def compute_persistence_2DImg(f, dimension=1.0, threshold=0.4):
"""
Copied from Hu's code under https://github.com/HuXiaoling/TopoLoss.
This function computes the persistence diagram of a 2D probability map and the corresponding critical points,
given a threshold.
:param f: numpy array of shape NxN
This is the input image/probability map from which e calculate the topological features.
:param dimension: float
Controls the dimension of the topoological features, that we want to calculate.
:param threshold: float
When calculating topological features, we have to say, which pixels belong to the boundary
and which pixels belong to the voids/holes. Everything above the threshold is boundary,
everything below is considered to belong to the hole.
We have the following color code: Black = 0 = hole, white = 1 = boundary
"""
# f has to be 2D function
assert len(f.shape) == 2
dim = 2
# Pad the function with a few pixels of maximum values
# This way one can compute the 1D topology as loops
# Remember to transform back to the original coordinates when finished
padwidth = 3
padvalue = min(f.min(), 0.0)
f_padded = np.pad(f, padwidth, 'constant', constant_values=padvalue)
start = time.time()
# Call persistence code to compute diagrams
# Loads PersistencePython.so (compiled from C++); should be in current dir
persistence_result = cubePers(
np.reshape(f_padded, f_padded.size).tolist(), list(f_padded.shape),
threshold)
end = time.time()
print('cubePers time elapsed ' + str(end - start))
# Only take 1-dim topology, first column of persistence_result is dimension
persistence_result_filtered = np.array(
list(filter(lambda x: x[0] == float(dimension), persistence_result)))
# Persistence diagram (second and third columns are coordinates)
# Check if filtration is not empty
if len(persistence_result_filtered.shape) < 2:
dgm = np.array([])
birth_cp_list = np.array([])
death_cp_list = np.array([])
else:
dgm = persistence_result_filtered[:, 1:3]
# Critical points
birth_cp_list = persistence_result_filtered[:, 4:4 + dim]
death_cp_list = persistence_result_filtered[:, 4 + dim:]
# When mapping back, shift critical points back to the original coordinates
birth_cp_list = birth_cp_list - padwidth
death_cp_list = death_cp_list - padwidth
return dgm, birth_cp_list, death_cp_list
def compute_persistence_2DImg_1DHom(f):
"""
compute persistence diagram in a 2D function (can be N-dim) and critical pts
only generate 1D homology dots and critical points
"""
#assert len(f.shape) == 2 # f has to be 2D function
#dim = 2
dim = len(f.shape)
# pad the function with a few pixels of minimum values
# this way one can compute the 1D topology as loops
# remember to transform back to the original coordinates when finished
padwidth = 2
padvalue = min(f.min(), 0.0)
print(padvalue)
f_padded = np.pad(f, padwidth, 'constant', constant_values=padvalue)
# call persistence code to compute diagrams
# loads PersistencePython.so (compiled from C++); should be in current dir
from PersistencePython import cubePers
# print (f_padded)
print((f_padded.shape))
print(f_padded.size)
print(type(f_padded))
print(type(np.reshape(f_padded, f_padded.size)))
print((np.reshape(f_padded, f_padded.size).tolist()))
print(type(list(f_padded.shape)))
# print (np.reshape(f_padded, f_padded.size).tolist())
persistence_result = cubePers(
np.reshape(f_padded, f_padded.size).tolist(), list(f_padded.shape),
0.001)
# print(type(persistence_result))
# print (persistence_result)
# print(len(persistence_result))
# only take 1-dim topology, first column of persistence_result is dimension
persistence_result_filtered = np.array(
list(filter(lambda x: x[0] == 1, persistence_result)))
# persistence diagram (second and third columns are coordinates)
# print (persistence_result_filtered)
dgm = persistence_result_filtered[:, 1:3]
# critical points
birth_cp_list = persistence_result_filtered[:, 4:4 + dim]
death_cp_list = persistence_result_filtered[:, 4 + dim:]
# when mapping back, shift critical points back to the original coordinates
birth_cp_list = birth_cp_list - padwidth
death_cp_list = death_cp_list - padwidth
return dgm, birth_cp_list, death_cp_list
def compute_persistence_2DImg_1DHom_gt(f,
padwidth=2,
homo_dim=1,
pers_thd=0.001):
"""
compute persistence diagram in a 2D function (can be N-dim) and critical pts
only generate 1D homology dots and critical points
"""
# print (len(f.shape))
assert len(f.shape) == 2 # f has to be 2D function
dim = 2
# pad the function with a few pixels of minimum values
# this way one can compute the 1D topology as loops
# remember to transform back to the original coordinates when finished
#padwidth = 2
# padvalue = min(f.min(), 0.0)
padvalue = f.min()
# print(f)
# print (type(f.cpu().numpy()))
if (not isinstance(f, np.ndarray)):
f_padded = np.pad(f.cpu().detach().numpy(),
padwidth,
'constant',
constant_values=padvalue.cpu().detach().numpy())
else:
f_padded = np.pad(f, padwidth, 'constant', constant_values=padvalue)
# call persistence code to compute diagrams
# loads PersistencePython.so (compiled from C++); should be in current dir
#from src.PersistencePython import cubePers
from PersistencePython import cubePers
# persistence_result = cubePers(a, list(f_padded.shape), 0.001)
persistence_result = cubePers(
np.reshape(f_padded, f_padded.size).tolist(), list(f_padded.shape),
pers_thd)
# print("persistence_result", type(persistence_result))
# print(type(persistence_result))
# print (persistence_result)
# print(len(persistence_result))
# only take 1-dim topology, first column of persistence_result is dimension
persistence_result_filtered = np.array(
list(filter(lambda x: x[0] == homo_dim, persistence_result)))
# persistence diagram (second and third columns are coordinates)
# print (persistence_result_filtered)
#print ('shape of persistence_result_filtered')
#print (persistence_result_filtered.shape)
if (persistence_result_filtered.shape[0] == 0):
return np.array([]), np.array([]), np.array([])
dgm = persistence_result_filtered[:, 1:3]
# critical points
birth_cp_list = persistence_result_filtered[:, 4:4 + dim]
death_cp_list = persistence_result_filtered[:, 4 + dim:]
# when mapping back, shift critical points back to the original coordinates
birth_cp_list = birth_cp_list - padwidth
death_cp_list = death_cp_list - padwidth
return dgm, birth_cp_list, death_cp_list