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scikit-image/skimage/measure/_regionprops.py
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Johannes L. Schönberger 6546b9dba4 Merge pull request #1007 from stefanv/label_refactor 
Move `morphology.label` to `measure.label` and prepare for 0-label transition
2014-05-25 21:56:42 -04:00

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# coding: utf-8
import warnings
from math import sqrt, atan2, pi as PI
import numpy as np
from scipy import ndimage
from ._label import label
from . import _moments
__all__ = ['regionprops', 'perimeter']
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)
PROPS = {
'Area': 'area',
'BoundingBox': 'bbox',
'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',
'Solidity': 'solidity',
# 'SubarrayIdx'
'WeightedCentralMoments': 'weighted_moments_central',
'WeightedCentroid': 'weighted_centroid',
'WeightedHuMoments': 'weighted_moments_hu',
'WeightedMoments': 'weighted_moments',
'WeightedNormalizedMoments': 'weighted_moments_normalized'
}
PROP_VALS = PROPS.values()
class _cached_property(object):
"""Decorator to use a function as a cached property.
The function is only called the first time and each successive call returns
the cached result of the first call.
class Foo(object):
@_cached_property
def foo(self):
return "Cached"
class Foo(object):
def __init__(self):
self._cache_active = False
@_cached_property
def foo(self):
return "Not cached"
Adapted from <http://wiki.python.org/moin/PythonDecoratorLibrary>.
"""
def __init__(self, func, name=None, doc=None):
self.__name__ = name or func.__name__
self.__module__ = func.__module__
self.__doc__ = doc or func.__doc__
self.func = func
def __get__(self, obj, type=None):
if obj is None:
return self
# call every time, if cache is not active
if not obj.__dict__.get('_cache_active', True):
return self.func(obj)
# try to retrieve from cache or call and store result in cache
try:
value = obj.__dict__[self.__name__]
except KeyError:
value = self.func(obj)
obj.__dict__[self.__name__] = value
return value
class _RegionProperties(object):
def __init__(self, slice, label, label_image, intensity_image,
cache_active):
self.label = label
self._slice = slice
self._label_image = label_image
self._intensity_image = intensity_image
self._cache_active = cache_active
@_cached_property
def area(self):
return self.moments[0, 0]
@_cached_property
def bbox(self):
return (self._slice[0].start, self._slice[1].start,
self._slice[0].stop, self._slice[1].stop)
@_cached_property
def centroid(self):
row, col = self.local_centroid
return row + self._slice[0].start, col + self._slice[1].start
@_cached_property
def convex_area(self):
return np.sum(self.convex_image)
@_cached_property
def convex_image(self):
from ..morphology.convex_hull import convex_hull_image
return convex_hull_image(self.image)
@_cached_property
def coords(self):
rr, cc = np.nonzero(self.image)
return np.vstack((rr + self._slice[0].start,
cc + self._slice[1].start)).T
@_cached_property
def eccentricity(self):
l1, l2 = self.inertia_tensor_eigvals
if l1 == 0:
return 0
return sqrt(1 - l2 / l1)
@_cached_property
def equivalent_diameter(self):
return sqrt(4 * self.moments[0, 0] / PI)
@_cached_property
def euler_number(self):
euler_array = self.filled_image != self.image
_, num = label(euler_array, neighbors=8, return_num=True)
return -num + 1
@_cached_property
def extent(self):
rows, cols = self.image.shape
return self.moments[0, 0] / (rows * cols)
@_cached_property
def filled_area(self):
return np.sum(self.filled_image)
@_cached_property
def filled_image(self):
return ndimage.binary_fill_holes(self.image, STREL_8)
@_cached_property
def image(self):
return self._label_image[self._slice] == self.label
@_cached_property
def _image_double(self):
return self.image.astype(np.double)
@_cached_property
def inertia_tensor(self):
mu = self.moments_central
a = mu[2, 0] / mu[0, 0]
b = -mu[1, 1] / mu[0, 0]
c = mu[0, 2] / mu[0, 0]
return np.array([[a, b], [b, c]])
@_cached_property
def inertia_tensor_eigvals(self):
a, b, b, c = self.inertia_tensor.flat
# eigen values of inertia tensor
l1 = (a + c) / 2 + sqrt(4 * b ** 2 + (a - c) ** 2) / 2
l2 = (a + c) / 2 - sqrt(4 * b ** 2 + (a - c) ** 2) / 2
return l1, l2
@_cached_property
def intensity_image(self):
if self._intensity_image is None:
raise AttributeError('No intensity image specified.')
return self._intensity_image[self._slice] * self.image
@_cached_property
def _intensity_image_double(self):
return self.intensity_image.astype(np.double)
@_cached_property
def local_centroid(self):
m = self.moments
row = m[0, 1] / m[0, 0]
col = m[1, 0] / m[0, 0]
return row, col
@_cached_property
def max_intensity(self):
return np.max(self.intensity_image[self.image])
@_cached_property
def mean_intensity(self):
return np.mean(self.intensity_image[self.image])
@_cached_property
def min_intensity(self):
return np.min(self.intensity_image[self.image])
@_cached_property
def major_axis_length(self):
l1, _ = self.inertia_tensor_eigvals
return 4 * sqrt(l1)
@_cached_property
def minor_axis_length(self):
_, l2 = self.inertia_tensor_eigvals
return 4 * sqrt(l2)
@_cached_property
def moments(self):
return _moments.moments(self._image_double, 3)
@_cached_property
def moments_central(self):
row, col = self.local_centroid
return _moments.moments_central(self._image_double, row, col, 3)
@_cached_property
def moments_hu(self):
return _moments.moments_hu(self.moments_normalized)
@_cached_property
def moments_normalized(self):
return _moments.moments_normalized(self.moments_central, 3)
@_cached_property
def orientation(self):
a, b, b, c = self.inertia_tensor.flat
b = -b
if a - c == 0:
if b > 0:
return -PI / 4.
else:
return PI / 4.
else:
return - 0.5 * atan2(2 * b, (a - c))
@_cached_property
def perimeter(self):
return perimeter(self.image, 4)
@_cached_property
def solidity(self):
return self.moments[0, 0] / np.sum(self.convex_image)
@_cached_property
def weighted_centroid(self):
row, col = self.weighted_local_centroid
return row + self._slice[0].start, col + self._slice[1].start
@_cached_property
def weighted_local_centroid(self):
m = self.weighted_moments
row = m[0, 1] / m[0, 0]
col = m[1, 0] / m[0, 0]
return row, col
@_cached_property
def weighted_moments(self):
return _moments.moments_central(self._intensity_image_double, 0, 0, 3)
@_cached_property
def weighted_moments_central(self):
row, col = self.weighted_local_centroid
return _moments.moments_central(self._intensity_image_double,
row, col, 3)
@_cached_property
def weighted_moments_hu(self):
return _moments.moments_hu(self.weighted_moments_normalized)
@_cached_property
def weighted_moments_normalized(self):
return _moments.moments_normalized(self.weighted_moments_central, 3)
def __iter__(self):
return iter(PROPS.values())
def __getitem__(self, key):
value = getattr(self, key, None)
if value is not None:
return value
else: # backwards compatability
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):
"""Measure properties of labeled image regions.
Parameters
----------
label_image : (N, M) ndarray
Labeled input image.
intensity_image : (N, M) ndarray, optional
Intensity 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.
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)``
**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 distance between its
minor and major axis length. The value is between 0 and 1.
**equivalent_diameter** : float
The diameter of a circle with the same area as the region.
**euler_number** : int
Euler number 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.
**label** : int
The label in the labeled input image.
**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
Angle between the X-axis and the major axis of the ellipse that has
the same second-moments as the region. Ranging from `-pi/2` to
`pi/2` in counter-clockwise direction.
**perimeter** : float
Perimeter of object which approximates the contour as a line
through the centers of border pixels using a 4-connectivity.
**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_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 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).
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] http://en.wikipedia.org/wiki/Image_moment
Examples
--------
>>> from skimage import data, util
>>> from skimage.morphology import label
>>> img = util.img_as_ubyte(data.coins()) > 110
>>> label_img = label(img)
>>> props = regionprops(label_img)
>>> props[0].centroid # centroid of first labeled object
(22.729879860483141, 81.912285234465827)
>>> props[0]['centroid'] # centroid of first labeled object
(22.729879860483141, 81.912285234465827)
"""
label_image = np.squeeze(label_image)
if label_image.ndim != 2:
raise TypeError('Only 2-D images supported.')
regions = []
objects = ndimage.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)
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 = ndimage.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 = ndimage.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 = np.dot(perimeter_histogram, perimeter_weights)
return total_perimeter
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