import numpy as np
import scipy as scipy
import matplotlib.pyplot as plt
from skimage.segmentation import watershed
# from pyewt.src.boundaries2d import ewt2d_spectrum_regularize, symmetrize_fourier, UnSymmetrize_Fourier, ewt2d_get_maxima
# from pyewt.src.ewt2dvoronoi import ewt2d_Voronoi_Filterbank, ewt2d_merge_symmetric
from .boundaries2d import ewt2d_spectrum_regularize, symmetrize_fourier, UnSymmetrize_Fourier, ewt2d_get_maxima
from .ewt2dvoronoi import ewt2d_Voronoi_Filterbank, ewt2d_merge_symmetric
[docs]
def ewt2d_watershed(f,params):
""" Compute the 2D EWT based on a Watershed partitioning of the Fourier domain.
Parameters
----------
f : 2D ndarray
Input image.
params : dict
Transform parameters.
Returns
-------
ewtw : list of 2D ndarray
Collection of outputs of each EW filter.
mfb : list of 2D ndarray
The built filter bank.
maxima : ndarray
Coordinates of each meaningful detected maxima.
waterpartition : 2D ndarray
Detected Voronoi partition.
plane : ndarray
Scale-space domain.
Notes
-----
If params["log"] is set to True, then the detection is performed on the logarithm
of the spectrum of f.
params["typeDetect"] must be set to the wanted classification
method. The available options are:
- "otsu" : uses Otsu's technique
- "halfnormal" : uses a half-normal law to model the problem
- "empiricallaw" : uses the data itself to build a model of
the problem
- "kmeans" : uses kmeans to classify
params["t"]: is the initial scale for the Gaussian kernel (0.8 is a good default value).
params["kn"]: is the kernel size for the Gaussian kernel (6 is a good default value).
params["niter"]: is the number of iterations through the scales (4 is a good default value).
params["edge"]: is the size (in pixels) of the strip to ignore at the edge of the image (0 is no strip).
params["includeCenter"]: if 1, the center of the image is included in the scale space maxima (0 is not included).
params["tau"]: is the half width of the transition area for the Voronoi partition (0.1 is a good default value).
params["complex"]: if 1, the watershed partition is complex, otherwise it is real (0 is real).
Though usually not providing better results, this function allows regularization of the spectrum of f using the
selected method set in params["reg"]. The available methods are:
- "none" : does nothing, returns f
- "gaussian" : convolve f with a Gaussian of length and standard
deviation given by params["lengthfilter"] and
params["sigmafilter"], respectively
- "average": convolve f with a constant filter of length given
by params["lengthfilter"]
Author: Jerome Gilles
Institution: San Diego State University
Version: 1.0 (07/28/2025)
"""
if f.dtype != np.complex128:
f = f.astype(np.complex128)
# Get Fourier transform and its magnitude
ff_orig = np.fft.fftshift(np.fft.fft2(f))
# Symmetrize the spectrum if needed
absff, extH, extW = symmetrize_fourier(np.abs(ff_orig))
if params.get("log", 0) == 1:
absff = np.log(absff)
# Regularization (if requested)
absff = ewt2d_spectrum_regularize(absff, params)
# Get meaningful maxima
maxima, plane = ewt2d_get_maxima(absff, params, extH, extW)
# create the image of markers for watershed
markers = np.zeros_like(absff, dtype=np.int32)
for i, (y, x) in enumerate(maxima):
markers[y, x] = i + 1
# Build the Watershed cells
labels = watershed(-absff, markers)
waterpartition = UnSymmetrize_Fourier(labels, extH, extW)
# Extract each Watershed cell mask
# Make sure the labels are continuous
lab = np.unique(labels).tolist()
watercel = []
for k in lab:
mask = np.zeros(absff.shape, dtype=int)
mask[labels == k] = 1
watercel.append(mask)
# Group symmetric cells if real transform is required
if params.get("complex", 0) != 1:
waterocells = ewt2d_merge_symmetric(watercel,maxima)
mfb = ewt2d_Voronoi_Filterbank(absff.shape, waterocells, params["tau"], extH, extW)
else:
mfb = ewt2d_Voronoi_Filterbank(absff.shape, watercel, params["tau"], extH, extW)
# Perform the filtering
ewtw = []
for filt in mfb:
filtered = np.fft.ifft2(np.fft.ifftshift(ff_orig * filt))
ewtw.append(filtered)
return ewtw, mfb, maxima, waterpartition, plane
[docs]
def iewt2d_watershed(ewtw, mfb):
"""
Performs the inverse Empirical Watershed Wavelet Transform,
returning a reconstruction of the image.
Parameters
----------
ewtw : list of 2D ndarray
Empirical wavelet coefficients.
mfb : list of 2D ndarray
Corresponding empirical wavelet filters.
Returns
-------
rec : 2D ndarray
Reconstructed image.
Author: Jerome Gilles
Institution: San Diego State University
Version: 1.0 (07/28/2025)
"""
dual_sum = mfb[0] ** 2
rec = np.fft.fftshift(np.fft.fft2(ewtw[0])) * mfb[0]
for i in range(1, len(mfb)):
rec += np.fft.fftshift(np.fft.fft2(ewtw[i])) * mfb[i]
dual_sum += mfb[i] ** 2
rec = np.fft.ifft2(np.fft.ifftshift(rec / dual_sum))
return rec
[docs]
def show_ewt2d_watershed_boundaries(f, wat, color=None, logspec=0):
""" Plots the edges of the watershed partition onto the magnitude of the Fourier spectrum of the input image.
Parameters:
f: ndarray
Input image.
wat: ndarray
Watershed partition image (same size as f).
color: list or tuple
RGB color for the partition edges, values in [0,1]. Default is red.
logspec: int
If 1, plot the logarithm of the spectrum. Default is 0.
Author: Jerome Gilles
Institution: San Diego State University
Version: 1.0 (07/28/2025)
"""
if color is None:
color = [1, 0, 0]
# Find the edges of the Watershed partition
gr = np.zeros_like(f)
gr[:-1, :] += np.abs(np.diff(wat, axis=0))
gr[:, :-1] += np.abs(np.diff(wat, axis=1))
# Get the magnitude of the Fourier spectrum of f
absff = np.abs(np.fft.fftshift(np.fft.fft2(f)))
if logspec == 1:
absff = np.log(1 + absff)
# Normalize between [0,1]
absff = (absff - absff.min()) / (absff.max() - absff.min())
# Make it an RGB image
rgb_img = np.stack([absff]*3, axis=-1)
# Tag each edge pixel to the wanted color
edge_pixels = gr != 0
for k in range(3):
rgb_img[..., k][edge_pixels] = color[k]
plt.figure()
plt.imshow(rgb_img)
plt.axis('off')
plt.show()