import os
import numpy as np
from polsartools.utils.proc_utils import process_chunks_parallel
from polsartools.utils.utils import conv2d,time_it
from polsartools.utils.convert_matrices import T3_C3_mat
from .fp_infiles import fp_c3t3files
[docs]
@time_it
def h_a_alpha_fp(in_dir, win=1, fmt="tif", cog=False,
ovr = [2, 4, 8, 16], comp = False,
max_workers=None,block_size=(512, 512),
progress_callback=None # for QGIS plugin
):
"""Perform H/A//α (Entropy/Anisotropy/Alpha) decomposition for full-pol SAR data.
This function implements the Cloude-Pottier decomposition, computing entropy (H),
alpha angle (α), anisotropy (A), and normalized eigenvalues from full-polarimetric
SAR coherency (T3) or covariance (C3) matrices. This decomposition is fundamental
for understanding scattering mechanisms in polarimetric SAR data.
Examples
--------
>>> # Basic usage with default parameters
>>> h_a_alpha_fp("/path/to/fullpol_data")
>>> # Advanced usage with custom parameters
>>> h_a_alpha_fp(
... in_dir="/path/to/fullpol_data",
... win=5,
... fmt="tif",
... cog=True,
... block_size=(1024, 1024)
... )
Parameters
----------
in_dir : str
Path to the input folder containing full-pol T3 or C3 matrix files.
win : int, default=1
Size of the spatial averaging window. Larger windows improve eigenvalue/eigenvector
estimation but decrease spatial resolution.
fmt : {'tif', 'bin'}, default='tif'
Output file format:
- 'tif': GeoTIFF format with georeferencing information
- 'bin': Raw binary format
cog : bool, default=False
If True, creates Cloud Optimized GeoTIFF (COG) outputs with internal tiling
and overviews for efficient web access.
ovr : list[int], default=[2, 4, 8, 16]
Overview levels for COG creation. Each number represents the
decimation factor for that overview level.
comp : bool, default=False
If True, uses LZW compression for GeoTIFF outputs.
max_workers : int | None, default=None
Maximum number of parallel processing workers. If None, uses
CPU count - 1 workers.
block_size : tuple[int, int], default=(512, 512)
Size of processing blocks (rows, cols) for parallel computation.
Larger blocks use more memory but may be more efficient.
Returns
-------
None
Writes six output files to disk:
1. H_fp: Entropy (H) [0-1]
2. alpha_fp: Alpha angle (α) [0°-90°]
3. anisotropy_fp: Anisotropy (A) [0-1]
4. e1_norm: Normalized first eigenvalue
5. e2_norm: Normalized second eigenvalue
6. e3_norm: Normalized third eigenvalue
Notes
-----
The H/α/A decomposition provides three main parameters:
1. Entropy (H):
- Range: [0, 1]
- H = 0: Single scattering mechanism
- H = 1: Random mixture of scattering mechanisms
- Formula: H = -∑(pᵢ log₃(pᵢ)), where pᵢ are normalized eigenvalues
2. Alpha angle (α):
- Range: [0°, 90°]
- α ≈ 0°: Surface scattering
- α ≈ 45°: Volume scattering
- α ≈ 90°: Double-bounce scattering
- Formula: α = ∑(pᵢαᵢ), where αᵢ are individual alpha angles
3. Anisotropy (A):
- Range: [0, 1]
- Measures relative importance of secondary mechanisms
- A = (λ₂ - λ₃)/(λ₂ + λ₃), where λᵢ are eigenvalues
References
----------
- Cloude, S.R. and Pottier, E., 2002. An entropy based classification scheme for land applications of polarimetric SAR. IEEE transactions on geoscience and remote sensing, 35(1), pp.68-78.
"""
write_flag=True
input_filepaths = fp_c3t3files(in_dir)
output_filepaths = []
if fmt == "bin":
output_filepaths.append(os.path.join(in_dir, "H_fp.bin"))
output_filepaths.append(os.path.join(in_dir, "alpha_fp.bin"))
output_filepaths.append(os.path.join(in_dir, "anisotropy_fp.bin"))
output_filepaths.append(os.path.join(in_dir, "e1_norm.bin"))
output_filepaths.append(os.path.join(in_dir, "e2_norm.bin"))
output_filepaths.append(os.path.join(in_dir, "e3_norm.bin"))
else:
output_filepaths.append(os.path.join(in_dir, "H_fp.tif"))
output_filepaths.append(os.path.join(in_dir, "alpha_fp.tif"))
output_filepaths.append(os.path.join(in_dir, "anisotropy_fp.tif"))
output_filepaths.append(os.path.join(in_dir, "e1_norm.tif"))
output_filepaths.append(os.path.join(in_dir, "e2_norm.tif"))
output_filepaths.append(os.path.join(in_dir, "e3_norm.tif"))
process_chunks_parallel(input_filepaths, list(output_filepaths),
window_size=win, write_flag=write_flag,
processing_func=process_chunk_halphafp,block_size=block_size,
max_workers=max_workers, num_outputs=len(output_filepaths),
cog=cog,ovr=ovr,comp=comp,
progress_callback=progress_callback
)
def process_chunk_halphafp(chunks, window_size, input_filepaths, *args):
# additional_arg1 = args[0] if len(args) > 0 else None
# additional_arg2 = args[1] if len(args) > 1 else None
if 'T11' in input_filepaths[0] and 'T22' in input_filepaths[5] and 'T33' in input_filepaths[8]:
t11_T1 = np.array(chunks[0])
t12_T1 = np.array(chunks[1])+1j*np.array(chunks[2])
t13_T1 = np.array(chunks[3])+1j*np.array(chunks[4])
t21_T1 = np.conj(t12_T1)
t22_T1 = np.array(chunks[5])
t23_T1 = np.array(chunks[6])+1j*np.array(chunks[7])
t31_T1 = np.conj(t13_T1)
t32_T1 = np.conj(t23_T1)
t33_T1 = np.array(chunks[8])
T_T1 = np.array([[t11_T1, t12_T1, t13_T1],
[t21_T1, t22_T1, t23_T1],
[t31_T1, t32_T1, t33_T1]])
# T_T1 = T3_C3_mat(T3)
elif 'C11' in input_filepaths[0] and 'C22' in input_filepaths[5] and 'C33' in input_filepaths[8]:
C11 = np.array(chunks[0])
C12 = np.array(chunks[1])+1j*np.array(chunks[2])
C13 = np.array(chunks[3])+1j*np.array(chunks[4])
C21 = np.conj(C12)
C22 = np.array(chunks[5])
C23 = np.array(chunks[6])+1j*np.array(chunks[7])
C31 = np.conj(C13)
C32 = np.conj(C23)
C33 = np.array(chunks[8])
T_T1 = np.array([[C11, C12, C13],
[C21, C22, C23],
[C31, C32, C33]])
else:
raise ValueError("Invalid input matrices. Ensure the input is either T3 or C3 matrix foolder.")
if window_size>1:
kernel = np.ones((window_size,window_size),np.float32)/(window_size*window_size)
t11f = conv2d(T_T1[0,0,:,:],kernel)
t12f = conv2d(np.real(T_T1[0,1,:,:]),kernel)+1j*conv2d(np.imag(T_T1[0,1,:,:]),kernel)
t13f = conv2d(np.real(T_T1[0,2,:,:]),kernel)+1j*conv2d(np.imag(T_T1[0,2,:,:]),kernel)
t21f = np.conj(t12f)
t22f = conv2d(T_T1[1,1,:,:],kernel)
t23f = conv2d(np.real(T_T1[1,2,:,:]),kernel)+1j*conv2d(np.imag(T_T1[1,2,:,:]),kernel)
t31f = np.conj(t13f)
t32f = np.conj(t23f)
t33f = conv2d(T_T1[2,2,:,:],kernel)
T_T1 = np.array([[t11f, t12f, t13f], [t21f, t22f, t23f], [t31f, t32f, t33f]])
_,_,rows,cols = np.shape(T_T1)
T_T1 = T_T1.reshape(9, rows, cols)
# Indices for vectorized access
i, j = np.indices((rows, cols))
T_T1 = np.dstack((T_T1[0,:,:],T_T1[1,:,:],T_T1[2,:,:],
T_T1[3,:,:],T_T1[4,:,:],T_T1[5,:,:],T_T1[6,:,:],T_T1[7,:,:],T_T1[8,:,:]))
data = T_T1.reshape( T_T1.shape[0]*T_T1.shape[1], T_T1.shape[2]).reshape((-1,3,3))
# infinity, nan handling
data = np.nan_to_num(data, nan=0.0, posinf=0, neginf=0)
# data = np.nan_to_num(data, nan=np.nan, posinf=np.nan, neginf=np.nan)
evals_, evecs_ = np.linalg.eig(data.reshape(-1, 3, 3))
# Sort eigenvalues for each pixel in descending order;
sorted_indices = np.argsort(evals_, axis=-1)[:, ::-1]
# Reorder eigenvalues and eigenvectors based on sorted indices
evals = np.take_along_axis(evals_, sorted_indices, axis=-1) # Reorder eigenvalues
# To reorder the eigenvectors, we use indexing
# Use `sorted_indices` to index along the second axis (the 3 components of the eigenvector)
evecs = np.array([evecs_[i, :, sorted_indices[i]] for i in range(evecs_.shape[0])])
# print('Eigen!')
# Not sure if this is required; if enabled entropy values are different between polsarpro and this code
# evals[:,0][evals[:,0] <0] = 0
# evals[:,1][evals[:,1] <0] = 0
# evals[:,2][evals[:,2] <0] = 0
# evals[:,0][evals[:,0] >1] = 1
# evals[:,1][evals[:,1] >1] = 1
# evals[:,2][evals[:,2] >1] = 1
eval_norm1 = (evals[:,0])/(evals[:,0] + evals[:,1]+ evals[:,2])
eval_norm1[eval_norm1<0]=0
# eval_norm1[eval_norm1>1]=1
eval_norm2 = (evals[:,1])/(evals[:,0] + evals[:,1]+ evals[:,2])
eval_norm2[eval_norm2<0]=0
# eval_norm2[eval_norm2>1]=1
eval_norm3 = (evals[:,2])/(evals[:,0] + evals[:,1]+evals[:,2])
eval_norm3[eval_norm3<0]=0
# eval_norm3[eval_norm3>1]=1
# # %Alpha 1
eig_vec_r1 = np.real(evecs[:,0,0])
eig_vec_c1 = np.imag(evecs[:,0,0])
alpha1 = np.arccos(np.sqrt(eig_vec_r1*eig_vec_r1 + eig_vec_c1*eig_vec_c1))*180/np.pi
# # %Alpha 2
eig_vec_r2 = np.real(evecs[:,0,1])
eig_vec_c2 = np.imag(evecs[:,0,1])
alpha2 = np.arccos(np.sqrt(eig_vec_r2*eig_vec_r2 + eig_vec_c2*eig_vec_c2))*180/np.pi
# # %Alpha 3
eig_vec_r3 = np.real(evecs[:,0,2])
eig_vec_c3 = np.imag(evecs[:,0,2])
alpha3 = np.arccos(np.sqrt(eig_vec_r3*eig_vec_r3 + eig_vec_c3*eig_vec_c3))*180/np.pi
# # %Cloude Alpha
alpha_ = (eval_norm1*alpha1 + eval_norm2*alpha2+ eval_norm3*alpha3)
alpha_ = np.real(alpha_.reshape(rows,cols))
# print('Alpha!')
# # %Entropy
H = - eval_norm1*np.log10(eval_norm1)/np.log10(3) - eval_norm2*np.log10(eval_norm2)/np.log10(3) - eval_norm3*np.log10(eval_norm3)/np.log10(3)
H = np.real(H.reshape(rows,cols))
# alpha1 = alpha1.reshape(rows,cols)
# alpha2 = alpha2.reshape(rows,cols)
# alpha3 = alpha3.reshape(rows,cols)
## POLARIMETRIC SCATTERING ANISOTROPY (A)
Anisotropy = (eval_norm2-eval_norm3)/(eval_norm2+eval_norm3)
Anisotropy = np.real(Anisotropy.reshape(rows,cols))
eval_norm1 = np.real(eval_norm1.reshape(rows,cols))
eval_norm2 = np.real(eval_norm2.reshape(rows,cols))
eval_norm3 = np.real(eval_norm3.reshape(rows,cols))
return H.astype(np.float32),alpha_.astype(np.float32),Anisotropy.astype(np.float32),\
eval_norm1.astype(np.float32),eval_norm2.astype(np.float32),eval_norm3.astype(np.float32)
