def __init__(self):
"""Initialize the distribution.
Load the values, tangents, and x-coordinate scaling of a spline that
approximates the partition function. The spline was produced by running
the script in fit_partition_spline.py.
"""
with util.get_resource_as_file(
'robust_loss/data/partition_spline.npz') as spline_file:
with np.load(spline_file, allow_pickle=False) as f:
self._spline_x_scale = f['x_scale']
self._spline_values = f['values']
self._spline_tangents = f['tangents']
def _load_golden_data(self):
"""Loads golden data: an RGBimage and its CDF9/7 decomposition.
This golden data was produced by running the code from
https://www.getreuer.info/projects/wavelet-cdf-97-implementation
on a test image.
Returns:
A tuple containing and image, its decomposition, and its wavelet type.
"""
with util.get_resource_as_file(
'robust_loss/data/wavelet_golden.mat') as golden_filename:
data = scipy.io.loadmat(golden_filename)
im = np.float32(data['I_color'])
pyr_true = data['pyr_color'][0, :].tolist()
for i in range(len(pyr_true) - 1):
pyr_true[i] = tuple(pyr_true[i].flatten())
pyr_true = tuple(pyr_true)
wavelet_type = 'CDF9/7'
return im, pyr_true, wavelet_type
def log_base_partition_function(alpha):
r"""Approximate the distribution's log-partition function with a 1D spline.
Because the partition function (Z(\alpha) in the paper) of the distribution is
difficult to model analytically, we approximate it with a (transformed) cubic
hermite spline: Each alpha is pushed through a nonlinearity before being used
to interpolate into a spline, which allows us to use a relatively small spline
to accurately model the log partition function over the range of all
non-negative input values.
Args:
alpha: A tensor or scalar of single or double precision floats containing
the set of alphas for which we would like an approximate log partition
function. Must be non-negative, as the partition function is undefined
when alpha < 0.
Returns:
An approximation of log(Z(alpha)) accurate to within 1e-6
"""
float_dtype = alpha.dtype
# Load the values, tangents, and x-coordinate scaling of a spline that
# approximates the partition function. This was produced by running
# the script in fit_partition_spline.py
with util.get_resource_as_file(
'robust_loss/data/partition_spline.npz') as spline_file:
with np.load(spline_file, allow_pickle=False) as f:
x_scale = tf.cast(f['x_scale'], float_dtype)
values = tf.cast(f['values'], float_dtype)
tangents = tf.cast(f['tangents'], float_dtype)
# The partition function is undefined when `alpha`< 0.
assert_ops = [tf.Assert(tf.reduce_all(alpha >= 0.), [alpha])]
with tf.control_dependencies(assert_ops):
# Transform `alpha` to the form expected by the spline.
x = partition_spline_curve(alpha)
# Interpolate into the spline.
return cubic_spline.interpolate1d(x * x_scale, values, tangents)
