kndvi.js

// Javacript for GEE
// kNDVI using the RBF kernel.
// nir and red are near-infrared and red bands, respectively.
// The example here assumes the values of these bands are *reflectances*.
// For instace, for MODIS you must divide the raw values by 10000.
// See the image collection documentation for specific instructions.

// We present two implementations which are equivalent: 
//      1. Using the definition of the RBF kernel k(nir,red)=exp(-(nir-red)^2/(2*sigma^2)) in the kNDVI=(1-k(nir,red))/(1+k(nir,red))
//      2. which is equivalent to kNDVI = tanh((nir-red)^2/(2*sigma)^2)
// Both obtain the same result, use the one you prefer!

var addKNDVI_RBF = function(image) {
  // Compute (nir-red)^2
  var D2 = nir.subtract(red).pow(2);
  // Fix or estimate a reasonable sigma value, e.g. sigma = 0.15
  var sigma = ee.Number(0.15);
  // Compute kernel (k) and kNDVI
  var k = D2.divide(sigma.pow(2).multiply(2)).multiply(-1).exp();
  var kndvi = ee.Image.constant(1).subtract(k)
      .divide(ee.Image.constant(1).add(k));
  return image.addBands(kndvi.select([0], ['kndvi']));
}

var addKNDVI_tanh = function(image) {
  // Compute (nir-red)^2
  var D2 = nir.subtract(red).pow(2);
  var sigma = ee.Number(0.15);
  var kndvi = D2.divide(sigma.multiply(2.0).pow(2)).tanh();
  return image.addBands(kndvi.select([0], ['kndvi']));
}