def q2c(y):
"""
Convert from quads in y to complex numbers in z.
"""
j2 = (np.sqrt(0.5) * np.array([1, 1j])).astype(appropriate_complex_type_for(y))
# Arrange pixels from the corners of the quads into
# 2 subimages of alternate real and imag pixels.
# a----b
# | |
# | |
# c----d
# Combine (a,b) and (d,c) to form two complex subimages.
p = y[0::2, 0::2]*j2[0] + y[0::2, 1::2]*j2[1] # p = (a + jb) / sqrt(2)
q = y[1::2, 1::2]*j2[0] - y[1::2, 0::2]*j2[1] # q = (d - jc) / sqrt(2)
# Form the 2 highpasses in z.
z = np.dstack((p-q,p+q))
return z
def q2c(y):
"""
Convert from quads in y to complex numbers in z.
"""
j2 = (np.sqrt(0.5) * np.array([1, 1j])).astype(
appropriate_complex_type_for(y))
# Arrange pixels from the corners of the quads into
# 2 subimages of alternate real and imag pixels.
# a----b
# | |
# | |
# c----d
# Combine (a,b) and (d,c) to form two complex subimages.
p = y[0::2, 0::2] * j2[0] + y[0::2, 1::2] * j2[1] # p = (a + jb) / sqrt(2)
q = y[1::2, 1::2] * j2[0] - y[1::2, 0::2] * j2[1] # q = (d - jc) / sqrt(2)
# Form the 2 highpasses in z.
z = np.dstack((p - q, p + q))
return z
def forward(self, X, nlevels=3, include_scale=False):
"""Perform a *n*-level DTCWT-2D decompostion on a 2D matrix *X*.
:param X: 2D real array
:param nlevels: Number of levels of wavelet decomposition
:returns: A :py:class:`dtcwt.Pyramid` compatible object representing the transform-domain signal
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, Sept 2001
.. codeauthor:: Cian Shaffrey, Cambridge University, Sept 2001
"""
# If biort has 6 elements instead of 4, then it's a modified
# rotationally symmetric wavelet
# FIXME: there's probably a nicer way to do this
if len(self.biort) == 4:
h0o, g0o, h1o, g1o = self.biort
elif len(self.biort) == 6:
h0o, g0o, h1o, g1o, h2o, g2o = self.biort
else:
raise ValueError('Biort wavelet must have 6 or 4 components.')
# If qshift has 12 elements instead of 8, then it's a modified
# rotationally symmetric wavelet
# FIXME: there's probably a nicer way to do this
if len(self.qshift) == 8:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = self.qshift
elif len(self.qshift) == 12:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b, h2a, h2b = self.qshift[:10]
else:
raise ValueError('Qshift wavelet must have 12 or 8 components.')
X = np.atleast_2d(asfarray(X))
original_size = X.shape
if len(X.shape) >= 3:
raise ValueError('The entered image is {0}, which is invalid '.
format('x'.join(list(str(s) for s in X.shape))) +
'for the 2D transform in a numpy backend. ' +
'Please enter each image slice separately.')
# The next few lines of code check to see if the image is odd in size, if so an extra ...
# row/column will be added to the bottom/right of the image
initial_row_extend = 0 #initialise
initial_col_extend = 0
if original_size[0] % 2 != 0:
# if X.shape[0] is not divisable by 2 then we need to extend X by adding a row at the bottom
X = np.vstack((X, X[[-1],:])) # Any further extension will be done in due course.
initial_row_extend = 1
if original_size[1] % 2 != 0:
# if X.shape[1] is not divisable by 2 then we need to extend X by adding a col to the left
X = np.hstack((X, X[:,[-1]]))
initial_col_extend = 1
extended_size = X.shape
if nlevels == 0:
if include_scale:
return Pyramid(X, (), ())
else:
return Pyramid(X, ())
# initialise
Yh = [None,] * nlevels
if include_scale:
# this is only required if the user specifies a third output component.
Yscale = [None,] * nlevels
complex_dtype = appropriate_complex_type_for(X)
if nlevels >= 1:
# Do odd top-level filters on cols.
Lo = colfilter(X,h0o).T
Hi = colfilter(X,h1o).T
if len(self.biort) >= 6:
Ba = colfilter(X,h2o).T
# Do odd top-level filters on rows.
LoLo = colfilter(Lo,h0o).T
Yh[0] = np.zeros((LoLo.shape[0] >> 1, LoLo.shape[1] >> 1, 6), dtype=complex_dtype)
Yh[0][:,:,0:6:5] = q2c(colfilter(Hi,h0o).T) # Horizontal pair
Yh[0][:,:,2:4:1] = q2c(colfilter(Lo,h1o).T) # Vertical pair
if len(self.biort) >= 6:
Yh[0][:,:,1:5:3] = q2c(colfilter(Ba,h2o).T) # Diagonal pair
else:
Yh[0][:,:,1:5:3] = q2c(colfilter(Hi,h1o).T) # Diagonal pair
if include_scale:
Yscale[0] = LoLo
for level in xrange(1, nlevels):
row_size, col_size = LoLo.shape
if row_size % 4 != 0:
# Extend by 2 rows if no. of rows of LoLo are not divisable by 4
LoLo = np.vstack((LoLo[:1,:], LoLo, LoLo[-1:,:]))
if col_size % 4 != 0:
# Extend by 2 cols if no. of cols of LoLo are not divisable by 4
LoLo = np.hstack((LoLo[:,:1], LoLo, LoLo[:,-1:]))
# Do even Qshift filters on rows.
Lo = coldfilt(LoLo,h0b,h0a).T
Hi = coldfilt(LoLo,h1b,h1a).T
if len(self.qshift) >= 12:
Ba = coldfilt(LoLo,h2b,h2a).T
# Do even Qshift filters on columns.
LoLo = coldfilt(Lo,h0b,h0a).T
Yh[level] = np.zeros((LoLo.shape[0]>>1, LoLo.shape[1]>>1, 6), dtype=complex_dtype)
Yh[level][:,:,0:6:5] = q2c(coldfilt(Hi,h0b,h0a).T) # Horizontal
Yh[level][:,:,2:4:1] = q2c(coldfilt(Lo,h1b,h1a).T) # Vertical
if len(self.qshift) >= 12:
Yh[level][:,:,1:5:3] = q2c(coldfilt(Ba,h2b,h2a).T) # Diagonal
else:
Yh[level][:,:,1:5:3] = q2c(coldfilt(Hi,h1b,h1a).T) # Diagonal
if include_scale:
Yscale[level] = LoLo
Yl = LoLo
if initial_row_extend == 1 and initial_col_extend == 1:
logging.warn('The image entered is now a {0} NOT a {1}.'.format(
'x'.join(list(str(s) for s in extended_size)),
'x'.join(list(str(s) for s in original_size))))
logging.warn(
'The bottom row and rightmost column have been duplicated, prior to decomposition.')
if initial_row_extend == 1 and initial_col_extend == 0:
logging.warn('The image entered is now a {0} NOT a {1}.'.format(
'x'.join(list(str(s) for s in extended_size)),
'x'.join(list(str(s) for s in original_size))))
logging.warn(
'The bottom row has been duplicated, prior to decomposition.')
if initial_row_extend == 0 and initial_col_extend == 1:
logging.warn('The image entered is now a {0} NOT a {1}.'.format(
'x'.join(list(str(s) for s in extended_size)),
'x'.join(list(str(s) for s in original_size))))
logging.warn(
'The rightmost column has been duplicated, prior to decomposition.')
if include_scale:
return Pyramid(Yl, tuple(Yh), tuple(Yscale))
else:
return Pyramid(Yl, tuple(Yh))
def forward(self, X, nlevels=3, include_scale=False):
"""Perform a *n*-level DTCWT-2D decompostion on a 2D matrix *X*.
:param X: 2D real array
:param nlevels: Number of levels of wavelet decomposition
:returns: A :py:class:`dtcwt.Pyramid` compatible object representing the transform-domain signal
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, Sept 2001
.. codeauthor:: Cian Shaffrey, Cambridge University, Sept 2001
"""
# If biort has 6 elements instead of 4, then it's a modified
# rotationally symmetric wavelet
# FIXME: there's probably a nicer way to do this
if len(self.biort) == 4:
h0o, g0o, h1o, g1o = self.biort
elif len(self.biort) == 6:
h0o, g0o, h1o, g1o, h2o, g2o = self.biort
else:
raise ValueError('Biort wavelet must have 6 or 4 components.')
# If qshift has 12 elements instead of 8, then it's a modified
# rotationally symmetric wavelet
# FIXME: there's probably a nicer way to do this
if len(self.qshift) == 8:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = self.qshift
elif len(self.qshift) == 12:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b, h2a, h2b = self.qshift[:10]
else:
raise ValueError('Qshift wavelet must have 12 or 8 components.')
X = np.atleast_2d(asfarray(X))
original_size = X.shape
if len(X.shape) >= 3:
raise ValueError(
'The entered image is {0}, please enter each image slice separately.'
.format('x'.join(list(str(s) for s in X.shape))))
# The next few lines of code check to see if the image is odd in size, if so an extra ...
# row/column will be added to the bottom/right of the image
initial_row_extend = 0 #initialise
initial_col_extend = 0
if original_size[0] % 2 != 0:
# if X.shape[0] is not divisable by 2 then we need to extend X by adding a row at the bottom
X = np.vstack(
(X, X[[-1], :]
)) # Any further extension will be done in due course.
initial_row_extend = 1
if original_size[1] % 2 != 0:
# if X.shape[1] is not divisable by 2 then we need to extend X by adding a col to the left
X = np.hstack((X, X[:, [-1]]))
initial_col_extend = 1
extended_size = X.shape
if nlevels == 0:
if include_scale:
return Pyramid(X, (), ())
else:
return Pyramid(X, ())
# initialise
Yh = [
None,
] * nlevels
if include_scale:
# this is only required if the user specifies a third output component.
Yscale = [
None,
] * nlevels
complex_dtype = appropriate_complex_type_for(X)
if nlevels >= 1:
# Do odd top-level filters on cols.
Lo = colfilter(X, h0o).T
Hi = colfilter(X, h1o).T
if len(self.biort) >= 6:
Ba = colfilter(X, h2o).T
# Do odd top-level filters on rows.
LoLo = colfilter(Lo, h0o).T
Yh[0] = np.zeros((LoLo.shape[0] >> 1, LoLo.shape[1] >> 1, 6),
dtype=complex_dtype)
Yh[0][:, :, 0:6:5] = q2c(colfilter(Hi, h0o).T) # Horizontal pair
Yh[0][:, :, 2:4:1] = q2c(colfilter(Lo, h1o).T) # Vertical pair
if len(self.biort) >= 6:
Yh[0][:, :, 1:5:3] = q2c(colfilter(Ba, h2o).T) # Diagonal pair
else:
Yh[0][:, :, 1:5:3] = q2c(colfilter(Hi, h1o).T) # Diagonal pair
if include_scale:
Yscale[0] = LoLo
for level in xrange(1, nlevels):
row_size, col_size = LoLo.shape
if row_size % 4 != 0:
# Extend by 2 rows if no. of rows of LoLo are not divisable by 4
LoLo = np.vstack((LoLo[:1, :], LoLo, LoLo[-1:, :]))
if col_size % 4 != 0:
# Extend by 2 cols if no. of cols of LoLo are not divisable by 4
LoLo = np.hstack((LoLo[:, :1], LoLo, LoLo[:, -1:]))
# Do even Qshift filters on rows.
Lo = coldfilt(LoLo, h0b, h0a).T
Hi = coldfilt(LoLo, h1b, h1a).T
if len(self.qshift) >= 12:
Ba = coldfilt(LoLo, h2b, h2a).T
# Do even Qshift filters on columns.
LoLo = coldfilt(Lo, h0b, h0a).T
Yh[level] = np.zeros((LoLo.shape[0] >> 1, LoLo.shape[1] >> 1, 6),
dtype=complex_dtype)
Yh[level][:, :, 0:6:5] = q2c(coldfilt(Hi, h0b,
h0a).T) # Horizontal
Yh[level][:, :, 2:4:1] = q2c(coldfilt(Lo, h1b, h1a).T) # Vertical
if len(self.qshift) >= 12:
Yh[level][:, :, 1:5:3] = q2c(coldfilt(Ba, h2b,
h2a).T) # Diagonal
else:
Yh[level][:, :, 1:5:3] = q2c(coldfilt(Hi, h1b,
h1a).T) # Diagonal
if include_scale:
Yscale[level] = LoLo
Yl = LoLo
if initial_row_extend == 1 and initial_col_extend == 1:
logging.warn('The image entered is now a {0} NOT a {1}.'.format(
'x'.join(list(str(s) for s in extended_size)),
'x'.join(list(str(s) for s in original_size))))
logging.warn(
'The bottom row and rightmost column have been duplicated, prior to decomposition.'
)
if initial_row_extend == 1 and initial_col_extend == 0:
logging.warn('The image entered is now a {0} NOT a {1}.'.format(
'x'.join(list(str(s) for s in extended_size)),
'x'.join(list(str(s) for s in original_size))))
logging.warn(
'The bottom row has been duplicated, prior to decomposition.')
if initial_row_extend == 0 and initial_col_extend == 1:
logging.warn('The image entered is now a {0} NOT a {1}.'.format(
'x'.join(list(str(s) for s in extended_size)),
'x'.join(list(str(s) for s in original_size))))
logging.warn(
'The rightmost column has been duplicated, prior to decomposition.'
)
if include_scale:
return Pyramid(Yl, tuple(Yh), tuple(Yscale))
else:
return Pyramid(Yl, tuple(Yh))
