When conducting remote sensing analysis, it can often be very instructive to evaluate the spectral similarity – or dissimilarity – of different image features.
Below we demonstrate the use of a dendrogram to quantitatively analyze and visually assess the similarity and hierarchical clustering of reflectance spectra.
Understanding spectral relationships can impart valuable information on: the potential spectral variability within a given scene, the capacity to differentiate certain unique features in an image, the need for clustering spectrally similar features, or the number of spectral endmembers that could be used to describe a particular area. Spectral analysis can therefore be an important first step in understanding the capabilities and limitations of different analysis methods and application objectives.
Spectra are typically obtained from field or laboratory measurements, from an existing spectral library, or derived from the image itself. Similarity between individual spectra, or between clusters of similar spectra, can be mathematically analyzed using different distance metrics, such as root-mean-square error or spectral angle. The magnitude of similarity amongst these distances can then be used as an indicator of the ability to differentiate and/or identify spectral features using different image processing techniques.
When analyzing a relatively small set of spectra, evaluating results from a similarity assessment can be easily achieved by simply examining the output directly. For example, if we consider a set of coral reef spectra representing coral, sponge, sand and submerged aquatic vegetation (SAV), analysis using spectral angle reveals measurable differences between all four spectra. This is also apparent by plotting the spectra themselves, and seeing that each feature exhibits unique characteristics.
However, when the number of spectra is increased, and the spectral relationships become more complex, visual assessment of both the spectral signatures and similarity output becomes more difficult to interpret. For example, expanding our coral reef analysis, we now investigate spectra from 10 individual sponge species, and find the interpretation of results to be less obvious. There are clearly species exhibiting close similarities, as well as differences, but it is not immediately apparent which species can be easily differentiated and which species need to be clustered.
A useful method that can assist with this analysis is utilizing output from the distance calculations to build a dendrogram. This provides a visual representation of spectral relationships, as well as quantitative information relevant to image analysis. For example, as shown below, of the 10 sponge species in our analysis, 6 of these species can be differentiated at 0.1 spectral angle; however, there are two sets of species, (i) Chondrilla spp. and C. caribensis and (ii) A. lacunosa and I. felix, that are closely similar at 0.1 spectral angle and would need to be clustered at this level of analysis.
To further illustrate the utility of using a “spectral dendrogram”, we expand our coral reef analysis to include spectra from 24 coral species, 3 SAV species and sand, in addition to the 10 sponge species. As evident from the dendrogram, spectral relationships in this analysis are significantly more complex. For example, at 0.1 spectra angle there are multiple situations where different spectral types (e.g., coral and sponge, or SAV and sponge) are closely similar and can’t be spectrally differentiated. This has important implications, and potential limitations, for subsequent spectral analysis and image classification results.
These are but a few examples illustrating the types of visualization and levels of information that can be derived from these plots. However, potential applications are as varied as your spectra, so we invite you to explore the use of dendrograms in your own spectral analysis.
Acknowledgement: Spectral data used in the above examples were collected using a GER-1500 spectrometer by M. Lucas at the University of Puerto Rico at Mayaguez for a NASA EPSCoR sponsored research project on the biodiversity of coastal and terrestrial ecosystems.