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 subbands 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 subbands in z.
z = np.dstack((p-q,p+q))
return z
def dtwavexfm2(X, nlevels=3, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, 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
:param biort: Level 1 wavelets to use. See :py:func:`biort`.
:param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
:returns Yl: The real lowpass image from the final level
:returns Yh: A tuple containing the complex highpass subimages for each level.
:returns Yscale: If *include_scale* is True, a tuple containing real lowpass coefficients for every scale.
If *biort* or *qshift* are strings, they are used as an argument to the
:py:func:`biort` or :py:func:`qshift` functions. Otherwise, they are
interpreted as tuples of vectors giving filter coefficients. In the *biort*
case, this should be (h0o, g0o, h1o, g1o). In the *qshift* case, this should
be (h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b).
Example::
# Performs a 3-level transform on the real image X using the 13,19-tap
# filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
Yl, Yh = dtwavexfm2(X, 3, 'near_sym_b', 'qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, Sept 2001
.. codeauthor:: Cian Shaffrey, Cambridge University, Sept 2001
"""
X = np.atleast_2d(asfarray(X))
# Try to load coefficients if biort is a string parameter
try:
h0o, g0o, h1o, g1o = _biort(biort)
except TypeError:
h0o, g0o, h1o, g1o = biort
# Try to load coefficients if qshift is a string parameter
try:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = _qshift(qshift)
except TypeError:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = qshift
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 X, (), ()
else:
return 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
# 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, 5]] = q2c(colfilter(Hi,h0o).T) # Horizontal pair
Yh[0][:,:,[2, 3]] = q2c(colfilter(Lo,h1o).T) # Vertical pair
Yh[0][:,:,[1, 4]] = 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[[0],:], 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[:,[0]], LoLo, LoLo[:,[-1]]))
# Do even Qshift filters on rows.
Lo = coldfilt(LoLo,h0b,h0a).T
Hi = coldfilt(LoLo,h1b,h1a).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, 5]] = q2c(coldfilt(Hi,h0b,h0a).T) # Horizontal
Yh[level][:,:,[2, 3]] = q2c(coldfilt(Lo,h1b,h1a).T) # Vertical
Yh[level][:,:,[1, 4]] = q2c(coldfilt(Hi,h1b,h1a).T) # Diagonal
if include_scale:
Yscale[0] = 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 Yl, tuple(Yh), tuple(Yscale)
else:
return Yl, tuple(Yh)
def dtwavexfm2(X, nlevels=3, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, 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
:param biort: Level 1 wavelets to use. See :py:func:`biort`.
:param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
:returns Yl: The real lowpass image from the final level
:returns Yh: A tuple containing the complex highpass subimages for each level.
:returns Yscale: If *include_scale* is True, a tuple containing real lowpass coefficients for every scale.
If *biort* or *qshift* are strings, they are used as an argument to the
:py:func:`biort` or :py:func:`qshift` functions. Otherwise, they are
interpreted as tuples of vectors giving filter coefficients. In the *biort*
case, this should be (h0o, g0o, h1o, g1o). In the *qshift* case, this should
be (h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b).
Example::
# Performs a 3-level transform on the real image X using the 13,19-tap
# filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
Yl, Yh = dtwavexfm2(X, 3, 'near_sym_b', 'qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, Sept 2001
.. codeauthor:: Cian Shaffrey, Cambridge University, Sept 2001
"""
X = np.atleast_2d(asfarray(X))
# Try to load coefficients if biort is a string parameter
try:
h0o, g0o, h1o, g1o = _biort(biort)
except TypeError:
h0o, g0o, h1o, g1o = biort
# Try to load coefficients if qshift is a string parameter
try:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = _qshift(qshift)
except TypeError:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = qshift
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 X, (), ()
else:
return 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
# 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, 5]] = q2c(colfilter(Hi, h0o).T) # Horizontal pair
Yh[0][:, :, [2, 3]] = q2c(colfilter(Lo, h1o).T) # Vertical pair
Yh[0][:, :, [1, 4]] = 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[[0], :], 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[:, [0]], LoLo, LoLo[:, [-1]]))
# Do even Qshift filters on rows.
Lo = coldfilt(LoLo, h0b, h0a).T
Hi = coldfilt(LoLo, h1b, h1a).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, 5]] = q2c(coldfilt(Hi, h0b, h0a).T) # Horizontal
Yh[level][:, :, [2, 3]] = q2c(coldfilt(Lo, h1b, h1a).T) # Vertical
Yh[level][:, :, [1, 4]] = q2c(coldfilt(Hi, h1b, h1a).T) # Diagonal
if include_scale:
Yscale[0] = 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 Yl, tuple(Yh), tuple(Yscale)
else:
return Yl, tuple(Yh)
