Perona-Malik filter

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// Import Sentinel-1 Collection 
var s1 =  ee.ImageCollection('COPERNICUS/S1_GRD')
			.filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VH'))
			.filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VV'))
			.filter(ee.Filter.eq('orbitProperties_pass', 'DESCENDING'))
			.filter(ee.Filter.eq('instrumentMode', 'IW'))
			.filterBounds(geometry)
			.filterDate("2020-10-01","2020-10-31");
			
var firstNoTerrainCorrection = ee.Image(s1.first());

Map.addLayer(firstNoTerrainCorrection,{min:-25,max:20},"no terrain correction");

s1 = s1.map(terrainCorrection);
var s1_pmf = s1.map(PeronaMalikFilter);
print(s1_pmf)

var firstTerrainCorrection = ee.Image(s1.first());
var s1_pmf  = ee.Image(s1_pmf.first());


Map.addLayer(firstTerrainCorrection,{min:-25,max:20},"Terrain corrected");
Map.addLayer(s1_pmf,{min:-25,max:20},"Perona Malik");


// Implementation by Andreas Vollrath (ESA), inspired by Johannes Reiche (Wageningen)
function terrainCorrection(image) { 
  var imgGeom = image.geometry();
  var srtm = ee.Image('USGS/SRTMGL1_003').clip(imgGeom); // 30m srtm 
  var sigma0Pow = ee.Image.constant(10).pow(image.divide(10.0));

  // Article ( numbers relate to chapters) 
  // 2.1.1 Radar geometry 
  var theta_i = image.select('angle');
  var phi_i = ee.Terrain.aspect(theta_i)
    .reduceRegion(ee.Reducer.mean(), theta_i.get('system:footprint'), 1000)
    .get('aspect');

  // 2.1.2 Terrain geometry
  var alpha_s = ee.Terrain.slope(srtm).select('slope');
  var phi_s = ee.Terrain.aspect(srtm).select('aspect');

  // 2.1.3 Model geometry
  // reduce to 3 angle
  var phi_r = ee.Image.constant(phi_i).subtract(phi_s);

  // convert all to radians
  var phi_rRad = phi_r.multiply(Math.PI / 180);
  var alpha_sRad = alpha_s.multiply(Math.PI / 180);
  var theta_iRad = theta_i.multiply(Math.PI / 180);
  var ninetyRad = ee.Image.constant(90).multiply(Math.PI / 180);

  // slope steepness in range (eq. 2)
  var alpha_r = (alpha_sRad.tan().multiply(phi_rRad.cos())).atan();

  // slope steepness in azimuth (eq 3)
  var alpha_az = (alpha_sRad.tan().multiply(phi_rRad.sin())).atan();

  // local incidence angle (eq. 4)
  var theta_lia = (alpha_az.cos().multiply((theta_iRad.subtract(alpha_r)).cos())).acos();
  var theta_liaDeg = theta_lia.multiply(180 / Math.PI);
  // 2.2 
  // Gamma_nought_flat
  var gamma0 = sigma0Pow.divide(theta_iRad.cos());
  var gamma0dB = ee.Image.constant(10).multiply(gamma0.log10());
  var ratio_1 = gamma0dB.select('VV').subtract(gamma0dB.select('VH'));

  // Volumetric Model
  var nominator = (ninetyRad.subtract(theta_iRad).add(alpha_r)).tan();
  var denominator = (ninetyRad.subtract(theta_iRad)).tan();
  var volModel = (nominator.divide(denominator)).abs();

  // apply model
  var gamma0_Volume = gamma0.divide(volModel);
  var gamma0_VolumeDB = ee.Image.constant(10).multiply(gamma0_Volume.log10());

  // we add a layover/shadow maskto the original implmentation
  // layover, where slope > radar viewing angle 
  var alpha_rDeg = alpha_r.multiply(180 / Math.PI);
  var layover = alpha_rDeg.lt(theta_i);

  // shadow where LIA > 90
  var shadow = theta_liaDeg.lt(85);

  // calculate the ratio for RGB vis
  var ratio = gamma0_VolumeDB.select('VV').subtract(gamma0_VolumeDB.select('VH'));

  var output = gamma0_VolumeDB.addBands(ratio).addBands(alpha_r).addBands(phi_s).addBands(theta_iRad)
    .addBands(layover).addBands(shadow).addBands(gamma0dB).addBands(ratio_1);

  return image.addBands(
    output.select(['VV', 'VH'], ['VV', 'VH']),
    null,
    true
  );
}


function powerToDb(img){
  return ee.Image(10).multiply(img.log10());
}

function dbToPower(img){
  return ee.Image(10).pow(img.divide(10));
}

/**
 * Perona-Malik (anisotropic diffusion) convolution
 * 
 * by Gennadii Donchyts see https://groups.google.com/forum/#!topic/google-earth-engine-developers/a9W0Nlrhoq0
 * I(n+1, i, j) = I(n, i, j) + lambda * (cN * dN(I) + cS * dS(I) + cE * dE(I), cW * dW(I))
 * 
 * iter: Number of interations to apply filter
 * K: kernal size
 * opt_method: choose method 1 (default) or 2
 * 
 * Returns: image 
 */

function PeronaMalikFilter(img) {
  
  var K = 3.5;
  var iter = 10;
  var method = 2;
  
  var dxW = ee.Kernel.fixed(3, 3,
                           [[ 0,  0,  0],
                            [ 1, -1,  0],
                            [ 0,  0,  0]]);
  
  var dxE = ee.Kernel.fixed(3, 3,
                           [[ 0,  0,  0],
                            [ 0, -1,  1],
                            [ 0,  0,  0]]);
  
  var dyN = ee.Kernel.fixed(3, 3,
                           [[ 0,  1,  0],
                            [ 0, -1,  0],
                            [ 0,  0,  0]]);
  
  var dyS = ee.Kernel.fixed(3, 3,
                           [[ 0,  0,  0],
                            [ 0, -1,  0],
                            [ 0,  1,  0]]);

  var lambda = 0.2;

  var k1 = ee.Image(-1.0/K);
  var k2 = ee.Image(K).multiply(ee.Image(K));

  for(var i = 0; i < iter; i++) {
    var dI_W = img.convolve(dxW)
    var dI_E = img.convolve(dxE)
    var dI_N = img.convolve(dyN)
    var dI_S = img.convolve(dyS)

    switch(method) {
      case 1:
        var cW = dI_W.multiply(dI_W).multiply(k1).exp();
        var cE = dI_E.multiply(dI_E).multiply(k1).exp();
        var cN = dI_N.multiply(dI_N).multiply(k1).exp();
        var cS = dI_S.multiply(dI_S).multiply(k1).exp();
    
        img = img.add(ee.Image(lambda).multiply(cN.multiply(dI_N).add(cS.multiply(dI_S)).add(cE.multiply(dI_E)).add(cW.multiply(dI_W))))
        break;
      case 2:
        var cW = ee.Image(1.0).divide(ee.Image(1.0).add(dI_W.multiply(dI_W).divide(k2)));
        var cE = ee.Image(1.0).divide(ee.Image(1.0).add(dI_E.multiply(dI_E).divide(k2)));
        var cN = ee.Image(1.0).divide(ee.Image(1.0).add(dI_N.multiply(dI_N).divide(k2)));
        var cS = ee.Image(1.0).divide(ee.Image(1.0).add(dI_S.multiply(dI_S).divide(k2)));
    
        img = img.add(ee.Image(lambda).multiply(cN.multiply(dI_N).add(cS.multiply(dI_S)).add(cE.multiply(dI_E)).add(cW.multiply(dI_W))))
        break;
    }
  }

  return img;
}