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import numpy as np
import tensorflow as tf
from ..cubical_complex import CubicalComplex
######################
# Cubical filtration #
######################
# The parameters of the model are the pixel values.
def _Cubical(X, dimension):
# Parameters: X (image),
# dimension (homology dimension)
# Compute the persistence pairs with Gudhi
cc = CubicalComplex(dimensions=X.shape, top_dimensional_cells=X.flatten())
cc.persistence()
try:
cof = cc.cofaces_of_persistence_pairs()[0][dimension]
except IndexError:
cof = np.array([])
if len(cof) > 0:
# Sort points with distance-to-diagonal
Xs = X.shape
pers = [X[np.unravel_index(cof[idx,1], Xs)] - X[np.unravel_index(cof[idx,0], Xs)] for idx in range(len(cof))]
perm = np.argsort(pers)
cof = cof[perm[::-1]]
# Retrieve and ouput image indices/pixels corresponding to positive and negative simplices
D = len(Xs) if len(cof) > 0 else 1
ocof = np.array([0 for _ in range(D*2*cof.shape[0])])
count = 0
for idx in range(0,2*cof.shape[0],2):
ocof[D*idx:D*(idx+1)] = np.unravel_index(cof[count,0], Xs)
ocof[D*(idx+1):D*(idx+2)] = np.unravel_index(cof[count,1], Xs)
count += 1
return np.array(ocof, dtype=np.int32)
class CubicalLayer(tf.keras.layers.Layer):
"""
TensorFlow layer for computing cubical persistence out of a cubical complex
Attributes:
dimension (int): homology dimension
"""
def __init__(self, dimension=1, **kwargs):
super().__init__(dynamic=True, **kwargs)
self.dimension = dimension
def build(self):
super.build()
def call(self, X):
"""
Compute persistence diagram associated to a cubical complex filtered by some pixel values
Parameters:
X (TensorFlow variable): pixel values of the cubical complex
"""
# Compute pixels associated to positive and negative simplices
# Don't compute gradient for this operation
indices = tf.stop_gradient(_Cubical(X.numpy(), self.dimension))
# Get persistence diagram by simply picking the corresponding entries in the image
dgm = tf.reshape(tf.gather_nd(X, tf.reshape(indices, [-1,len(X.shape)])), [-1,2])
return dgm
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