def test_output_size():
Y = coldfilt(lena, (-1,1), (1,-1))
assert Y.shape == (lena.shape[0]/2, lena.shape[1])
def dtwavexfm(X,
nlevels=3,
biort=DEFAULT_BIORT,
qshift=DEFAULT_QSHIFT,
include_scale=False):
"""Perform a *n*-level DTCWT decompostion on a 1D column vector *X* (or on
the columns of a matrix *X*).
:param X: 1D real array or 2D real array whose columns are to be transformed
: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 (N, M, 6) shape 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 5-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 = dtwavexfm(X,5,'near_sym_b','qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
# Need this because colfilter and friends assumes input is 2d
X = asfarray(X)
if len(X.shape) == 1:
X = np.atleast_2d(X).T
# 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
L = np.asanyarray(X.shape)
# ensure that X is an even length, thus enabling it to be extended if needs be.
if X.shape[0] % 2 != 0:
raise ValueError('Size of input X must be a multiple of 2')
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 scales are to be outputted
Yscale = [
None,
] * nlevels
# Level 1.
Hi = colfilter(X, h1o)
Lo = colfilter(X, h0o)
Yh[0] = Hi[::2, :] + 1j * Hi[1::2, :] # Convert Hi to complex form.
if include_scale:
Yscale[0] = Lo
# Levels 2 and above.
for level in xrange(1, nlevels):
# Check to see if height of Lo is divisable by 4, if not extend.
if Lo.shape[0] % 4 != 0:
Lo = np.vstack((Lo[0, :], Lo, Lo[-1, :]))
Hi = coldfilt(Lo, h1b, h1a)
Lo = coldfilt(Lo, h0b, h0a)
Yh[level] = Hi[::2, :] + 1j * Hi[1::
2, :] # Convert Hi to complex form.
if include_scale:
Yscale[level] = Lo
Yl = Lo
if include_scale:
return Yl, Yh, Yscale
else:
return Yl, Yh
def test_good_input_size():
coldfilt(lena[:,:511], (-1,1), (1,-1))
def test_good_input_size_non_orthogonal():
coldfilt(lena[:,:511], (1,1), (1,1))
def test_different_size():
coldfilt(lena, (-0.5,-1,2,1,0.5), (-1,2,-1))
def test_bad_input_size():
coldfilt(lena[:511,:], (-1,1), (1,-1))
def test_odd_filter():
coldfilt(lena, (-1,2,-1), (-1,2,1))
def _level2_xfm(X, h0a, h0b, h1a, h1b, ext_mode):
"""Perform level 2 or greater of the 3d transform.
"""
if ext_mode == 4:
if X.shape[0] % 4 != 0:
X = np.concatenate((X[[0],:,:], X, X[[-1],:,:]), 0)
if X.shape[1] % 4 != 0:
X = np.concatenate((X[:,[0],:], X, X[:,[-1],:]), 1)
if X.shape[2] % 4 != 0:
X = np.concatenate((X[:,:,[0]], X, X[:,:,[-1]]), 2)
elif ext_mode == 8:
if X.shape[0] % 8 != 0:
X = np.concatenate((X[(0,0),:,:], X, X[(-1,-1),:,:]), 0)
if X.shape[1] % 8 != 0:
X = np.concatenate((X[:,(0,0),:], X, X[:,(-1,-1),:]), 1)
if X.shape[2] % 8 != 0:
X = np.concatenate((X[:,:,(0,0)], X, X[:,:,(-1,-1)]), 2)
# Create work area
work_shape = np.asanyarray(X.shape)
work = np.zeros(work_shape, dtype=X.dtype)
# Form some useful slices
s0a = slice(None, work.shape[0] >> 1)
s1a = slice(None, work.shape[1] >> 1)
s2a = slice(None, work.shape[2] >> 1)
s0b = slice(work.shape[0] >> 1, None)
s1b = slice(work.shape[1] >> 1, None)
s2b = slice(work.shape[2] >> 1, None)
# Assign input
work = X
# Loop over 2nd dimension extracting 2D slice from first and 3rd dimensions
for f in xrange(work.shape[1]):
# extract slice (copy required because we overwrite the work array)
y = work[:, f, :].T.copy()
# Do even Qshift filters on 3rd dim.
work[:, f, s2b] = coldfilt(y, h1b, h1a).T
work[:, f, s2a] = coldfilt(y, h0b, h0a).T
# Loop over 3rd dimension extracting 2D slice from first and 2nd dimensions
for f in xrange(work.shape[2]):
# Do even Qshift filters on rows.
y1 = work[:, :, f].T
y2 = np.vstack((coldfilt(y1, h0b, h0a), coldfilt(y1, h1b, h1a))).T
# Do even Qshift filters on columns.
work[s0a, :, f] = coldfilt(y2, h0b, h0a)
work[s0b, :, f] = coldfilt(y2, h1b, h1a)
# Return appropriate slices of output
return (
work[s0a, s1a, s2a], # LLL
np.concatenate((
cube2c(work[s0a, s1b, s2a]), # HLL
cube2c(work[s0b, s1a, s2a]), # LHL
cube2c(work[s0b, s1b, s2a]), # HHL
cube2c(work[s0a, s1a, s2b]), # LLH
cube2c(work[s0a, s1b, s2b]), # HLH
cube2c(work[s0b, s1a, s2b]), # LHH
cube2c(work[s0b, s1b, s2b]), # HLH
), axis=3)
)
def dtwavexfm(X, nlevels=3, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, include_scale=False):
"""Perform a *n*-level DTCWT decompostion on a 1D column vector *X* (or on
the columns of a matrix *X*).
:param X: 1D real array or 2D real array whose columns are to be transformed
: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 (N, M, 6) shape 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 5-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 = dtwavexfm(X,5,'near_sym_b','qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
# Need this because colfilter and friends assumes input is 2d
X = asfarray(X)
if len(X.shape) == 1:
X = np.atleast_2d(X).T
# 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
L = np.asanyarray(X.shape)
# ensure that X is an even length, thus enabling it to be extended if needs be.
if X.shape[0] % 2 != 0:
raise ValueError('Size of input X must be a multiple of 2')
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 scales are to be outputted
Yscale = [None,] * nlevels
# Level 1.
Hi = colfilter(X, h1o)
Lo = colfilter(X, h0o)
Yh[0] = Hi[::2,:] + 1j*Hi[1::2,:] # Convert Hi to complex form.
if include_scale:
Yscale[0] = Lo
# Levels 2 and above.
for level in xrange(1, nlevels):
# Check to see if height of Lo is divisable by 4, if not extend.
if Lo.shape[0] % 4 != 0:
Lo = np.vstack((Lo[0,:], Lo, Lo[-1,:]))
Hi = coldfilt(Lo,h1b,h1a)
Lo = coldfilt(Lo,h0b,h0a)
Yh[level] = Hi[::2,:] + 1j*Hi[1::2,:] # Convert Hi to complex form.
if include_scale:
Yscale[level] = Lo
Yl = Lo
if include_scale:
return Yl, Yh, Yscale
else:
return Yl, 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)
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)
