grayscale plot, black represents the closest match and pure white (DN=255) is the farthest distance.

The following image shows the Euclidean Distance plot. The bright red areas correspond to the minimum Euclidean Distance and therefore the best match with the target vector. The purple areas are the worst matches, i.e. the farthest Euclidean Distances. The red areas correspond to the obvious snow areas in the band images, with the orange and yellow areas being probable matches as well in this case. Note that you can turn off the color scale by unchecking the 'Display Euclidean Distance Scale' check box on the Spectral Criteria form.

This technique can also be used for SPOT, ASTER, and EO-1 data as well. The following example used the Point Spectrum Generator to identify target crops.

EO-1 Hyperion data can also be used for Euclidean Distance analysis. This can be done by selecting any 9 of the 122 total Hyperion bands. The following image shows such an analysis for bands 81-89 of a Hyperion scene.

Note: in order to get the best classification with EO-1 data it is often best to select your points using the RGB composite image selection. This is because areas that appear very distinctive in one band can be virtually non-existent in other bands. This will lead to confusing results because you will think you are selecting points that have similar reflectances across all band when in reality they may only be similar in a single band.