def testImageDctPreservesVolume(self):
"""Tests that image_dct() is volume preserving."""
for _ in range(4):
im = np.float32(np.random.uniform(size=(4, 4, 2)))
jacobian = util.compute_jacobian(util.image_dct, im)
# Assert that the determinant of the Jacobian is close to 1.
det = np.linalg.det(jacobian)
self.assertAllClose(det, 1., atol=1e-5, rtol=1e-5)
def testRgbToSyuvPreservesVolume(self):
"""Tests that rgb_to_syuv() is volume preserving."""
for _ in range(4):
im = np.float32(np.random.uniform(size=(1, 1, 3)))
jacobian = util.compute_jacobian(util.rgb_to_syuv, im)
# Assert that the determinant of the Jacobian is close to 1.
det = np.linalg.det(jacobian)
self.assertAllClose(det, 1., atol=1e-5, rtol=1e-5)
def testWaveletTransformationIsVolumePreserving(self):
"""Tests that construct() is volume preserving when size is a power of 2."""
sz = (1, 4, 4)
num_levels = 2
im = np.float32(np.random.uniform(0., 1., sz))
for wavelet_type in wavelet.generate_filters():
# Construct the Jacobian of construct().
def fun(z):
# pylint: disable=cell-var-from-loop
return wavelet.flatten(wavelet.construct(z, num_levels, wavelet_type))
jacobian = util.compute_jacobian(fun, im)
# Assert that the determinant of the Jacobian is close to 1.
det = np.linalg.det(jacobian)
self.assertAllClose(det, 1., atol=1e-5, rtol=1e-5)
