def blur(field, radius, cutoff=None, kernel="1/1+x"):
"""
Warning: This function can cause NaN in the gradients, reason unknown.
Runs a blur kernel over the given tensor.
:param field: tensor
:param radius: weight function curve scale
:param cutoff: kernel size
:param kernel: Type of blur kernel (str). Must be in ('1/1+x', 'gauss')
:return:
"""
if cutoff is None:
cutoff = min(int(round(radius * 3)), *field.shape[1:-1])
xyz = np.meshgrid(
*[range(-int(cutoff), (cutoff) + 1) for _ in field.shape[1:-1]])
d = math.to_float(np.sqrt(np.sum([x**2 for x in xyz], axis=0)))
if kernel == "1/1+x":
weights = math.to_float(1) / (d / radius + 1)
elif kernel.lower() == "gauss":
weights = math.exp(-d / radius / 2)
else:
raise ValueError("Unknown kernel: %s" % kernel)
weights /= math.sum(weights)
weights = math.reshape(weights, list(weights.shape) + [1, 1])
return math.conv(field, weights)
def frequency_loss(tensor, frequency_falloff=100, reduce_batches=True):
"""
Instead of minimizing each entry of the tensor, minimize the frequencies of the tensor, emphasizing lower frequencies over higher ones.
:param reduce_batches: whether to reduce the batch dimension of the loss by adding the losses along the first dimension
:param tensor: typically actual - target
:param frequency_falloff: large values put more emphasis on lower frequencies, 1.0 weights all frequencies equally.
:return: scalar loss value
"""
if struct.isstruct(tensor):
all_tensors = struct.flatten(tensor)
return sum(
frequency_loss(tensor, frequency_falloff, reduce_batches)
for tensor in all_tensors)
diff_fft = abs_square(math.fft(tensor))
k = fftfreq(tensor.shape[1:-1], mode='absolute')
weights = math.exp(-0.5 * k**2 * frequency_falloff**2)
return l1_loss(diff_fft * weights, reduce_batches=reduce_batches)