Spectral Transformations

Arithmetic Operations/Band Calculations

Arithmetic operations (addition, subtraction, multiplication, division) or band calculations can be carried out on any data set of at least two spectral bands of the same geographical area. They allow the generation of a new image with properties that are more suited to a particular purpose than the original ones. The most widely used arithmetic operation in remote sensing image analysis is the division or rationing of spectral bands with the aim of emphasizing the differences between them. These differences may be quantified to estimate, for example, the biophysical or geochemical properties of the land surface (see next section). Another widely used application of image division is the normalization of spectral response patterns by rationing two spectral bands. This technique makes use of the fact that illuminated surfaces reflect more solar radiation than shaded surfaces of the same nature and that the relation between those two can roughly be described by a multiplicative spectral component.

Many cases of band calculations combine at least two arithmetic operations, for example, image addition and division. For example, the average spectral reflectance in visible light (VIS) is calculated by summing the digital numbers of the respective channels in the blue, green, and red parts of the spectrum and dividing the sum by the number of bands (i.e., VIS = (B + G + R)/3).

A special case of band calculations is that of conditional operations that do not make use of the total amount of incoming data for a calculation but use a selection of the data set. An example is the common method of selecting the maximum spectral reflectance value for the same spectral band over the same geographical area out of a collection of n subsequent (e.g., daily) [Page 2679]data takes. This method, known as the maximum value composite method, is widely used in generating coarse-resolution temporal composites of global coverage remote sensing products (e.g., MODIS, Spot-VEGETATION, NOAA-AVHRR).

Spectral Ratios and Vegetation Indices

Spectral ratios describe a group of band calculations that use the spectral reflection in two bands. Modification and extension of ratios to multiple complex band calculations resulted in the emergence of the term (spectral) vegetation indices (VIs). This term accounts for the fact that the amount of solar radiation that is reflected from a land surface object is a function of wavelength and object characteristics, especially the type and biophysical properties of the vegetated fraction of the object (e.g., fraction-absorbed photosynthetically active radiation, chlorophyll, leaf area index, or biomass). In particular, VIs parameterize the relation between the absorption maximum in the red (R) region and the reflectance maximum of the near-infrared region (NIR) of the electromagnetic spectrum, which is characteristic of vital vegetation. These circumstances have led to the development of a vast number of VIs that are widely applied in any spatially explicit Earth science application of remote sensing data. Among others, the Normalized Difference Vegetation Index (NDVI) is representative of the group of dual-band VIs. It is the ratio of the difference of NIR and R to their

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