The term band maths denotes the arithmetic combination (addition/subtraction, multiplication/division) of two or more spectral bands in an early stage of image analysis. The resulting scalar values represent the spectral behaviour in different bands in a single value; such procedure makes particular sense, when spectral behaviour varies in those bands (like the red edge of vegetation spectra in the NIR band). There are several reasons for applying band maths when working with multispectral imagery: (1) A single range of values rather than multiple bands is easier to comprehend and interpret; (2) Thresholds or class limits are applied more intuitively in a grey scale image; (3) Indices can be easily calculated and compared across different sensors; they are implemented as standard routines in many software environments as well as cloud processing environments (such as Google Earth Engine or the Proba-V exploitation platform) Out of the many possible, literature suggests a few arithmetic band combinations as application-specific quasi-standards. Band ratios (e.g. red band divided by NIR band) and indices (such as the normalised difference vegetation index, NDVI) belong to this group. Indices have the advantage over simple ratios in constraining the value range, e.g. [-1 | 1]. Designated to indicate specific land cover types (such as water index, snow index, soil index, etc.) such indices are widely used as a basis for operational information products. Another index is the normalised burn ratio (NBR) which relates near infrared and short-wave infrared reflectance to measure burn severity taking into consideration the increasing of SWIR reflectance in the course of a fire. Pre-processing such as dark object subtraction and radiometric or even atmospheric correction is a key requirement prior to indexing. The coding in digital numbers (DN) is a function of the sensitivity and the radiometric resolution of the sensor. The actual recording depends on atmospheric conditions (additional brightness, haze, etc.). Therefore, in order to make the resulting values comparable among different types of sensors and scenes, radiometric correction is mandatory, converting DNs into radiances, i.e. true reflectance values as physical measurement units. Two advanced examples of band maths beyond rationing are the perpendicular vegetation index (PVI) and the tasselled cap (TC) transformation. PVI is based on the assumption that vegetation pixels are generally separable from soil pixels (at least after unmixing or for pure pixels), and thus pixel values are located in a perpendicular direction from the soil line in a NIR/red feature space. The Euclidean distance from the soil line, determined by Pythagorean triangle, yields the PVI. Tasselled cap instead rests on the notion of a cap-like histogram shape when plotting pixels on a brightness vs. greenness plot, with the latter determined by linear combinations of VIS and NIR bands, along with empirically determined coefficients. TC 1 as a weighted sum corresponds to brightness, TC 2 to greenness, TC 3 to yellowness, sometimes referred to as wetness. A fourth TC called nonesuch likely corresponds to noise and atmospheric disturbance effects in the image.
Explain how band maths can be applied to derive an index that indicates a specific land cover type like vegetation
Explain why radiometric correction is a key requirement for deriving indices with band maths
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