def skeletonize_index(binary,
points=None,
steps=None,
removals=False,
radii=False,
return_points=False,
check_border=True,
delete_border=False,
verbose=True):
"""Skeletonize a binary 3d array using PK12 algorithm via index coordinates.
Arguments
---------
binary : array
Binary image to be skeletonized.
steps : int or None
Number of maximal iteration steps. If None, use maximal reduction.
removals :bool
If True, returns the steps in which the pixels in the input data
were removed.
radii :bool
If True, the estimate of the local radius is returned.
verbose :bool
If True, print progress info.
Returns
-------
skeleton : array
The skeleton of the binary input.
points : nxd array
The point coordinates of the skeleton.
"""
if verbose:
print('#############################################################')
print('Skeletonization PK12 [convolution, index]')
timer = tmr.Timer()
#TODO: make this work for any memmapable source
if not isinstance(binary, np.ndarray):
raise ValueError('Numpy array required for binary in skeletonization!')
if binary.ndim != 3:
raise ValueError('The binary array dimension is %d, 3 is required!' %
binary.ndim)
if delete_border:
binary = t3d.delete_border(binary)
check_border = False
if check_border:
if not t3d.check_border(binary):
raise ValueError(
'The binary array needs to have not points on the border!')
binary_flat = binary.reshape(-1, order='A')
# detect points
if points is None:
points = ap.where(binary_flat).array
npoints = points.shape[0]
if verbose:
timer.print_elapsed_time('Foreground points: %d' % (points.shape[0], ))
if removals is True or radii is True:
#birth = np.zeros(binary.shape, dtype = 'uint16');
order = 'C'
if binary.flags.f_contiguous:
order = 'F'
death = np.zeros(binary.shape, dtype='uint16', order=order)
deathflat = death.reshape(-1, order='A')
with_info = True
else:
with_info = False
# iterate
if steps is None:
steps = -1
step = 1
nnonrem = 0
while True:
if verbose:
print(
'#############################################################'
)
print('Iteration %d' % step)
timer_iter = tmr.Timer()
print(type(points), points.dtype, binary.dtype)
border = cpl.convolve_3d_indices_if_smaller_than(
binary, t3d.n6, points, 6)
borderpoints = points[border]
#borderids = np.nonzero(border)[0];
borderids = ap.where(border).array
keep = np.ones(len(border), dtype=bool)
if verbose:
timer_iter.print_elapsed_time('Border points: %d' %
(len(borderpoints), ))
#if info is not None:
# b = birth[borderpoints[:,0], borderpoints[:,1], borderpoints[:,2]];
# bids = b == 0;
# birth[borderpoints[bids,0], borderpoints[bids,1], borderpoints[bids,2]] = step;
# sub iterations
remiter = 0
for i in range(12):
if verbose:
print(
'-------------------------------------------------------------'
)
print('Sub-Iteration %d' % i)
timer_sub_iter = tmr.Timer()
remborder = delete[cpl.convolve_3d_indices(binary, rotations[i],
borderpoints)]
rempoints = borderpoints[remborder]
if verbose:
timer_sub_iter.print_elapsed_time('Matched points : %d' %
(len(rempoints), ))
binary_flat[rempoints] = 0
keep[borderids[remborder]] = False
rem = len(rempoints)
remiter += rem
#death times
if with_info is True:
#remo = np.logical_not(keep);
deathflat[rempoints] = 12 * step + i
if verbose:
timer_sub_iter.print_elapsed_time('Sub-Iteration %d' % (i, ))
if verbose:
print(
'-------------------------------------------------------------'
)
#update foregroud
points = points[keep]
if step % 3 == 0:
npts = len(points)
points = points[consider[cpl.convolve_3d_indices(
binary, base, points)]]
nnonrem += npts - len(points)
if verbose:
print('Non-removable points: %d' % (npts - len(points)))
if verbose:
print('Foreground points : %d' % points.shape[0])
if verbose:
print(
'-------------------------------------------------------------'
)
timer_iter.print_elapsed_time('Iteration %d' % (step, ))
step += 1
if steps >= 0 and step >= steps:
break
if remiter == 0:
break
if verbose:
print('#############################################################')
timer.print_elapsed_time('Skeletonization done')
print('Total removed: %d' % (npoints - (len(points) + nnonrem)))
print('Total remaining: %d' % (len(points) + nnonrem))
if radii is True or return_points is True:
points = ap.where(binary_flat).array
if radii is True:
#calculate average diameter as death average death of neighbourhood
radii = cpl.convolve_3d_indices(death,
t3d.n18,
points,
out_dtype='uint16')
else:
radii = None
result = [binary]
if return_points:
result.append(points)
if removals is True:
result.append(death)
if radii is not None:
result.append(radii)
if len(result) > 1:
return tuple(result)
else:
return result[0]
def graph_from_skeleton(skeleton, points = None, radii = None, vertex_coordinates = True,
check_border = True, delete_border = False, verbose = False):
"""Converts a binary skeleton image to a graph-tool graph.
Arguments
---------
skeleton : array
Source with 2d/3d binary skeleton.
points : array
List of skeleton points as 1d indices of flat skeleton array (optional to save processing time).
radii : array
List of radii associated with each vertex.
vertex_coordinates : bool
If True, store coordiantes of the vertices / edges.
check_border : bool
If True, check if the boder is empty. The algorithm reuqires this.
delete_border : bool
If True, delete the border.
verbose : bool
If True, print progress information.
Returns
-------
graph : Graph class
The graph corresponding to the skeleton.
Note
----
Edges are detected between neighbouring foreground pixels using 26-connectivty.
"""
skeleton = io.as_source(skeleton);
if delete_border:
skeleton = t3d.delete_border(skeleton);
check_border = False;
if check_border:
if not t3d.check_border(skeleton):
raise ValueError('The skeleton array needs to have no points on the border!');
if verbose:
timer = tmr.Timer();
timer_all = tmr.Timer();
print('Graph from skeleton calculation initialize.!');
if points is None:
points = ap.where(skeleton.reshape(-1, order = 'A')).array;
if verbose:
timer.print_elapsed_time('Point list generation');
timer.reset();
#create graph
n_vertices = points.shape[0];
g = ggt.Graph(n_vertices=n_vertices, directed=False);
g.shape = skeleton.shape;
if verbose:
timer.print_elapsed_time('Graph initialized with %d vertices' % n_vertices);
timer.reset();
#detect edges
edges_all = np.zeros((0,2), dtype = int);
for i,o in enumerate(t3d.orientations()):
# calculate off set
offset = np.sum((np.hstack(np.where(o))-[1,1,1]) * skeleton.strides)
edges = ap.neighbours(points, offset);
if len(edges) > 0:
edges_all = np.vstack([edges_all, edges]);
if verbose:
timer.print_elapsed_time('%d edges with orientation %d/13 found' % (edges.shape[0], i+1));
timer.reset();
if edges_all.shape[0] > 0:
g.add_edge(edges_all);
if verbose:
timer.print_elapsed_time('Added %d edges to graph' % (edges_all.shape[0]));
timer.reset();
if vertex_coordinates:
vertex_coordinates = np.array(np.unravel_index(points, skeleton.shape, order=skeleton.order)).T;
g.set_vertex_coordinates(vertex_coordinates);
if radii is not None:
g.set_vertex_radius(radii);
if verbose:
timer_all.print_elapsed_time('Skeleton to Graph');
return g;
def skeletonize(binary,
points=None,
steps=None,
removals=False,
radii=False,
check_border=True,
delete_border=False,
return_points=False,
verbose=True):
"""Skeletonize a binary 3d array using PK12 algorithm.
Arguments
---------
binary : array
Binary image to skeletonize.
points : array or None.
Optional list of points in the binary to speed up processing.
steps : int or None
Number of maximal iteration steps (if None maximal reduction).
removals : bool
If True, returns also the steps at which the pixels in the input data
where removed.
radii : bool
If True, the estimate of the local radius is returned.
check_border : bool
If True, check if the boder is empty. The algorithm reuqires this.
delete_border : bool
If True, delete the border.
verbose : bool
If True print progress info.
Returns
-------
skeleton : array
The skeleton of the binary.
points : array
The point coordinates of the skeleton nx3
Note
----
The skeletonization is done in place on the binary. Copy the binary if
needed for further processing.
"""
if verbose:
print('#############################################################')
print('Skeletonization PK12 [convolution]')
timer = tmr.Timer()
#TODO: make this work for any memmapable source !
if not isinstance(binary, np.ndarray):
raise ValueError('Numpy array required for binary in skeletonization!')
if binary.ndim != 3:
raise ValueError('The binary array dimension is %d, 3 is required!' %
binary.ndim)
if delete_border:
binary = t3d.delete_border(binary)
check_border = False
if check_border:
if not t3d.check_border(binary):
raise ValueError(
'The binary array needs to have no points on the border!')
# detect points
#points = np.array(np.nonzero(binary)).T;
if points is None:
points = ap.where(binary).array
if verbose:
timer.print_elapsed_time(head='Foreground points: %d' %
(points.shape[0], ))
if removals is True or radii is True:
#birth = np.zeros(binary.shape, dtype = 'uint16');
death = np.zeros(binary.shape, dtype='uint16')
with_info = True
else:
with_info = False
# iterate
if steps is None:
steps = -1
step = 1
removed = 0
while True:
if verbose:
print(
'#############################################################'
)
print('Iteration %d' % step)
timer_iter = tmr.Timer()
border = cpl.convolve_3d_points(binary, t3d.n6, points) < 6
borderpoints = points[border]
borderids = np.nonzero(border)[0]
keep = np.ones(len(border), dtype=bool)
if verbose:
timer_iter.print_elapsed_time('Border points: %d' %
(len(borderpoints), ))
#if info is not None:
# b = birth[borderpoints[:,0], borderpoints[:,1], borderpoints[:,2]];
# bids = b == 0;
# birth[borderpoints[bids,0], borderpoints[bids,1], borderpoints[bids,2]] = step;
# sub iterations
remiter = 0
for i in range(12):
if verbose:
print(
'-------------------------------------------------------------'
)
print('Sub-Iteration %d' % i)
timer_sub_iter = tmr.Timer()
remborder = delete[cpl.convolve_3d_points(binary, rotations[i],
borderpoints)]
rempoints = borderpoints[remborder]
if verbose:
timer_sub_iter.print_elapsed_time('Matched points: %d' %
(len(rempoints), ))
binary[rempoints[:, 0], rempoints[:, 1], rempoints[:, 2]] = 0
keep[borderids[remborder]] = False
rem = len(rempoints)
remiter += rem
removed += rem
if verbose:
print('Deleted points: %d' % (rem))
timer_sub_iter.print_elapsed_time('Sub-Iteration %d' % (i))
#death times
if with_info is True:
#remo = np.logical_not(keep);
death[rempoints[:, 0], rempoints[:, 1],
rempoints[:, 2]] = 12 * step + i
#update foreground
points = points[keep]
if verbose:
print('Foreground points: %d' % points.shape[0])
if verbose:
print(
'-------------------------------------------------------------'
)
timer_iter.print_elapsed_time('Iteration %d' % (step, ))
step += 1
if steps >= 0 and step >= steps:
break
if remiter == 0:
break
if verbose:
print('#############################################################')
print('Total removed: %d' % (removed))
print('Total remaining: %d' % (len(points)))
timer.print_elapsed_time('Skeletonization')
result = [binary]
if return_points:
result.append(points)
if removals is True:
result.append(death)
if radii is True:
#calculate average diameter as average death of neighbourhood
radii = cpl.convolve_3d(death, np.array(t3d.n18, dtype='uint16'),
points)
result.append(radii)
if len(result) > 1:
return tuple(result)
else:
return result[0]