def testDecompositionIsNonRedundant(self):
"""Test that wavelet construction is not redundant.
If the wavelet decompositon is not redundant, then we should be able to
1) Construct a wavelet decomposition
2) Alter a single coefficient in the decomposition
3) Collapse that decomposition into an image and back
and the two wavelet decompositions should be the same.
"""
for wavelet_type in wavelet.generate_filters():
for _ in range(4):
# Construct an image and a wavelet decomposition of it.
num_levels = np.int32(np.ceil(4 * np.random.uniform()))
sz_clamp = 2**(num_levels - 1) + 1
sz = np.maximum(
np.int32(
np.ceil(
np.array([2, 32, 32]) *
np.random.uniform(size=3))),
np.array([0, sz_clamp, sz_clamp]),
)
im = np.random.uniform(size=sz)
pyr = wavelet.construct(im, num_levels, wavelet_type)
# Pick a coefficient at random in the decomposition to alter.
d = np.int32(np.floor(np.random.uniform() * len(pyr)))
v = np.random.uniform()
if d == (len(pyr) - 1):
if np.prod(pyr[d].shape) > 0:
c, i, j = np.int32(
np.floor(
np.array(np.random.uniform(size=3)) *
pyr[d].shape)).tolist()
pyr[d][c, i, j] = v
else:
b = np.int32(np.floor(np.random.uniform() * len(pyr[d])))
if np.prod(pyr[d][b].shape) > 0:
c, i, j = np.int32(
np.floor(
np.array(np.random.uniform(size=3)) *
pyr[d][b].shape)).tolist()
pyr[d][b][c, i, j] = v
# Collapse and then reconstruct the wavelet decomposition, and check
# that it is unchanged.
recon = wavelet.collapse(pyr, wavelet_type)
pyr_again = wavelet.construct(recon, num_levels, wavelet_type)
self._assert_pyramids_close(pyr, pyr_again, 1e-8)
def transform_to_mat(self, x):
"""Transforms a batch of images to a matrix."""
assert len(x.shape) == 4
x = torch.as_tensor(x)
if self.color_space == 'YUV':
x = util.rgb_to_syuv(x)
# If `color_space` == 'RGB', do nothing.
# Reshape `x` from
# (num_batches, width, height, num_channels) to
# (num_batches * num_channels, width, height)
_, width, height, num_channels = x.shape
x_stack = torch.reshape(x.permute(0, 3, 1, 2), (-1, width, height))
# Turn each channel in `x_stack` into the spatial representation specified
# by `representation`.
if self.representation in wavelet.generate_filters():
x_stack = wavelet.flatten(
wavelet.rescale(
wavelet.construct(x_stack, self.wavelet_num_levels,
self.representation),
self.wavelet_scale_base))
elif self.representation == 'DCT':
x_stack = util.image_dct(x_stack)
# If `representation` == 'PIXEL', do nothing.
# Reshape `x_stack` from
# (num_batches * num_channels, width, height) to
# (num_batches, num_channels * width * height)
x_mat = torch.reshape(
torch.reshape(x_stack, (-1, num_channels, width, height)).permute(
0, 2, 3, 1), [-1, width * height * num_channels])
return x_mat
def testRescaleAndUnrescaleReproducesInput(self):
"""Tests that rescale(rescale(x, k), 1/k) = x."""
im = np.random.uniform(size=(2, 32, 32))
scale_base = np.exp(np.random.normal())
pyr = wavelet.construct(im, 4, 'LeGall5/3')
pyr_rescaled = wavelet.rescale(pyr, scale_base)
pyr_recon = wavelet.rescale(pyr_rescaled, 1. / scale_base)
self._assert_pyramids_close(pyr, pyr_recon, 1e-8)
def testRescaleOneHalfIsNormalized(self):
"""Tests that rescale(construct(k), 0.5)[-1] = k for constant image k."""
for num_levels in range(5):
k = np.random.uniform()
im = k * np.ones((2, 32, 32))
pyr = wavelet.construct(im, num_levels, 'LeGall5/3')
pyr_rescaled = wavelet.rescale(pyr, 0.5)
np.testing.assert_allclose(pyr_rescaled[-1],
k * np.ones_like(pyr_rescaled[-1]),
atol=1e-8,
rtol=1e-8)
def testAccurateRoundTripWithSmallRandomImages(self):
"""Tests that collapse(construct(x)) == x for x = [1, k, k], k in [1, 4]."""
for wavelet_type in wavelet.generate_filters():
for width in range(0, 5):
sz = [1, width, width]
num_levels = wavelet.get_max_num_levels(sz)
im = np.random.uniform(size=sz)
pyr = wavelet.construct(im, num_levels, wavelet_type)
recon = wavelet.collapse(pyr, wavelet_type)
np.testing.assert_allclose(recon, im, atol=1e-8, rtol=1e-8)
def testAccurateRoundTripWithLargeRandomImages(self):
"""Tests that collapse(construct(x)) == x for large random x's."""
for wavelet_type in wavelet.generate_filters():
for _ in range(4):
num_levels = np.int32(np.ceil(4 * np.random.uniform()))
sz_clamp = 2**(num_levels - 1) + 1
sz = np.maximum(
np.int32(
np.ceil(np.array([2, 32, 32]) * np.random.uniform(size=3))),
np.array([0, sz_clamp, sz_clamp]))
im = np.random.uniform(size=sz)
pyr = wavelet.construct(im, num_levels, wavelet_type)
recon = wavelet.collapse(pyr, wavelet_type)
np.testing.assert_allclose(recon, im, atol=1e-8, rtol=1e-8)
def testConstructMatchesGoldenData(self, device):
"""Tests construct() against golden data."""
im, pyr_true, wavelet_type = self._load_golden_data()
im = torch.tensor(im, device=device)
pyr = wavelet.construct(im, len(pyr_true) - 1, wavelet_type)
pyr = list(pyr)
for d in range(len(pyr) - 1):
pyr[d] = list(pyr[d])
for b in range(3):
pyr[d][b] = pyr[d][b].cpu().detach()
d = len(pyr) - 1
pyr[d] = pyr[d].cpu().detach()
self._assert_pyramids_close(pyr, pyr_true, 1e-5)
def testWaveletTransformationIsVolumePreserving(self):
"""Tests that construct() is volume preserving when size is a power of 2."""
for wavelet_type in wavelet.generate_filters():
sz = (1, 4, 4)
num_levels = 2
# Construct the Jacobian of construct().
im = np.float32(np.random.uniform(0., 1., sz))
jacobian = []
vec = lambda x: torch.reshape(x, [-1])
for d in range(im.size):
var_im = torch.autograd.Variable(torch.tensor(im), requires_grad=True)
coeff = vec(
wavelet.flatten(
wavelet.construct(var_im, num_levels, wavelet_type)))[d]
coeff.backward()
jacobian.append(np.reshape(var_im.grad.detach().numpy(), [-1]))
jacobian = np.stack(jacobian, 1)
# Assert that the determinant of the Jacobian is close to 1.
det = np.linalg.det(jacobian)
np.testing.assert_allclose(det, 1., atol=1e-5, rtol=1e-5)
def testRescaleDoesNotAffectTheFirstLevel(self):
"""Tests that rescale(x, s)[0] = x[0] for any s."""
im = np.random.uniform(size=(2, 32, 32))
pyr = wavelet.construct(im, 4, 'LeGall5/3')
pyr_rescaled = wavelet.rescale(pyr, np.exp(np.random.normal()))
self._assert_pyramids_close(pyr[0:1], pyr_rescaled[0:1], 1e-8)
def testRescaleOneIsANoOp(self):
"""Tests that rescale(x, 1) = x."""
im = np.random.uniform(size=(2, 32, 32))
pyr = wavelet.construct(im, 4, 'LeGall5/3')
pyr_rescaled = wavelet.rescale(pyr, 1.)
self._assert_pyramids_close(pyr, pyr_rescaled, 1e-8)
def _construct_preserves_dtype(self, float_dtype):
"""Checks that construct()'s output has the same precision as its input."""
x = float_dtype(np.random.normal(size=(3, 16, 16)))
for wavelet_type in wavelet.generate_filters():
y = wavelet.flatten(wavelet.construct(x, 3, wavelet_type))
np.testing.assert_equal(y.detach().numpy().dtype, float_dtype)
def testConstructMatchesGoldenData(self):
"""Tests construct() against golden data."""
im, pyr_true, wavelet_type = self._load_golden_data()
pyr = wavelet.construct(im, len(pyr_true) - 1, wavelet_type)
self._assert_pyramids_close(pyr, pyr_true, 1e-5)
