Refined Lee Filter is an enhancement of Lee filter and can preserve prominent edges, linear features, point target, and texture information
See the code below or click here!
/*Copyright (c) 2021 SERVIR-Mekong
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// Algorithm adapted from https://groups.google.com/g/google-earth-engine-developers/c/ExepnAmP-hQ/m/7e5DnjXXAQAJ
// 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_lee_sigma = s1.map(refinedLee);
var firstTerrainCorrection = ee.Image(s1.first());
var s1_refinedLee = ee.Image(s1_lee_sigma.first());
Map.addLayer(firstTerrainCorrection,{min:-25,max:20},"Terrain corrected");
Map.addLayer(s1_refinedLee,{min:-25,max:20},"lee sigma");
// 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));
}
// The RL speckle filter
function refinedLee(image) {
var bandNames = image.bandNames();
image = dbToPower(image);
var result = ee.ImageCollection(bandNames.map(function(b){
var img = image.select([b]);
// img must be in natural units, i.e. not in dB!
// Set up 3x3 kernels
var weights3 = ee.List.repeat(ee.List.repeat(1,3),3);
var kernel3 = ee.Kernel.fixed(3,3, weights3, 1, 1, false);
var mean3 = img.reduceNeighborhood(ee.Reducer.mean(), kernel3);
var variance3 = img.reduceNeighborhood(ee.Reducer.variance(), kernel3);
// Use a sample of the 3x3 windows inside a 7x7 windows to determine gradients and directions
var sample_weights = ee.List([[0,0,0,0,0,0,0], [0,1,0,1,0,1,0],[0,0,0,0,0,0,0], [0,1,0,1,0,1,0], [0,0,0,0,0,0,0], [0,1,0,1,0,1,0],[0,0,0,0,0,0,0]]);
var sample_kernel = ee.Kernel.fixed(7,7, sample_weights, 3,3, false);
// Calculate mean and variance for the sampled windows and store as 9 bands
var sample_mean = mean3.neighborhoodToBands(sample_kernel);
var sample_var = variance3.neighborhoodToBands(sample_kernel);
// Determine the 4 gradients for the sampled windows
var gradients = sample_mean.select(1).subtract(sample_mean.select(7)).abs();
gradients = gradients.addBands(sample_mean.select(6).subtract(sample_mean.select(2)).abs());
gradients = gradients.addBands(sample_mean.select(3).subtract(sample_mean.select(5)).abs());
gradients = gradients.addBands(sample_mean.select(0).subtract(sample_mean.select(8)).abs());
// And find the maximum gradient amongst gradient bands
var max_gradient = gradients.reduce(ee.Reducer.max());
// Create a mask for band pixels that are the maximum gradient
var gradmask = gradients.eq(max_gradient);
// duplicate gradmask bands: each gradient represents 2 directions
gradmask = gradmask.addBands(gradmask);
// Determine the 8 directions
var directions = sample_mean.select(1).subtract(sample_mean.select(4)).gt(sample_mean.select(4).subtract(sample_mean.select(7))).multiply(1);
directions = directions.addBands(sample_mean.select(6).subtract(sample_mean.select(4)).gt(sample_mean.select(4).subtract(sample_mean.select(2))).multiply(2));
directions = directions.addBands(sample_mean.select(3).subtract(sample_mean.select(4)).gt(sample_mean.select(4).subtract(sample_mean.select(5))).multiply(3));
directions = directions.addBands(sample_mean.select(0).subtract(sample_mean.select(4)).gt(sample_mean.select(4).subtract(sample_mean.select(8))).multiply(4));
// The next 4 are the not() of the previous 4
directions = directions.addBands(directions.select(0).not().multiply(5));
directions = directions.addBands(directions.select(1).not().multiply(6));
directions = directions.addBands(directions.select(2).not().multiply(7));
directions = directions.addBands(directions.select(3).not().multiply(8));
// Mask all values that are not 1-8
directions = directions.updateMask(gradmask);
// "collapse" the stack into a singe band image (due to masking, each pixel has just one value (1-8) in it's directional band, and is otherwise masked)
directions = directions.reduce(ee.Reducer.sum());
//var pal = ['ffffff','ff0000','ffff00', '00ff00', '00ffff', '0000ff', 'ff00ff', '000000'];
//Map.addLayer(directions.reduce(ee.Reducer.sum()), {min:1, max:8, palette: pal}, 'Directions', false);
var sample_stats = sample_var.divide(sample_mean.multiply(sample_mean));
// Calculate localNoiseVariance
var sigmaV = sample_stats.toArray().arraySort().arraySlice(0,0,5).arrayReduce(ee.Reducer.mean(), [0]);
// Set up the 7*7 kernels for directional statistics
var rect_weights = ee.List.repeat(ee.List.repeat(0,7),3).cat(ee.List.repeat(ee.List.repeat(1,7),4));
var diag_weights = ee.List([[1,0,0,0,0,0,0], [1,1,0,0,0,0,0], [1,1,1,0,0,0,0],
[1,1,1,1,0,0,0], [1,1,1,1,1,0,0], [1,1,1,1,1,1,0], [1,1,1,1,1,1,1]]);
var rect_kernel = ee.Kernel.fixed(7,7, rect_weights, 3, 3, false);
var diag_kernel = ee.Kernel.fixed(7,7, diag_weights, 3, 3, false);
// Create stacks for mean and variance using the original kernels. Mask with relevant direction.
var dir_mean = img.reduceNeighborhood(ee.Reducer.mean(), rect_kernel).updateMask(directions.eq(1));
var dir_var = img.reduceNeighborhood(ee.Reducer.variance(), rect_kernel).updateMask(directions.eq(1));
dir_mean = dir_mean.addBands(img.reduceNeighborhood(ee.Reducer.mean(), diag_kernel).updateMask(directions.eq(2)));
dir_var = dir_var.addBands(img.reduceNeighborhood(ee.Reducer.variance(), diag_kernel).updateMask(directions.eq(2)));
// and add the bands for rotated kernels
for (var i=1; i<4; i++) {
dir_mean = dir_mean.addBands(img.reduceNeighborhood(ee.Reducer.mean(), rect_kernel.rotate(i)).updateMask(directions.eq(2*i+1)));
dir_var = dir_var.addBands(img.reduceNeighborhood(ee.Reducer.variance(), rect_kernel.rotate(i)).updateMask(directions.eq(2*i+1)));
dir_mean = dir_mean.addBands(img.reduceNeighborhood(ee.Reducer.mean(), diag_kernel.rotate(i)).updateMask(directions.eq(2*i+2)));
dir_var = dir_var.addBands(img.reduceNeighborhood(ee.Reducer.variance(), diag_kernel.rotate(i)).updateMask(directions.eq(2*i+2)));
}
// "collapse" the stack into a single band image (due to masking, each pixel has just one value in it's directional band, and is otherwise masked)
dir_mean = dir_mean.reduce(ee.Reducer.sum());
dir_var = dir_var.reduce(ee.Reducer.sum());
// A finally generate the filtered value
var varX = dir_var.subtract(dir_mean.multiply(dir_mean).multiply(sigmaV)).divide(sigmaV.add(1.0));
var b = varX.divide(dir_var);
return dir_mean.add(b.multiply(img.subtract(dir_mean)))
.arrayProject([0])
// Get a multi-band image bands.
.arrayFlatten([['sum']])
.float();
})).toBands().rename(bandNames);
return powerToDb(ee.Image(result));
}
