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Merge pull request #82 from zachrahan/find-contours

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Add contour finding.
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Stefan van der Walt
2011-12-01 12:53:55 -08:00
parent 8bd4637fc0 fbb07734fc
commit 207079ff1d
8 changed files with 520 additions and 1 deletions
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CONTRIBUTORS.txt
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Code to generate skimage logo.
- Zachary Pincus
Tracing of low cost paths, FreeImage I/O plugin
Tracing of low cost paths, FreeImage I/O plugin, iso-contours
- Almar Klein
Binary heap class for graph algorithms
doc/examples/plot_contours.py
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"""
===============
Contour finding
===============
``skimage.measure.find_contours`` uses a marching squares method to find
constant valued contours in an image. Array values are linearly interpolated
to provide better precision of the output contours. Contours which intersect
the image edge are open; all others are closed.
The `marching squares algorithm
<http://www.essi.fr/~lingrand/MarchingCubes/algo.html>`__ 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).
"""
from skimage import data
from skimage import measure
import numpy as np
import matplotlib.pyplot as plt
# Construct some test data
x, y = np.ogrid[-np.pi:np.pi:100j, -np.pi:np.pi:100j]
r = np.sin(np.exp((np.sin(x)**3 + np.cos(y)**2)))
# Find contours at a constant value of 0.8
contours = measure.find_contours(r, 0.8)
# Display the image and plot all contours found
plt.imshow(r, interpolation='nearest')
for n, contour in enumerate(contours):
plt.plot(contour[:, 1], contour[:, 0], linewidth=2)
plt.axis('image')
plt.xticks([])
plt.yticks([])
plt.show()
skimage/measure/__init__.py
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from find_contours import find_contours
skimage/measure/_find_contours.pyx
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# -*- python -*-
# cython: cdivision=True
import numpy as np
cimport numpy as np
np.import_array()
cdef inline double _get_fraction(double from_value, double to_value,
double level):
if (to_value == from_value):
return 0
return ((level - from_value) / (to_value - from_value))
def iterate_and_store(np.ndarray[double, ndim=2, mode='c'] array,
double level, int vertex_connect_high):
"""Iterate across the given array in a marching-squares fashion,
looking for segments that cross 'level'. If such a segment is
found, its coordinates are added to a growing list of segments,
which is returned by the function. if vertex_connect_high is
nonzero, high-values pixels are considered to be face+vertex
connected into objects; otherwise low-valued pixels are.
"""
if array.shape[0] < 2 or array.shape[1] < 2:
raise ValueError("Input array must be at least 2x2.")
cdef list arc_list = []
cdef int n
# The plan is to iterate a 2x2 square across the input array. This means
# that the upper-left corner of the square needs to iterate across a
# sub-array that's one-less-large in each direction (so that the square
# never steps out of bounds). The square is represented by four pointers:
# ul, ur, ll, and lr (for 'upper left', etc.). We also maintain the current
# 2D coordinates for the position of the upper-left pointer. Note that we
# ensured that the array is of type 'double' and is C-contiguous (last
# index varies the fastest).
# Current coords start at 0,0.
cdef int[2] coords
coords[0] = 0
coords[1] = 0
# Calculate the number of iterations we'll need
cdef int num_square_steps = (array.shape[0] - 1) * (array.shape[1] - 1)
cdef unsigned char square_case = 0
cdef tuple top, bottom, left, right
cdef double ul, ur, ll, lr
cdef int r0, r1, c0, c1
for n in range(num_square_steps):
# There are sixteen different possible square types, diagramed below.
# A + indicates that the vertex is above the contour value, and a -
# indicates that the vertex is below or equal to the contour value.
# The vertices of each square are:
# ul ur
# ll lr
# and can be treated as a binary value with the bits in that order. Thus
# each square case can be numbered:
# 0-- 1+- 2-+ 3++ 4-- 5+- 6-+ 7++
# -- -- -- -- +- +- +- +-
#
# 8-- 9+- 10-+ 11++ 12-- 13+- 14-+ 15++
# -+ -+ -+ -+ ++ ++ ++ ++
#
# The position of the line segment that cuts through (or
# doesn't, in case 0 and 15) each square is clear, except in
# cases 6 and 9. In this case, where the segments are placed
# is determined by vertex_connect_high. If
# vertex_connect_high is false, then lines like \\ are drawn
# through square 6, and lines like // are drawn through square
# 9. Otherwise, the situation is reversed.
# Finally, recall that we draw the lines so that (moving from tail to
# head) the lower-valued pixels are on the left of the line. So, for
# example, case 1 entails a line slanting from the middle of the top of
# the square to the middle of the left side of the square.
r0, c0 = coords[0], coords[1]
r1, c1 = r0 + 1, c0 + 1
ul = array[r0, c0]
ur = array[r0, c1]
ll = array[r1, c0]
lr = array[r1, c1]
# now in advance the coords indices
if coords[1] < array.shape[1] - 2:
coords[1] += 1
else:
coords[0] += 1
coords[1] = 0
square_case = 0
if (ul > level): square_case += 1
if (ur > level): square_case += 2
if (ll > level): square_case += 4
if (lr > level): square_case += 8
if (square_case != 0 and square_case != 15):
# only do anything if there's a line passing through the
# square. Cases 0 and 15 are entirely below/above the contour.
top = r0, c0 + _get_fraction(ul, ur, level)
bottom = r1, c0 + _get_fraction(ll, lr, level)
left = r0 + _get_fraction(ul, ll, level), c0
right = r0 + _get_fraction(ur, lr, level), c1
if (square_case == 1):
# top to left
arc_list.append(top)
arc_list.append(left)
elif (square_case == 2):
# right to top
arc_list.append(right)
arc_list.append(top)
elif (square_case == 3):
# right to left
arc_list.append(right)
arc_list.append(left)
elif (square_case == 4):
# left to bottom
arc_list.append(left)
arc_list.append(bottom)
elif (square_case == 5):
# top to bottom
arc_list.append(top)
arc_list.append(bottom)
elif (square_case == 6):
if vertex_connect_high:
arc_list.append(left)
arc_list.append(top)
arc_list.append(right)
arc_list.append(bottom)
else:
arc_list.append(right)
arc_list.append(top)
arc_list.append(left)
arc_list.append(bottom)
elif (square_case == 7):
# right to bottom
arc_list.append(right)
arc_list.append(bottom)
elif (square_case == 8):
# bottom to right
arc_list.append(bottom)
arc_list.append(right)
elif (square_case == 9):
if vertex_connect_high:
arc_list.append(top)
arc_list.append(right)
arc_list.append(bottom)
arc_list.append(left)
else:
arc_list.append(top)
arc_list.append(left)
arc_list.append(bottom)
arc_list.append(right)
elif (square_case == 10):
# bottom to top
arc_list.append(bottom)
arc_list.append(top)
elif (square_case == 11):
# bottom to left
arc_list.append(bottom)
arc_list.append(left)
elif (square_case == 12):
# lef to right
arc_list.append(left)
arc_list.append(right)
elif (square_case == 13):
# top to right
arc_list.append(top)
arc_list.append(right)
elif (square_case == 14):
# left to top
arc_list.append(left)
arc_list.append(top)
return arc_list
skimage/measure/find_contours.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 : 2D ndarray of double
Input data in which to find contours.
level : float
Value along which to find contours in the array.
fully_connected : str, {'low', '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 notes 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
-------
contours : list of (n,2)-ndarrays
Each contour is an ndarray of shape ``(n, 2)``,
consisting of n ``(x, y)`` coordinates along the contour.
Notes
-----
The marching squares algorithm is a special case of the marching cubes
algorithm [1]_. 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 ``2 x 2``-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 considered 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.
.. warning::
Array coordinates/values are assumed to refer to the *center* of the
array element. Take a simple example input: ``[0, 1]``. The interpolated
position of 0.5 in this array is midway between the 0-element (at
``x=0``) and the 1-element (at ``x=1``), and thus would fall at
``x=0.5``.
This means that to find reasonable contours, it is best to find contours
midway between the expected "light" and "dark" values. In particular,
given a binarized array, *do not* choose to find contours at the low or high
value of the array. This will often yield degenerate contours, especially
around structures that are a single array element wide. Instead choose
a middle value, as above.
References
----------
.. [1] 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).
"""
array = np.asarray(array, dtype=np.double)
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/measure/setup.py
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#!/usr/bin/env python
from skimage._build import cython
import os
base_path = os.path.abspath(os.path.dirname(__file__))
def configuration(parent_package='', top_path=None):
from numpy.distutils.misc_util import Configuration, get_numpy_include_dirs
config = Configuration('measure', parent_package, top_path)
config.add_data_dir('tests')
cython(['_find_contours.pyx'], working_path=base_path)
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/measure/tests/test_find_contours.py
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import numpy as np
from numpy.testing import *
from skimage.measure 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)
x,y = np.mgrid[-1:1:5j,-1:1:5j]
r = np.sqrt(x**2 + y**2)
def test_binary():
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]])
def test_float():
contours = find_contours(r, 0.5)
assert len(contours) == 1
assert_array_equal(contours[0],
[[ 2., 3.],
[ 1., 2.],
[ 2., 1.],
[ 3., 2.],
[ 2., 3.]])
if __name__ == '__main__':
from numpy.testing import run_module_suite
run_module_suite()
skimage/setup.py
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@@ -15,6 +15,7 @@ def configuration(parent_package='', top_path=None):
config.add_subpackage('color')
config.add_subpackage('draw')
config.add_subpackage('feature')
config.add_subpackage('measure')
def add_test_directories(arg, dirname, fnames):
if dirname.split(os.path.sep)[-1] == 'tests':