The PANCROMA™ Spectral Angle Analyzer™ is an alternative method for matching image pixel reflectances with target spectra. As in Euclidean Distance analysis, SAA also considers each image reflectance value and the target spectrum as an n-dimensional vector, where n is the number of multispectral bands. The algorithm determines the spectral similarity between each image reflectance vector and the target vector by calculating the angle between each image reflectance and the target. As in Euclidean Distance comparisons, target spectra used by the Spectral Angle Analyzer™ can come from ASCII files or spectral libraries, or you can extract them directly from an image using the Point Spectrum Generator™.
Spectral Angle comparisons can often be more discriminating and can yield more accurate matches than corresponding Euclidean Distance analyses. This is because, when used with calibrated reflectance data, Spectral Angle comparisons are often relatively insensitive to illumination and albedo effects that can sometimes confound Euclidean Distance analyses.
In order to use the method for Landsat 7 data, open six or seven Landsat multispectral band files. Then select 'Spectral Analysis' | 'Landsat Spectral Analyzer' | 'Six/Seven 8-Bit DN Bands' | 'Spectral Angle'. (Or alternatively, if you are using Landsat 7 reflectance data choose the corresponding 'Six/Seven 16-Bit Reflectance Bands' submenu selection).
When you do, the same Spectral Criteria form used for Euclidean Distance analysis will become visible. The target spectrum can be entered in the same way as for Euclidean Distance analysis, either manually, by reading in ASCII spectra, or by using the Point Spectrum Generator™.
The following images show a comparison between target discrimination results using the two methods. Both images were generated using the same target spectrum generated using the PANCROMA™ Point Spectrum Generator™, targeting the river.
There are interesting differences between the two plots. Both have successfully identified the water bodies. The main difference between the two plots is how they separated the target from the background. The Spectral Angle plot exhibits a much greater distance between the target (the river) and the background (farm and urban land). That is, the vector distances between the target and the background is relatively less than the vector angles between the target and the background. The Spectral Angle plot also shows more discrimination within the target itself, as it has picked up subtle differences between the reflectances of the water closer to the shore and the deeper water toward the middle of the river. The tributary stream in the Spectral Angle plot is also differentiated from the main river body, unlike the Euclidean Distance plot of the tributary. There are also differences in the secondary features that the two methods have identified as well.
However it is important to remember that PANCROMA™ Spectral Analyzer™ tools are designed for target identification, not classification. Classification attempts to assign all surface features in an image to groups, typically using statistical methods. Usually the user specifies the number of groups in the classification. Target identification on the other hand is designed to indicate all instances of a single surface feature, i.e. the instances that best match the target reflectance spectrum. In a strict mathematical sense, targeting treats all image pixels as a single group, with some members being geometrically closer to the target than others in a mathematical continuum. Classification relates pixels to each other rather than to a target, and attempts to make a statement about which pixels are likely to represent the same surface features as other pixels.
The following images show a comparison between cloud shadow masking results using the two methods. The first pair of images, a Euclidean Distance plot and a corresponding cloud mask (see next section) were generated using the Point Spectrum Generator™ and Euclidean Distance Analysis, with the mask track bar on setting zero.
The next pair of images were generated using the same target spectrum and Spectral Angle analysis
The SAA method resulted in a more discriminating match and it also excluded the false positives from the nearby water bodies that had similar reflectance spectra as the cloud shadows. In addition to Landsat 7, Spectral Analysis is currently implemented for NAIC and SPOT data as well.
IMPORTANT NOTE: Although it is possible to conduct multispectral analysis using entire Landsat scenes, be advised that the edges of the individual Landsat multispectral bands do not match exactly. This can produce border regions containing invalid distance or angular values because some of the multispectral band values are zero and some are non-zero. This can also influence the min and max value computations that set the color range scale. It is better for most work to crop off these regions before conducting multispectral analyses.