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Map Algebra

Map algebra is a way to perform raster calculations using mathematical expressions. The expression can be a simple arithmetic operation or a complex combination of multiple operations. The expression can be applied to a single raster band or multiple raster bands. The result of the expression is a new raster. Apache Sedona provides two ways to perform map algebra operations:
  1. Using the RS_MapAlgebra function.
  2. Using RS_BandAsArray and array based map algebra functions, such as RS_Add, RS_Multiply, etc.
Generally, the RS_MapAlgebra function is more flexible and can be used to perform more complex operations. The function takes three to four arguments: 
RS_MapAlgebra(rast: Raster, pixelType: String, script: String, [noDataValue: Double])
  • rast: The raster to apply the map algebra expression to.
  • pixelType: The data type of the output raster. This can be one of D (double), F (float), I (integer), S (short), US (unsigned short) or B (byte). If specified NULL, the output raster will have the same data type as the input raster.
  • script: The map algebra script. (For guidance on scripting for map algebra, refer to the Jiffle documentation.)
  • noDataValue: (Optional) The nodata value of the output raster.
RS_MapAlgebra function allows two raster column inputs, with multi-band rasters supported. The function accepts 5 parameters: 
RS_MapAlgebra(rast0: Raster, rast1: Raster, pixelType: String, script: String, noDataValue: Double)
  • rast0: The first raster to apply the map algebra expression to.
  • rast1: The second raster to apply the map algebra expression to.
  • pixelType: The data type of the output raster. This can be one of D (double), F (float), I (integer), S (short), US (unsigned short) or B (byte). If specified NULL, the output raster will have the same data type as the input raster.
  • script: The map algebra script. Refer to the NDVI section for more details on the format.
  • noDataValue: (Not optional) The nodata value of the output raster, null is allowed.
SQL Example for two raster input RS_MapAlgebra: 
RS_MapAlgebra(rast0, rast1, 'D', 'out = rast0[0] * 0.5 + rast1[0] * 0.5;', null)
RS_MapAlgebra function supports returning multi-band rasters: 
RS_MapAlgebra(rast: Raster, pixelType: String, script: String, noDataValue: Double, numBands: Int)
RS_MapAlgebra(rast0: Raster, rast1: Raster, pixelType: String, script: String, noDataValue: Double, numBands: Int)
The number of bands in the output raster should be passed into the numBands parameter. The output band can be specified in the same way as with the input rasters in the script, e.g: 
SELECT RS_MapAlgebra(rast, 'D', 'out[0] = rast[0] - rast[1]; out[1] = rast[0] + rast[1];', null, 2) FROM raster_table
RS_MapAlgebra also has good performance, since it is backed by Jiffle and can be compiled to Java bytecode for execution. We’ll demonstrate both approaches to implementing commonly used map algebra operations.
The RS_MapAlgebra function can cast the output raster to a different data type specified by pixelType:
  • If pixelType is smaller than the input raster data type, narrowing casts will be performed, which may result in loss of data.
  • If pixelType is larger, widening casts will retain data accuracy.
  • If pixelType matches the input raster data type, no casting occurs.
This allows controlling the output pixel data type. Users should consider potential precision impacts when coercing to a smaller type.

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NDVI

The Normalized Difference Vegetation Index (NDVI) is a simple graphical indicator that can be used to analyze remote sensing measurements, typically, but not necessarily, from a space platform, and assess whether the target being observed contains live green vegetation or not. NDVI has become a de facto standard index used to determine whether a given area contains live green vegetation or not. The NDVI is calculated from these individual measurements as follows: 
NDVI = (NIR - Red) / (NIR + Red)
where NIR is the near-infrared band and Red is the red band. Assume that we have a bunch of rasters with 4 bands: red, green, blue, and near-infrared. We want to calculate the NDVI for each raster. We can use the RS_MapAlgebra function to do this: 
SELECT RS_MapAlgebra(rast, 'D', 'out = (rast[3] - rast[0]) / (rast[3] + rast[0]);') as ndvi FROM raster_table
The Jiffle script is out = (rast[3] - rast[0]) / (rast[3] + rast[0]);. The rast variable is always bound to the input raster, and the out variable is bound to the output raster. Jiffle iterates over all the pixels in the input raster and executes the script for each pixel. the rast[3] and rast[0] refers to the current pixel values of the near-infrared and red bands, respectively. The out variable is the current output pixel value. The result of the RS_MapAlgebra function is a raster with a single band. The band is of type double, since we specified D as the pixelType argument. We can implement the same NDVI calculation using the array based map algebra functions: 
SELECT RS_Divide(
        RS_Subtract(RS_BandAsArray(rast, 1), RS_BandAsArray(rast, 4)),
        RS_Add(RS_BandAsArray(rast, 1), RS_BandAsArray(rast, 4))) as ndvi FROM raster_table
The RS_BandAsArray function extracts the specified band of the input raster to an array of double, and the RS_Add, RS_Subtract, and RS_Divide functions perform the arithmetic operations on the arrays. The code using the array based map algebra functions is more verbose. However, there is a RS_NormalizedDifference function that can be used to calculate the NDVI more concisely: 
SELECT RS_NormalizedDifference(RS_BandAsArray(rast, 1), RS_BandAsArray(rast, 4)) as ndvi FROM raster_table
The result of array based map algebra functions is an array of double. User can use RS_AddBandFromArray to add the array to a raster as a new band.

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AWEI

The Automated Water Extraction Index (AWEI) is a spectral index that can be used to extract water bodies from remote sensing imagery. The AWEI is calculated from these individual measurements as follows: 
AWEI = 4 * (Green - SWIR2) - (0.25 * NIR + 2.75 * SWIR1)
AWEI can be implemented easily using RS_MapAlgebra: 
-- Assume that the raster includes all 13 Sentinel-2 bands
SELECT RS_MapAlgebra(rast, 'D', 'out = 4 * (rast[2] - rast[11]) - (0.25 * rast[7] + 2.75 * rast[12]);') as awei FROM raster_table
We can also implement the same AWEI calculation using array based map algebra functions. The code looks more verbose: 
SELECT RS_Subtract(
    RS_Add(RS_MultiplyFactor(band_nir, 0.25), RS_MultiplyFactor(band_swir1, 2.75)),
    RS_MultiplyFactor(RS_Subtract(band_swir2, band_green), 4)) as awei
FROM (
SELECT RS_BandAsArray(rast, 3) AS band_green,
       RS_BandAsArray(rast, 12) AS band_swir2,
       RS_BandAsArray(rast, 13) AS band_swir1,
       RS_BandAsArray(rast, 8) AS band_nir
FROM raster_table) t

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Further Reading