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Merge pull request #1 from stefanv/find-contours

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Convert contour finding code to Cython and add an example.
This commit is contained in:
zachrahan
2011-12-01 09:11:52 -08:00
parent 1cb10a5bd9 8579ef0183
commit 60abf40c39
9 changed files with 305 additions and 324 deletions
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CONTRIBUTORS.txt
+1 -1
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@@ -28,7 +28,7 @@
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
+42
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@@ -0,0 +1,42 @@
"""
===============
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/io/collection.py
+1 -1
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@@ -8,7 +8,7 @@ from glob import glob
import os.path
import numpy as np
from io import imread
from ._io import imread
class MultiImage(object):
skimage/measure/__init__.py
+1 -1
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@@ -1 +1 @@
from find_contours import find_contours
from find_contours import find_contours
skimage/measure/_find_contours.c
-262
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@@ -1,262 +0,0 @@
#include <Python.h>
#include "numpy/arrayobject.h"
static char _find_contours_doc[] =
"This module defines C helper functions for find_contours";
static char iterate_and_store_doc[] =
"iterate_and_store(array, level, vertex_connect_high)\n\
\n\
Iterate across the given array in a marching-squares fashion, looking for\n\
segments that cross 'level'. If such a segment is found, its coordinates are\n\
added to a growing list of segments, which is returned by the function.\n\
if vertex_connect_high is nonzero, high-values pixels are considered to be\n\
face+vertex connected into objects; otherwise low-valued pixels are.";
// Nasty macros to inline the inner loop of interpolating the position of
// the contour and add an appropriate tuple to the output list.
// These macros define blocks of code that can only be used within the inner
// loop of 'iterate_and_store' because they use variables therefrom.
#define GET_FRACTION(from_value, to_value) \
((level - from_value) / (to_value - from_value))
#define TOP { \
output0 = coords[0]; \
output1 = coords[1] + GET_FRACTION(*ul_ptr, *ur_ptr); \
}
#define BOTTOM { \
output0 = coords[0] + 1; \
output1 = coords[1] + GET_FRACTION(*ll_ptr, *lr_ptr); \
}
#define LEFT { \
output0 = coords[0] + GET_FRACTION(*ul_ptr, *ll_ptr); \
output1 = coords[1]; \
}
#define RIGHT { \
output0 = coords[0] + GET_FRACTION(*ur_ptr, *lr_ptr); \
output1 = coords[1] + 1; \
}
#define ADD_TUPLE { \
PyObject* tuple = Py_BuildValue("(dd)", output0, output1); \
if (!tuple) { \
Py_DECREF(double_array); \
Py_DECREF(arc_list); \
return NULL; \
} \
char res = PyList_Append(arc_list, tuple); \
Py_DECREF(tuple); \
if (res < 0) { \
Py_DECREF(double_array); \
Py_DECREF(arc_list); \
return NULL; \
} \
}
#define ADD_SEGMENT(START, END) { \
double output0, output1; \
START \
ADD_TUPLE \
END \
ADD_TUPLE \
}
static PyObject*
iterate_and_store(PyObject *self, PyObject *args)
{
PyObject* array;
double level;
int vertex_connect_high;
if (!PyArg_ParseTuple(args, "Odi:iterate_and_store", &array, &level,
&vertex_connect_high)) {
return NULL;
}
PyObject* double_array = PyArray_FromAny(array,
PyArray_DescrFromType(NPY_DOUBLE), 2, 2, NPY_CONTIGUOUS | NPY_ALIGNED,
NULL);
if (!double_array) {
return NULL;
}
npy_intp *dims = PyArray_DIMS(double_array);
if (dims[0] < 2 || dims[1] < 2) {
Py_DECREF(double_array);
PyErr_SetString(PyExc_ValueError, "Input array must be at least 2x2.");
return NULL;
}
// 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.
npy_intp coords[2] = {0,0};
// Precompute the size of the array minus 2 in each direction, so we'll know
// when to update the coordinates and double-increment the square pointers
// so that the upper-left pointer never visits the last column.
npy_intp dims_m2[2];
dims_m2[0] = dims[0] - 2;
dims_m2[1] = dims[1] - 2;
// Calculate the number of iterations we'll need
npy_intp num_square_steps = (dims[0] - 1) * (dims[1] - 1);
// and set up the square pointers.
double* ul_ptr = PyArray_DATA(double_array);
double* ur_ptr = ul_ptr + 1;
double* ll_ptr = ul_ptr + dims[1];
double* lr_ptr = ll_ptr + 1;
// make a list to hold the returned coordinates
PyObject* arc_list = PyList_New(0);
if (!arc_list) {
Py_DECREF(double_array);
return NULL;
}
while(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.
unsigned char square_case = 0;
if ((*ul_ptr) > level) square_case += 1;
if ((*ur_ptr) > level) square_case += 2;
if ((*ll_ptr) > level) square_case += 4;
if ((*lr_ptr) > level) square_case += 8;
switch(square_case)
{
case 0: // no line
break;
case 1: // top to left
ADD_SEGMENT(TOP, LEFT);
break;
case 2: // right to top
ADD_SEGMENT(RIGHT, TOP);
break;
case 3: // right to left
ADD_SEGMENT(RIGHT, LEFT);
break;
case 4: // left to bottom
ADD_SEGMENT(LEFT, BOTTOM);
break;
case 5: // top to bottom
ADD_SEGMENT(TOP, BOTTOM);
break;
case 6:
if (vertex_connect_high)
{
// left to top
ADD_SEGMENT(LEFT, TOP);
// right to bottom
ADD_SEGMENT(RIGHT, BOTTOM);
}
else
{
// right to top
ADD_SEGMENT(RIGHT, TOP);
// left to bottom
ADD_SEGMENT(LEFT, BOTTOM);
}
break;
case 7: // right to bottom
ADD_SEGMENT(RIGHT, BOTTOM);
break;
case 8: // bottom to right
ADD_SEGMENT(BOTTOM, RIGHT);
break;
case 9:
if (vertex_connect_high)
{
// top to right
ADD_SEGMENT(TOP, RIGHT);
// bottom to left
ADD_SEGMENT(BOTTOM, LEFT);
}
else
{
// top to left
ADD_SEGMENT(TOP, LEFT);
// bottom to right
ADD_SEGMENT(BOTTOM, RIGHT);
}
break;
case 10: // bottom to top
ADD_SEGMENT(BOTTOM, TOP);
break;
case 11: // bottom to left
ADD_SEGMENT(BOTTOM, LEFT);
break;
case 12: // left to right
ADD_SEGMENT(LEFT, RIGHT);
break;
case 13: // top to right
ADD_SEGMENT(TOP, RIGHT);
break;
case 14: // left to top
ADD_SEGMENT(LEFT, TOP);
break;
case 15: // no line
break;
} // switch square_case
if (coords[1] < dims_m2[1]) {
coords[1]++;
} else {
coords[1] = 0;
coords[0]++;
// Double-increment pointers to advance them to the next row, since
// we're skipping the last column, as far as ul_ptr is concerned.
ul_ptr++; ur_ptr++; ll_ptr++; lr_ptr++;
}
ul_ptr++; ur_ptr++; ll_ptr++; lr_ptr++;
} // iteration
// get rid of the double array reference that we own
Py_DECREF(double_array);
return arc_list;
}
static PyMethodDef _find_contours_methods[] = {
{"iterate_and_store", iterate_and_store, METH_VARARGS, iterate_and_store_doc},
{NULL, NULL, 0, NULL}
};
PyMODINIT_FUNC
init_find_contours(void)
{
Py_InitModule3("_find_contours", _find_contours_methods, _find_contours_doc);
import_array();
}
skimage/measure/_find_contours.pyx
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@@ -0,0 +1,185 @@
# -*- python -*-
# cython: cdivision=True
import numpy as np
cimport numpy as np
np.import_array()
cdef 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, c0 + 1]
ll = array[r0 + 1, c0]
lr = array[r0 + 1, c0 + 1]
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
top = coords[0], coords[1] + _get_fraction(ul, ur, level)
bottom = coords[0] + 1, coords[1] + _get_fraction(ll, lr, level)
left = coords[0] + _get_fraction(ul, ll, level), coords[1]
right = coords[0] + _get_fraction(ur, lr, level), coords[1] + 1
if (square_case == 0):
# no line
pass
elif (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)
elif (square_case == 15):
# no line
pass
if coords[1] < array.shape[1] - 2:
coords[1] += 1
else:
coords[0] += 1
coords[1] = 0
return arc_list
skimage/measure/find_contours.py
+68 -58
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@@ -5,44 +5,46 @@ 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.
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
----------
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 : 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.)
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.)
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.
-------
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 (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
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 2x2-element square has two high-valued and two low-valued
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
@@ -50,45 +52,54 @@ def find_contours(array, level, fully_connected='low', positive_orientation='low
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
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.
IMPORTANT NOTE ON COORDINATES AND VALUES:
Array coordinates/values are assumed to refer to the _center_ of the
array element. Take a simple example: [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.
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
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.'''
array = np.asarray(array)
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
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".')
@@ -98,7 +109,7 @@ def find_contours(array, level, fully_connected='low', positive_orientation='low
if positive_orientation == 'high':
contours = [c[::-1] for c in contours]
return contours
def _take_2(seq):
iterator = iter(seq)
while(True):
@@ -117,24 +128,24 @@ def _assemble_contours(points_iterator):
# 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.
# 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
# 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
# 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.
@@ -166,7 +177,7 @@ def _assemble_contours(points_iterator):
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
# We've found a single contour to which the new segment should be
# prepended.
tail.appendleft(from_point)
del starts[to_point]
@@ -179,6 +190,5 @@ def _assemble_contours(points_iterator):
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
+6
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@@ -1,11 +1,17 @@
#!/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()])
skimage/measure/tests/test_find_contours.py
+1 -1
View File
@@ -1,7 +1,7 @@
import numpy as np
from numpy.testing import *
from skimage.find_contours import find_contours
from skimage.measure import find_contours
a = np.ones((8,8), dtype=np.float32)
a[1:-1, 1] = 0