IV.3.2 Spectral ratios

IV - FROM DATA TO INFORMATION

3- HOW CAN WE EMPHASISE CERTAIN IMAGE CHARACTERISTICS (IMAGE TRANSFORMATION)?

3.2- Spectral ratios (Indices)

We can represent remote sensing images as a collection of number grids (matrices) consisting of a number of rows and columns. Each spectral channel is represented by a separate grid. Thus, a multispectral image with k spectral channels that is n pixels high and m pixels wide consists of k grids of n rows on m columns. The numbers in the grid represent the observed spectral response of the part of the Earth's surface corresponding to the position of the grid cell (see What is a digital image?).

Source: Planetscope Visual Mosaic - NICFI Satellite Data Program (Planet University)

The big advantage of storing remote sensing data in matrices is that calculations in linear algebra are possible (e.g. matrix multiplications) and that computers (and especially graphics processors) can calculate with them very quickly.

By performing more or less complex mathematical operations for each pixel, involving the numerical values observed for that pixel in different spectral bands, we can derive spectral indices that can be very useful for the analysis of remote sensing data.

For example, one could calculate the sum of the spectral values of an image with three components: the calculation is done for each pixel, and the result is stored in a digital image with the same number of pixels as the base images.

In some cases, the outcome of the operations may be negative, or greater than 255, the maximum value an image processing system can handle. One then resorts to coefficients and/or a constant. For example, if the 2 components A and B each vary between 0 and 255, then C= (A-B) x 0.5 + 127 will certainly be between 0 and 255.

The most commonly used indices are the so-called Normalised Difference Indices (NDI).

An NDI is designed as the ratio of the difference between the spectral reflectance values of two bands and the sum of the same values:

where ρ1 and ρ2 are the reflectance for two specific spectral channels.The denominator normalises the exposure ratio.

With an NDI, we basically calculate a new image grid that allows us to highlight or study certain features of the Earth's surface. The most commonly used NDIs serve to study the presence or characteristics of vegetation, water, soil or snow.

Of all the NDIs, NDVI (Normalised Difference Vegetation Index) is probably the most widely used. NDVI is a vegetation index calculated as follows::

where NIR is the reflectance in the near infrared channel and R is the reflectance in the red image channel.

To understand the principle of the vegetation index NDVI, we recall that the spectral signature of plants is very special, as it shows a clear peak in the near infrared, and a lower reflectance in the red.

The denominator of the formula serves to reduce the effect of different illumination: the spectral signature of the same object maintains the same appearance globally, but is shifted upwards when the object is better illuminated (object 1).The calculation of the simple difference IR-R is very sensitive to the difference in global illumination, while the normalised difference is constant.

NDVI is a simple index used to quantify green vegetation and distinguish it from other surfaces such as buildings. NDVI is also an indicator of the health status of vegetation based on how plants reflect certain wavelengths. Indeed, the chlorophyll of healthy vegetation reflects more near-infrared and green light while absorbing blue and red light.

The index takes values between -1 and 1. Negative values correspond to water, values around 0 usually correspond to bare soil, rock, sand or buildings. Lower, positive values usually represent grass, shrubs or less healthy vegetation while high values represent, for example, healthy trees and agricultural crops with high photosynthetic activity.

The Normalised Difference Vegetation Index (NDVI) shown above was calculated from band 8 (near-infrared) and band 4 (red) of a Sentinel-2 image taken over Brussels on 2 May 2022. The densely built-up urban fabric with low NDVI values contrasts sharply with the high values of the Sonian Forest to the south-east, as well as the urban parks and the few vegetated agricultural lands to the north-east. Credit European Union - Contains modified Copernicus Sentinel data 2022 processed with Sentinel Hub EO Browser

Besides NDVI, other NDIs such as NDWI (Normalized Difference Water Index), SAVI (Soil Adjusted Vegetation Index), NDSI (Normalized Difference Snow Index),.... are also used.

Some normalised difference indices calculated on Planet NICFI images. NDVI (left), NDWI (centre) and MSAVI2 (modified soil- adjusted vegetation index - a variant of NDVI corrected for the influence of soil reflectance in areas with little vegetation). Data source: Planet University. Visualisations réalisées avec Sentinel Hub EO Browser.