python分水嶺アルゴリズムの実現
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「watershed.py-分水嶺アルゴリズムこのモジュールは分水嶺アルゴリズムを実現し、ピクセルをタグの盆地に割り当てることができる.このアルゴリズムは優先キューを使用してピクセルを保存し、優先キューのメトリック基準はピクセル値であり、キューの時間を入力する-これは関係をより緊密にし、最も近いタグに有利にする.いくつかのアイデアはSoilleから取られ、「数学的形態を用いてデジタル高距離モデルから自動的に盆地を画定する」信号処理20(1990)171-182.この論文の最も重要な見解は、キューに入る時間が2つの問題を解決した:最大勾配を持つ隣人にピクセルを割り当てるべきか、勾配がなければ高原のピクセルを反対側のタグの間に割り当てるべきか.最初はCellProfilerの一部であり、コードはGPLとBSDの許可を得た.URL:http://www.cellprofiler.org著作権所有(c)2003-2009マサチューセッツ工科大学著作権所有(c)2009-2011 Broad Institute著作権所有.原作者:Lee Kamentsky
Examples
分水嶺アルゴリズムは、重複するオブジェクトを分離するために使用することができる.
まず、2つの重なり合う円を持つ初期画像を生成します.
>>> x, y = np.indices((80, 80))
>>> x1, y1, x2, y2 = 28, 28, 44, 52
>>> r1, r2 = 16, 20
>>> mask_circle1 = (x - x1)**2 + (y - y1)**2 < r1**2
>>> mask_circle2 = (x - x2)**2 + (y - y2)**2 < r2**2
>>> image = np.logical_or(mask_circle1, mask_circle2)
次に、2つの円を分けます.背景からの最大距離でタグを生成します.
>>> from scipy import ndimage as ndi
>>> distance = ndi.distance_transform_edt(image)
>>> from skimage.feature import peak_local_max
>>> local_maxi = peak_local_max(distance, labels=image,
... footprint=np.ones((3, 3)),
... indices=False)
>>> markers = ndi.label(local_maxi)[0]
最後に、画像とタグに対して分水嶺を実行します.
>>> labels = watershed(-distance, markers, mask=image)
import numpy as np
from scipy import ndimage as ndi
from . import _watershed
from ..util import crop, regular_seeds
def _validate_inputs(image, markers, mask):
""" 。
Parameters
----------
image : array
The input image.
markers : int or array of int
The marker image.
mask : array, or None
A boolean mask, True where we want to compute the watershed.
Returns
-------
image, markers, mask : arrays
The validated and formatted arrays. Image will have dtype float64,
markers int32, and mask int8. If ``None`` was given for the mask,
it is a volume of all 1s.
Raises
------
ValueError
If the shapes of the given arrays don't match.
"""
if not isinstance(markers, (np.ndarray, list, tuple)):
# not array-like, assume int
markers = regular_seeds(image.shape, markers)
elif markers.shape != image.shape:
raise ValueError("`markers` (shape {}) must have same shape "
"as `image` (shape {})".format(markers.shape, image.shape))
if mask is not None and mask.shape != image.shape:
raise ValueError("`mask` must have same shape as `image`")
if mask is None:
# Use a complete `True` mask if none is provided
mask = np.ones(image.shape, bool)
return (image.astype(np.float64),
markers.astype(np.int32),
mask.astype(np.int8))
def _validate_connectivity(image_dim, connectivity, offset):
"""Convert any valid connectivity to a structuring element and offset.
Parameters
----------
image_dim : int
The number of dimensions of the input image.
connectivity : int, array, or None
The neighborhood connectivity. An integer is interpreted as in
``scipy.ndimage.generate_binary_structure``, as the maximum number
of orthogonal steps to reach a neighbor. An array is directly
interpreted as a structuring element and its shape is validated against
the input image shape. ``None`` is interpreted as a connectivity of 1.
offset : tuple of int, or None
The coordinates of the center of the structuring element.
Returns
-------
c_connectivity : array of bool
The structuring element corresponding to the input `connectivity`.
offset : array of int
The offset corresponding to the center of the structuring element.
Raises
------
ValueError:
If the image dimension and the connectivity or offset dimensions don't
match.
"""
if connectivity is None:
connectivity = 1
if np.isscalar(connectivity):
c_connectivity = ndi.generate_binary_structure(image_dim, connectivity)
else:
c_connectivity = np.array(connectivity, bool)
if c_connectivity.ndim != image_dim:
raise ValueError("Connectivity dimension must be same as image")
if offset is None:
if any([x % 2 == 0 for x in c_connectivity.shape]):
raise ValueError("Connectivity array must have an unambiguous "
"center")
offset = np.array(c_connectivity.shape) // 2
return c_connectivity, offset
def _compute_neighbors(image, structure, offset):
"""Compute neighborhood as an array of linear offsets into the image.
These are sorted according to Euclidean distance from the center (given
by `offset`), ensuring that immediate neighbors are visited first.
"""
structure[tuple(offset)] = 0 # ignore the center; it's not a neighbor
locations = np.transpose(np.nonzero(structure))
sqdistances = np.sum((locations - offset)**2, axis=1)
neighborhood = (np.ravel_multi_index(locations.T, image.shape) -
np.ravel_multi_index(offset, image.shape)).astype(np.int32)
sorted_neighborhood = neighborhood[np.argsort(sqdistances)]
return sorted_neighborhood
def watershed(image, markers, connectivity=1, offset=None, mask=None,
compactness=0, watershed_line=False):
"""Find watershed basins in `image` flooded from given `markers`.
Parameters
----------
image: ndarray (2-D, 3-D, ...) of integers
Data array where the lowest value points are labeled first.
markers: int, or ndarray of int, same shape as `image`
The desired number of markers, or an array marking the basins with the
values to be assigned in the label matrix. Zero means not a marker.
connectivity: ndarray, optional
An array with the same number of dimensions as `image` whose
non-zero elements indicate neighbors for connection.
Following the scipy convention, default is a one-connected array of
the dimension of the image.
offset: array_like of shape image.ndim, optional
offset of the connectivity (one offset per dimension)
mask: ndarray of bools or 0s and 1s, optional
Array of same shape as `image`. Only points at which mask == True
will be labeled.
compactness : float, optional
Use compact watershed [3]_ with given compactness parameter.
Higher values result in more regularly-shaped watershed basins.
watershed_line : bool, optional
If watershed_line is True, a one-pixel wide line separates the regions
obtained by the watershed algorithm. The line has the label 0.
Returns
-------
out: ndarray
A labeled matrix of the same type and shape as markers
See also
--------
skimage.segmentation.random_walker: random walker segmentation
A segmentation algorithm based on anisotropic diffusion, usually
slower than the watershed but with good results on noisy data and
boundaries with holes.
Notes
-----
[1] _ [2] _， 。
， ， - ，
。
Some ideas taken from
Soille, "Automated Basin Delineation from Digital Elevation Models Using
Mathematical Morphology", Signal Processing 20 (1990) 171-182
， ： ， ， ， 。
This implementation converts all arguments to specific, lowest common
denominator types, then passes these to a C algorithm.
Markers can be determined manually, or automatically using for example
the local minima of the gradient of the image, or the local maxima of the
distance function to the background for separating overlapping objects
(see example).
References
----------
.. [1] http://en.wikipedia.org/wiki/Watershed_%28image_processing%29
.. [2] http://cmm.ensmp.fr/~beucher/wtshed.html
.. [3] Peer Neubert & Peter Protzel (2014). Compact Watershed and
Preemptive SLIC: On Improving Trade-offs of Superpixel Segmentation
Algorithms. ICPR 2014, pp 996-1001. DOI:10.1109/ICPR.2014.181
https://www.tu-chemnitz.de/etit/proaut/forschung/rsrc/cws_pSLIC_ICPR.pdfExamples
分水嶺アルゴリズムは、重複するオブジェクトを分離するために使用することができる.
まず、2つの重なり合う円を持つ初期画像を生成します.
>>> x, y = np.indices((80, 80))
>>> x1, y1, x2, y2 = 28, 28, 44, 52
>>> r1, r2 = 16, 20
>>> mask_circle1 = (x - x1)**2 + (y - y1)**2 < r1**2
>>> mask_circle2 = (x - x2)**2 + (y - y2)**2 < r2**2
>>> image = np.logical_or(mask_circle1, mask_circle2)
次に、2つの円を分けます.背景からの最大距離でタグを生成します.
>>> from scipy import ndimage as ndi
>>> distance = ndi.distance_transform_edt(image)
>>> from skimage.feature import peak_local_max
>>> local_maxi = peak_local_max(distance, labels=image,
... footprint=np.ones((3, 3)),
... indices=False)
>>> markers = ndi.label(local_maxi)[0]
最後に、画像とタグに対して分水嶺を実行します.
>>> labels = watershed(-distance, markers, mask=image)