Permalink
654 lines (537 sloc) 21.8 KB
from math import sqrt, atan2, pi as PI
import itertools
from warnings import warn
import numpy as np
from scipy import ndimage as ndi
from ._label import label
from . import _moments
from functools import wraps
__all__ = ['regionprops', 'perimeter']
XY_TO_RC_DEPRECATION_MESSAGE = (
'regionprops and image moments (including moments, normalized moments, '
'central moments, and inertia tensor) of 2D images will change from xy '
'coordinates to rc coordinates in version 0.16.\nSee '
'https://scikit-image.org/docs/0.14.x/release_notes_and_installation.html#deprecations '
'for details on how to avoid this message.'
)
STREL_4 = np.array([[0, 1, 0],
[1, 1, 1],
[0, 1, 0]], dtype=np.uint8)
STREL_8 = np.ones((3, 3), dtype=np.uint8)
STREL_26_3D = np.ones((3, 3, 3), dtype=np.uint8)
PROPS = {
'Area': 'area',
'BoundingBox': 'bbox',
'BoundingBoxArea': 'bbox_area',
'CentralMoments': 'moments_central',
'Centroid': 'centroid',
'ConvexArea': 'convex_area',
# 'ConvexHull',
'ConvexImage': 'convex_image',
'Coordinates': 'coords',
'Eccentricity': 'eccentricity',
'EquivDiameter': 'equivalent_diameter',
'EulerNumber': 'euler_number',
'Extent': 'extent',
# 'Extrema',
'FilledArea': 'filled_area',
'FilledImage': 'filled_image',
'HuMoments': 'moments_hu',
'Image': 'image',
'Label': 'label',
'MajorAxisLength': 'major_axis_length',
'MaxIntensity': 'max_intensity',
'MeanIntensity': 'mean_intensity',
'MinIntensity': 'min_intensity',
'MinorAxisLength': 'minor_axis_length',
'Moments': 'moments',
'NormalizedMoments': 'moments_normalized',
'Orientation': 'orientation',
'Perimeter': 'perimeter',
# 'PixelIdxList',
# 'PixelList',
'Slice': 'slice',
'Solidity': 'solidity',
# 'SubarrayIdx'
'WeightedCentralMoments': 'weighted_moments_central',
'WeightedCentroid': 'weighted_centroid',
'WeightedHuMoments': 'weighted_moments_hu',
'WeightedMoments': 'weighted_moments',
'WeightedNormalizedMoments': 'weighted_moments_normalized'
}
PROP_VALS = set(PROPS.values())
def _cached(f):
@wraps(f)
def wrapper(obj):
cache = obj._cache
prop = f.__name__
if not ((prop in cache) and obj._cache_active):
cache[prop] = f(obj)
return cache[prop]
return wrapper
def only2d(method):
@wraps(method)
def func2d(self, *args, **kwargs):
if self._ndim > 2:
raise NotImplementedError('Property %s is not implemented for '
'3D images' % method.__name__)
return method(self, *args, **kwargs)
return func2d
class _RegionProperties(object):
"""Please refer to `skimage.measure.regionprops` for more information
on the available region properties.
"""
def __init__(self, slice, label, label_image, intensity_image,
cache_active, coordinates):
if intensity_image is not None:
if not intensity_image.shape == label_image.shape:
raise ValueError('Label and intensity image must have the'
'same shape.')
self.label = label
self._slice = slice
self.slice = slice
self._label_image = label_image
self._intensity_image = intensity_image
self._cache_active = cache_active
self._cache = {}
self._ndim = label_image.ndim
# Note: in PR 2603, we added support for nD moments in regionprops.
# Many properties used xy coordinates, instead of rc. This attribute
# helps with the deprecation process and should be removed in 0.16.
if label_image.ndim > 2 or coordinates == 'rc':
self._use_xy_warning = False
self._transpose_moments = False
elif coordinates == 'xy':
self._use_xy_warning = False # don't warn if 'xy' given explicitly
self._transpose_moments = True
elif coordinates is None:
self._use_xy_warning = True
self._transpose_moments = True
else:
raise ValueError('Incorrect value for regionprops coordinates: %s.'
' Possible values are: "rc", "xy", or None')
@_cached
def area(self):
return np.sum(self.image)
def bbox(self):
"""
Returns
-------
A tuple of the bounding box's start coordinates for each dimension,
followed by the end coordinates for each dimension
"""
return tuple([self.slice[i].start for i in range(self._ndim)] +
[self.slice[i].stop for i in range(self._ndim)])
def bbox_area(self):
return self.image.size
def centroid(self):
return tuple(self.coords.mean(axis=0))
@_cached
def convex_area(self):
return np.sum(self.convex_image)
@_cached
def convex_image(self):
from ..morphology.convex_hull import convex_hull_image
return convex_hull_image(self.image)
def coords(self):
indices = np.nonzero(self.image)
return np.vstack([indices[i] + self.slice[i].start
for i in range(self._ndim)]).T
@only2d
def eccentricity(self):
l1, l2 = self.inertia_tensor_eigvals
if l1 == 0:
return 0
return sqrt(1 - l2 / l1)
def equivalent_diameter(self):
if self._ndim == 2:
return sqrt(4 * self.area / PI)
elif self._ndim == 3:
return (6 * self.area / PI) ** (1. / 3)
def euler_number(self):
euler_array = self.filled_image != self.image
_, num = label(euler_array, connectivity=self._ndim, return_num=True,
background=0)
return -num + 1
def extent(self):
return self.area / self.image.size
def filled_area(self):
return np.sum(self.filled_image)
@_cached
def filled_image(self):
structure = np.ones((3,) * self._ndim)
return ndi.binary_fill_holes(self.image, structure)
@_cached
def image(self):
return self._label_image[self.slice] == self.label
@_cached
def inertia_tensor(self):
mu = self.moments_central
return _moments.inertia_tensor(self.image, mu)
@_cached
def inertia_tensor_eigvals(self):
return _moments.inertia_tensor_eigvals(self.image,
T=self.inertia_tensor)
@_cached
def intensity_image(self):
if self._intensity_image is None:
raise AttributeError('No intensity image specified.')
return self._intensity_image[self.slice] * self.image
def _intensity_image_double(self):
return self.intensity_image.astype(np.double)
def local_centroid(self):
M = self.moments
if self._transpose_moments:
M = M.T
return tuple(M[tuple(np.eye(self._ndim, dtype=int))] /
M[(0,) * self._ndim])
def max_intensity(self):
return np.max(self.intensity_image[self.image])
def mean_intensity(self):
return np.mean(self.intensity_image[self.image])
def min_intensity(self):
return np.min(self.intensity_image[self.image])
def major_axis_length(self):
l1 = self.inertia_tensor_eigvals[0]
return 4 * sqrt(l1)
def minor_axis_length(self):
l2 = self.inertia_tensor_eigvals[-1]
return 4 * sqrt(l2)
@_cached
def moments(self):
M = _moments.moments(self.image.astype(np.uint8), 3)
if self._use_xy_warning:
warn(XY_TO_RC_DEPRECATION_MESSAGE)
if self._transpose_moments:
M = M.T
return M
@_cached
def moments_central(self):
mu = _moments.moments_central(self.image.astype(np.uint8),
self.local_centroid, order=3)
if self._use_xy_warning:
warn(XY_TO_RC_DEPRECATION_MESSAGE)
if self._transpose_moments:
mu = mu.T
return mu
@only2d
def moments_hu(self):
return _moments.moments_hu(self.moments_normalized)
@_cached
def moments_normalized(self):
return _moments.moments_normalized(self.moments_central, 3)
@only2d
def orientation(self):
a, b, b, c = self.inertia_tensor.flat
sign = -1 if self._transpose_moments else 1
if a - c == 0:
if b < 0:
return -PI / 4.
else:
return PI / 4.
else:
return sign * 0.5 * atan2(-2 * b, c - a)
@only2d
def perimeter(self):
return perimeter(self.image, 4)
def solidity(self):
return self.area / self.convex_area
def weighted_centroid(self):
ctr = self.weighted_local_centroid
return tuple(idx + slc.start
for idx, slc in zip(ctr, self.slice))
def weighted_local_centroid(self):
M = self.weighted_moments
return (M[tuple(np.eye(self._ndim, dtype=int))] /
M[(0,) * self._ndim])
@_cached
def weighted_moments(self):
return _moments.moments(self._intensity_image_double(), 3)
@_cached
def weighted_moments_central(self):
ctr = self.weighted_local_centroid
return _moments.moments_central(self._intensity_image_double(),
center=ctr, order=3)
@only2d
def weighted_moments_hu(self):
return _moments.moments_hu(self.weighted_moments_normalized)
@_cached
def weighted_moments_normalized(self):
return _moments.moments_normalized(self.weighted_moments_central, 3)
def __iter__(self):
props = PROP_VALS
if self._intensity_image is None:
unavailable_props = ('intensity_image',
'max_intensity',
'mean_intensity',
'min_intensity',
'weighted_moments',
'weighted_moments_central',
'weighted_centroid',
'weighted_local_centroid',
'weighted_moments_hu',
'weighted_moments_normalized')
props = props.difference(unavailable_props)
return iter(sorted(props))
def __getitem__(self, key):
value = getattr(self, key, None)
if value is not None:
return value
else: # backwards compatibility
return getattr(self, PROPS[key])
def __eq__(self, other):
if not isinstance(other, _RegionProperties):
return False
for key in PROP_VALS:
try:
# so that NaNs are equal
np.testing.assert_equal(getattr(self, key, None),
getattr(other, key, None))
except AssertionError:
return False
return True
def regionprops(label_image, intensity_image=None, cache=True,
coordinates=None):
"""Measure properties of labeled image regions.
Parameters
----------
label_image : (N, M) ndarray
Labeled input image. Labels with value 0 are ignored.
.. versionchanged:: 0.14.1
Previously, ``label_image`` was processed by ``numpy.squeeze`` and
so any number of singleton dimensions was allowed. This resulted in
inconsistent handling of images with singleton dimensions. To
recover the old behaviour, use
``regionprops(np.squeeze(label_image), ...)``.
intensity_image : (N, M) ndarray, optional
Intensity (i.e., input) image with same size as labeled image.
Default is None.
cache : bool, optional
Determine whether to cache calculated properties. The computation is
much faster for cached properties, whereas the memory consumption
increases.
coordinates : 'rc' or 'xy', optional
Coordinate conventions for 2D images. (Only 'rc' coordinates are
supported for 3D images.)
Returns
-------
properties : list of RegionProperties
Each item describes one labeled region, and can be accessed using the
attributes listed below.
Notes
-----
The following properties can be accessed as attributes or keys:
**area** : int
Number of pixels of region.
**bbox** : tuple
Bounding box ``(min_row, min_col, max_row, max_col)``.
Pixels belonging to the bounding box are in the half-open interval
``[min_row; max_row)`` and ``[min_col; max_col)``.
**bbox_area** : int
Number of pixels of bounding box.
**centroid** : array
Centroid coordinate tuple ``(row, col)``.
**convex_area** : int
Number of pixels of convex hull image.
**convex_image** : (H, J) ndarray
Binary convex hull image which has the same size as bounding box.
**coords** : (N, 2) ndarray
Coordinate list ``(row, col)`` of the region.
**eccentricity** : float
Eccentricity of the ellipse that has the same second-moments as the
region. The eccentricity is the ratio of the focal distance
(distance between focal points) over the major axis length.
The value is in the interval [0, 1).
When it is 0, the ellipse becomes a circle.
**equivalent_diameter** : float
The diameter of a circle with the same area as the region.
**euler_number** : int
Euler characteristic of region. Computed as number of objects (= 1)
subtracted by number of holes (8-connectivity).
**extent** : float
Ratio of pixels in the region to pixels in the total bounding box.
Computed as ``area / (rows * cols)``
**filled_area** : int
Number of pixels of filled region.
**filled_image** : (H, J) ndarray
Binary region image with filled holes which has the same size as
bounding box.
**image** : (H, J) ndarray
Sliced binary region image which has the same size as bounding box.
**inertia_tensor** : (2, 2) ndarray
Inertia tensor of the region for the rotation around its mass.
**inertia_tensor_eigvals** : tuple
The two eigen values of the inertia tensor in decreasing order.
**intensity_image** : ndarray
Image inside region bounding box.
**label** : int
The label in the labeled input image.
**local_centroid** : array
Centroid coordinate tuple ``(row, col)``, relative to region bounding
box.
**major_axis_length** : float
The length of the major axis of the ellipse that has the same
normalized second central moments as the region.
**max_intensity** : float
Value with the greatest intensity in the region.
**mean_intensity** : float
Value with the mean intensity in the region.
**min_intensity** : float
Value with the least intensity in the region.
**minor_axis_length** : float
The length of the minor axis of the ellipse that has the same
normalized second central moments as the region.
**moments** : (3, 3) ndarray
Spatial moments up to 3rd order::
m_ji = sum{ array(x, y) * x^j * y^i }
where the sum is over the `x`, `y` coordinates of the region.
**moments_central** : (3, 3) ndarray
Central moments (translation invariant) up to 3rd order::
mu_ji = sum{ array(x, y) * (x - x_c)^j * (y - y_c)^i }
where the sum is over the `x`, `y` coordinates of the region,
and `x_c` and `y_c` are the coordinates of the region's centroid.
**moments_hu** : tuple
Hu moments (translation, scale and rotation invariant).
**moments_normalized** : (3, 3) ndarray
Normalized moments (translation and scale invariant) up to 3rd order::
nu_ji = mu_ji / m_00^[(i+j)/2 + 1]
where `m_00` is the zeroth spatial moment.
**orientation** : float
In 'rc' coordinates, angle between the 0th axis (rows) and the major
axis of the ellipse that has the same second moments as the region,
ranging from `-pi/2` to `pi/2` counter-clockwise.
In `xy` coordinates, as above but the angle is now measured from the
"x" or horizontal axis.
**perimeter** : float
Perimeter of object which approximates the contour as a line
through the centers of border pixels using a 4-connectivity.
**slice** : tuple of slices
A slice to extract the object from the source image.
**solidity** : float
Ratio of pixels in the region to pixels of the convex hull image.
**weighted_centroid** : array
Centroid coordinate tuple ``(row, col)`` weighted with intensity
image.
**weighted_local_centroid** : array
Centroid coordinate tuple ``(row, col)``, relative to region bounding
box, weighted with intensity image.
**weighted_moments** : (3, 3) ndarray
Spatial moments of intensity image up to 3rd order::
wm_ji = sum{ array(x, y) * x^j * y^i }
where the sum is over the `x`, `y` coordinates of the region.
**weighted_moments_central** : (3, 3) ndarray
Central moments (translation invariant) of intensity image up to
3rd order::
wmu_ji = sum{ array(x, y) * (x - x_c)^j * (y - y_c)^i }
where the sum is over the `x`, `y` coordinates of the region,
and `x_c` and `y_c` are the coordinates of the region's weighted
centroid.
**weighted_moments_hu** : tuple
Hu moments (translation, scale and rotation invariant) of intensity
image.
**weighted_moments_normalized** : (3, 3) ndarray
Normalized moments (translation and scale invariant) of intensity
image up to 3rd order::
wnu_ji = wmu_ji / wm_00^[(i+j)/2 + 1]
where ``wm_00`` is the zeroth spatial moment (intensity-weighted area).
Each region also supports iteration, so that you can do::
for prop in region:
print(prop, region[prop])
See Also
--------
label
References
----------
.. [1] Wilhelm Burger, Mark Burge. Principles of Digital Image Processing:
Core Algorithms. Springer-Verlag, London, 2009.
.. [2] B. Jähne. Digital Image Processing. Springer-Verlag,
Berlin-Heidelberg, 6. edition, 2005.
.. [3] T. H. Reiss. Recognizing Planar Objects Using Invariant Image
Features, from Lecture notes in computer science, p. 676. Springer,
Berlin, 1993.
.. [4] https://en.wikipedia.org/wiki/Image_moment
Examples
--------
>>> from skimage import data, util
>>> from skimage.measure import label
>>> img = util.img_as_ubyte(data.coins()) > 110
>>> label_img = label(img, connectivity=img.ndim)
>>> props = regionprops(label_img)
>>> # centroid of first labeled object
>>> props[0].centroid
(22.729879860483141, 81.912285234465827)
>>> # centroid of first labeled object
>>> props[0]['centroid']
(22.729879860483141, 81.912285234465827)
"""
if label_image.ndim not in (2, 3):
raise TypeError('Only 2-D and 3-D images supported.')
if not np.issubdtype(label_image.dtype, np.integer):
raise TypeError('Label image must be of integer type.')
regions = []
objects = ndi.find_objects(label_image)
for i, sl in enumerate(objects):
if sl is None:
continue
label = i + 1
props = _RegionProperties(sl, label, label_image, intensity_image,
cache, coordinates=coordinates)
regions.append(props)
return regions
def perimeter(image, neighbourhood=4):
"""Calculate total perimeter of all objects in binary image.
Parameters
----------
image : array
Binary image.
neighbourhood : 4 or 8, optional
Neighborhood connectivity for border pixel determination.
Returns
-------
perimeter : float
Total perimeter of all objects in binary image.
References
----------
.. [1] K. Benkrid, D. Crookes. Design and FPGA Implementation of
a Perimeter Estimator. The Queen's University of Belfast.
http://www.cs.qub.ac.uk/~d.crookes/webpubs/papers/perimeter.doc
"""
if neighbourhood == 4:
strel = STREL_4
else:
strel = STREL_8
image = image.astype(np.uint8)
eroded_image = ndi.binary_erosion(image, strel, border_value=0)
border_image = image - eroded_image
perimeter_weights = np.zeros(50, dtype=np.double)
perimeter_weights[[5, 7, 15, 17, 25, 27]] = 1
perimeter_weights[[21, 33]] = sqrt(2)
perimeter_weights[[13, 23]] = (1 + sqrt(2)) / 2
perimeter_image = ndi.convolve(border_image, np.array([[10, 2, 10],
[ 2, 1, 2],
[10, 2, 10]]),
mode='constant', cval=0)
# You can also write
# return perimeter_weights[perimeter_image].sum()
# but that was measured as taking much longer than bincount + np.dot (5x
# as much time)
perimeter_histogram = np.bincount(perimeter_image.ravel(), minlength=50)
total_perimeter = perimeter_histogram @ perimeter_weights
return total_perimeter
def _parse_docs():
import re
import textwrap
doc = regionprops.__doc__ or ''
matches = re.finditer(r'\*\*(\w+)\*\* \:.*?\n(.*?)(?=\n [\*\S]+)',
doc, flags=re.DOTALL)
prop_doc = dict((m.group(1), textwrap.dedent(m.group(2))) for m in matches)
return prop_doc
def _install_properties_docs():
prop_doc = _parse_docs()
for p in [member for member in dir(_RegionProperties)
if not member.startswith('_')]:
getattr(_RegionProperties, p).__doc__ = prop_doc[p]
setattr(_RegionProperties, p, property(getattr(_RegionProperties, p)))
if __debug__:
# don't install docstrings when in optimized/non-debug mode
_install_properties_docs()