def upsample(image, method=None):
"""Specialised function to upsample an image by a factor of two using
a specified sampling method. If *image* is an array of shape (NxMx...) then
the output will have shape (2Nx2Mx...). Only rows and columns are
upsampled, depth axes and greater are interpolated but are not upsampled.
:param image: an array containing the image to upsample
:param method: if non-None, a string specifying the sampling method to use.
If *method* is ``None``, the default sampling method ``'lanczos'`` is used.
The following sampling methods are supported:
=========== ===========
Name Description
=========== ===========
nearest Nearest-neighbour sampling
bilinear Bilinear sampling
lanczos Lanczos sampling with window radius of 3
=========== ===========
"""
image = np.atleast_2d(asfarray(image))
# The default '.T' operator doesn't quite do what we want since it
# reverses the axes rather than only swapping the first two
def _t(X):
axes = np.arange(len(X.shape))
axes[:2] = (1,0)
return np.transpose(X, axes)
return _upsample_columns(_t(_upsample_columns(_t(image), method)), method)
def upsample(image, method=None):
"""Specialised function to upsample an image by a factor of two using
a specified sampling method. If *image* is an array of shape (NxMx...) then
the output will have shape (2Nx2Mx...). Only rows and columns are
upsampled, depth axes and greater are interpolated but are not upsampled.
:param image: an array containing the image to upsample
:param method: if non-None, a string specifying the sampling method to use.
If *method* is ``None``, the default sampling method ``'lanczos'`` is used.
The following sampling methods are supported:
=========== ===========
Name Description
=========== ===========
nearest Nearest-neighbour sampling
bilinear Bilinear sampling
lanczos Lanczos sampling with window radius of 3
=========== ===========
"""
image = np.atleast_2d(asfarray(image))
# The default '.T' operator doesn't quite do what we want since it
# reverses the axes rather than only swapping the first two
def _t(X):
axes = np.arange(len(X.shape))
axes[:2] = (1, 0)
return np.transpose(X, axes)
return _upsample_columns(_t(_upsample_columns(_t(image), method)), method)
def _upsample_columns(X, method=None):
"""
The centre of columns of X, an M-columned matrix, are assumed to have co-ordinates
{ 0, 1, 2, ... , M-1 } which means that the up-sampled matrix's columns should sample
from { -0.25, 0.25, 0.75, ... , M-1.25 }. We can view that as an interleaved set of teo
*convolutions* of X. The first, A, using a kernel equivalent to sampling the { -0.25, 0.75,
1.75, 2.75, ... M-1.25 } columns and the second, B, sampling the { 0.25, 1.25, ... , M-0.75 }
columns.
"""
if method is None:
method = 'lanczos'
X = np.atleast_2d(asfarray(X))
out_shape = list(X.shape)
out_shape[1] *= 2
output = np.zeros(out_shape, dtype=X.dtype)
# Centres of sampling for A and B convolutions
M = X.shape[1]
A_columns = np.linspace(-0.25, M-1.25, M)
B_columns = A_columns + 0.5
# For A columns sample at x = ceil(x) - 0.25 with ceil(x) = { 0, 1, 2, ..., M-1 }
# For B columns sample at x = floor(x) + 0.25 with floor(x) = { 0, 1, 2, ..., M-1 }
int_columns = np.linspace(0, M-1, M)
if method == 'lanczos':
# Lanczos kernel width
a = 3.0
sample_offsets = np.arange(-a, a+1)
# For A: if i = ceil(x) + di, => ceil(x) - i = -0.25 - di
# For B: if i = floor(x) + di, => floor(x) - i = 0.25 - di
l_as = np.sinc(-0.25-sample_offsets)*np.sinc((-0.25-sample_offsets)/a)
l_bs = np.sinc(0.25-sample_offsets)*np.sinc((0.25-sample_offsets)/a)
elif method == 'nearest':
# Nearest neighbour kernel width is 1
sample_offsets = [0,]
l_as = l_bs = [1,]
elif method == 'bilinear':
# Bilinear kernel width is technically 2 but we need to offset the kernels differently
# for A and B columns:
sample_offsets = [-1,0,1]
l_as = [0.25, 0.75, 0]
l_bs = [0, 0.75, 0.25]
else:
raise ValueError('Unknown interpolation mode: {0}'.format(mode))
# Convolve
for di, l_a, l_b in zip(sample_offsets, l_as, l_bs):
columns = reflect(int_columns + di, -0.5, M-0.5).astype(np.int)
output[:,0::2,...] += l_a * X[:,columns,...]
output[:,1::2,...] += l_b * X[:,columns,...]
return output
def upsample_highpass(im, method=None):
"""As :py:func:`upsample` except that the highpass image is first phase
rolled so that the filter has approximate DC centre frequency. The upshot
is that this is the function to use when re-sampling complex subband
images.
"""
im = np.atleast_2d(asfarray(im))
# Sampled co-ordinates
dxs, dys = np.meshgrid(np.arange(im.shape[1]*2), np.arange(im.shape[0]*2))
sxs = 0.5 * (dxs + 0.5) - 0.5
sys = 0.5 * (dys + 0.5) - 0.5
# phase unwrap
X, Y = np.meshgrid(np.arange(im.shape[1]), np.arange(im.shape[0]))
im_unwrap = im * _phase_image(X, Y, True)
# sample
im_sampled = upsample(im_unwrap, method)
# re-wrap
return im_sampled * _phase_image(sxs, sys, False)
def upsample_highpass(im, method=None):
"""As :py:func:`upsample` except that the highpass image is first phase
rolled so that the filter has approximate DC centre frequency. The upshot
is that this is the function to use when re-sampling complex subband
images.
"""
im = np.atleast_2d(asfarray(im))
# Sampled co-ordinates
dxs, dys = np.meshgrid(np.arange(im.shape[1] * 2),
np.arange(im.shape[0] * 2))
sxs = 0.5 * (dxs + 0.5) - 0.5
sys = 0.5 * (dys + 0.5) - 0.5
# phase unwrap
X, Y = np.meshgrid(np.arange(im.shape[1]), np.arange(im.shape[0]))
im_unwrap = im * _phase_image(X, Y, True)
# sample
im_sampled = upsample(im_unwrap, method)
# re-wrap
return im_sampled * _phase_image(sxs, sys, False)
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 dtwavexfm3(X, nlevels=3, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, ext_mode=4, discard_level_1=False):
"""Perform a *n*-level DTCWT-3D decompostion on a 3D matrix *X*.
:param X: 3D real array-like object
: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`.
:param ext_mode: Extension mode. See below.
:param discard_level_1: True if level 1 high-pass bands are to be discarded.
:returns Yl: The real lowpass image from the final level
:returns Yh: A tuple containing the complex highpass subimages for each level.
Each element of *Yh* is a 4D complex array with the 4th dimension having
size 28. The 3D slice ``Yh[l][:,:,:,d]`` corresponds to the complex higpass
coefficients for direction d at level l where d and l are both 0-indexed.
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).
There are two values for *ext_mode*, either 4 or 8. If *ext_mode* = 4,
check whether 1st level is divisible by 2 (if not we raise a
``ValueError``). Also check whether from 2nd level onwards, the coefs can
be divided by 4. If any dimension size is not a multiple of 4, append extra
coefs by repeating the edges. If *ext_mode* = 8, check whether 1st level is
divisible by 4 (if not we raise a ``ValueError``). Also check whether from
2nd level onwards, the coeffs can be divided by 8. If any dimension size is
not a multiple of 8, append extra coeffs by repeating the edges twice.
If *discard_level_1* is True the highpass coefficients at level 1 will be
discarded. (And, in fact, will never be calculated.) This turns the
transform from being 8:1 redundant to being 1:1 redundant at the cost of
no-longer allowing perfect reconstruction. If this option is selected then
`Yh[0]` will be `None`. Note that :py:func:`dtwaveifm3` will accepts
`Yh[0]` being `None` and will treat it as being zero.
Example::
# Performs a 3-level transform on the real 3D array X using the 13,19-tap
# filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
Yl, Yh = dtwavexfm3(X, 3, 'near_sym_b', 'qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Huizhong Chen, Jan 2009
.. codeauthor:: Nick Kingsbury, Cambridge University, July 1999.
"""
X = np.atleast_3d(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
# Check value of ext_mode. TODO: this should really be an enum :S
if ext_mode != 4 and ext_mode != 8:
raise ValueError('ext_mode must be one of 4 or 8')
Yl = X
Yh = [None,] * nlevels
# level is 0-indexed
for level in xrange(nlevels):
# Transform
if level == 0 and discard_level_1:
Yl = _level1_xfm_no_highpass(Yl, h0o, h1o, ext_mode)
elif level == 0 and not discard_level_1:
Yl, Yh[level] = _level1_xfm(Yl, h0o, h1o, ext_mode)
else:
Yl, Yh[level] = _level2_xfm(Yl, h0a, h0b, h1a, h1b, ext_mode)
return Yl, tuple(Yh)
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 _upsample_columns(X, method=None):
"""
The centre of columns of X, an M-columned matrix, are assumed to have co-ordinates
{ 0, 1, 2, ... , M-1 } which means that the up-sampled matrix's columns should sample
from { -0.25, 0.25, 0.75, ... , M-1.25 }. We can view that as an interleaved set of teo
*convolutions* of X. The first, A, using a kernel equivalent to sampling the { -0.25, 0.75,
1.75, 2.75, ... M-1.25 } columns and the second, B, sampling the { 0.25, 1.25, ... , M-0.75 }
columns.
"""
if method is None:
method = 'lanczos'
X = np.atleast_2d(asfarray(X))
out_shape = list(X.shape)
out_shape[1] *= 2
output = np.zeros(out_shape, dtype=X.dtype)
# Centres of sampling for A and B convolutions
M = X.shape[1]
A_columns = np.linspace(-0.25, M - 1.25, M)
B_columns = A_columns + 0.5
# For A columns sample at x = ceil(x) - 0.25 with ceil(x) = { 0, 1, 2, ..., M-1 }
# For B columns sample at x = floor(x) + 0.25 with floor(x) = { 0, 1, 2, ..., M-1 }
int_columns = np.linspace(0, M - 1, M)
if method == 'lanczos':
# Lanczos kernel width
a = 3.0
sample_offsets = np.arange(-a, a + 1)
# For A: if i = ceil(x) + di, => ceil(x) - i = -0.25 - di
# For B: if i = floor(x) + di, => floor(x) - i = 0.25 - di
l_as = np.sinc(-0.25 - sample_offsets) * np.sinc(
(-0.25 - sample_offsets) / a)
l_bs = np.sinc(0.25 - sample_offsets) * np.sinc(
(0.25 - sample_offsets) / a)
elif method == 'nearest':
# Nearest neighbour kernel width is 1
sample_offsets = [
0,
]
l_as = l_bs = [
1,
]
elif method == 'bilinear':
# Bilinear kernel width is technically 2 but we need to offset the kernels differently
# for A and B columns:
sample_offsets = [-1, 0, 1]
l_as = [0.25, 0.75, 0]
l_bs = [0, 0.75, 0.25]
else:
raise ValueError('Unknown interpolation mode: {0}'.format(mode))
# Convolve
for di, l_a, l_b in zip(sample_offsets, l_as, l_bs):
columns = reflect(int_columns + di, -0.5, M - 0.5).astype(np.int)
output[:, 0::2, ...] += l_a * X[:, columns, ...]
output[:, 1::2, ...] += l_b * X[:, columns, ...]
return output
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)