def gamma_map(img, window=7, enl=4.9):
"""Gamma Map speckle filtering algorithm.
Algorithm adapted from https://groups.google.com/g/google-earth-engine-developers/c/a9W0Nlrhoq0/m/tnGMC45jAgAJ.
args:
img (ee.Image): Earth engine image object. Expects that imagery is a SAR image
window (int, optional): moving window size to apply filter (i.e. a value of 7 == 7x7 window). default = 7
enl (float, optional): equivalent number of looks (enl) per pixel from a SAR scan.
See https://sentinel.esa.int/web/sentinel/user-guides/sentinel-1-sar/resolutions/level-1-ground-range-detected.
default = 4.9
returns:
ee.Image: filtered SAR image using the Gamma Map algorithm
"""
bandNames = img.bandNames()
# Square kernel, window should be odd (typically 3, 5 or 7)
weights = ee.List.repeat(ee.List.repeat(1, window), window)
midPt = (window // 2) + 1 if (window % 2) != 0 else window // 2
# ~~(window/2) does integer division in JavaScript
kernel = ee.Kernel.fixed(window, window, weights, midPt, midPt, False)
# Convert image from dB to natural values
nat_img = geeutils.db_to_power(img)
# Get mean and variance
mean = nat_img.reduceNeighborhood(ee.Reducer.mean(), kernel)
variance = nat_img.reduceNeighborhood(ee.Reducer.variance(), kernel)
# "Pure speckle" threshold
ci = variance.sqrt().divide(mean) # square root of inverse of enl
# If ci <= cu, the kernel lies in a "pure speckle" area -> return simple mean
cu = 1.0 / math.sqrt(enl)
# If cu < ci < cmax the kernel lies in the low textured speckle area -> return the filtered value
cmax = math.sqrt(2.0) * cu
alpha = ee.Image(1.0 + cu * cu).divide(ci.multiply(ci).subtract(cu * cu))
b = alpha.subtract(enl + 1.0)
d = (mean.multiply(mean).multiply(b).multiply(b).add(
alpha.multiply(mean).multiply(nat_img).multiply(4.0 * enl)))
f = b.multiply(mean).add(d.sqrt()).divide(alpha.multiply(2.0))
caster = ee.Dictionary.fromLists(
bandNames, ee.List.repeat("float", bandNames.length()))
img1 = (geeutils.power_to_db(mean.updateMask(
ci.lte(cu))).rename(bandNames).cast(caster))
img2 = (geeutils.power_to_db(
f.updateMask(ci.gt(cu)).updateMask(
ci.lt(cmax))).rename(bandNames).cast(caster))
img3 = img.updateMask(ci.gte(cmax)).rename(bandNames).cast(caster)
# If ci > cmax do not filter at all (i.e. we don't do anything, other then masking)
result = (ee.ImageCollection([img1, img2, img3]).reduce(
ee.Reducer.firstNonNull()).rename(bandNames).clip(img.geometry()))
# Compose a 3 band image with the mean filtered "pure speckle", the "low textured" filtered and the unfiltered portions
return result
def gamma_map(img, window=7, enl=5):
bandNames = img.bandNames()
# Square kernel, window should be odd (typically 3, 5 or 7)
weights = ee.List.repeat(ee.List.repeat(1, window), window)
midPt = (window // 2) + 1 if (window % 2) != 0 else window // 2
# ~~(window/2) does integer division in JavaScript
kernel = ee.Kernel.fixed(window, window, weights, midPt, midPt, False)
# Convert image from dB to natural values
nat_img = geeutils.db_to_power(img)
# Get mean and variance
mean = nat_img.reduceNeighborhood(ee.Reducer.mean(), kernel)
variance = nat_img.reduceNeighborhood(ee.Reducer.variance(), kernel)
# "Pure speckle" threshold
ci = variance.sqrt().divide(mean) # square root of inverse of enl
# If ci <= cu, the kernel lies in a "pure speckle" area -> return simple mean
cu = 1.0 / math.sqrt(enl)
# If cu < ci < cmax the kernel lies in the low textured speckle area -> return the filtered value
cmax = math.sqrt(2.0) * cu
alpha = ee.Image(1.0 + cu * cu).divide(ci.multiply(ci).subtract(cu * cu))
b = alpha.subtract(enl + 1.0)
d = (mean.multiply(mean).multiply(b).multiply(b).add(
alpha.multiply(mean).multiply(nat_img).multiply(4.0 * enl)))
f = b.multiply(mean).add(d.sqrt()).divide(alpha.multiply(2.0))
caster = ee.Dictionary.fromLists(bandNames, ee.List.repeat("float", 3))
img1 = (geeutils.power_to_db(mean.updateMask(
ci.lte(cu))).rename(bandNames).cast(caster))
img2 = (geeutils.power_to_db(
f.updateMask(ci.gt(cu)).updateMask(
ci.lt(cmax))).rename(bandNames).cast(caster))
img3 = img.updateMask(ci.gte(cmax)).rename(bandNames).cast(caster)
# If ci > cmax do not filter at all (i.e. we don't do anything, other then masking)
result = (ee.ImageCollection([img1, img2, img3]).reduce(
ee.Reducer.firstNonNull()).rename(bandNames).clip(img.geometry()))
# Compose a 3 band image with the mean filtered "pure speckle", the "low textured" filtered and the unfiltered portions
return result
def lee_sigma(img, window=9, sigma=0.9, looks=4, tk=7, keep_bands=["angle"]):
"""Lee Sigma speckle filtering algorithm.
Implemented from interpreting https://doi.org/10.1109/TGRS.2008.2002881
args:
img (ee.Image): Earth engine image object. Expects that imagery is a SAR image
window (int, optional): moving window size to apply filter (i.e. a value of 9 == 9x9 window). default = 9
sigma (float, optional): sigma lookup value from table 1 in paper. default = 0.9
looks (int, optional): look intensity value from table 1 in paper. default = 4
tk (int, optional): threshold value to determine values in window as point targets. default = 7
keep_bands (list[str], optional): list of band names to drop during filtering and include in the result
default = ["angle"]
returns:
ee.Image: filtered SAR image using the Lee Sigma algorithm
"""
band_names = img.bandNames()
if keep_bands is not None:
keep_img = img.select(keep_bands)
proc_bands = band_names.removeAll(keep_bands)
else:
proc_bands = band_names
img = img.select(proc_bands)
midPt = (window // 2) + 1 if (window % 2) != 0 else window // 2
kernelWeights = ee.List.repeat(ee.List.repeat(1, window), window)
kernel = ee.Kernel.fixed(window, window, kernelWeights, midPt, midPt)
targetWeights = ee.List.repeat(ee.List.repeat(1, 3), 3)
targetkernel = ee.Kernel.fixed(3, 3, targetWeights, 1, 1)
# Lookup table for range and eta values for intensity
sigmaLookup = ee.Dictionary({
1:
ee.Dictionary({
0.5:
ee.Dictionary({
"A1": 0.436,
"A2": 1.92,
"η": 0.4057
}),
0.6:
ee.Dictionary({
"A1": 0.343,
"A2": 2.21,
"η": 0.4954
}),
0.7:
ee.Dictionary({
"A1": 0.254,
"A2": 2.582,
"η": 0.5911
}),
0.8:
ee.Dictionary({
"A1": 0.168,
"A2": 3.094,
"η": 0.6966
}),
0.9:
ee.Dictionary({
"A1": 0.084,
"A2": 3.941,
"η": 0.8191
}),
0.95:
ee.Dictionary({
"A1": 0.043,
"A2": 4.840,
"η": 0.8599
}),
}),
2:
ee.Dictionary({
0.5:
ee.Dictionary({
"A1": 0.582,
"A2": 1.584,
"η": 0.2763
}),
0.6:
ee.Dictionary({
"A1": 0.501,
"A2": 1.755,
"η": 0.3388
}),
0.7:
ee.Dictionary({
"A1": 0.418,
"A2": 1.972,
"η": 0.4062
}),
0.8:
ee.Dictionary({
"A1": 0.327,
"A2": 2.260,
"η": 0.4819
}),
0.9:
ee.Dictionary({
"A1": 0.221,
"A2": 2.744,
"η": 0.5699
}),
0.95:
ee.Dictionary({
"A1": 0.152,
"A2": 3.206,
"η": 0.6254
}),
}),
3:
ee.Dictionary({
0.5:
ee.Dictionary({
"A1": 0.652,
"A2": 1.458,
"η": 0.2222
}),
0.6:
ee.Dictionary({
"A1": 0.580,
"A2": 1.586,
"η": 0.2736
}),
0.7:
ee.Dictionary({
"A1": 0.505,
"A2": 1.751,
"η": 0.3280
}),
0.8:
ee.Dictionary({
"A1": 0.419,
"A2": 1.865,
"η": 0.3892
}),
0.9:
ee.Dictionary({
"A1": 0.313,
"A2": 2.320,
"η": 0.4624
}),
0.95:
ee.Dictionary({
"A1": 0.238,
"A2": 2.656,
"η": 0.5084
}),
}),
4:
ee.Dictionary({
0.5:
ee.Dictionary({
"A1": 0.694,
"A2": 1.385,
"η": 0.1921
}),
0.6:
ee.Dictionary({
"A1": 0.630,
"A2": 1.495,
"η": 0.2348
}),
0.7:
ee.Dictionary({
"A1": 0.560,
"A2": 1.627,
"η": 0.2825
}),
0.8:
ee.Dictionary({
"A1": 0.480,
"A2": 1.804,
"η": 0.3354
}),
0.9:
ee.Dictionary({
"A1": 0.378,
"A2": 2.094,
"η": 0.3991
}),
0.95:
ee.Dictionary({
"A1": 0.302,
"A2": 2.360,
"η": 0.4391
}),
}),
})
# extract data from lookup
looksDict = ee.Dictionary(sigmaLookup.get(ee.String(str(looks))))
sigmaImage = ee.Dictionary(looksDict.get(ee.String(str(sigma)))).toImage()
a1 = sigmaImage.select("A1")
a2 = sigmaImage.select("A2")
aRange = a2.subtract(a1)
eta = sigmaImage.select("η").pow(2)
img = geeutils.db_to_power(img)
# MMSE estimator
mmseMask = img.gte(a1).Or(img.lte(a2))
mmseIn = img.updateMask(mmseMask)
oneImg = ee.Image(1)
z = mmseIn.reduceNeighborhood(ee.Reducer.mean(), kernel, None, True)
varz = mmseIn.reduceNeighborhood(ee.Reducer.variance(), kernel)
varx = (varz.subtract(z.abs().pow(2).multiply(eta))).divide(
oneImg.add(eta))
b = varx.divide(varz)
mmse = oneImg.subtract(b).multiply(z.abs()).add(b.multiply(mmseIn))
# workflow
z99 = ee.Dictionary(
img.reduceRegion(
reducer=ee.Reducer.percentile([99], None, 255, 0.001, 1e6),
geometry=img.geometry(),
scale=10,
bestEffort=True,
)).toImage()
overThresh = img.gte(z99)
K = overThresh.reduceNeighborhood(ee.Reducer.sum(), targetkernel, None,
True)
retainPixel = K.gte(tk)
xHat = geeutils.power_to_db(img.updateMask(retainPixel).unmask(mmse))
output = ee.Image(xHat).rename(proc_bands)
if keep_bands is not None:
output = output.addBands(keep_img)
return output
def perona_malik(img, n_iters=10, K=3, method=1):
"""Perona-Malik (anisotropic diffusion) convolution
Developed by Gennadii Donchyts see https://groups.google.com/g/google-earth-engine-developers/c/umGlt5qIN1I/m/PD8lsJ7qBAAJ
I(n+1, i, j) = I(n, i, j) + lambda * (cN * dN(I) + cS * dS(I) + cE * dE(I), cW * dW(I))
args:
img (ee.Image): Earth engine image object. Expects that imagery is a SAR image
n_iters (int, optional): Number of interations to apply filter
K (int,optional): moving window size to apply filter (i.e. a value of 7 == 7x7 window). default = 3
method (int, optional): choose method 1 (default) or 2
returns:
ee.Image: filtered SAR image using the perona malik algorithm
"""
def _method_1(dI_W, dI_E, dI_N, dI_S):
cW = dI_W.pow(2).multiply(k1).exp()
cE = dI_E.pow(2).multiply(k1).exp()
cN = dI_N.pow(2).multiply(k1).exp()
cS = dI_S.pow(2).multiply(k1).exp()
return cW, cE, cN, cS
def _method_2(dI_W, dI_E, dI_N, dI_S):
cW = one.divide(one.add(dI_W.pow(2).divide(k2)))
cE = one.divide(one.add(dI_E.pow(2).divide(k2)))
cN = one.divide(one.add(dI_N.pow(2).divide(k2)))
cS = one.divide(one.add(dI_S.pow(2).divide(k2)))
return cW, cE, cN, cS
# covnert db to natural units before applying filter
power = geeutils.db_to_power(img)
dxW = ee.Kernel.fixed(3, 3, [[0, 0, 0], [1, -1, 0], [0, 0, 0]])
dxE = ee.Kernel.fixed(3, 3, [[0, 0, 0], [0, -1, 1], [0, 0, 0]])
dyN = ee.Kernel.fixed(3, 3, [[0, 1, 0], [0, -1, 0], [0, 0, 0]])
dyS = ee.Kernel.fixed(3, 3, [[0, 0, 0], [0, -1, 0], [0, 1, 0]])
one = ee.Image.constant(1.0)
l = ee.Image.constant(0.2)
k = ee.Image.constant(K)
k1 = ee.Image.constant(-1.0 / K)
k2 = k.pow(2)
if method == 1:
_method = _method_1
elif method == 2:
_method = _method_2
else:
raise NotImplementedError(
"Could not determine algorithm to apply filter...options for `method` are 1 or 2"
)
for i in range(n_iters):
dI_W = power.convolve(dxW)
dI_E = power.convolve(dxE)
dI_N = power.convolve(dyN)
dI_S = power.convolve(dyS)
cW, cE, cN, cS = _method(dI_W, dI_E, dI_N, dI_S)
power = power.add(
l.multiply(
cN.multiply(dI_N).add(cS.multiply(dI_S)).add(
cE.multiply(dI_E)).add(cW.multiply(dI_W))))
# covnert natural to db units after filter is done
img = geeutils.power_to_db(power)
return img
def refined_lee(image, keep_bands=["angle"]):
"""Refined Lee speckle filtering algorithm.
Algorithm adapted from https://groups.google.com/g/google-earth-engine-developers/c/ExepnAmP-hQ/m/7e5DnjXXAQAJ
args:
image (ee.Image): Earth engine image object. Expects that imagery is a SAR image
returns:
ee.Image: filtered SAR image using the Refined Lee algorithm
"""
# TODO: include keep bands...maybe one-shot filtering if using keep_bands???
def apply_filter(b):
"""Closure function to apply the refined lee algorithm on individual bands"""
b = ee.String(b)
img = power.select(b)
# img must be in natural units, i.e. not in dB!
# Set up 3x3 kernels
weights3 = ee.List.repeat(ee.List.repeat(1, 3), 3)
kernel3 = ee.Kernel.fixed(3, 3, weights3, 1, 1, False)
mean3 = img.reduceNeighborhood(ee.Reducer.mean(), kernel3)
variance3 = img.reduceNeighborhood(ee.Reducer.variance(), kernel3)
# Use a sample of the 3x3 windows inside a 7x7 windows to determine gradients and directions
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],
])
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
sample_mean = mean3.neighborhoodToBands(sample_kernel)
sample_var = variance3.neighborhoodToBands(sample_kernel)
# Determine the 4 gradients for the sampled windows
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
max_gradient = gradients.reduce(ee.Reducer.max())
# Create a mask for band pixels that are the maximum gradient
gradmask = gradients.eq(max_gradient)
# duplicate gradmask bands: each gradient represents 2 directions
gradmask = gradmask.addBands(gradmask)
# Determine the 8 directions
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())
sample_stats = sample_var.divide(sample_mean.multiply(sample_mean))
# Calculate localNoiseVariance
sigmaV = (sample_stats.toArray().arraySort().arraySlice(
0, 0, 5).arrayReduce(ee.Reducer.mean(), [0]))
# Set up the 7*7 kernels for directional statistics
rect_weights = ee.List.repeat(ee.List.repeat(0, 7), 3).cat(
ee.List.repeat(ee.List.repeat(1, 7), 4))
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],
])
rect_kernel = ee.Kernel.fixed(7, 7, rect_weights, 3, 3, False)
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.
dir_mean = img.reduceNeighborhood(ee.Reducer.mean(),
rect_kernel).updateMask(
directions.eq(1))
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 i in range(1, 4):
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
varX = dir_var.subtract(
dir_mean.multiply(dir_mean).multiply(sigmaV)).divide(
sigmaV.add(1.0))
b = varX.divide(dir_var)
# return multi-band image band from array
return (dir_mean.add(b.multiply(img.subtract(dir_mean))).arrayProject(
[0]).arrayFlatten([["sum"]]).float())
band_names = image.bandNames()
if keep_bands is not None:
keep_img = image.select(keep_bands)
proc_bands = band_names.removeAll(keep_bands)
else:
proc_bands = band_names
image = image.select(proc_bands)
power = geeutils.db_to_power(image)
result = ee.ImageCollection(proc_bands.map(apply_filter)).toBands()
output = geeutils.power_to_db(ee.Image(result)).rename(proc_bands)
if keep_bands is not None:
output = output.addBands(keep_img)
return output
def lee_sigma(img, window=9, sigma=0.9, looks=4, tk=7, keep_bands="angle"):
band_names = img.bandNames()
proc_bands = band_names.remove(keep_bands)
keep_img = img.select(keep_bands)
img = img.select(proc_bands)
midPt = (window // 2) + 1 if (window % 2) != 0 else window // 2
kernelWeights = ee.List.repeat(ee.List.repeat(1, window), window)
kernel = ee.Kernel.fixed(window, window, kernelWeights, midPt, midPt)
targetWeights = ee.List.repeat(ee.List.repeat(1, 3), 3)
targetkernel = ee.Kernel.fixed(3, 3, targetWeights, 1, 1)
# Lookup table for range and eta values for intensity
sigmaLookup = ee.Dictionary({
1:
ee.Dictionary({
0.5:
ee.Dictionary({
"A1": 0.436,
"A2": 1.92,
"η": 0.4057
}),
0.6:
ee.Dictionary({
"A1": 0.343,
"A2": 2.21,
"η": 0.4954
}),
0.7:
ee.Dictionary({
"A1": 0.254,
"A2": 2.582,
"η": 0.5911
}),
0.8:
ee.Dictionary({
"A1": 0.168,
"A2": 3.094,
"η": 0.6966
}),
0.9:
ee.Dictionary({
"A1": 0.084,
"A2": 3.941,
"η": 0.8191
}),
0.95:
ee.Dictionary({
"A1": 0.043,
"A2": 4.840,
"η": 0.8599
}),
}),
2:
ee.Dictionary({
0.5:
ee.Dictionary({
"A1": 0.582,
"A2": 1.584,
"η": 0.2763
}),
0.6:
ee.Dictionary({
"A1": 0.501,
"A2": 1.755,
"η": 0.3388
}),
0.7:
ee.Dictionary({
"A1": 0.418,
"A2": 1.972,
"η": 0.4062
}),
0.8:
ee.Dictionary({
"A1": 0.327,
"A2": 2.260,
"η": 0.4819
}),
0.9:
ee.Dictionary({
"A1": 0.221,
"A2": 2.744,
"η": 0.5699
}),
0.95:
ee.Dictionary({
"A1": 0.152,
"A2": 3.206,
"η": 0.6254
}),
}),
3:
ee.Dictionary({
0.5:
ee.Dictionary({
"A1": 0.652,
"A2": 1.458,
"η": 0.2222
}),
0.6:
ee.Dictionary({
"A1": 0.580,
"A2": 1.586,
"η": 0.2736
}),
0.7:
ee.Dictionary({
"A1": 0.505,
"A2": 1.751,
"η": 0.3280
}),
0.8:
ee.Dictionary({
"A1": 0.419,
"A2": 1.865,
"η": 0.3892
}),
0.9:
ee.Dictionary({
"A1": 0.313,
"A2": 2.320,
"η": 0.4624
}),
0.95:
ee.Dictionary({
"A1": 0.238,
"A2": 2.656,
"η": 0.5084
}),
}),
4:
ee.Dictionary({
0.5:
ee.Dictionary({
"A1": 0.694,
"A2": 1.385,
"η": 0.1921
}),
0.6:
ee.Dictionary({
"A1": 0.630,
"A2": 1.495,
"η": 0.2348
}),
0.7:
ee.Dictionary({
"A1": 0.560,
"A2": 1.627,
"η": 0.2825
}),
0.8:
ee.Dictionary({
"A1": 0.480,
"A2": 1.804,
"η": 0.3354
}),
0.9:
ee.Dictionary({
"A1": 0.378,
"A2": 2.094,
"η": 0.3991
}),
0.95:
ee.Dictionary({
"A1": 0.302,
"A2": 2.360,
"η": 0.4391
}),
}),
})
# extract data from lookup
looksDict = ee.Dictionary(sigmaLookup.get(ee.String(str(looks))))
sigmaImage = ee.Dictionary(looksDict.get(ee.String(str(sigma)))).toImage()
a1 = sigmaImage.select("A1")
a2 = sigmaImage.select("A2")
aRange = a2.subtract(a1)
eta = sigmaImage.select("η").pow(2)
img = geeutils.db_to_power(img)
# MMSE estimator
mmseMask = img.gte(a1).Or(img.lte(a2))
mmseIn = img.updateMask(mmseMask)
oneImg = ee.Image(1)
z = mmseIn.reduceNeighborhood(ee.Reducer.mean(), kernel, None, True)
varz = mmseIn.reduceNeighborhood(ee.Reducer.variance(), kernel)
varx = (varz.subtract(z.abs().pow(2).multiply(eta))).divide(
oneImg.add(eta))
b = varx.divide(varz)
mmse = oneImg.subtract(b).multiply(z.abs()).add(b.multiply(mmseIn))
# workflow
z99 = ee.Dictionary(
img.reduceRegion(
reducer=ee.Reducer.percentile([99], None, 255, 0.001, 1e6),
geometry=img.geometry(),
scale=10,
bestEffort=True,
)).toImage()
overThresh = img.gte(z99)
K = overThresh.reduceNeighborhood(ee.Reducer.sum(), targetkernel, None,
True)
retainPixel = K.gte(tk)
xHat = geeutils.power_to_db(img.updateMask(retainPixel).unmask(mmse))
return ee.Image(xHat).rename(proc_bands).addBands(keep_img)
def refined_lee(image):
def apply_filter(b):
img = power.select([b])
# img must be in natural units, i.e. not in dB!
# Set up 3x3 kernels
weights3 = ee.List.repeat(ee.List.repeat(1, 3), 3)
kernel3 = ee.Kernel.fixed(3, 3, weights3, 1, 1, False)
mean3 = img.reduceNeighborhood(ee.Reducer.mean(), kernel3)
variance3 = img.reduceNeighborhood(ee.Reducer.variance(), kernel3)
# Use a sample of the 3x3 windows inside a 7x7 windows to determine gradients and directions
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],
])
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
sample_mean = mean3.neighborhoodToBands(sample_kernel)
sample_var = variance3.neighborhoodToBands(sample_kernel)
# Determine the 4 gradients for the sampled windows
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
max_gradient = gradients.reduce(ee.Reducer.max())
# Create a mask for band pixels that are the maximum gradient
gradmask = gradients.eq(max_gradient)
# duplicate gradmask bands: each gradient represents 2 directions
gradmask = gradmask.addBands(gradmask)
# Determine the 8 directions
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())
sample_stats = sample_var.divide(sample_mean.multiply(sample_mean))
# Calculate localNoiseVariance
sigmaV = (sample_stats.toArray().arraySort().arraySlice(
0, 0, 5).arrayReduce(ee.Reducer.mean(), [0]))
# Set up the 7*7 kernels for directional statistics
rect_weights = ee.List.repeat(ee.List.repeat(0, 7), 3).cat(
ee.List.repeat(ee.List.repeat(1, 7), 4))
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],
])
rect_kernel = ee.Kernel.fixed(7, 7, rect_weights, 3, 3, False)
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.
dir_mean = img.reduceNeighborhood(ee.Reducer.mean(),
rect_kernel).updateMask(
directions.eq(1))
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 i in range(1, 4):
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
varX = dir_var.subtract(
dir_mean.multiply(dir_mean).multiply(sigmaV)).divide(
sigmaV.add(1.0))
b = varX.divide(dir_var)
# return multi-band image band from array
return (dir_mean.add(b.multiply(img.subtract(dir_mean))).arrayProject(
[0]).arrayFlatten([["sum"]]).float())
bandNames = image.bandNames()
power = geeutils.db_to_power(image)
result = ee.ImageCollection(
bandNames.map(apply_filter)).toBands().rename(bandNames)
return geeutils.power_to_db(ee.Image(result))
def slope_correction(image, elevation, model="volume", buffer=0, scale=1000):
"""This function applies the slope correction on a Sentinel-1 image.
Function based on https:# doi.org/10.3390/rs12111867.
Adapted from https:# github.com/ESA-PhiLab/radiometric-slope-correction/blob/master/notebooks/1%20-%20Generate%20Data.ipynb
args:
image (ee.Image): Sentinel-1 to perform correction on
elevation (ee.Image): Input DEM to calculate slope corrections from
model (str, optional): physical reference model to be applied. Options are 'volume' or 'surface'.
default = volume
buffer (int, optional): buffer in meters for layover/shadow mask. If zero then no buffer will be applied. default = 0
scale (int, optional): reduction scale to process satellite heading compared to ground. Increasing will reduce
chance of OOM errors but reduce local scale correction accuracy. default = 1000
returns:
ee.Image: slope corrected SAR imagery with look and local incidence angle bands
raises:
NotImplementedError: when keyword model is not of 'volume' or 'surface'
"""
def _volumetric_model_SCF(theta_iRad, alpha_rRad):
"""Closure funnction for calculation of volumetric model SCF
args:
theta_iRad (ee.Image): incidence angle in radians
alpha_rRad (ee.Image): slope steepness in range
returns:
ee.Image
"""
# model
nominator = (ninetyRad.subtract(theta_iRad).add(alpha_rRad)).tan()
denominator = (ninetyRad.subtract(theta_iRad)).tan()
return nominator.divide(denominator)
def _surface_model_SCF(theta_iRad, alpha_rRad, alpha_azRad):
"""Closure funnction for calculation of direct model SCF
args:
theta_iRad (ee.Image): incidence angle in radians
alpha_rRad (ee.Image): slope steepness in range
alpha_azRad (ee.Image): slope steepness in azimuth
returns:
ee.Image
"""
# model
nominator = (ninetyRad.subtract(theta_iRad)).cos()
denominator = alpha_azRad.cos().multiply(
(ninetyRad.subtract(theta_iRad).add(alpha_rRad)).cos())
return nominator.divide(denominator)
def _erode(image, distance):
"""Closure function to buffer raster values
args:
image (ee.Image): image that should be buffered
distance (int): distance of buffer in meters
returns:
ee.Image
"""
d = (image.Not().unmask(1).fastDistanceTransform(10).sqrt().multiply(
ee.Image.pixelArea().sqrt()))
return image.updateMask(d.gt(distance))
def _masking(alpha_rRad, theta_iRad, buffer):
"""Closure function for masking of layover and shadow
args:
alpha_rRad (ee.Image): slope steepness in range
theta_iRad (ee.Image): incidence angle in radians
buffer (int): buffer in meters
returns:
ee.Image
"""
# layover, where slope > radar viewing angle
layover = alpha_rRad.lt(theta_iRad).rename("layover")
# shadow
shadow = alpha_rRad.gt(
ee.Image.constant(-1).multiply(
ninetyRad.subtract(theta_iRad))).rename("shadow")
# add buffer to layover and shadow
if buffer > 0:
layover = _erode(layover, buffer)
shadow = _erode(shadow, buffer)
# combine layover and shadow
no_data_mask = layover.And(shadow).rename("no_data_mask")
return no_data_mask
# get the image geometry and projection
geom = image.geometry(scale)
proj = image.select(1).projection()
# image to convert angle to radians
to_radians = ee.Image.constant((math.pi / 180))
# create a 90 degree image in radians
ninetyRad = ee.Image.constant(90).multiply(to_radians)
# calculate the look direction
heading = (ee.Terrain.aspect(image.select("angle")).reduceRegion(
ee.Reducer.mean(), geom, scale).get("aspect"))
# Sigma0 to Power of input image
sigma0Pow = geeutils.db_to_power(image)
# the numbering follows the article chapters
# 2.1.1 Radar geometry
theta_iRad = image.select("angle").multiply(to_radians)
phi_iRad = ee.Image.constant(heading).multiply(to_radians)
# 2.1.2 Terrain geometry
alpha_sRad = (ee.Terrain.slope(elevation).select("slope").multiply(
to_radians).setDefaultProjection(proj))
phi_sRad = (ee.Terrain.aspect(elevation).select("aspect").multiply(
to_radians).setDefaultProjection(proj))
# 2.1.3 Model geometry
# reduce to 3 angle
phi_rRad = phi_iRad.subtract(phi_sRad)
# slope steepness in range (eq. 2)
alpha_rRad = (alpha_sRad.tan().multiply(phi_rRad.cos())).atan()
# slope steepness in azimuth (eq 3)
alpha_azRad = (alpha_sRad.tan().multiply(phi_rRad.sin())).atan()
# local incidence angle (eq. 4)
theta_liaRad = (alpha_azRad.cos().multiply(
(theta_iRad.subtract(alpha_rRad)).cos())).acos()
theta_liaDeg = theta_liaRad.multiply(180 / math.pi)
# 2.2
# Gamma_nought
gamma0 = sigma0Pow.divide(theta_iRad.cos())
gamma0dB = geeutils.db_to_power(gamma0).select(["VV", "VH"],
["VV_gamma0", "VH_gamma0"])
if model == "volume":
scf = _volumetric_model_SCF(theta_iRad, alpha_rRad)
elif model == "surface":
scf = _surface_model_SCF(theta_iRad, alpha_rRad, alpha_azRad)
else:
raise NotImplementedError(
f"Defined model, {model}, has not been implemented. Options are 'volume' or 'surface'"
)
# apply model for Gamm0_f
gamma0_flat = gamma0.divide(scf)
gamma0_flatDB = geeutils.power_to_db(gamma0_flat).select(["VV", "VH"])
# calculate layover and shadow mask
masks = _masking(alpha_rRad, theta_iRad, buffer)
return (gamma0_flatDB.updateMask(masks).addBands(
image.select("angle")).addBands(
theta_liaDeg.rename("local_inc_angle")))