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Add contour-finding

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Bring some old code for "marching-squares" contour-finding into
skimage. Only one crummy test and c code may not be up to style
standards...
This commit is contained in:
Zach Pincus
2011-11-26 00:23:03 -05:00
parent 4c88f94508
commit 51d643c527
3 changed files with 248 additions and 0 deletions
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skimage/find_contours/__init__.py
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import numpy as np
import _find_contours
from collections import deque
_param_options = ('high', 'low')
def find_contours(array, level, fully_connected='low', positive_orientation='low'):
'''Find iso-valued contours in a 2D array for a given level value.
Uses the "marching squares" method to compute a the iso-valued contours of
the input 2D array for a particular level value. Array values are linearly
interpolated to provide better precision for the output contours.
Parameters
----------
array : convertible to a 2D ndarray object
Input data in which to find isocontours.
level : float
Value along which to find contours in the array.
fully_connected : either 'low' or 'high'
Indicates whether array elements below the given level value are to
be considered fully- connected (and hence elements above the value
will only be face connected), or vice-versa. (See below for details.)
positive_orientation : either 'low' or 'high'
Indicates whether the output contours will produce
positively-oriented polygons around islands of low- or high-valued
elements. If 'low' then contours will wind counter- clockwise around
elements below the iso-value. Alternately, this means that low-valued
elements are always on the left of the contour. (See below for
details.)
Returns
-------
A list of contours, where each contour is an ndarray of shape (n, 2)
consisting of n (x,y) coordinates along the contour.
The marching squares algorithm is a special case of the marching cubes
algorithm (Lorensen, William and Harvey E. Cline. Marching Cubes: A High
Resolution 3D Surface Construction Algorithm. Computer Graphics (SIGGRAPH
87 Proceedings) 21(4) July 1987, p. 163-170). A simple explanation is
available here: http://www.essi.fr/~lingrand/MarchingCubes/algo.html
There is a single ambiguous case in the marching squares algorithm: when
a given 2x2-element square has two high-valued and two low-valued
elements, each pair diagonally adjacent. (Where high- and low-valued is
with respect to the contour value sought.) In this case, either the
high-valued elements can be 'connected together' via a thin isthmus that
separates the low-valued elements, or vice-versa. When elements are
connected together across a diagonal, they are considered 'fully
connected' (also known as 'face+vertex-connected' or '8-connected'). Only
high-valued or low-valued elements can be fully-connected, the other set
will be considred as 'face-connected' or '4-connected'. By default,
low-valued elements are considered fully-connected; this can be altered
with the 'fully_connected' parameter.
Output contours are not guaranteed to be closed: contours which intersect
the array edge will be left open. All other contours will be closed. (The
closed-ness of a contours can be tested by checking whether the beginning
point is the same as the end point.)
Contours are oriented. By default, array values lower than the contour
value are to the left of the contour and values greater than the contour
value are to the right. This means that contours will wind
counter-clockwise (i.e. in 'positive orientation') around islands of
low-valued pixels. This behavior can be altered with the
'positive_orientation' parameter.
The order of the contours in the output list is determined by the position
of the smallest x,y (in lexicographical order) coordinate in the contour.
This is a side-effect of how the input array is traversed, but can be
relied upon.'''
array = np.asarray(array)
if array.ndim != 2:
raise RuntimeError('Only 2D arrays are supported.')
level = float(level)
if fully_connected not in _param_options or
positive_orientation not in _param_options:
raise ValueError('Parameters "fully_connected" and'
' "positive_orientation" must be either "high" or "low".')
point_list = _find_contours.iterate_and_store(array, level,
fully_connected == 'high')
contours = _assemble_contours(_take_2(point_list))
if positive_orientation == 'high':
contours = [c[::-1] for c in contours]
return contours
def _take_2(seq):
iterator = iter(seq)
while(True):
n1 = iterator.next()
n2 = iterator.next()
yield (n1, n2)
def _assemble_contours(points_iterator):
current_index = 0
contours = {}
starts = {}
ends = {}
for from_point, to_point in points_iterator:
# Ignore degenerate segments.
# This happens when (and only when) one vertex of the square is
# exactly the contour level, and the rest are above or below.
# This degnerate vertex will be picked up later by neighboring squares.
if from_point == to_point: continue
tail_data = starts.get(to_point)
head_data = ends.get(from_point)
if tail_data is not None and head_data is not None:
tail, tail_num = tail_data
head, head_num = head_data
# We need to connect these two contours.
if tail is head:
# We need to closed a contour.
# Add the end point, and remove the contour from the
# 'starts' and 'ends' dicts.
head.append(to_point)
del starts[to_point]
del ends[from_point]
else: # tail is not head
# We need to join two distinct contours.
# We want to keep the first contour segment created, so that
# the final contours are ordered left->right, top->bottom.
if tail_num > head_num:
# tail was created second. Append tail to head.
head.extend(tail)
# remove all traces of tail:
del starts[to_point]
del ends[tail[-1]]
del contours[tail_num]
# remove the old end of head and add the new end.
del ends[from_point]
ends[head[-1]] = (head, head_num)
else: # tail_num <= head_num
# head was created second. Prepend head to tail.
tail.extendleft(reversed(head))
# remove all traces of head:
del starts[head[0]]
del ends[from_point]
del contours[head_num]
# remove the old start of tail and add the new start.
del starts[to_point]
starts[tail[0]] = (tail, tail_num)
elif tail_data is None and head_data is None:
# we need to add a new contour
current_index += 1
new_num = current_index
new_contour = deque((from_point, to_point))
contours[new_num] = new_contour
starts[from_point] = (new_contour, new_num)
ends[to_point] = (new_contour, new_num)
elif tail_data is not None and head_data is None:
tail, tail_num = tail_data
# We've found a single contour to which the new segment should be
# prepended.
tail.appendleft(from_point)
del starts[to_point]
starts[from_point] = (tail, tail_num)
elif tail_data is None and head_data is not None:
head, head_num = head_data
# We've found a single contour to which the new segment should be
# appended
head.append(to_point)
del ends[from_point]
ends[to_point] = (head, head_num)
# end iteration over from_ and to_ points
return [np.array(contour) for (num, contour) in sorted(contours.items())]
skimage/find_contours/setup.py
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#!/usr/bin/env python
def configuration(parent_package='', top_path=None):
from numpy.distutils.misc_util import Configuration, get_numpy_include_dirs
config = Configuration('find_contours', parent_package, top_path)
config.add_data_dir('tests')
config.add_extension('_find_contours', sources=['_find_contours.c'],
include_dirs=[get_numpy_include_dirs()])
return config
if __name__ == '__main__':
from numpy.distutils.core import setup
setup(maintainer = 'scikits.image Developers',
maintainer_email = 'scikits-image@googlegroups.com',
description = 'Graph-based Image-processing Algorithms',
url = 'https://github.com/scikits-image/scikits.image',
license = 'Modified BSD',
**(configuration(top_path='').todict())
)
skimage/find_contours/tests/test_find_contours.py
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import numpy as np
from numpy.testing import *
from skimage.find_contours import find_contours
a = np.ones((8,8), dtype=np.float32)
a[1:-1, 1] = 0
a[1, 1:-1] = 0
## array([[ 1., 1., 1., 1., 1., 1., 1., 1.],
## [ 1., 0., 0., 0., 0., 0., 0., 1.],
## [ 1., 0., 1., 1., 1., 1., 1., 1.],
## [ 1., 0., 1., 1., 1., 1., 1., 1.],
## [ 1., 0., 1., 1., 1., 1., 1., 1.],
## [ 1., 0., 1., 1., 1., 1., 1., 1.],
## [ 1., 0., 1., 1., 1., 1., 1., 1.],
## [ 1., 1., 1., 1., 1., 1., 1., 1.]], dtype=float32)
def test_find_contours():
contours = find_contours(a, 0.5)
assert len(contours) == 1
assert_array_equal(contours[0],
[[ 6. , 1.5],
[ 5. , 1.5],
[ 4. , 1.5],
[ 3. , 1.5],
[ 2. , 1.5],
[ 1.5, 2. ],
[ 1.5, 3. ],
[ 1.5, 4. ],
[ 1.5, 5. ],
[ 1.5, 6. ],
[ 1. , 6.5],
[ 0.5, 6. ],
[ 0.5, 5. ],
[ 0.5, 4. ],
[ 0.5, 3. ],
[ 0.5, 2. ],
[ 0.5, 1. ],
[ 1. , 0.5],
[ 2. , 0.5],
[ 3. , 0.5],
[ 4. , 0.5],
[ 5. , 0.5],
[ 6. , 0.5],
[ 6.5, 1. ],
[ 6. , 1.5]])
if __name__ == '__main__':
from numpy.testing import run_module_suite
run_module_suite()