_id
stringlengths 2
7
| title
stringlengths 1
88
| partition
stringclasses 3
values | text
stringlengths 75
19.8k
| language
stringclasses 1
value | meta_information
dict |
|---|---|---|---|---|---|
q17700
|
ParallelRunner.launch_simulation
|
train
|
def launch_simulation(self, parameter):
"""
Launch a single simulation, using SimulationRunner's facilities.
This function is used by ParallelRunner's run_simulations to map
simulation running over the parameter list.
Args:
parameter (dict): the parameter combination to simulate.
"""
return next(SimulationRunner.run_simulations(self, [parameter],
self.data_folder))
|
python
|
{
"resource": ""
}
|
q17701
|
JsonHelper.stringify
|
train
|
def stringify(self, obj, beautify=False, raise_exception=False):
"""Alias of helper.string.serialization.json.stringify"""
return self.helper.string.serialization.json.stringify(
obj=obj,
beautify=beautify,
raise_exception=raise_exception)
|
python
|
{
"resource": ""
}
|
q17702
|
JsonHelper.parse
|
train
|
def parse(self, text, encoding='utf8', raise_exception=False):
"""Alias of helper.string.serialization.json.parse"""
return self.helper.string.serialization.json.parse(
text=text,
encoding=encoding,
raise_exception=raise_exception)
|
python
|
{
"resource": ""
}
|
q17703
|
DatabaseManager.new
|
train
|
def new(cls, script, commit, params, campaign_dir, overwrite=False):
"""
Initialize a new class instance with a set configuration and filename.
The created database has the same name of the campaign directory.
Args:
script (str): the ns-3 name of the script that will be used in this
campaign;
commit (str): the commit of the ns-3 installation that is used to
run the simulations.
params (list): a list of the parameters that can be used on the
script.
campaign_dir (str): The path of the file where to save the DB.
overwrite (bool): Whether or not existing directories should be
overwritten.
"""
# We only accept absolute paths
if not Path(campaign_dir).is_absolute():
raise ValueError("Path is not absolute")
# Make sure the directory does not exist already
if Path(campaign_dir).exists() and not overwrite:
raise FileExistsError("The specified directory already exists")
elif Path(campaign_dir).exists() and overwrite:
# Verify we are not deleting files belonging to the user
campaign_dir_name = os.path.basename(campaign_dir)
folder_contents = set(os.listdir(campaign_dir))
allowed_files = set(
['data', '%s.json' % campaign_dir_name] +
# Allow hidden files (like .DS_STORE in macos)
[os.path.basename(os.path.normpath(f)) for f in
glob.glob(os.path.join(campaign_dir, ".*"))])
if(not folder_contents.issubset(allowed_files)):
raise ValueError("The specified directory cannot be overwritten"
" because it contains user files.")
# This operation destroys data.
shutil.rmtree(campaign_dir)
# Create the directory and database file in it
# The indent and separators ensure the database is human readable.
os.makedirs(campaign_dir)
tinydb = TinyDB(os.path.join(campaign_dir, "%s.json" %
os.path.basename(campaign_dir)))
# Save the configuration in the database
config = {
'script': script,
'commit': commit,
'params': sorted(params)
}
tinydb.table('config').insert(config)
return cls(tinydb, campaign_dir)
|
python
|
{
"resource": ""
}
|
q17704
|
DatabaseManager.load
|
train
|
def load(cls, campaign_dir):
"""
Initialize from an existing database.
It is assumed that the database json file has the same name as its
containing folder.
Args:
campaign_dir (str): The path to the campaign directory.
"""
# We only accept absolute paths
if not Path(campaign_dir).is_absolute():
raise ValueError("Path is not absolute")
# Verify file exists
if not Path(campaign_dir).exists():
raise ValueError("Directory does not exist")
# Extract filename from campaign dir
filename = "%s.json" % os.path.split(campaign_dir)[1]
filepath = os.path.join(campaign_dir, filename)
try:
# Read TinyDB instance from file
tinydb = TinyDB(filepath)
# Make sure the configuration is a valid dictionary
assert set(
tinydb.table('config').all()[0].keys()) == set(['script',
'params',
'commit'])
except:
# Remove the database instance created by tinydb
os.remove(filepath)
raise ValueError("Specified campaign directory seems corrupt")
return cls(tinydb, campaign_dir)
|
python
|
{
"resource": ""
}
|
q17705
|
DatabaseManager.get_next_rngruns
|
train
|
def get_next_rngruns(self):
"""
Yield the next RngRun values that can be used in this campaign.
"""
available_runs = [result['params']['RngRun'] for result in
self.get_results()]
yield from DatabaseManager.get_next_values(available_runs)
|
python
|
{
"resource": ""
}
|
q17706
|
DatabaseManager.insert_result
|
train
|
def insert_result(self, result):
"""
Insert a new result in the database.
This function also verifies that the result dictionaries saved in the
database have the following structure (with {'a': 1} representing a
dictionary, 'a' a key and 1 its value)::
{
'params': {
'param1': value1,
'param2': value2,
...
'RngRun': value3
},
'meta': {
'elapsed_time': value4,
'id': value5
}
}
Where elapsed time is a float representing the seconds the simulation
execution took, and id is a UUID uniquely identifying the result, and
which is used to locate the output files in the campaign_dir/data
folder.
"""
# This dictionary serves as a model for how the keys in the newly
# inserted result should be structured.
example_result = {
'params': {k: ['...'] for k in self.get_params() + ['RngRun']},
'meta': {k: ['...'] for k in ['elapsed_time', 'id']},
}
# Verify result format is correct
if not(DatabaseManager.have_same_structure(result, example_result)):
raise ValueError(
'%s:\nExpected: %s\nGot: %s' % (
"Result dictionary does not correspond to database format",
pformat(example_result, depth=1),
pformat(result, depth=1)))
# Insert result
self.db.table('results').insert(result)
|
python
|
{
"resource": ""
}
|
q17707
|
DatabaseManager.get_results
|
train
|
def get_results(self, params=None, result_id=None):
"""
Return all the results available from the database that fulfill some
parameter combinations.
If params is None (or not specified), return all results.
If params is specified, it must be a dictionary specifying the result
values we are interested in, with multiple values specified as lists.
For example, if the following params value is used::
params = {
'param1': 'value1',
'param2': ['value2', 'value3']
}
the database will be queried for results having param1 equal to value1,
and param2 equal to value2 or value3.
Not specifying a value for all the available parameters is allowed:
unspecified parameters are assumed to be 'free', and can take any
value.
Returns:
A list of results matching the query. Returned results have the
same structure as results inserted with the insert_result method.
"""
# In this case, return all results
# A cast to dict is necessary, since self.db.table() contains TinyDB's
# Document object (which is simply a wrapper for a dictionary, thus the
# simple cast).
if result_id is not None:
return [dict(i) for i in self.db.table('results').all() if
i['meta']['id'] == result_id]
if params is None:
return [dict(i) for i in self.db.table('results').all()]
# Verify parameter format is correct
all_params = set(['RngRun'] + self.get_params())
param_subset = set(params.keys())
if (not all_params.issuperset(param_subset)):
raise ValueError(
'%s:\nParameters: %s\nQuery: %s' % (
'Specified parameter keys do not match database format',
all_params,
param_subset))
# Convert values that are not lists into lists to later perform
# iteration over values more naturally. Perform this on a new
# dictionary not to modify the original copy.
query_params = {}
for key in params:
if not isinstance(params[key], list):
query_params[key] = [params[key]]
else:
query_params[key] = params[key]
# Handle case where query params has no keys
if not query_params.keys():
return [dict(i) for i in self.db.table('results').all()]
# Create the TinyDB query
# In the docstring example above, this is equivalent to:
# AND(OR(param1 == value1), OR(param2 == value2, param2 == value3))
query = reduce(and_, [reduce(or_, [
where('params')[key] == v for v in value]) for key, value in
query_params.items()])
return [dict(i) for i in self.db.table('results').search(query)]
|
python
|
{
"resource": ""
}
|
q17708
|
DatabaseManager.wipe_results
|
train
|
def wipe_results(self):
"""
Remove all results from the database.
This also removes all output files, and cannot be undone.
"""
# Clean results table
self.db.purge_table('results')
# Get rid of contents of data dir
map(shutil.rmtree, glob.glob(os.path.join(self.get_data_dir(), '*.*')))
|
python
|
{
"resource": ""
}
|
q17709
|
DatabaseManager.get_all_values_of_all_params
|
train
|
def get_all_values_of_all_params(self):
"""
Return a dictionary containing all values that are taken by all
available parameters.
Always returns the parameter list in alphabetical order.
"""
values = collections.OrderedDict([[p, []] for p in
sorted(self.get_params())])
for result in self.get_results():
for param in self.get_params():
values[param] += [result['params'][param]]
sorted_values = collections.OrderedDict([[k,
sorted(list(set(values[k])))]
for k in values.keys()])
for k in sorted_values.keys():
if sorted_values[k] == []:
sorted_values[k] = None
return sorted_values
|
python
|
{
"resource": ""
}
|
q17710
|
SerializationHelper.serialize
|
train
|
def serialize(self, obj, method='json', beautify=False, raise_exception=False):
"""Alias of helper.string.serialization.serialize"""
return self.helper.string.serialization.serialize(
obj=obj, method=method, beautify=beautify, raise_exception=raise_exception)
|
python
|
{
"resource": ""
}
|
q17711
|
SerializationHelper.deserialize
|
train
|
def deserialize(self, text, method='json', encoding='utf8', raise_exception=False):
"""Alias of helper.string.serialization.deserialize"""
return self.helper.string.serialization.deserialize(
text, method=method, encoding=encoding, raise_exception=raise_exception)
|
python
|
{
"resource": ""
}
|
q17712
|
GridRunner.run_program
|
train
|
def run_program(self, command, working_directory=os.getcwd(),
environment=None, cleanup_files=True,
native_spec="-l cputype=intel"):
"""
Run a program through the grid, capturing the standard output.
"""
try:
s = drmaa.Session()
s.initialize()
jt = s.createJobTemplate()
jt.remoteCommand = os.path.dirname(
os.path.abspath(__file__)) + '/run_program.sh'
jt.args = [command]
if environment is not None:
jt.jobEnvironment = environment
jt.workingDirectory = working_directory
jt.nativeSpecification = native_spec
output_filename = os.path.join(working_directory, 'output.txt')
jt.outputPath = ':' + output_filename
jt.joinFiles = True
jobid = s.runJob(jt)
s.wait(jobid, drmaa.Session.TIMEOUT_WAIT_FOREVER)
with open(output_filename, 'r') as output:
stdout = output.read()
# Clean up
if cleanup_files:
os.remove(output_filename)
finally:
try:
s.control(drmaa.JOB_IDS_SESSION_ALL,
drmaa.JobControlAction.TERMINATE)
s.synchronize([drmaa.JOB_IDS_SESSION_ALL], dispose=True)
s.exit()
except(drmaa.errors.NoActiveSessionException):
pass
return stdout
|
python
|
{
"resource": ""
}
|
q17713
|
adjacent
|
train
|
def adjacent(labels):
'''Return a binary mask of all pixels which are adjacent to a pixel of
a different label.
'''
high = labels.max()+1
if high > np.iinfo(labels.dtype).max:
labels = labels.astype(np.int)
image_with_high_background = labels.copy()
image_with_high_background[labels == 0] = high
min_label = scind.minimum_filter(image_with_high_background,
footprint=np.ones((3,3),bool),
mode = 'constant',
cval = high)
max_label = scind.maximum_filter(labels,
footprint=np.ones((3,3),bool),
mode = 'constant',
cval = 0)
return (min_label != max_label) & (labels > 0)
|
python
|
{
"resource": ""
}
|
q17714
|
binary_thin
|
train
|
def binary_thin(image, strel1, strel2):
"""Morphologically thin an image
strel1 - the required values of the pixels in order to survive
strel2 - at each pixel, the complement of strel1 if we care about the value
"""
hit_or_miss = scind.binary_hit_or_miss(image, strel1, strel2)
return np.logical_and(image,np.logical_not(hit_or_miss))
|
python
|
{
"resource": ""
}
|
q17715
|
strel_disk
|
train
|
def strel_disk(radius):
"""Create a disk structuring element for morphological operations
radius - radius of the disk
"""
iradius = int(radius)
x,y = np.mgrid[-iradius:iradius+1,-iradius:iradius+1]
radius2 = radius * radius
strel = np.zeros(x.shape)
strel[x*x+y*y <= radius2] = 1
return strel
|
python
|
{
"resource": ""
}
|
q17716
|
strel_octagon
|
train
|
def strel_octagon(radius):
"""Create an octagonal structuring element for morphological operations
radius - the distance from the origin to each edge of the octagon
"""
#
# Inscribe a diamond in a square to get an octagon.
#
iradius = int(radius)
i, j = np.mgrid[-iradius:(iradius + 1), -iradius:(iradius+1)]
#
# The distance to the diagonal side is also iradius:
#
# iradius ** 2 = i**2 + j**2 and i = j
# iradius ** 2 = 2 * i ** 2
# i = iradius / sqrt(2)
# i + j = iradius * sqrt(2)
#
dradius = float(iradius) * np.sqrt(2)
strel = (((i+j) <= dradius) & ((i+j) >= -dradius) &
((i-j) <= dradius) & ((i-j) >= -dradius))
return strel
|
python
|
{
"resource": ""
}
|
q17717
|
strel_pair
|
train
|
def strel_pair(x, y):
"""Create a structing element composed of the origin and another pixel
x, y - x and y offsets of the other pixel
returns a structuring element
"""
x_center = int(np.abs(x))
y_center = int(np.abs(y))
result = np.zeros((y_center * 2 + 1, x_center * 2 + 1), bool)
result[y_center, x_center] = True
result[y_center + int(y), x_center + int(x)] = True
return result
|
python
|
{
"resource": ""
}
|
q17718
|
cpmaximum
|
train
|
def cpmaximum(image, structure=np.ones((3,3),dtype=bool),offset=None):
"""Find the local maximum at each point in the image, using the given structuring element
image - a 2-d array of doubles
structure - a boolean structuring element indicating which
local elements should be sampled
offset - the offset to the center of the structuring element
"""
center = np.array(structure.shape) // 2
if offset is None:
offset = center
origin = np.array(offset) - center
return scind.maximum_filter(image, footprint=structure, origin=origin,
mode='constant', cval=np.min(image))
|
python
|
{
"resource": ""
}
|
q17719
|
convex_hull_image
|
train
|
def convex_hull_image(image):
'''Given a binary image, return an image of the convex hull'''
labels = image.astype(int)
points, counts = convex_hull(labels, np.array([1]))
output = np.zeros(image.shape, int)
for i in range(counts[0]):
inext = (i+1) % counts[0]
draw_line(output, points[i,1:], points[inext,1:],1)
output = fill_labeled_holes(output)
return output == 1
|
python
|
{
"resource": ""
}
|
q17720
|
triangle_areas
|
train
|
def triangle_areas(p1,p2,p3):
"""Compute an array of triangle areas given three arrays of triangle pts
p1,p2,p3 - three Nx2 arrays of points
"""
v1 = (p2 - p1).astype(np.float)
v2 = (p3 - p1).astype(np.float)
# Original:
# cross1 = v1[:,1] * v2[:,0]
# cross2 = v2[:,1] * v1[:,0]
# a = (cross1-cross2) / 2
# Memory reduced:
cross1 = v1[:, 1]
cross1 *= v2[:, 0]
cross2 = v2[:, 1]
cross2 *= v1[:, 0]
a = cross1
a -= cross2
a /= 2.0
del v1, v2, cross1, cross2
a = a.copy() # a is a view on v1; shed one dimension.
a = np.abs(a)
#
# Handle small round-off errors
#
a[a<np.finfo(np.float32).eps] = 0
return a
|
python
|
{
"resource": ""
}
|
q17721
|
minimum_distance2
|
train
|
def minimum_distance2(hull_a, center_a, hull_b, center_b):
'''Return the minimum distance or 0 if overlap between 2 convex hulls
hull_a - list of points in clockwise direction
center_a - a point within the hull
hull_b - list of points in clockwise direction
center_b - a point within the hull
'''
if hull_a.shape[0] < 3 or hull_b.shape[0] < 3:
return slow_minimum_distance2(hull_a, hull_b)
else:
return faster_minimum_distance2(hull_a, center_a, hull_b, center_b)
|
python
|
{
"resource": ""
}
|
q17722
|
slow_minimum_distance2
|
train
|
def slow_minimum_distance2(hull_a, hull_b):
'''Do the minimum distance by exhaustive examination of all points'''
d2_min = np.iinfo(int).max
for a in hull_a:
if within_hull(a, hull_b):
return 0
for b in hull_b:
if within_hull(b, hull_a):
return 0
for pt_a in hull_a:
for pt_b in hull_b:
d2_min = min(d2_min, np.sum((pt_a - pt_b)**2))
for h1, h2 in ((hull_a, hull_b), (hull_b, hull_a)):
# Find the distance from a vertex in h1 to an edge in h2
for pt1 in h1:
prev_pt2 = h2[-1,:]
for pt2 in h2:
if (np.dot(pt2-prev_pt2,pt1-prev_pt2) > 0 and
np.dot(prev_pt2-pt2,pt1-pt2) > 0):
# points form an acute triangle, so edge is closer
# than vertices
d2_min = min(d2_min, distance2_to_line(pt1, prev_pt2, pt2))
prev_pt2 = pt2
return d2_min
|
python
|
{
"resource": ""
}
|
q17723
|
lines_intersect
|
train
|
def lines_intersect(pt1_p, pt2_p, pt1_q, pt2_q):
'''Return true if two line segments intersect
pt1_p, pt2_p - endpoints of first line segment
pt1_q, pt2_q - endpoints of second line segment
'''
#
# The idea here is to do the cross-product of the vector from
# point 1 to point 2 of one segment against the cross products from
# both points of the other segment. If any of the cross products are zero,
# the point is colinear with the line. If the cross products differ in
# sign, then one point is on one side of the line and the other is on
# the other. If that happens for both, then the lines must cross.
#
for pt1_a, pt2_a, pt1_b, pt2_b in ((pt1_p, pt2_p, pt1_q, pt2_q),
(pt1_q, pt2_q, pt1_p, pt2_p)):
v_a = pt2_a-pt1_a
cross_a_1b = np.cross(v_a, pt1_b-pt2_a)
if cross_a_1b == 0 and colinear_intersection_test(pt1_a, pt2_a, pt1_b):
return True
cross_a_2b = np.cross(v_a, pt2_b-pt2_a)
if cross_a_2b == 0 and colinear_intersection_test(pt1_a, pt2_a, pt2_b):
return True
if (cross_a_1b < 0) == (cross_a_2b < 0):
return False
return True
|
python
|
{
"resource": ""
}
|
q17724
|
find_farthest
|
train
|
def find_farthest(point, hull):
'''Find the vertex in hull farthest away from a point'''
d_start = np.sum((point-hull[0,:])**2)
d_end = np.sum((point-hull[-1,:])**2)
if d_start > d_end:
# Go in the forward direction
i = 1
inc = 1
term = hull.shape[0]
d2_max = d_start
else:
# Go in the reverse direction
i = hull.shape[0]-2
inc = -1
term = -1
d2_max = d_end
while i != term:
d2 = np.sum((point - hull[i,:])**2)
if d2 < d2_max:
break
i += inc
d2_max = d2
return i-inc
|
python
|
{
"resource": ""
}
|
q17725
|
find_visible
|
train
|
def find_visible(hull, observer, background):
'''Given an observer location, find the first and last visible
points in the hull
The observer at "observer" is looking at the hull whose most distant
vertex from the observer is "background. Find the vertices that are
the furthest distance from the line between observer and background.
These will be the start and ends in the vertex chain of vertices
visible by the observer.
'''
pt_background = hull[background,:]
vector = pt_background - observer
i = background
dmax = 0
while True:
i_next = (i+1) % hull.shape[0]
pt_next = hull[i_next,:]
d = -np.cross(vector, pt_next-pt_background)
if d < dmax or i_next == background:
i_min = i
break
dmax = d
i = i_next
dmax = 0
i = background
while True:
i_next = (i+hull.shape[0]-1) % hull.shape[0]
pt_next = hull[i_next,:]
d = np.cross(vector, pt_next-pt_background)
if d < dmax or i_next == background:
i_max = i
break
dmax = d
i = i_next
return (i_min, i_max)
|
python
|
{
"resource": ""
}
|
q17726
|
distance2_to_line
|
train
|
def distance2_to_line(pt, l0, l1):
'''The perpendicular distance squared from a point to a line
pt - point in question
l0 - one point on the line
l1 - another point on the line
'''
pt = np.atleast_1d(pt)
l0 = np.atleast_1d(l0)
l1 = np.atleast_1d(l1)
reshape = pt.ndim == 1
if reshape:
pt.shape = l0.shape = l1.shape = (1, pt.shape[0])
result = (((l0[:,0] - l1[:,0]) * (l0[:,1] - pt[:,1]) -
(l0[:,0] - pt[:,0]) * (l0[:,1] - l1[:,1]))**2 /
np.sum((l1-l0)**2, 1))
if reshape:
result = result[0]
return result
|
python
|
{
"resource": ""
}
|
q17727
|
within_hull
|
train
|
def within_hull(point, hull):
'''Return true if the point is within the convex hull'''
h_prev_pt = hull[-1,:]
for h_pt in hull:
if np.cross(h_pt-h_prev_pt, point - h_pt) >= 0:
return False
h_prev_pt = h_pt
return True
|
python
|
{
"resource": ""
}
|
q17728
|
calculate_extents
|
train
|
def calculate_extents(labels, indexes):
"""Return the area of each object divided by the area of its bounding box"""
fix = fixup_scipy_ndimage_result
areas = fix(scind.sum(np.ones(labels.shape),labels,np.array(indexes, dtype=np.int32)))
y,x = np.mgrid[0:labels.shape[0],0:labels.shape[1]]
xmin = fix(scind.minimum(x, labels, indexes))
xmax = fix(scind.maximum(x, labels, indexes))
ymin = fix(scind.minimum(y, labels, indexes))
ymax = fix(scind.maximum(y, labels, indexes))
bbareas = (xmax-xmin+1)*(ymax-ymin+1)
return areas / bbareas
|
python
|
{
"resource": ""
}
|
q17729
|
calculate_perimeters
|
train
|
def calculate_perimeters(labels, indexes):
"""Count the distances between adjacent pixels in the perimeters of the labels"""
#
# Create arrays that tell whether a pixel is like its neighbors.
# index = 0 is the pixel -1,-1 from the pixel of interest, 1 is -1,0, etc.
#
m = table_idx_from_labels(labels)
pixel_score = __perimeter_scoring[m]
return fixup_scipy_ndimage_result(scind.sum(pixel_score, labels, np.array(indexes,dtype=np.int32)))
|
python
|
{
"resource": ""
}
|
q17730
|
calculate_solidity
|
train
|
def calculate_solidity(labels,indexes=None):
"""Calculate the area of each label divided by the area of its convex hull
labels - a label matrix
indexes - the indexes of the labels to measure
"""
if indexes is not None:
""" Convert to compat 32bit integer """
indexes = np.array(indexes,dtype=np.int32)
areas = scind.sum(np.ones(labels.shape),labels,indexes)
convex_hull_areas = calculate_convex_hull_areas(labels, indexes)
return areas / convex_hull_areas
|
python
|
{
"resource": ""
}
|
q17731
|
white_tophat
|
train
|
def white_tophat(image, radius=None, mask=None, footprint=None):
'''White tophat filter an image using a circular structuring element
image - image in question
radius - radius of the circular structuring element. If no radius, use
an 8-connected structuring element.
mask - mask of significant pixels in the image. Points outside of
the mask will not participate in the morphological operations
'''
#
# Subtract the opening to get the tophat
#
final_image = image - opening(image, radius, mask, footprint)
#
# Paint the masked pixels into the final image
#
if not mask is None:
not_mask = np.logical_not(mask)
final_image[not_mask] = image[not_mask]
return final_image
|
python
|
{
"resource": ""
}
|
q17732
|
black_tophat
|
train
|
def black_tophat(image, radius=None, mask=None, footprint=None):
'''Black tophat filter an image using a circular structuring element
image - image in question
radius - radius of the circular structuring element. If no radius, use
an 8-connected structuring element.
mask - mask of significant pixels in the image. Points outside of
the mask will not participate in the morphological operations
'''
#
# Subtract the image from the closing to get the bothat
#
final_image = closing(image, radius, mask, footprint) - image
#
# Paint the masked pixels into the final image
#
if not mask is None:
not_mask = np.logical_not(mask)
final_image[not_mask] = image[not_mask]
return final_image
|
python
|
{
"resource": ""
}
|
q17733
|
grey_erosion
|
train
|
def grey_erosion(image, radius=None, mask=None, footprint=None):
'''Perform a grey erosion with masking'''
if footprint is None:
if radius is None:
footprint = np.ones((3,3),bool)
radius = 1
else:
footprint = strel_disk(radius)==1
else:
radius = max(1, np.max(np.array(footprint.shape) // 2))
iradius = int(np.ceil(radius))
#
# Do a grey_erosion with masked pixels = 1 so they don't participate
#
big_image = np.ones(np.array(image.shape)+iradius*2)
big_image[iradius:-iradius,iradius:-iradius] = image
if not mask is None:
not_mask = np.logical_not(mask)
big_image[iradius:-iradius,iradius:-iradius][not_mask] = 1
processed_image = scind.grey_erosion(big_image, footprint=footprint)
final_image = processed_image[iradius:-iradius,iradius:-iradius]
if not mask is None:
final_image[not_mask] = image[not_mask]
return final_image
|
python
|
{
"resource": ""
}
|
q17734
|
opening
|
train
|
def opening(image, radius=None, mask=None, footprint=None):
'''Do a morphological opening
image - pixel image to operate on
radius - use a structuring element with the given radius. If no radius,
use an 8-connected structuring element.
mask - if present, only use unmasked pixels for operations
'''
eroded_image = grey_erosion(image, radius, mask, footprint)
return grey_dilation(eroded_image, radius, mask, footprint)
|
python
|
{
"resource": ""
}
|
q17735
|
closing
|
train
|
def closing(image, radius=None, mask=None, footprint = None):
'''Do a morphological closing
image - pixel image to operate on
radius - use a structuring element with the given radius. If no structuring
element, use an 8-connected structuring element.
mask - if present, only use unmasked pixels for operations
'''
dilated_image = grey_dilation(image, radius, mask, footprint)
return grey_erosion(dilated_image, radius, mask, footprint)
|
python
|
{
"resource": ""
}
|
q17736
|
openlines
|
train
|
def openlines(image, linelength=10, dAngle=10, mask=None):
"""
Do a morphological opening along lines of different angles.
Return difference between max and min response to different angles for each pixel.
This effectively removes dots and only keeps lines.
image - pixel image to operate on
length - length of the structural element
angluar_resolution - angle step for the rotating lines
mask - if present, only use unmasked pixels for operations
"""
nAngles = 180//dAngle
openingstack = np.zeros((nAngles,image.shape[0],image.shape[1]),image.dtype)
for iAngle in range(nAngles):
angle = dAngle * iAngle
se = strel_line(linelength,angle)
openingstack[iAngle,:,:] = opening(image, mask=mask, footprint=se)
imLines = np.max(openingstack,axis=0) - np.min(openingstack,axis=0)
return imLines
|
python
|
{
"resource": ""
}
|
q17737
|
pattern_of
|
train
|
def pattern_of(index):
'''Return the pattern represented by an index value'''
return np.array([[index & 2**0,index & 2**1,index & 2**2],
[index & 2**3,index & 2**4,index & 2**5],
[index & 2**6,index & 2**7,index & 2**8]], bool)
|
python
|
{
"resource": ""
}
|
q17738
|
index_of
|
train
|
def index_of(pattern):
'''Return the index of a given pattern'''
return (pattern[0,0] * 2**0 + pattern[0,1] * 2**1 + pattern[0,2] * 2**2 +
pattern[1,0] * 2**3 + pattern[1,1] * 2**4 + pattern[1,2] * 2**5 +
pattern[2,0] * 2**6 + pattern[2,1] * 2**7 + pattern[2,2] * 2**8)
|
python
|
{
"resource": ""
}
|
q17739
|
make_table
|
train
|
def make_table(value, pattern, care=np.ones((3,3),bool)):
'''Return a table suitable for table_lookup
value - set all table entries matching "pattern" to "value", all others
to not "value"
pattern - a 3x3 boolean array with the pattern to match
care - a 3x3 boolean array where each value is true if the pattern
must match at that position and false if we don't care if
the pattern matches at that position.
'''
def fn(index, p,i,j):
'''Return true if bit position "p" in index matches pattern'''
return ((((index & 2**p) > 0) == pattern[i,j]) or not care[i,j])
return np.array([value
if (fn(i,0,0,0) and fn(i,1,0,1) and fn(i,2,0,2) and
fn(i,3,1,0) and fn(i,4,1,1) and fn(i,5,1,2) and
fn(i,6,2,0) and fn(i,7,2,1) and fn(i,8,2,2))
else not value
for i in range(512)], bool)
|
python
|
{
"resource": ""
}
|
q17740
|
branchpoints
|
train
|
def branchpoints(image, mask=None):
'''Remove all pixels from an image except for branchpoints
image - a skeletonized image
mask - a mask of pixels excluded from consideration
1 0 1 ? 0 ?
0 1 0 -> 0 1 0
0 1 0 0 ? 0
'''
global branchpoints_table
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = False
result = table_lookup(masked_image, branchpoints_table, False, 1)
if not mask is None:
result[~mask] = image[~mask]
return result
|
python
|
{
"resource": ""
}
|
q17741
|
branchings
|
train
|
def branchings(image, mask=None):
'''Count the number of branches eminating from each pixel
image - a binary image
mask - optional mask of pixels not to consider
This is the count of the number of branches that
eminate from a pixel. A pixel with neighbors fore
and aft has branches fore and aft = 2. An endpoint
has one branch. A fork has 3. Finally, there's
the quadrabranch which has 4:
1 0 1
0 1 0 -> 4
1 0 1
'''
global branchings_table
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = False
#
# Not a binary operation, so we do a convolution with the following
# kernel to get the indices into the table.
#
kernel = np.array([[1,2,4],
[8,16,32],
[64,128,256]])
indexer = scind.convolve(masked_image.astype(int), kernel,
mode='constant').astype(int)
result = branchings_table[indexer]
return result
|
python
|
{
"resource": ""
}
|
q17742
|
bridge
|
train
|
def bridge(image, mask=None, iterations = 1):
'''Fill in pixels that bridge gaps.
1 0 0 1 0 0
0 0 0 -> 0 1 0
0 0 1 0 0 1
'''
global bridge_table
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = False
result = table_lookup(masked_image, bridge_table, False, iterations)
if not mask is None:
result[~mask] = image[~mask]
return result
|
python
|
{
"resource": ""
}
|
q17743
|
clean
|
train
|
def clean(image, mask=None, iterations = 1):
'''Remove isolated pixels
0 0 0 0 0 0
0 1 0 -> 0 0 0
0 0 0 0 0 0
Border pixels and pixels adjoining masks are removed unless one valid
neighbor is true.
'''
global clean_table
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = False
result = table_lookup(masked_image, clean_table, False, iterations)
if not mask is None:
result[~mask] = image[~mask]
return result
|
python
|
{
"resource": ""
}
|
q17744
|
diag
|
train
|
def diag(image, mask=None, iterations=1):
'''4-connect pixels that are 8-connected
0 0 0 0 0 ?
0 0 1 -> 0 1 1
0 1 0 ? 1 ?
'''
global diag_table
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = False
result = table_lookup(masked_image, diag_table, False, iterations)
if not mask is None:
result[~mask] = image[~mask]
return result
|
python
|
{
"resource": ""
}
|
q17745
|
endpoints
|
train
|
def endpoints(image, mask=None):
'''Remove all pixels from an image except for endpoints
image - a skeletonized image
mask - a mask of pixels excluded from consideration
1 0 0 ? 0 0
0 1 0 -> 0 1 0
0 0 0 0 0 0
'''
global endpoints_table
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = False
result = table_lookup(masked_image, endpoints_table, False, 1)
if not mask is None:
result[~mask] = image[~mask]
return result
|
python
|
{
"resource": ""
}
|
q17746
|
fill
|
train
|
def fill(image, mask=None, iterations=1):
'''Fill isolated black pixels
1 1 1 1 1 1
1 0 1 -> 1 1 1
1 1 1 1 1 1
'''
global fill_table
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = True
result = table_lookup(masked_image, fill_table, True, iterations)
if not mask is None:
result[~mask] = image[~mask]
return result
|
python
|
{
"resource": ""
}
|
q17747
|
fill4
|
train
|
def fill4(image, mask=None, iterations=1):
'''Fill 4-connected black pixels
x 1 x x 1 x
1 0 1 -> 1 1 1
x 1 x x 1 x
'''
global fill4_table
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = True
result = table_lookup(masked_image, fill4_table, True, iterations)
if not mask is None:
result[~mask] = image[~mask]
return result
|
python
|
{
"resource": ""
}
|
q17748
|
majority
|
train
|
def majority(image, mask=None, iterations=1):
'''A pixel takes the value of the majority of its neighbors
'''
global majority_table
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = False
result = table_lookup(masked_image, majority_table, False, iterations)
if not mask is None:
result[~mask] = image[~mask]
return result
|
python
|
{
"resource": ""
}
|
q17749
|
remove
|
train
|
def remove(image, mask=None, iterations=1):
'''Turn 1 pixels to 0 if their 4-connected neighbors are all 0
? 1 ? ? 1 ?
1 1 1 -> 1 0 1
? 1 ? ? 1 ?
'''
global remove_table
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = False
result = table_lookup(masked_image, remove_table, False)
if not mask is None:
result[~mask] = image[~mask]
return result
|
python
|
{
"resource": ""
}
|
q17750
|
spur
|
train
|
def spur(image, mask=None, iterations=1):
'''Remove spur pixels from an image
0 0 0 0 0 0
0 1 0 -> 0 0 0
0 0 1 0 0 ?
'''
global spur_table_1,spur_table_2
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = False
index_i, index_j, masked_image = prepare_for_index_lookup(masked_image,
False)
if iterations is None:
iterations = len(index_i)
for i in range(iterations):
for table in (spur_table_1, spur_table_2):
index_i, index_j = index_lookup(index_i, index_j,
masked_image, table, 1)
masked_image = extract_from_image_lookup(image, index_i, index_j)
if not mask is None:
masked_image[~mask] = image[~mask]
return masked_image
|
python
|
{
"resource": ""
}
|
q17751
|
thicken
|
train
|
def thicken(image, mask=None, iterations=1):
'''Thicken the objects in an image where doing so does not connect them
0 0 0 ? ? ?
0 0 0 -> ? 1 ?
0 0 1 ? ? ?
1 0 0 ? ? ?
0 0 0 -> ? 0 ?
0 0 1 ? ? ?
'''
global thicken_table
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = False
result = table_lookup(masked_image, thicken_table, False, iterations)
if not mask is None:
result[~mask] = image[~mask]
return result
|
python
|
{
"resource": ""
}
|
q17752
|
distance_color_labels
|
train
|
def distance_color_labels(labels):
'''Recolor a labels matrix so that adjacent labels have distant numbers
'''
#
# Color labels so adjacent ones are most distant
#
colors = color_labels(labels, True)
#
# Order pixels by color, then label #
#
rlabels = labels.ravel()
order = np.lexsort((rlabels, colors.ravel()))
#
# Construct color indices with the cumsum trick:
# cumsum([0,0,1,0,1]) = [0,0,1,1,2]
# and copy back into the color array, using the order.
#
different = np.hstack([[rlabels[order[0]] > 0],
rlabels[order[1:]] != rlabels[order[:-1]]])
# We need to careful about ravel() returning a new object, but in the usual
# case of colors having order='C', this won't create any copies.
rcolor = colors.ravel()
rcolor[order] = np.cumsum(different).astype(colors.dtype)
return rcolor.reshape(colors.shape).astype(labels.dtype)
|
python
|
{
"resource": ""
}
|
q17753
|
skeletonize
|
train
|
def skeletonize(image, mask=None, ordering = None):
'''Skeletonize the image
Take the distance transform.
Order the 1 points by the distance transform.
Remove a point if it has more than 1 neighbor and if removing it
does not change the Euler number.
image - the binary image to be skeletonized
mask - only skeletonize pixels within the mask
ordering - a matrix of the same dimensions as the image. The matrix
provides the ordering of the erosion with the lowest values
being eroded first. The default is to use the distance transform.
'''
global eight_connect
if mask is None:
masked_image = image
else:
masked_image = image.astype(bool).copy()
masked_image[~mask] = False
#
# Lookup table - start with only positive pixels.
# Keep if # pixels in neighborhood is 2 or less
# Keep if removing the pixel results in a different connectivity
#
table = (make_table(True,np.array([[0,0,0],[0,1,0],[0,0,0]],bool),
np.array([[0,0,0],[0,1,0],[0,0,0]],bool)) &
(np.array([scind.label(pattern_of(index), eight_connect)[1] !=
scind.label(pattern_of(index & ~ 2**4),
eight_connect)[1]
for index in range(512) ]) |
np.array([np.sum(pattern_of(index))<3 for index in range(512)])))
if ordering is None:
distance = scind.distance_transform_edt(masked_image)
else:
distance = ordering
#
# The processing order along the edge is critical to the shape of the
# resulting skeleton: if you process a corner first, that corner will
# be eroded and the skeleton will miss the arm from that corner. Pixels
# with fewer neighbors are more "cornery" and should be processed last.
#
cornerness_table = np.array([9-np.sum(pattern_of(index))
for index in range(512)])
corner_score = table_lookup(masked_image, cornerness_table, False,1)
i,j = np.mgrid[0:image.shape[0],0:image.shape[1]]
result=masked_image.copy()
distance = distance[result]
i = np.ascontiguousarray(i[result],np.int32)
j = np.ascontiguousarray(j[result],np.int32)
result=np.ascontiguousarray(result,np.uint8)
#
# We use a random # for tiebreaking. Assign each pixel in the image a
# predictable, random # so that masking doesn't affect arbitrary choices
# of skeletons
#
np.random.seed(0)
tiebreaker=np.random.permutation(np.arange(np.product(masked_image.shape)))
tiebreaker.shape=masked_image.shape
order = np.lexsort((tiebreaker[masked_image],
corner_score[masked_image],
distance))
order = np.ascontiguousarray(order, np.int32)
table = np.ascontiguousarray(table, np.uint8)
skeletonize_loop(result, i, j, order, table)
result = result.astype(bool)
if not mask is None:
result[~mask] = image[~mask]
return result
|
python
|
{
"resource": ""
}
|
q17754
|
skeletonize_labels
|
train
|
def skeletonize_labels(labels):
'''Skeletonize a labels matrix'''
#
# The trick here is to separate touching labels by coloring the
# labels matrix and then processing each color separately
#
colors = color_labels(labels)
max_color = np.max(colors)
if max_color == 0:
return labels
result = np.zeros(labels.shape, labels.dtype)
for i in range(1,max_color+1):
mask = skeletonize(colors==i)
result[mask] = labels[mask]
return result
|
python
|
{
"resource": ""
}
|
q17755
|
skeleton_length
|
train
|
def skeleton_length(labels, indices=None):
'''Compute the length of all skeleton branches for labeled skeletons
labels - a labels matrix
indices - the indexes of the labels to be measured. Default is all
returns an array of one skeleton length per label.
'''
global __skel_length_table
if __skel_length_table is None:
tbl = np.zeros(512, np.float32)
for ii in range(-1, 2):
for jj in range(-1, 2):
if ii == 0 and jj == 0:
continue
#
# Set the bit to search for and the center bit
#
idx = 2 ** (ii + 1 + (jj + 1) * 3) | 16
mask = (np.arange(512) & idx) == idx
#
# If we are four-connected to another pixel that is
# connected to this one, they are 8-connected and that
# is the distance.
#
# bad good
# x 1 0 0 0 0
# x 1 1 0 1 0
# x x x 0 x 1
if ii != 0 and jj != 0:
for adjacent_i, adjacent_j in (
(ii-1, jj), (ii, jj-1), (ii+1, jj), (ii, jj+1)):
if any([_ < -1 or _ > 1
for _ in (adjacent_i, adjacent_j)]):
continue
aidx = 2 ** (adjacent_i+1 + (adjacent_j + 1) * 3)
mask = mask & ((np.arange(512) & aidx) != aidx)
tbl[mask] += np.sqrt(ii*ii + jj*jj) / 2
__skel_length_table = tbl
if indices is None:
indices = np.arange(1, np.max(labels)+1)
else:
indices = np.asanyarray(indices)
if len(indices) == 0:
return np.zeros(0)
score = __skel_length_table[table_idx_from_labels(labels)]
result = np.bincount(labels.ravel(),
weights = score.ravel(),
minlength=np.max(indices)+1)
return result[indices]
|
python
|
{
"resource": ""
}
|
q17756
|
distance_to_edge
|
train
|
def distance_to_edge(labels):
'''Compute the distance of a pixel to the edge of its object
labels - a labels matrix
returns a matrix of distances
'''
colors = color_labels(labels)
max_color = np.max(colors)
result = np.zeros(labels.shape)
if max_color == 0:
return result
for i in range(1, max_color+1):
mask = (colors==i)
result[mask] = scind.distance_transform_edt(mask)[mask]
return result
|
python
|
{
"resource": ""
}
|
q17757
|
is_local_maximum
|
train
|
def is_local_maximum(image, labels, footprint):
'''Return a boolean array of points that are local maxima
image - intensity image
labels - find maxima only within labels. Zero is reserved for background.
footprint - binary mask indicating the neighborhood to be examined
must be a matrix with odd dimensions, center is taken to
be the point in question.
'''
assert((np.all(footprint.shape) & 1) == 1)
footprint = (footprint != 0)
footprint_extent = (np.array(footprint.shape)-1) // 2
if np.all(footprint_extent == 0):
return labels > 0
result = (labels > 0).copy()
#
# Create a labels matrix with zeros at the borders that might be
# hit by the footprint.
#
big_labels = np.zeros(np.array(labels.shape) + footprint_extent*2,
labels.dtype)
big_labels[[slice(fe,-fe) for fe in footprint_extent]] = labels
#
# Find the relative indexes of each footprint element
#
image_strides = np.array(image.strides) // image.dtype.itemsize
big_strides = np.array(big_labels.strides) // big_labels.dtype.itemsize
result_strides = np.array(result.strides) // result.dtype.itemsize
footprint_offsets = np.mgrid[[slice(-fe,fe+1) for fe in footprint_extent]]
footprint_offsets = footprint_offsets[:, footprint]
#
# Order by distance, low to high and get rid of center pt.
#
d = np.sum(footprint_offsets **2, 0)
footprint_offsets, d = footprint_offsets[:, d > 0], d[d > 0]
footprint_offsets = footprint_offsets[:, np.lexsort([d])]
fp_image_offsets = np.sum(image_strides[:, np.newaxis] *
footprint_offsets, 0)
fp_big_offsets = np.sum(big_strides[:, np.newaxis] *
footprint_offsets, 0)
#
# Get the index of each labeled pixel in the image and big_labels arrays
#
indexes = np.mgrid[[slice(0,x) for x in labels.shape]][:, labels > 0]
image_indexes = np.sum(image_strides[:, np.newaxis] * indexes, 0)
big_indexes = np.sum(big_strides[:, np.newaxis] *
(indexes + footprint_extent[:, np.newaxis]), 0)
result_indexes = np.sum(result_strides[:, np.newaxis] * indexes, 0)
#
# Now operate on the raveled images
#
big_labels_raveled = big_labels.ravel()
image_raveled = image.ravel()
result_raveled = result.ravel()
#
# A hit is a hit if the label at the offset matches the label at the pixel
# and if the intensity at the pixel is greater or equal to the intensity
# at the offset.
#
for fp_image_offset, fp_big_offset in zip(fp_image_offsets, fp_big_offsets):
same_label = (big_labels_raveled[big_indexes + fp_big_offset] ==
big_labels_raveled[big_indexes])
less_than = (image_raveled[image_indexes[same_label]] <
image_raveled[image_indexes[same_label]+ fp_image_offset])
mask = ~same_label
mask[same_label] = ~less_than
result_raveled[result_indexes[~mask]] = False
result_indexes = result_indexes[mask]
big_indexes = big_indexes[mask]
image_indexes = image_indexes[mask]
return result
|
python
|
{
"resource": ""
}
|
q17758
|
is_obtuse
|
train
|
def is_obtuse(p1, v, p2):
'''Determine whether the angle, p1 - v - p2 is obtuse
p1 - N x 2 array of coordinates of first point on edge
v - N x 2 array of vertex coordinates
p2 - N x 2 array of coordinates of second point on edge
returns vector of booleans
'''
p1x = p1[:,1]
p1y = p1[:,0]
p2x = p2[:,1]
p2y = p2[:,0]
vx = v[:,1]
vy = v[:,0]
Dx = vx - p2x
Dy = vy - p2y
Dvp1x = p1x - vx
Dvp1y = p1y - vy
return Dvp1x * Dx + Dvp1y * Dy > 0
|
python
|
{
"resource": ""
}
|
q17759
|
stretch
|
train
|
def stretch(image, mask=None):
'''Normalize an image to make the minimum zero and maximum one
image - pixel data to be normalized
mask - optional mask of relevant pixels. None = don't mask
returns the stretched image
'''
image = np.array(image, float)
if np.product(image.shape) == 0:
return image
if mask is None:
minval = np.min(image)
maxval = np.max(image)
if minval == maxval:
if minval < 0:
return np.zeros_like(image)
elif minval > 1:
return np.ones_like(image)
return image
else:
return (image - minval) / (maxval - minval)
else:
significant_pixels = image[mask]
if significant_pixels.size == 0:
return image
minval = np.min(significant_pixels)
maxval = np.max(significant_pixels)
if minval == maxval:
transformed_image = minval
else:
transformed_image = ((significant_pixels - minval) /
(maxval - minval))
result = image.copy()
image[mask] = transformed_image
return image
|
python
|
{
"resource": ""
}
|
q17760
|
median_filter
|
train
|
def median_filter(data, mask, radius, percent=50):
'''Masked median filter with octagonal shape
data - array of data to be median filtered.
mask - mask of significant pixels in data
radius - the radius of a circle inscribed into the filtering octagon
percent - conceptually, order the significant pixels in the octagon,
count them and choose the pixel indexed by the percent
times the count divided by 100. More simply, 50 = median
returns a filtered array. In areas where the median filter does
not overlap the mask, the filtered result is undefined, but in
practice, it will be the lowest value in the valid area.
'''
if mask is None:
mask = np.ones(data.shape, dtype=bool)
if np.all(~ mask):
return data.copy()
#
# Normalize the ranked data to 0-255
#
if (not np.issubdtype(data.dtype, np.int) or
np.min(data) < 0 or np.max(data) > 255):
ranked_data, translation = rank_order(data[mask], nbins=255)
was_ranked = True
else:
ranked_data = data[mask]
was_ranked = False
input = np.zeros(data.shape, np.uint8 )
input[mask] = ranked_data
mmask = np.ascontiguousarray(mask, np.uint8)
output = np.zeros(data.shape, np.uint8)
_filter.median_filter(input, mmask, output, radius, percent)
if was_ranked:
result = translation[output]
else:
result = output
return result
|
python
|
{
"resource": ""
}
|
q17761
|
bilateral_filter
|
train
|
def bilateral_filter(image, mask, sigma_spatial, sigma_range,
sampling_spatial = None, sampling_range = None):
"""Bilateral filter of an image
image - image to be bilaterally filtered
mask - mask of significant points in image
sigma_spatial - standard deviation of the spatial Gaussian
sigma_range - standard deviation of the range Gaussian
sampling_spatial - amt to reduce image array extents when sampling
default is 1/2 sigma_spatial
sampling_range - amt to reduce the range of values when sampling
default is 1/2 sigma_range
The bilateral filter is described by the following equation:
sum(Fs(||p - q||)Fr(|Ip - Iq|)Iq) / sum(Fs(||p-q||)Fr(|Ip - Iq))
where the sum is over all points in the kernel
p is all coordinates in the image
q is the coordinates as perturbed by the mask
Ip is the intensity at p
Iq is the intensity at q
Fs is the spatial convolution function, for us a Gaussian that
falls off as the distance between falls off
Fr is the "range" distance which falls off as the difference
in intensity increases.
1 / sum(Fs(||p-q||)Fr(|Ip - Iq)) is the weighting for point p
"""
# The algorithm is taken largely from code by Jiawen Chen which miraculously
# extends to the masked case:
# http://groups.csail.mit.edu/graphics/bilagrid/bilagrid_web.pdf
#
# Form a 3-d array whose extent is reduced in the i,j directions
# by the spatial sampling parameter and whose extent is reduced in the
# z (image intensity) direction by the range sampling parameter.
# Scatter each significant pixel in the image into the nearest downsampled
# array address where the pixel's i,j coordinate gives the corresponding
# i and j in the matrix and the intensity value gives the corresponding z
# in the array.
# Count the # of values entered into each 3-d array element to form a
# weight.
# Similarly convolve the downsampled value and weight arrays with a 3-d
# Gaussian kernel whose i and j Gaussian is the sigma_spatial and whose
# z is the sigma_range.
#
# Divide the value by the weight to scale each z value appropriately
#
# Linearly interpolate using an i x j x 3 array where [:,:,0] is the
# i coordinate in the downsampled array, [:,:,1] is the j coordinate
# and [:,:,2] is the unrounded index of the z-slot
#
# One difference is that I don't pad the intermediate arrays. The
# weights bleed off the edges of the intermediate arrays and this
# accounts for the ring of zero values used at the border bleeding
# back into the intermediate arrays during convolution
#
if sampling_spatial is None:
sampling_spatial = sigma_spatial / 2.0
if sampling_range is None:
sampling_range = sigma_range / 2.0
if np.all(np.logical_not(mask)):
return image
masked_image = image[mask]
image_min = np.min(masked_image)
image_max = np.max(masked_image)
image_delta = image_max - image_min
if image_delta == 0:
return image
#
# ds = downsampled. Calculate the ds array sizes and sigmas.
#
ds_sigma_spatial = sigma_spatial / sampling_spatial
ds_sigma_range = sigma_range / sampling_range
ds_i_limit = int(image.shape[0] / sampling_spatial) + 2
ds_j_limit = int(image.shape[1] / sampling_spatial) + 2
ds_z_limit = int(image_delta / sampling_range) + 2
grid_data = np.zeros((ds_i_limit, ds_j_limit, ds_z_limit))
grid_weights = np.zeros((ds_i_limit, ds_j_limit, ds_z_limit))
#
# Compute the downsampled i, j and z coordinates at each point
#
di,dj = np.mgrid[0:image.shape[0],
0:image.shape[1]].astype(float) / sampling_spatial
dz = (masked_image - image_min) / sampling_range
#
# Treat this as a list of 3-d coordinates from now on
#
di = di[mask]
dj = dj[mask]
#
# scatter the unmasked image points into the data array and
# scatter a value of 1 per point into the weights
#
grid_data[(di + .5).astype(int),
(dj + .5).astype(int),
(dz + .5).astype(int)] += masked_image
grid_weights[(di + .5).astype(int),
(dj + .5).astype(int),
(dz + .5).astype(int)] += 1
#
# Make a Gaussian kernel
#
kernel_spatial_limit = int(2 * ds_sigma_spatial) + 1
kernel_range_limit = int(2 * ds_sigma_range) + 1
ki,kj,kz = np.mgrid[-kernel_spatial_limit : kernel_spatial_limit+1,
-kernel_spatial_limit : kernel_spatial_limit+1,
-kernel_range_limit : kernel_range_limit+1]
kernel = np.exp(-.5 * ((ki**2 + kj**2) / ds_sigma_spatial ** 2 +
kz**2 / ds_sigma_range ** 2))
blurred_grid_data = convolve(grid_data, kernel, mode='constant')
blurred_weights = convolve(grid_weights, kernel, mode='constant')
weight_mask = blurred_weights > 0
normalized_blurred_grid = np.zeros(grid_data.shape)
normalized_blurred_grid[weight_mask] = ( blurred_grid_data[weight_mask] /
blurred_weights[weight_mask])
#
# Now use di, dj and dz to find the coordinate of the point within
# the blurred grid to use. We actually interpolate between points
# here (both in the i,j direction to get intermediate z values and in
# the z direction to get the slot, roughly where we put our original value)
#
dijz = np.vstack((di, dj, dz))
image_copy = image.copy()
image_copy[mask] = map_coordinates(normalized_blurred_grid, dijz,
order = 1)
return image_copy
|
python
|
{
"resource": ""
}
|
q17762
|
laplacian_of_gaussian
|
train
|
def laplacian_of_gaussian(image, mask, size, sigma):
'''Perform the Laplacian of Gaussian transform on the image
image - 2-d image array
mask - binary mask of significant pixels
size - length of side of square kernel to use
sigma - standard deviation of the Gaussian
'''
half_size = size//2
i,j = np.mgrid[-half_size:half_size+1,
-half_size:half_size+1].astype(float) / float(sigma)
distance = (i**2 + j**2)/2
gaussian = np.exp(-distance)
#
# Normalize the Gaussian
#
gaussian = gaussian / np.sum(gaussian)
log = (distance - 1) * gaussian
#
# Normalize the kernel to have a sum of zero
#
log = log - np.mean(log)
if mask is None:
mask = np.ones(image.shape[:2], bool)
masked_image = image.copy()
masked_image[~mask] = 0
output = convolve(masked_image, log, mode='constant', cval=0)
#
# Do the LoG of the inverse of the mask. This finds the magnitude of the
# contribution of the masked pixels. We then fudge by multiplying by the
# value at the pixel of interest - this effectively sets the value at a
# masked pixel to that of the pixel of interest.
#
# It underestimates the LoG, that's not a terrible thing.
#
correction = convolve((~ mask).astype(float), log, mode='constant', cval = 1)
output += correction * image
output[~ mask] = image[~ mask]
return output
|
python
|
{
"resource": ""
}
|
q17763
|
roberts
|
train
|
def roberts(image, mask=None):
'''Find edges using the Roberts algorithm
image - the image to process
mask - mask of relevant points
The algorithm returns the magnitude of the output of the two Roberts
convolution kernels.
The following is the canonical citation for the algorithm:
L. Roberts Machine Perception of 3-D Solids, Optical and
Electro-optical Information Processing, MIT Press 1965.
The following website has a tutorial on the algorithm:
http://homepages.inf.ed.ac.uk/rbf/HIPR2/roberts.htm
'''
result = np.zeros(image.shape)
#
# Four quadrants and two convolutions:
#
# q0,0 | q0,1 1 | 0 anti-diagonal
# q1,0 | q1,1 0 | -1
#
# q-1,0 | q0,0 0 | 1 diagonal
# q-1,1 | q0,1 -1 | 0
#
# Points near the mask edges and image edges are computed unreliably
# so make them zero (no edge) in the result
#
if mask is None:
mask = np.ones(image.shape, bool)
big_mask = binary_erosion(mask,
generate_binary_structure(2,2),
border_value = 0)
result[big_mask==False] = 0
q00 = image[:,:][big_mask]
q11 = image[1:,1:][big_mask[:-1,:-1]]
qm11 = image[:-1,1:][big_mask[1:,:-1]]
diagonal = q00 - qm11
anti_diagonal = q00 - q11
result[big_mask] = np.sqrt(diagonal*diagonal + anti_diagonal*anti_diagonal)
return result
|
python
|
{
"resource": ""
}
|
q17764
|
sobel
|
train
|
def sobel(image, mask=None):
'''Calculate the absolute magnitude Sobel to find the edges
image - image to process
mask - mask of relevant points
Take the square root of the sum of the squares of the horizontal and
vertical Sobels to get a magnitude that's somewhat insensitive to
direction.
Note that scipy's Sobel returns a directional Sobel which isn't
useful for edge detection in its raw form.
'''
return np.sqrt(hsobel(image,mask)**2 + vsobel(image,mask)**2)
|
python
|
{
"resource": ""
}
|
q17765
|
prewitt
|
train
|
def prewitt(image, mask=None):
'''Find the edge magnitude using the Prewitt transform
image - image to process
mask - mask of relevant points
Return the square root of the sum of squares of the horizontal
and vertical Prewitt transforms.
'''
return np.sqrt(hprewitt(image,mask)**2 + vprewitt(image,mask)**2)
|
python
|
{
"resource": ""
}
|
q17766
|
hprewitt
|
train
|
def hprewitt(image, mask=None):
'''Find the horizontal edges of an image using the Prewitt transform
image - image to process
mask - mask of relevant points
We use the following kernel and return the absolute value of the
result at each point:
1 1 1
0 0 0
-1 -1 -1
'''
if mask is None:
mask = np.ones(image.shape, bool)
big_mask = binary_erosion(mask,
generate_binary_structure(2,2),
border_value = 0)
result = np.abs(convolve(image, np.array([[ 1, 1, 1],
[ 0, 0, 0],
[-1,-1,-1]]).astype(float)/3.0))
result[big_mask==False] = 0
return result
|
python
|
{
"resource": ""
}
|
q17767
|
gabor
|
train
|
def gabor(image, labels, frequency, theta):
'''Gabor-filter the objects in an image
image - 2-d grayscale image to filter
labels - a similarly shaped labels matrix
frequency - cycles per trip around the circle
theta - angle of the filter. 0 to 2 pi
Calculate the Gabor filter centered on the centroids of each object
in the image. Summing the resulting image over the labels matrix will
yield a texture measure per object.
'''
#
# The code inscribes the X and Y position of each pixel relative to
# the centroid of that pixel's object. After that, the Gabor filter
# for the image can be calculated per-pixel and the image can be
# multiplied by the filter to get the filtered image.
#
nobjects = np.max(labels)
if nobjects == 0:
return image
centers = centers_of_labels(labels)
areas = fix(scind.sum(np.ones(image.shape),labels, np.arange(nobjects, dtype=np.int32)+1))
mask = labels > 0
i,j = np.mgrid[0:image.shape[0],0:image.shape[1]].astype(float)
i = i[mask]
j = j[mask]
image = image[mask]
lm = labels[mask] - 1
i -= centers[0,lm]
j -= centers[1,lm]
sigma = np.sqrt(areas/np.pi) / 3.0
sigma = sigma[lm]
g_exp = 1000.0/(2.0*np.pi*sigma**2) * np.exp(-(i**2 + j**2)/(2*sigma**2))
g_angle = 2*np.pi/frequency*(i*np.cos(theta)+j*np.sin(theta))
g_cos = g_exp * np.cos(g_angle)
g_sin = g_exp * np.sin(g_angle)
#
# Normalize so that the sum of the filter over each object is zero
# and so that there is no bias-value within each object.
#
g_cos_mean = fix(scind.mean(g_cos,lm, np.arange(nobjects)))
i_mean = fix(scind.mean(image, lm, np.arange(nobjects)))
i_norm = image - i_mean[lm]
g_sin_mean = fix(scind.mean(g_sin,lm, np.arange(nobjects)))
g_cos -= g_cos_mean[lm]
g_sin -= g_sin_mean[lm]
g = np.zeros(mask.shape,dtype=np.complex)
g[mask] = i_norm *g_cos+i_norm * g_sin*1j
return g
|
python
|
{
"resource": ""
}
|
q17768
|
enhance_dark_holes
|
train
|
def enhance_dark_holes(image, min_radius, max_radius, mask=None):
'''Enhance dark holes using a rolling ball filter
image - grayscale 2-d image
radii - a vector of radii: we enhance holes at each given radius
'''
#
# Do 4-connected erosion
#
se = np.array([[False, True, False],
[True, True, True],
[False, True, False]])
#
# Invert the intensities
#
inverted_image = image.max() - image
previous_reconstructed_image = inverted_image
eroded_image = inverted_image
smoothed_image = np.zeros(image.shape)
for i in range(max_radius+1):
eroded_image = grey_erosion(eroded_image, mask=mask, footprint = se)
reconstructed_image = grey_reconstruction(eroded_image, inverted_image,
footprint = se)
output_image = previous_reconstructed_image - reconstructed_image
if i >= min_radius:
smoothed_image = np.maximum(smoothed_image,output_image)
previous_reconstructed_image = reconstructed_image
return smoothed_image
|
python
|
{
"resource": ""
}
|
q17769
|
granulometry_filter
|
train
|
def granulometry_filter(image, min_radius, max_radius, mask=None):
'''Enhances bright structures within a min and max radius using a rolling ball filter
image - grayscale 2-d image
radii - a vector of radii: we enhance holes at each given radius
'''
#
# Do 4-connected erosion
#
se = np.array([[False, True, False],
[True, True, True],
[False, True, False]])
#
# Initialize
#
inverted_image = image.max() - image
previous_opened_image = image
eroded_image = image
selected_granules_image = np.zeros(image.shape)
#
# Select granules by successive morphological openings
#
for i in range(max_radius+1):
eroded_image = grey_erosion(eroded_image, mask=mask, footprint = se)
opened_image = grey_dilation(eroded_image, inverted_image, footprint = se)
output_image = previous_opened_image - opened_image
if i >= min_radius:
selected_granules_image = np.maximum(selected_granules_image, output_image)
previous_opened_image = opened_image
return selected_granules_image
|
python
|
{
"resource": ""
}
|
q17770
|
velocity_kalman_model
|
train
|
def velocity_kalman_model():
'''Return a KalmanState set up to model objects with constant velocity
The observation and measurement vectors are i,j.
The state vector is i,j,vi,vj
'''
om = np.array([[1,0,0,0], [0, 1, 0, 0]])
tm = np.array([[1,0,1,0],
[0,1,0,1],
[0,0,1,0],
[0,0,0,1]])
return KalmanState(om, tm)
|
python
|
{
"resource": ""
}
|
q17771
|
reverse_velocity_kalman_model
|
train
|
def reverse_velocity_kalman_model():
'''Return a KalmanState set up to model going backwards in time'''
om = np.array([[1,0,0,0], [0, 1, 0, 0]])
tm = np.array([[1,0,-1,0],
[0,1,0,-1],
[0,0,1,0],
[0,0,0,1]])
return KalmanState(om, tm)
|
python
|
{
"resource": ""
}
|
q17772
|
line_integration
|
train
|
def line_integration(image, angle, decay, sigma):
'''Integrate the image along the given angle
DIC images are the directional derivative of the underlying
image. This filter reconstructs the original image by integrating
along that direction.
image - a 2-dimensional array
angle - shear angle in radians. We integrate perpendicular to this angle
decay - an exponential decay applied to the integration
sigma - the standard deviation of a Gaussian which is used to
smooth the image in the direction parallel to the shear angle.
'''
#
# Normalize the image so that the mean is zero
#
normalized = image - np.mean(image)
#
# Rotate the image so the J direction is perpendicular to the shear angle.
#
rotated = scind.rotate(normalized, -angle)
#
# Smooth in only the i direction
#
smoothed = scind.gaussian_filter1d(rotated, sigma) if sigma > 0 else rotated
#
# We want img_out[:,j+1] to be img_out[:,j] * decay + img[j+1]
# Could be done by convolution with a ramp, maybe in FFT domain,
# but we just do a bunch of steps here.
#
result_fwd = smoothed.copy()
for i in range(1,result_fwd.shape[0]):
result_fwd[i] += result_fwd[i-1] * decay
result_rev = smoothed.copy()
for i in reversed(range(result_rev.shape[0]-1)):
result_rev[i] += result_rev[i+1] * decay
result = (result_fwd - result_rev) / 2
#
# Rotate and chop result
#
result = scind.rotate(result, angle)
ipad = int((result.shape[0] - image.shape[0]) / 2)
jpad = int((result.shape[1] - image.shape[1]) / 2)
result = result[ipad:(ipad + image.shape[0]),
jpad:(jpad + image.shape[1])]
#
# Scale the resultant image similarly to the output.
#
img_min, img_max = np.min(image), np.max(image)
result_min, result_max = np.min(result), np.max(result)
if (img_min == img_max) or (result_min == result_max):
return np.zeros(result.shape)
result = (result - result_min) / (result_max - result_min)
result = img_min + result * (img_max - img_min)
return result
|
python
|
{
"resource": ""
}
|
q17773
|
variance_transform
|
train
|
def variance_transform(img, sigma, mask=None):
'''Calculate a weighted variance of the image
This function caluclates the variance of an image, weighting the
local contributions by a Gaussian.
img - image to be transformed
sigma - standard deviation of the Gaussian
mask - mask of relevant pixels in the image
'''
if mask is None:
mask = np.ones(img.shape, bool)
else:
img = img.copy()
img[~mask] = 0
#
# This is the Gaussian of the mask... so we can normalize for
# pixels near the edge of the mask
#
gmask = scind.gaussian_filter(mask.astype(float), sigma,
mode = 'constant')
img_mean = scind.gaussian_filter(img, sigma,
mode = 'constant') / gmask
img_squared = scind.gaussian_filter(img ** 2, sigma,
mode = 'constant') / gmask
var = img_squared - img_mean ** 2
return var
|
python
|
{
"resource": ""
}
|
q17774
|
inv_n
|
train
|
def inv_n(x):
'''given N matrices, return N inverses'''
#
# The inverse of a small matrix (e.g. 3x3) is
#
# 1
# ----- C(j,i)
# det(A)
#
# where C(j,i) is the cofactor of matrix A at position j,i
#
assert x.ndim == 3
assert x.shape[1] == x.shape[2]
c = np.array([ [cofactor_n(x, j, i) * (1 - ((i+j) % 2)*2)
for j in range(x.shape[1])]
for i in range(x.shape[1])]).transpose(2,0,1)
return c / det_n(x)[:, np.newaxis, np.newaxis]
|
python
|
{
"resource": ""
}
|
q17775
|
det_n
|
train
|
def det_n(x):
'''given N matrices, return N determinants'''
assert x.ndim == 3
assert x.shape[1] == x.shape[2]
if x.shape[1] == 1:
return x[:,0,0]
result = np.zeros(x.shape[0])
for permutation in permutations(np.arange(x.shape[1])):
sign = parity(permutation)
result += np.prod([x[:, i, permutation[i]]
for i in range(x.shape[1])], 0) * sign
sign = - sign
return result
|
python
|
{
"resource": ""
}
|
q17776
|
parity
|
train
|
def parity(x):
'''The parity of a permutation
The parity of a permutation is even if the permutation can be
formed by an even number of transpositions and is odd otherwise.
The parity of a permutation is even if there are an even number of
compositions of even size and odd otherwise. A composition is a cycle:
for instance in (1, 2, 0, 3), there is the cycle: (0->1, 1->2, 2->0)
and the cycle, (3->3). Both cycles are odd, so the parity is even:
you can exchange 0 and 1 giving (0, 2, 1, 3) and 2 and 1 to get
(0, 1, 2, 3)
'''
order = np.lexsort((x,))
hit = np.zeros(len(x), bool)
p = 0
for j in range(len(x)):
if not hit[j]:
cycle = 1
i = order[j]
# mark every node in a cycle
while i != j:
hit[i] = True
i = order[i]
cycle += 1
p += cycle - 1
return 1 if p % 2 == 0 else -1
|
python
|
{
"resource": ""
}
|
q17777
|
dot_n
|
train
|
def dot_n(x, y):
'''given two tensors N x I x K and N x K x J return N dot products
If either x or y is 2-dimensional, broadcast it over all N.
Dot products are size N x I x J.
Example:
x = np.array([[[1,2], [3,4], [5,6]],[[7,8], [9,10],[11,12]]])
y = np.array([[[1,2,3], [4,5,6]],[[7,8,9],[10,11,12]]])
print dot_n(x,y)
array([[[ 9, 12, 15],
[ 19, 26, 33],
[ 29, 40, 51]],
[[129, 144, 159],
[163, 182, 201],
[197, 220, 243]]])
'''
if x.ndim == 2:
if y.ndim == 2:
return np.dot(x, y)
x3 = False
y3 = True
nlen = y.shape[0]
elif y.ndim == 2:
nlen = x.shape[0]
x3 = True
y3 = False
else:
assert x.shape[0] == y.shape[0]
nlen = x.shape[0]
x3 = True
y3 = True
assert x.shape[1+x3] == y.shape[0+y3]
n, i, j, k = np.mgrid[0:nlen, 0:x.shape[0+x3], 0:y.shape[1+y3],
0:y.shape[0+y3]]
return np.sum((x[n, i, k] if x3 else x[i,k]) *
(y[n, k, j] if y3 else y[k,j]), 3)
|
python
|
{
"resource": ""
}
|
q17778
|
permutations
|
train
|
def permutations(x):
'''Given a listlike, x, return all permutations of x
Returns the permutations of x in the lexical order of their indices:
e.g.
>>> x = [ 1, 2, 3, 4 ]
>>> for p in permutations(x):
>>> print p
[ 1, 2, 3, 4 ]
[ 1, 2, 4, 3 ]
[ 1, 3, 2, 4 ]
[ 1, 3, 4, 2 ]
[ 1, 4, 2, 3 ]
[ 1, 4, 3, 2 ]
[ 2, 1, 3, 4 ]
...
[ 4, 3, 2, 1 ]
'''
#
# The algorithm is attributed to Narayana Pandit from his
# Ganita Kaumundi (1356). The following is from
#
# http://en.wikipedia.org/wiki/Permutation#Systematic_generation_of_all_permutations
#
# 1. Find the largest index k such that a[k] < a[k + 1].
# If no such index exists, the permutation is the last permutation.
# 2. Find the largest index l such that a[k] < a[l].
# Since k + 1 is such an index, l is well defined and satisfies k < l.
# 3. Swap a[k] with a[l].
# 4. Reverse the sequence from a[k + 1] up to and including the final
# element a[n].
#
yield list(x) # don't forget to do the first one
x = np.array(x)
a = np.arange(len(x))
while True:
# 1 - find largest or stop
ak_lt_ak_next = np.argwhere(a[:-1] < a[1:])
if len(ak_lt_ak_next) == 0:
raise StopIteration()
k = ak_lt_ak_next[-1, 0]
# 2 - find largest a[l] < a[k]
ak_lt_al = np.argwhere(a[k] < a)
l = ak_lt_al[-1, 0]
# 3 - swap
a[k], a[l] = (a[l], a[k])
# 4 - reverse
if k < len(x)-1:
a[k+1:] = a[:k:-1].copy()
yield x[a].tolist()
|
python
|
{
"resource": ""
}
|
q17779
|
circular_hough
|
train
|
def circular_hough(img, radius, nangles = None, mask=None):
'''Circular Hough transform of an image
img - image to be transformed.
radius - radius of circle
nangles - # of angles to measure, e.g. nangles = 4 means accumulate at
0, 90, 180 and 270 degrees.
Return the Hough transform of the image which is the accumulators
for the transform x + r cos t, y + r sin t.
'''
a = np.zeros(img.shape)
m = np.zeros(img.shape)
if nangles is None:
# if no angle specified, take the circumference
# Round to a multiple of 4 to make it bilaterally stable
nangles = int(np.pi * radius + 3.5) & (~ 3)
for i in range(nangles):
theta = 2*np.pi * float(i) / float(nangles)
x = int(np.round(radius * np.cos(theta)))
y = int(np.round(radius * np.sin(theta)))
xmin = max(0, -x)
xmax = min(img.shape[1] - x, img.shape[1])
ymin = max(0, -y)
ymax = min(img.shape[0] - y, img.shape[0])
dest = (slice(ymin, ymax),
slice(xmin, xmax))
src = (slice(ymin+y, ymax+y), slice(xmin+x, xmax+x))
if mask is not None:
a[dest][mask[src]] += img[src][mask[src]]
m[dest][mask[src]] += 1
else:
a[dest] += img[src]
m[dest] += 1
a[m > 0] /= m[m > 0]
return a
|
python
|
{
"resource": ""
}
|
q17780
|
poisson_equation
|
train
|
def poisson_equation(image, gradient=1, max_iter=100, convergence=.01, percentile = 90.0):
'''Estimate the solution to the Poisson Equation
The Poisson Equation is the solution to gradient(x) = h^2/4 and, in this
context, we use a boundary condition where x is zero for background
pixels. Also, we set h^2/4 = 1 to indicate that each pixel is a distance
of 1 from its neighbors.
The estimation exits after max_iter iterations or if the given percentile
of foreground pixels differ by less than the convergence fraction
from one pass to the next.
Some ideas taken from Gorelick, "Shape representation and classification
using the Poisson Equation", IEEE Transactions on Pattern Analysis and
Machine Intelligence V28, # 12, 2006
image - binary image with foreground as True
gradient - the target gradient between 4-adjacent pixels
max_iter - maximum # of iterations at a given level
convergence - target fractional difference between values from previous
and next pass
percentile - measure convergence at this percentile
'''
# Evaluate the poisson equation with zero-padded boundaries
pe = np.zeros((image.shape[0]+2, image.shape[1]+2))
if image.shape[0] > 64 and image.shape[1] > 64:
#
# Sub-sample to get seed values
#
sub_image = image[::2, ::2]
sub_pe = poisson_equation(sub_image,
gradient=gradient*2,
max_iter=max_iter,
convergence=convergence)
coordinates = np.mgrid[0:(sub_pe.shape[0]*2),
0:(sub_pe.shape[1]*2)].astype(float) / 2
pe[1:(sub_image.shape[0]*2+1), 1:(sub_image.shape[1]*2+1)] = \
scind.map_coordinates(sub_pe, coordinates, order=1)
pe[:image.shape[0], :image.shape[1]][~image] = 0
else:
pe[1:-1,1:-1] = image
#
# evaluate only at i and j within the foreground
#
i, j = np.mgrid[0:pe.shape[0], 0:pe.shape[1]]
mask = (i>0) & (i<pe.shape[0]-1) & (j>0) & (j<pe.shape[1]-1)
mask[mask] = image[i[mask]-1, j[mask]-1]
i = i[mask]
j = j[mask]
if len(i) == 0:
return pe[1:-1, 1:-1]
if len(i) == 1:
# Just in case "percentile" can't work when unable to interpolate
# between a single value... Isolated pixels have value = 1
#
pe[mask] = 1
return pe[1:-1, 1:-1]
for itr in range(max_iter):
next_pe = (pe[i+1, j] + pe[i-1, j] + pe[i, j+1] + pe[i, j-1]) / 4 + 1
difference = np.abs((pe[mask] - next_pe) / next_pe)
pe[mask] = next_pe
if np.percentile(difference, percentile) <= convergence:
break
return pe[1:-1, 1:-1]
|
python
|
{
"resource": ""
}
|
q17781
|
KalmanState.predicted_state_vec
|
train
|
def predicted_state_vec(self):
'''The predicted state vector for the next time point
From Welch eqn 1.9
'''
if not self.has_cached_predicted_state_vec:
self.p_state_vec = dot_n(
self.translation_matrix,
self.state_vec[:, :, np.newaxis])[:,:,0]
return self.p_state_vec
|
python
|
{
"resource": ""
}
|
q17782
|
KalmanState.predicted_obs_vec
|
train
|
def predicted_obs_vec(self):
'''The predicted observation vector
The observation vector for the next step in the filter.
'''
if not self.has_cached_obs_vec:
self.obs_vec = dot_n(
self.observation_matrix,
self.predicted_state_vec[:,:,np.newaxis])[:,:,0]
return self.obs_vec
|
python
|
{
"resource": ""
}
|
q17783
|
KalmanState.map_frames
|
train
|
def map_frames(self, old_indices):
'''Rewrite the feature indexes based on the next frame's identities
old_indices - for each feature in the new frame, the index of the
old feature
'''
nfeatures = len(old_indices)
noldfeatures = len(self.state_vec)
if nfeatures > 0:
self.state_vec = self.state_vec[old_indices]
self.state_cov = self.state_cov[old_indices]
self.noise_var = self.noise_var[old_indices]
if self.has_cached_obs_vec:
self.obs_vec = self.obs_vec[old_indices]
if self.has_cached_predicted_state_vec:
self.p_state_vec = self.p_state_vec[old_indices]
if len(self.state_noise_idx) > 0:
#
# We have to renumber the new_state_noise indices and get rid
# of those that don't map to numbers. Typical index trick here:
# * create an array for each legal old element: -1 = no match
# * give each old element in the array the new number
# * Filter out the "no match" elements.
#
reverse_indices = -np.ones(noldfeatures, int)
reverse_indices[old_indices] = np.arange(nfeatures)
self.state_noise_idx = reverse_indices[self.state_noise_idx]
self.state_noise = self.state_noise[self.state_noise_idx != -1,:]
self.state_noise_idx = self.state_noise_idx[self.state_noise_idx != -1]
|
python
|
{
"resource": ""
}
|
q17784
|
KalmanState.add_features
|
train
|
def add_features(self, kept_indices, new_indices,
new_state_vec, new_state_cov, new_noise_var):
'''Add new features to the state
kept_indices - the mapping from all indices in the state to new
indices in the new version
new_indices - the indices of the new features in the new version
new_state_vec - the state vectors for the new indices
new_state_cov - the covariance matrices for the new indices
new_noise_var - the noise variances for the new indices
'''
assert len(kept_indices) == len(self.state_vec)
assert len(new_indices) == len(new_state_vec)
assert len(new_indices) == len(new_state_cov)
assert len(new_indices) == len(new_noise_var)
if self.has_cached_obs_vec:
del self.obs_vec
if self.has_cached_predicted_state_vec:
del self.predicted_obs_vec
nfeatures = len(kept_indices) + len(new_indices)
next_state_vec = np.zeros((nfeatures, self.state_len))
next_state_cov = np.zeros((nfeatures, self.state_len, self.state_len))
next_noise_var = np.zeros((nfeatures, self.state_len))
if len(kept_indices) > 0:
next_state_vec[kept_indices] = self.state_vec
next_state_cov[kept_indices] = self.state_cov
next_noise_var[kept_indices] = self.noise_var
if len(self.state_noise_idx) > 0:
self.state_noise_idx = kept_indices[self.state_noise_idx]
if len(new_indices) > 0:
next_state_vec[new_indices] = new_state_vec
next_state_cov[new_indices] = new_state_cov
next_noise_var[new_indices] = new_noise_var
self.state_vec = next_state_vec
self.state_cov = next_state_cov
self.noise_var = next_noise_var
|
python
|
{
"resource": ""
}
|
q17785
|
KalmanState.deep_copy
|
train
|
def deep_copy(self):
'''Return a deep copy of the state'''
c = KalmanState(self.observation_matrix, self.translation_matrix)
c.state_vec = self.state_vec.copy()
c.state_cov = self.state_cov.copy()
c.noise_var = self.noise_var.copy()
c.state_noise = self.state_noise.copy()
c.state_noise_idx = self.state_noise_idx.copy()
return c
|
python
|
{
"resource": ""
}
|
q17786
|
spline_factors
|
train
|
def spline_factors(u):
'''u is np.array'''
X = np.array([(1.-u)**3 , 4-(6.*(u**2))+(3.*(u**3)) , 1.+(3.*u)+(3.*(u**2))-(3.*(u**3)) , u**3]) * (1./6)
return X
|
python
|
{
"resource": ""
}
|
q17787
|
gauss
|
train
|
def gauss(x,m_y,sigma):
'''returns the gaussian with mean m_y and std. dev. sigma,
calculated at the points of x.'''
e_y = [np.exp((1.0/(2*float(sigma)**2)*-(n-m_y)**2)) for n in np.array(x)]
y = [1.0/(float(sigma) * np.sqrt(2 * np.pi)) * e for e in e_y]
return np.array(y)
|
python
|
{
"resource": ""
}
|
q17788
|
d2gauss
|
train
|
def d2gauss(x,m_y,sigma):
'''returns the second derivative of the gaussian with mean m_y,
and standard deviation sigma, calculated at the points of x.'''
return gauss(x,m_y,sigma)*[-1/sigma**2 + (n-m_y)**2/sigma**4 for n in x]
|
python
|
{
"resource": ""
}
|
q17789
|
spline_matrix2d
|
train
|
def spline_matrix2d(x,y,px,py,mask=None):
'''For boundary constraints, the first two and last two spline pieces are constrained
to be part of the same cubic curve.'''
V = np.kron(spline_matrix(x,px),spline_matrix(y,py))
lenV = len(V)
if mask is not None:
indices = np.nonzero(mask.T.flatten())
if len(indices)>1:
indices = np.nonzero(mask.T.flatten())[1][0]
newV=V.T[indices]
V=newV.T
V=V.reshape((V.shape[0],V.shape[1]))
return V
|
python
|
{
"resource": ""
}
|
q17790
|
otsu
|
train
|
def otsu(data, min_threshold=None, max_threshold=None,bins=256):
"""Compute a threshold using Otsu's method
data - an array of intensity values between zero and one
min_threshold - only consider thresholds above this minimum value
max_threshold - only consider thresholds below this maximum value
bins - we bin the data into this many equally-spaced bins, then pick
the bin index that optimizes the metric
"""
assert min_threshold is None or max_threshold is None or min_threshold < max_threshold
def constrain(threshold):
if not min_threshold is None and threshold < min_threshold:
threshold = min_threshold
if not max_threshold is None and threshold > max_threshold:
threshold = max_threshold
return threshold
data = np.atleast_1d(data)
data = data[~ np.isnan(data)]
if len(data) == 0:
return (min_threshold if not min_threshold is None
else max_threshold if not max_threshold is None
else 0)
elif len(data) == 1:
return constrain(data[0])
if bins > len(data):
bins = len(data)
data.sort()
var = running_variance(data)
rvar = np.flipud(running_variance(np.flipud(data)))
thresholds = data[1:len(data):len(data)//bins]
score_low = (var[0:len(data)-1:len(data)//bins] *
np.arange(0,len(data)-1,len(data)//bins))
score_high = (rvar[1:len(data):len(data)//bins] *
(len(data) - np.arange(1,len(data),len(data)//bins)))
scores = score_low + score_high
if len(scores) == 0:
return constrain(thresholds[0])
index = np.argwhere(scores == scores.min()).flatten()
if len(index)==0:
return constrain(thresholds[0])
#
# Take the average of the thresholds to either side of
# the chosen value to get an intermediate in cases where there is
# a steep step between the background and foreground
index = index[0]
if index == 0:
index_low = 0
else:
index_low = index-1
if index == len(thresholds)-1:
index_high = len(thresholds)-1
else:
index_high = index+1
return constrain((thresholds[index_low]+thresholds[index_high]) / 2)
|
python
|
{
"resource": ""
}
|
q17791
|
entropy
|
train
|
def entropy(data, bins=256):
"""Compute a threshold using Ray's entropy measurement
data - an array of intensity values between zero and one
bins - we bin the data into this many equally-spaced bins, then pick
the bin index that optimizes the metric
"""
data = np.atleast_1d(data)
data = data[~ np.isnan(data)]
if len(data) == 0:
return 0
elif len(data) == 1:
return data[0]
if bins > len(data):
bins = len(data)
data.sort()
var = running_variance(data)+1.0/512.0
rvar = np.flipud(running_variance(np.flipud(data)))+1.0/512.0
thresholds = data[1:len(data):len(data)//bins]
w = np.arange(0,len(data)-1,len(data)//bins)
score_low = w * np.log(var[0:len(data)-1:len(data)//bins] *
w * np.sqrt(2*np.pi*np.exp(1)))
score_low[np.isnan(score_low)]=0
w = len(data) - np.arange(1,len(data),len(data)//bins)
score_high = w * np.log(rvar[1:len(data):len(data)//bins] * w *
np.sqrt(2*np.pi*np.exp(1)))
score_high[np.isnan(score_high)]=0
scores = score_low + score_high
index = np.argwhere(scores == scores.min()).flatten()
if len(index)==0:
return thresholds[0]
#
# Take the average of the thresholds to either side of
# the chosen value to get an intermediate in cases where there is
# a steep step between the background and foreground
index = index[0]
if index == 0:
index_low = 0
else:
index_low = index-1
if index == len(thresholds)-1:
index_high = len(thresholds)-1
else:
index_high = index+1
return (thresholds[index_low]+thresholds[index_high]) / 2
|
python
|
{
"resource": ""
}
|
q17792
|
otsu3
|
train
|
def otsu3(data, min_threshold=None, max_threshold=None,bins=128):
"""Compute a threshold using a 3-category Otsu-like method
data - an array of intensity values between zero and one
min_threshold - only consider thresholds above this minimum value
max_threshold - only consider thresholds below this maximum value
bins - we bin the data into this many equally-spaced bins, then pick
the bin index that optimizes the metric
We find the maximum weighted variance, breaking the histogram into
three pieces.
Returns the lower and upper thresholds
"""
assert min_threshold is None or max_threshold is None or min_threshold < max_threshold
#
# Compute the running variance and reverse running variance.
#
data = np.atleast_1d(data)
data = data[~ np.isnan(data)]
data.sort()
if len(data) == 0:
return 0
var = running_variance(data)
rvar = np.flipud(running_variance(np.flipud(data)))
if bins > len(data):
bins = len(data)
bin_len = int(len(data)//bins)
thresholds = data[0:len(data):bin_len]
score_low = (var[0:len(data):bin_len] *
np.arange(0,len(data),bin_len))
score_high = (rvar[0:len(data):bin_len] *
(len(data) - np.arange(0,len(data),bin_len)))
#
# Compute the middles
#
cs = data.cumsum()
cs2 = (data**2).cumsum()
i,j = np.mgrid[0:score_low.shape[0],0:score_high.shape[0]]*bin_len
diff = (j-i).astype(float)
w = diff
mean = (cs[j] - cs[i]) / diff
mean2 = (cs2[j] - cs2[i]) / diff
score_middle = w * (mean2 - mean**2)
score_middle[i >= j] = np.Inf
score = score_low[i*bins//len(data)] + score_middle + score_high[j*bins//len(data)]
best_score = np.min(score)
best_i_j = np.argwhere(score==best_score)
return (thresholds[best_i_j[0,0]],thresholds[best_i_j[0,1]])
|
python
|
{
"resource": ""
}
|
q17793
|
outline
|
train
|
def outline(labels):
"""Given a label matrix, return a matrix of the outlines of the labeled objects
If a pixel is not zero and has at least one neighbor with a different
value, then it is part of the outline.
"""
output = numpy.zeros(labels.shape, labels.dtype)
lr_different = labels[1:,:]!=labels[:-1,:]
ud_different = labels[:,1:]!=labels[:,:-1]
d1_different = labels[1:,1:]!=labels[:-1,:-1]
d2_different = labels[1:,:-1]!=labels[:-1,1:]
different = numpy.zeros(labels.shape, bool)
different[1:,:][lr_different] = True
different[:-1,:][lr_different] = True
different[:,1:][ud_different] = True
different[:,:-1][ud_different] = True
different[1:,1:][d1_different] = True
different[:-1,:-1][d1_different] = True
different[1:,:-1][d2_different] = True
different[:-1,1:][d2_different] = True
#
# Labels on edges need outlines
#
different[0,:] = True
different[:,0] = True
different[-1,:] = True
different[:,-1] = True
output[different] = labels[different]
return output
|
python
|
{
"resource": ""
}
|
q17794
|
euclidean_dist
|
train
|
def euclidean_dist(point1, point2):
"""Compute the Euclidean distance between two points.
Parameters
----------
point1, point2 : 2-tuples of float
The input points.
Returns
-------
d : float
The distance between the input points.
Examples
--------
>>> point1 = (1.0, 2.0)
>>> point2 = (4.0, 6.0) # (3., 4.) away, simplest Pythagorean triangle
>>> euclidean_dist(point1, point2)
5.0
"""
(x1, y1) = point1
(x2, y2) = point2
return math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)
|
python
|
{
"resource": ""
}
|
q17795
|
Trace.from_detections_assignment
|
train
|
def from_detections_assignment(detections_1, detections_2, assignments):
"""
Creates traces out of given assignment and cell data.
"""
traces = []
for d1n, d2n in six.iteritems(assignments):
# check if the match is between existing cells
if d1n < len(detections_1) and d2n < len(detections_2):
traces.append(Trace(detections_1[d1n], detections_2[d2n]))
return traces
|
python
|
{
"resource": ""
}
|
q17796
|
NeighbourMovementTracking.run_tracking
|
train
|
def run_tracking(self, label_image_1, label_image_2):
"""
Tracks cells between input label images.
@returns: injective function from old objects to new objects (pairs of [old, new]). Number are compatible with labels.
"""
self.scale = self.parameters_tracking["avgCellDiameter"] / 35.0
detections_1 = self.derive_detections(label_image_1)
detections_2 = self.derive_detections(label_image_2)
# Calculate tracking based on cell features and position.
traces = self.find_initials_traces(detections_1, detections_2)
# Use neighbourhoods to improve tracking.
for _ in range(int(self.parameters_tracking["iterations"])):
traces = self.improve_traces(detections_1, detections_2, traces)
# Filter traces.
return [(trace.previous_cell.number, trace.current_cell.number) for trace in traces]
|
python
|
{
"resource": ""
}
|
q17797
|
NeighbourMovementTracking.is_cell_big
|
train
|
def is_cell_big(self, cell_detection):
"""
Check if the cell is considered big.
@param CellFeature cell_detection:
@return:
"""
return cell_detection.area > self.parameters_tracking["big_size"] * self.scale * self.scale
|
python
|
{
"resource": ""
}
|
q17798
|
NeighbourMovementTracking.calculate_basic_cost
|
train
|
def calculate_basic_cost(self, d1, d2):
"""
Calculates assignment cost between two cells.
"""
distance = euclidean_dist(d1.center, d2.center) / self.scale
area_change = 1 - min(d1.area, d2.area) / max(d1.area, d2.area)
return distance + self.parameters_cost_initial["area_weight"] * area_change
|
python
|
{
"resource": ""
}
|
q17799
|
NeighbourMovementTracking.calculate_localised_cost
|
train
|
def calculate_localised_cost(self, d1, d2, neighbours, motions):
"""
Calculates assignment cost between two cells taking into account the movement of cells neighbours.
:param CellFeatures d1: detection in first frame
:param CellFeatures d2: detection in second frame
"""
my_nbrs_with_motion = [n for n in neighbours[d1] if n in motions]
my_motion = (d1.center[0] - d2.center[0], d1.center[1] - d2.center[1])
if my_nbrs_with_motion == []:
distance = euclidean_dist(d1.center, d2.center) / self.scale
else:
# it is not in motions if there is no trace (cell is considered to vanish)
distance = min([euclidean_dist(my_motion, motions[n]) for n in my_nbrs_with_motion]) / self.scale
area_change = 1 - min(d1.area, d2.area) / max(d1.area, d2.area)
return distance + self.parameters_cost_iteration["area_weight"] * area_change
|
python
|
{
"resource": ""
}
|
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