2231 lines
81 KiB
Python
2231 lines
81 KiB
Python
# Copyright (C) 2003-2005 Peter J. Verveer
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#
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# Redistribution and use in source and binary forms, with or without
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# modification, are permitted provided that the following conditions
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# are met:
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#
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# 1. Redistributions of source code must retain the above copyright
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# notice, this list of conditions and the following disclaimer.
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#
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# 2. Redistributions in binary form must reproduce the above
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# copyright notice, this list of conditions and the following
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# disclaimer in the documentation and/or other materials provided
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# with the distribution.
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#
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# 3. The name of the author may not be used to endorse or promote
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# products derived from this software without specific prior
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# written permission.
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#
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# THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
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# OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
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# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
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# GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
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# WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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from __future__ import division, print_function, absolute_import
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import warnings
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import operator
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import numpy
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from . import _ni_support
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from . import _nd_image
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from . import filters
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__all__ = ['iterate_structure', 'generate_binary_structure', 'binary_erosion',
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'binary_dilation', 'binary_opening', 'binary_closing',
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'binary_hit_or_miss', 'binary_propagation', 'binary_fill_holes',
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'grey_erosion', 'grey_dilation', 'grey_opening', 'grey_closing',
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'morphological_gradient', 'morphological_laplace', 'white_tophat',
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'black_tophat', 'distance_transform_bf', 'distance_transform_cdt',
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'distance_transform_edt']
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def _center_is_true(structure, origin):
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structure = numpy.array(structure)
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coor = tuple([oo + ss // 2 for ss, oo in zip(structure.shape,
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origin)])
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return bool(structure[coor])
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def iterate_structure(structure, iterations, origin=None):
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"""
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Iterate a structure by dilating it with itself.
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Parameters
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----------
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structure : array_like
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Structuring element (an array of bools, for example), to be dilated with
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itself.
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iterations : int
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number of dilations performed on the structure with itself
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origin : optional
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If origin is None, only the iterated structure is returned. If
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not, a tuple of the iterated structure and the modified origin is
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returned.
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Returns
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-------
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iterate_structure : ndarray of bools
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A new structuring element obtained by dilating `structure`
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(`iterations` - 1) times with itself.
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See also
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--------
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generate_binary_structure
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Examples
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--------
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>>> from scipy import ndimage
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>>> struct = ndimage.generate_binary_structure(2, 1)
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>>> struct.astype(int)
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array([[0, 1, 0],
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[1, 1, 1],
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[0, 1, 0]])
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>>> ndimage.iterate_structure(struct, 2).astype(int)
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array([[0, 0, 1, 0, 0],
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[0, 1, 1, 1, 0],
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[1, 1, 1, 1, 1],
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[0, 1, 1, 1, 0],
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[0, 0, 1, 0, 0]])
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>>> ndimage.iterate_structure(struct, 3).astype(int)
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array([[0, 0, 0, 1, 0, 0, 0],
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[0, 0, 1, 1, 1, 0, 0],
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[0, 1, 1, 1, 1, 1, 0],
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[1, 1, 1, 1, 1, 1, 1],
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[0, 1, 1, 1, 1, 1, 0],
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[0, 0, 1, 1, 1, 0, 0],
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[0, 0, 0, 1, 0, 0, 0]])
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"""
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structure = numpy.asarray(structure)
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if iterations < 2:
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return structure.copy()
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ni = iterations - 1
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shape = [ii + ni * (ii - 1) for ii in structure.shape]
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pos = [ni * (structure.shape[ii] // 2) for ii in range(len(shape))]
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slc = tuple(slice(pos[ii], pos[ii] + structure.shape[ii], None)
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for ii in range(len(shape)))
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out = numpy.zeros(shape, bool)
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out[slc] = structure != 0
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out = binary_dilation(out, structure, iterations=ni)
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if origin is None:
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return out
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else:
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origin = _ni_support._normalize_sequence(origin, structure.ndim)
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origin = [iterations * o for o in origin]
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return out, origin
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def generate_binary_structure(rank, connectivity):
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"""
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Generate a binary structure for binary morphological operations.
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Parameters
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----------
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rank : int
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Number of dimensions of the array to which the structuring element
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will be applied, as returned by `np.ndim`.
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connectivity : int
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`connectivity` determines which elements of the output array belong
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to the structure, i.e. are considered as neighbors of the central
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element. Elements up to a squared distance of `connectivity` from
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the center are considered neighbors. `connectivity` may range from 1
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(no diagonal elements are neighbors) to `rank` (all elements are
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neighbors).
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Returns
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-------
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output : ndarray of bools
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Structuring element which may be used for binary morphological
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operations, with `rank` dimensions and all dimensions equal to 3.
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See also
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--------
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iterate_structure, binary_dilation, binary_erosion
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Notes
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-----
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`generate_binary_structure` can only create structuring elements with
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dimensions equal to 3, i.e. minimal dimensions. For larger structuring
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elements, that are useful e.g. for eroding large objects, one may either
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use `iterate_structure`, or create directly custom arrays with
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numpy functions such as `numpy.ones`.
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Examples
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--------
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>>> from scipy import ndimage
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>>> struct = ndimage.generate_binary_structure(2, 1)
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>>> struct
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array([[False, True, False],
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[ True, True, True],
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[False, True, False]], dtype=bool)
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>>> a = np.zeros((5,5))
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>>> a[2, 2] = 1
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>>> a
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array([[ 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0.],
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[ 0., 0., 1., 0., 0.],
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[ 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0.]])
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>>> b = ndimage.binary_dilation(a, structure=struct).astype(a.dtype)
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>>> b
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array([[ 0., 0., 0., 0., 0.],
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[ 0., 0., 1., 0., 0.],
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[ 0., 1., 1., 1., 0.],
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[ 0., 0., 1., 0., 0.],
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[ 0., 0., 0., 0., 0.]])
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>>> ndimage.binary_dilation(b, structure=struct).astype(a.dtype)
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array([[ 0., 0., 1., 0., 0.],
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[ 0., 1., 1., 1., 0.],
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[ 1., 1., 1., 1., 1.],
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[ 0., 1., 1., 1., 0.],
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[ 0., 0., 1., 0., 0.]])
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>>> struct = ndimage.generate_binary_structure(2, 2)
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>>> struct
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array([[ True, True, True],
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[ True, True, True],
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[ True, True, True]], dtype=bool)
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>>> struct = ndimage.generate_binary_structure(3, 1)
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>>> struct # no diagonal elements
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array([[[False, False, False],
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[False, True, False],
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[False, False, False]],
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[[False, True, False],
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[ True, True, True],
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[False, True, False]],
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[[False, False, False],
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[False, True, False],
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[False, False, False]]], dtype=bool)
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"""
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if connectivity < 1:
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connectivity = 1
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if rank < 1:
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return numpy.array(True, dtype=bool)
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output = numpy.fabs(numpy.indices([3] * rank) - 1)
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output = numpy.add.reduce(output, 0)
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return output <= connectivity
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def _binary_erosion(input, structure, iterations, mask, output,
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border_value, origin, invert, brute_force):
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try:
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iterations = operator.index(iterations)
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except TypeError:
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raise TypeError('iterations parameter should be an integer')
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input = numpy.asarray(input)
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if numpy.iscomplexobj(input):
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raise TypeError('Complex type not supported')
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if structure is None:
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structure = generate_binary_structure(input.ndim, 1)
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else:
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structure = numpy.asarray(structure, dtype=bool)
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if structure.ndim != input.ndim:
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raise RuntimeError('structure and input must have same dimensionality')
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if not structure.flags.contiguous:
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structure = structure.copy()
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if numpy.prod(structure.shape, axis=0) < 1:
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raise RuntimeError('structure must not be empty')
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if mask is not None:
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mask = numpy.asarray(mask)
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if mask.shape != input.shape:
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raise RuntimeError('mask and input must have equal sizes')
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origin = _ni_support._normalize_sequence(origin, input.ndim)
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cit = _center_is_true(structure, origin)
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if isinstance(output, numpy.ndarray):
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if numpy.iscomplexobj(output):
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raise TypeError('Complex output type not supported')
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else:
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output = bool
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output = _ni_support._get_output(output, input)
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if iterations == 1:
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_nd_image.binary_erosion(input, structure, mask, output,
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border_value, origin, invert, cit, 0)
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return output
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elif cit and not brute_force:
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changed, coordinate_list = _nd_image.binary_erosion(
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input, structure, mask, output,
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border_value, origin, invert, cit, 1)
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structure = structure[tuple([slice(None, None, -1)] *
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structure.ndim)]
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for ii in range(len(origin)):
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origin[ii] = -origin[ii]
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if not structure.shape[ii] & 1:
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origin[ii] -= 1
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if mask is not None:
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mask = numpy.asarray(mask, dtype=numpy.int8)
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if not structure.flags.contiguous:
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structure = structure.copy()
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_nd_image.binary_erosion2(output, structure, mask, iterations - 1,
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origin, invert, coordinate_list)
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return output
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else:
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tmp_in = numpy.empty_like(input, dtype=bool)
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tmp_out = output
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if iterations >= 1 and not iterations & 1:
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tmp_in, tmp_out = tmp_out, tmp_in
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changed = _nd_image.binary_erosion(
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input, structure, mask, tmp_out,
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border_value, origin, invert, cit, 0)
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ii = 1
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while ii < iterations or (iterations < 1 and changed):
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tmp_in, tmp_out = tmp_out, tmp_in
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changed = _nd_image.binary_erosion(
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tmp_in, structure, mask, tmp_out,
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border_value, origin, invert, cit, 0)
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ii += 1
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return output
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def binary_erosion(input, structure=None, iterations=1, mask=None, output=None,
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border_value=0, origin=0, brute_force=False):
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"""
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Multi-dimensional binary erosion with a given structuring element.
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Binary erosion is a mathematical morphology operation used for image
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processing.
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Parameters
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----------
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input : array_like
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Binary image to be eroded. Non-zero (True) elements form
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the subset to be eroded.
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structure : array_like, optional
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Structuring element used for the erosion. Non-zero elements are
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considered True. If no structuring element is provided, an element
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is generated with a square connectivity equal to one.
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iterations : int, optional
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The erosion is repeated `iterations` times (one, by default).
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If iterations is less than 1, the erosion is repeated until the
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result does not change anymore.
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mask : array_like, optional
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If a mask is given, only those elements with a True value at
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the corresponding mask element are modified at each iteration.
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output : ndarray, optional
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Array of the same shape as input, into which the output is placed.
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By default, a new array is created.
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border_value : int (cast to 0 or 1), optional
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Value at the border in the output array.
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origin : int or tuple of ints, optional
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Placement of the filter, by default 0.
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brute_force : boolean, optional
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Memory condition: if False, only the pixels whose value was changed in
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the last iteration are tracked as candidates to be updated (eroded) in
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the current iteration; if True all pixels are considered as candidates
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for erosion, regardless of what happened in the previous iteration.
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False by default.
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Returns
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-------
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binary_erosion : ndarray of bools
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Erosion of the input by the structuring element.
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See also
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--------
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grey_erosion, binary_dilation, binary_closing, binary_opening,
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generate_binary_structure
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Notes
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-----
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Erosion [1]_ is a mathematical morphology operation [2]_ that uses a
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structuring element for shrinking the shapes in an image. The binary
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erosion of an image by a structuring element is the locus of the points
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where a superimposition of the structuring element centered on the point
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is entirely contained in the set of non-zero elements of the image.
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References
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----------
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.. [1] https://en.wikipedia.org/wiki/Erosion_%28morphology%29
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.. [2] https://en.wikipedia.org/wiki/Mathematical_morphology
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Examples
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--------
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>>> from scipy import ndimage
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>>> a = np.zeros((7,7), dtype=int)
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>>> a[1:6, 2:5] = 1
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>>> a
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array([[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 0, 0],
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[0, 0, 1, 1, 1, 0, 0],
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[0, 0, 0, 0, 0, 0, 0]])
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>>> ndimage.binary_erosion(a).astype(a.dtype)
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array([[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 1, 0, 0, 0],
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[0, 0, 0, 1, 0, 0, 0],
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[0, 0, 0, 1, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0]])
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>>> #Erosion removes objects smaller than the structure
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>>> ndimage.binary_erosion(a, structure=np.ones((5,5))).astype(a.dtype)
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array([[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0]])
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"""
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return _binary_erosion(input, structure, iterations, mask,
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output, border_value, origin, 0, brute_force)
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def binary_dilation(input, structure=None, iterations=1, mask=None,
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output=None, border_value=0, origin=0,
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brute_force=False):
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"""
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Multi-dimensional binary dilation with the given structuring element.
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Parameters
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----------
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input : array_like
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Binary array_like to be dilated. Non-zero (True) elements form
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the subset to be dilated.
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structure : array_like, optional
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Structuring element used for the dilation. Non-zero elements are
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considered True. If no structuring element is provided an element
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is generated with a square connectivity equal to one.
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iterations : int, optional
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The dilation is repeated `iterations` times (one, by default).
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If iterations is less than 1, the dilation is repeated until the
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result does not change anymore. Only an integer of iterations is
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accepted.
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mask : array_like, optional
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If a mask is given, only those elements with a True value at
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the corresponding mask element are modified at each iteration.
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output : ndarray, optional
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Array of the same shape as input, into which the output is placed.
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By default, a new array is created.
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border_value : int (cast to 0 or 1), optional
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Value at the border in the output array.
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origin : int or tuple of ints, optional
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Placement of the filter, by default 0.
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brute_force : boolean, optional
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Memory condition: if False, only the pixels whose value was changed in
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the last iteration are tracked as candidates to be updated (dilated)
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in the current iteration; if True all pixels are considered as
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candidates for dilation, regardless of what happened in the previous
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iteration. False by default.
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Returns
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-------
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binary_dilation : ndarray of bools
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Dilation of the input by the structuring element.
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See also
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--------
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grey_dilation, binary_erosion, binary_closing, binary_opening,
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generate_binary_structure
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Notes
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-----
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Dilation [1]_ is a mathematical morphology operation [2]_ that uses a
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structuring element for expanding the shapes in an image. The binary
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dilation of an image by a structuring element is the locus of the points
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covered by the structuring element, when its center lies within the
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non-zero points of the image.
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References
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----------
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.. [1] https://en.wikipedia.org/wiki/Dilation_%28morphology%29
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.. [2] https://en.wikipedia.org/wiki/Mathematical_morphology
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Examples
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--------
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|
>>> from scipy import ndimage
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>>> a = np.zeros((5, 5))
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>>> a[2, 2] = 1
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>>> a
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array([[ 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0.],
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[ 0., 0., 1., 0., 0.],
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[ 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0.]])
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>>> ndimage.binary_dilation(a)
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array([[False, False, False, False, False],
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[False, False, True, False, False],
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[False, True, True, True, False],
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[False, False, True, False, False],
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[False, False, False, False, False]], dtype=bool)
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>>> ndimage.binary_dilation(a).astype(a.dtype)
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array([[ 0., 0., 0., 0., 0.],
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[ 0., 0., 1., 0., 0.],
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[ 0., 1., 1., 1., 0.],
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[ 0., 0., 1., 0., 0.],
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[ 0., 0., 0., 0., 0.]])
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>>> # 3x3 structuring element with connectivity 1, used by default
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>>> struct1 = ndimage.generate_binary_structure(2, 1)
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>>> struct1
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array([[False, True, False],
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[ True, True, True],
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[False, True, False]], dtype=bool)
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>>> # 3x3 structuring element with connectivity 2
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>>> struct2 = ndimage.generate_binary_structure(2, 2)
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>>> struct2
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array([[ True, True, True],
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[ True, True, True],
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[ True, True, True]], dtype=bool)
|
|
>>> ndimage.binary_dilation(a, structure=struct1).astype(a.dtype)
|
|
array([[ 0., 0., 0., 0., 0.],
|
|
[ 0., 0., 1., 0., 0.],
|
|
[ 0., 1., 1., 1., 0.],
|
|
[ 0., 0., 1., 0., 0.],
|
|
[ 0., 0., 0., 0., 0.]])
|
|
>>> ndimage.binary_dilation(a, structure=struct2).astype(a.dtype)
|
|
array([[ 0., 0., 0., 0., 0.],
|
|
[ 0., 1., 1., 1., 0.],
|
|
[ 0., 1., 1., 1., 0.],
|
|
[ 0., 1., 1., 1., 0.],
|
|
[ 0., 0., 0., 0., 0.]])
|
|
>>> ndimage.binary_dilation(a, structure=struct1,\\
|
|
... iterations=2).astype(a.dtype)
|
|
array([[ 0., 0., 1., 0., 0.],
|
|
[ 0., 1., 1., 1., 0.],
|
|
[ 1., 1., 1., 1., 1.],
|
|
[ 0., 1., 1., 1., 0.],
|
|
[ 0., 0., 1., 0., 0.]])
|
|
|
|
"""
|
|
input = numpy.asarray(input)
|
|
if structure is None:
|
|
structure = generate_binary_structure(input.ndim, 1)
|
|
origin = _ni_support._normalize_sequence(origin, input.ndim)
|
|
structure = numpy.asarray(structure)
|
|
structure = structure[tuple([slice(None, None, -1)] *
|
|
structure.ndim)]
|
|
for ii in range(len(origin)):
|
|
origin[ii] = -origin[ii]
|
|
if not structure.shape[ii] & 1:
|
|
origin[ii] -= 1
|
|
|
|
return _binary_erosion(input, structure, iterations, mask,
|
|
output, border_value, origin, 1, brute_force)
|
|
|
|
|
|
def binary_opening(input, structure=None, iterations=1, output=None,
|
|
origin=0, mask=None, border_value=0, brute_force=False):
|
|
"""
|
|
Multi-dimensional binary opening with the given structuring element.
|
|
|
|
The *opening* of an input image by a structuring element is the
|
|
*dilation* of the *erosion* of the image by the structuring element.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Binary array_like to be opened. Non-zero (True) elements form
|
|
the subset to be opened.
|
|
structure : array_like, optional
|
|
Structuring element used for the opening. Non-zero elements are
|
|
considered True. If no structuring element is provided an element
|
|
is generated with a square connectivity equal to one (i.e., only
|
|
nearest neighbors are connected to the center, diagonally-connected
|
|
elements are not considered neighbors).
|
|
iterations : int, optional
|
|
The erosion step of the opening, then the dilation step are each
|
|
repeated `iterations` times (one, by default). If `iterations` is
|
|
less than 1, each operation is repeated until the result does
|
|
not change anymore. Only an integer of iterations is accepted.
|
|
output : ndarray, optional
|
|
Array of the same shape as input, into which the output is placed.
|
|
By default, a new array is created.
|
|
origin : int or tuple of ints, optional
|
|
Placement of the filter, by default 0.
|
|
mask : array_like, optional
|
|
If a mask is given, only those elements with a True value at
|
|
the corresponding mask element are modified at each iteration.
|
|
|
|
.. versionadded:: 1.1.0
|
|
border_value : int (cast to 0 or 1), optional
|
|
Value at the border in the output array.
|
|
|
|
.. versionadded:: 1.1.0
|
|
brute_force : boolean, optional
|
|
Memory condition: if False, only the pixels whose value was changed in
|
|
the last iteration are tracked as candidates to be updated in the
|
|
current iteration; if true all pixels are considered as candidates for
|
|
update, regardless of what happened in the previous iteration.
|
|
False by default.
|
|
|
|
.. versionadded:: 1.1.0
|
|
|
|
Returns
|
|
-------
|
|
binary_opening : ndarray of bools
|
|
Opening of the input by the structuring element.
|
|
|
|
See also
|
|
--------
|
|
grey_opening, binary_closing, binary_erosion, binary_dilation,
|
|
generate_binary_structure
|
|
|
|
Notes
|
|
-----
|
|
*Opening* [1]_ is a mathematical morphology operation [2]_ that
|
|
consists in the succession of an erosion and a dilation of the
|
|
input with the same structuring element. Opening therefore removes
|
|
objects smaller than the structuring element.
|
|
|
|
Together with *closing* (`binary_closing`), opening can be used for
|
|
noise removal.
|
|
|
|
References
|
|
----------
|
|
.. [1] https://en.wikipedia.org/wiki/Opening_%28morphology%29
|
|
.. [2] https://en.wikipedia.org/wiki/Mathematical_morphology
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy import ndimage
|
|
>>> a = np.zeros((5,5), dtype=int)
|
|
>>> a[1:4, 1:4] = 1; a[4, 4] = 1
|
|
>>> a
|
|
array([[0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 0, 0, 0, 1]])
|
|
>>> # Opening removes small objects
|
|
>>> ndimage.binary_opening(a, structure=np.ones((3,3))).astype(int)
|
|
array([[0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 0, 0, 0, 0]])
|
|
>>> # Opening can also smooth corners
|
|
>>> ndimage.binary_opening(a).astype(int)
|
|
array([[0, 0, 0, 0, 0],
|
|
[0, 0, 1, 0, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 0, 1, 0, 0],
|
|
[0, 0, 0, 0, 0]])
|
|
>>> # Opening is the dilation of the erosion of the input
|
|
>>> ndimage.binary_erosion(a).astype(int)
|
|
array([[0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0],
|
|
[0, 0, 1, 0, 0],
|
|
[0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0]])
|
|
>>> ndimage.binary_dilation(ndimage.binary_erosion(a)).astype(int)
|
|
array([[0, 0, 0, 0, 0],
|
|
[0, 0, 1, 0, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 0, 1, 0, 0],
|
|
[0, 0, 0, 0, 0]])
|
|
|
|
"""
|
|
input = numpy.asarray(input)
|
|
if structure is None:
|
|
rank = input.ndim
|
|
structure = generate_binary_structure(rank, 1)
|
|
|
|
tmp = binary_erosion(input, structure, iterations, mask, None,
|
|
border_value, origin, brute_force)
|
|
return binary_dilation(tmp, structure, iterations, mask, output,
|
|
border_value, origin, brute_force)
|
|
|
|
|
|
def binary_closing(input, structure=None, iterations=1, output=None,
|
|
origin=0, mask=None, border_value=0, brute_force=False):
|
|
"""
|
|
Multi-dimensional binary closing with the given structuring element.
|
|
|
|
The *closing* of an input image by a structuring element is the
|
|
*erosion* of the *dilation* of the image by the structuring element.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Binary array_like to be closed. Non-zero (True) elements form
|
|
the subset to be closed.
|
|
structure : array_like, optional
|
|
Structuring element used for the closing. Non-zero elements are
|
|
considered True. If no structuring element is provided an element
|
|
is generated with a square connectivity equal to one (i.e., only
|
|
nearest neighbors are connected to the center, diagonally-connected
|
|
elements are not considered neighbors).
|
|
iterations : int, optional
|
|
The dilation step of the closing, then the erosion step are each
|
|
repeated `iterations` times (one, by default). If iterations is
|
|
less than 1, each operations is repeated until the result does
|
|
not change anymore. Only an integer of iterations is accepted.
|
|
output : ndarray, optional
|
|
Array of the same shape as input, into which the output is placed.
|
|
By default, a new array is created.
|
|
origin : int or tuple of ints, optional
|
|
Placement of the filter, by default 0.
|
|
mask : array_like, optional
|
|
If a mask is given, only those elements with a True value at
|
|
the corresponding mask element are modified at each iteration.
|
|
|
|
.. versionadded:: 1.1.0
|
|
border_value : int (cast to 0 or 1), optional
|
|
Value at the border in the output array.
|
|
|
|
.. versionadded:: 1.1.0
|
|
brute_force : boolean, optional
|
|
Memory condition: if False, only the pixels whose value was changed in
|
|
the last iteration are tracked as candidates to be updated in the
|
|
current iteration; if true al pixels are considered as candidates for
|
|
update, regardless of what happened in the previous iteration.
|
|
False by default.
|
|
|
|
.. versionadded:: 1.1.0
|
|
|
|
Returns
|
|
-------
|
|
binary_closing : ndarray of bools
|
|
Closing of the input by the structuring element.
|
|
|
|
See also
|
|
--------
|
|
grey_closing, binary_opening, binary_dilation, binary_erosion,
|
|
generate_binary_structure
|
|
|
|
Notes
|
|
-----
|
|
*Closing* [1]_ is a mathematical morphology operation [2]_ that
|
|
consists in the succession of a dilation and an erosion of the
|
|
input with the same structuring element. Closing therefore fills
|
|
holes smaller than the structuring element.
|
|
|
|
Together with *opening* (`binary_opening`), closing can be used for
|
|
noise removal.
|
|
|
|
References
|
|
----------
|
|
.. [1] https://en.wikipedia.org/wiki/Closing_%28morphology%29
|
|
.. [2] https://en.wikipedia.org/wiki/Mathematical_morphology
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy import ndimage
|
|
>>> a = np.zeros((5,5), dtype=int)
|
|
>>> a[1:-1, 1:-1] = 1; a[2,2] = 0
|
|
>>> a
|
|
array([[0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 0, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 0, 0, 0, 0]])
|
|
>>> # Closing removes small holes
|
|
>>> ndimage.binary_closing(a).astype(int)
|
|
array([[0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 0, 0, 0, 0]])
|
|
>>> # Closing is the erosion of the dilation of the input
|
|
>>> ndimage.binary_dilation(a).astype(int)
|
|
array([[0, 1, 1, 1, 0],
|
|
[1, 1, 1, 1, 1],
|
|
[1, 1, 1, 1, 1],
|
|
[1, 1, 1, 1, 1],
|
|
[0, 1, 1, 1, 0]])
|
|
>>> ndimage.binary_erosion(ndimage.binary_dilation(a)).astype(int)
|
|
array([[0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 0, 0, 0, 0]])
|
|
|
|
|
|
>>> a = np.zeros((7,7), dtype=int)
|
|
>>> a[1:6, 2:5] = 1; a[1:3,3] = 0
|
|
>>> a
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 0, 1, 0, 0],
|
|
[0, 0, 1, 0, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> # In addition to removing holes, closing can also
|
|
>>> # coarsen boundaries with fine hollows.
|
|
>>> ndimage.binary_closing(a).astype(int)
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 0, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> ndimage.binary_closing(a, structure=np.ones((2,2))).astype(int)
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
|
|
"""
|
|
input = numpy.asarray(input)
|
|
if structure is None:
|
|
rank = input.ndim
|
|
structure = generate_binary_structure(rank, 1)
|
|
|
|
tmp = binary_dilation(input, structure, iterations, mask, None,
|
|
border_value, origin, brute_force)
|
|
return binary_erosion(tmp, structure, iterations, mask, output,
|
|
border_value, origin, brute_force)
|
|
|
|
|
|
def binary_hit_or_miss(input, structure1=None, structure2=None,
|
|
output=None, origin1=0, origin2=None):
|
|
"""
|
|
Multi-dimensional binary hit-or-miss transform.
|
|
|
|
The hit-or-miss transform finds the locations of a given pattern
|
|
inside the input image.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like (cast to booleans)
|
|
Binary image where a pattern is to be detected.
|
|
structure1 : array_like (cast to booleans), optional
|
|
Part of the structuring element to be fitted to the foreground
|
|
(non-zero elements) of `input`. If no value is provided, a
|
|
structure of square connectivity 1 is chosen.
|
|
structure2 : array_like (cast to booleans), optional
|
|
Second part of the structuring element that has to miss completely
|
|
the foreground. If no value is provided, the complementary of
|
|
`structure1` is taken.
|
|
output : ndarray, optional
|
|
Array of the same shape as input, into which the output is placed.
|
|
By default, a new array is created.
|
|
origin1 : int or tuple of ints, optional
|
|
Placement of the first part of the structuring element `structure1`,
|
|
by default 0 for a centered structure.
|
|
origin2 : int or tuple of ints, optional
|
|
Placement of the second part of the structuring element `structure2`,
|
|
by default 0 for a centered structure. If a value is provided for
|
|
`origin1` and not for `origin2`, then `origin2` is set to `origin1`.
|
|
|
|
Returns
|
|
-------
|
|
binary_hit_or_miss : ndarray
|
|
Hit-or-miss transform of `input` with the given structuring
|
|
element (`structure1`, `structure2`).
|
|
|
|
See also
|
|
--------
|
|
binary_erosion
|
|
|
|
References
|
|
----------
|
|
.. [1] https://en.wikipedia.org/wiki/Hit-or-miss_transform
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy import ndimage
|
|
>>> a = np.zeros((7,7), dtype=int)
|
|
>>> a[1, 1] = 1; a[2:4, 2:4] = 1; a[4:6, 4:6] = 1
|
|
>>> a
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 1, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 1, 0, 0, 0],
|
|
[0, 0, 1, 1, 0, 0, 0],
|
|
[0, 0, 0, 0, 1, 1, 0],
|
|
[0, 0, 0, 0, 1, 1, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> structure1 = np.array([[1, 0, 0], [0, 1, 1], [0, 1, 1]])
|
|
>>> structure1
|
|
array([[1, 0, 0],
|
|
[0, 1, 1],
|
|
[0, 1, 1]])
|
|
>>> # Find the matches of structure1 in the array a
|
|
>>> ndimage.binary_hit_or_miss(a, structure1=structure1).astype(int)
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 1, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> # Change the origin of the filter
|
|
>>> # origin1=1 is equivalent to origin1=(1,1) here
|
|
>>> ndimage.binary_hit_or_miss(a, structure1=structure1,\\
|
|
... origin1=1).astype(int)
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 1, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 1, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
|
|
"""
|
|
input = numpy.asarray(input)
|
|
if structure1 is None:
|
|
structure1 = generate_binary_structure(input.ndim, 1)
|
|
if structure2 is None:
|
|
structure2 = numpy.logical_not(structure1)
|
|
origin1 = _ni_support._normalize_sequence(origin1, input.ndim)
|
|
if origin2 is None:
|
|
origin2 = origin1
|
|
else:
|
|
origin2 = _ni_support._normalize_sequence(origin2, input.ndim)
|
|
|
|
tmp1 = _binary_erosion(input, structure1, 1, None, None, 0, origin1,
|
|
0, False)
|
|
inplace = isinstance(output, numpy.ndarray)
|
|
result = _binary_erosion(input, structure2, 1, None, output, 0,
|
|
origin2, 1, False)
|
|
if inplace:
|
|
numpy.logical_not(output, output)
|
|
numpy.logical_and(tmp1, output, output)
|
|
else:
|
|
numpy.logical_not(result, result)
|
|
return numpy.logical_and(tmp1, result)
|
|
|
|
|
|
def binary_propagation(input, structure=None, mask=None,
|
|
output=None, border_value=0, origin=0):
|
|
"""
|
|
Multi-dimensional binary propagation with the given structuring element.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Binary image to be propagated inside `mask`.
|
|
structure : array_like, optional
|
|
Structuring element used in the successive dilations. The output
|
|
may depend on the structuring element, especially if `mask` has
|
|
several connex components. If no structuring element is
|
|
provided, an element is generated with a squared connectivity equal
|
|
to one.
|
|
mask : array_like, optional
|
|
Binary mask defining the region into which `input` is allowed to
|
|
propagate.
|
|
output : ndarray, optional
|
|
Array of the same shape as input, into which the output is placed.
|
|
By default, a new array is created.
|
|
border_value : int (cast to 0 or 1), optional
|
|
Value at the border in the output array.
|
|
origin : int or tuple of ints, optional
|
|
Placement of the filter, by default 0.
|
|
|
|
Returns
|
|
-------
|
|
binary_propagation : ndarray
|
|
Binary propagation of `input` inside `mask`.
|
|
|
|
Notes
|
|
-----
|
|
This function is functionally equivalent to calling binary_dilation
|
|
with the number of iterations less than one: iterative dilation until
|
|
the result does not change anymore.
|
|
|
|
The succession of an erosion and propagation inside the original image
|
|
can be used instead of an *opening* for deleting small objects while
|
|
keeping the contours of larger objects untouched.
|
|
|
|
References
|
|
----------
|
|
.. [1] http://cmm.ensmp.fr/~serra/cours/pdf/en/ch6en.pdf, slide 15.
|
|
.. [2] I.T. Young, J.J. Gerbrands, and L.J. van Vliet, "Fundamentals of
|
|
image processing", 1998
|
|
ftp://qiftp.tudelft.nl/DIPimage/docs/FIP2.3.pdf
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy import ndimage
|
|
>>> input = np.zeros((8, 8), dtype=int)
|
|
>>> input[2, 2] = 1
|
|
>>> mask = np.zeros((8, 8), dtype=int)
|
|
>>> mask[1:4, 1:4] = mask[4, 4] = mask[6:8, 6:8] = 1
|
|
>>> input
|
|
array([[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0]])
|
|
>>> mask
|
|
array([[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 1, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 1, 1],
|
|
[0, 0, 0, 0, 0, 0, 1, 1]])
|
|
>>> ndimage.binary_propagation(input, mask=mask).astype(int)
|
|
array([[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0]])
|
|
>>> ndimage.binary_propagation(input, mask=mask,\\
|
|
... structure=np.ones((3,3))).astype(int)
|
|
array([[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 1, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0, 0]])
|
|
|
|
>>> # Comparison between opening and erosion+propagation
|
|
>>> a = np.zeros((6,6), dtype=int)
|
|
>>> a[2:5, 2:5] = 1; a[0, 0] = 1; a[5, 5] = 1
|
|
>>> a
|
|
array([[1, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 1, 1, 0],
|
|
[0, 0, 1, 1, 1, 0],
|
|
[0, 0, 1, 1, 1, 0],
|
|
[0, 0, 0, 0, 0, 1]])
|
|
>>> ndimage.binary_opening(a).astype(int)
|
|
array([[0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0],
|
|
[0, 0, 0, 1, 0, 0],
|
|
[0, 0, 0, 0, 0, 0]])
|
|
>>> b = ndimage.binary_erosion(a)
|
|
>>> b.astype(int)
|
|
array([[0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 1, 0, 0],
|
|
[0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0]])
|
|
>>> ndimage.binary_propagation(b, mask=a).astype(int)
|
|
array([[0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 1, 1, 0],
|
|
[0, 0, 1, 1, 1, 0],
|
|
[0, 0, 1, 1, 1, 0],
|
|
[0, 0, 0, 0, 0, 0]])
|
|
|
|
"""
|
|
return binary_dilation(input, structure, -1, mask, output,
|
|
border_value, origin)
|
|
|
|
|
|
def binary_fill_holes(input, structure=None, output=None, origin=0):
|
|
"""
|
|
Fill the holes in binary objects.
|
|
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
n-dimensional binary array with holes to be filled
|
|
structure : array_like, optional
|
|
Structuring element used in the computation; large-size elements
|
|
make computations faster but may miss holes separated from the
|
|
background by thin regions. The default element (with a square
|
|
connectivity equal to one) yields the intuitive result where all
|
|
holes in the input have been filled.
|
|
output : ndarray, optional
|
|
Array of the same shape as input, into which the output is placed.
|
|
By default, a new array is created.
|
|
origin : int, tuple of ints, optional
|
|
Position of the structuring element.
|
|
|
|
Returns
|
|
-------
|
|
out : ndarray
|
|
Transformation of the initial image `input` where holes have been
|
|
filled.
|
|
|
|
See also
|
|
--------
|
|
binary_dilation, binary_propagation, label
|
|
|
|
Notes
|
|
-----
|
|
The algorithm used in this function consists in invading the complementary
|
|
of the shapes in `input` from the outer boundary of the image,
|
|
using binary dilations. Holes are not connected to the boundary and are
|
|
therefore not invaded. The result is the complementary subset of the
|
|
invaded region.
|
|
|
|
References
|
|
----------
|
|
.. [1] https://en.wikipedia.org/wiki/Mathematical_morphology
|
|
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy import ndimage
|
|
>>> a = np.zeros((5, 5), dtype=int)
|
|
>>> a[1:4, 1:4] = 1
|
|
>>> a[2,2] = 0
|
|
>>> a
|
|
array([[0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 0, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 0, 0, 0, 0]])
|
|
>>> ndimage.binary_fill_holes(a).astype(int)
|
|
array([[0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 0, 0, 0, 0]])
|
|
>>> # Too big structuring element
|
|
>>> ndimage.binary_fill_holes(a, structure=np.ones((5,5))).astype(int)
|
|
array([[0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 1, 0, 1, 0],
|
|
[0, 1, 1, 1, 0],
|
|
[0, 0, 0, 0, 0]])
|
|
|
|
"""
|
|
mask = numpy.logical_not(input)
|
|
tmp = numpy.zeros(mask.shape, bool)
|
|
inplace = isinstance(output, numpy.ndarray)
|
|
if inplace:
|
|
binary_dilation(tmp, structure, -1, mask, output, 1, origin)
|
|
numpy.logical_not(output, output)
|
|
else:
|
|
output = binary_dilation(tmp, structure, -1, mask, None, 1,
|
|
origin)
|
|
numpy.logical_not(output, output)
|
|
return output
|
|
|
|
|
|
def grey_erosion(input, size=None, footprint=None, structure=None,
|
|
output=None, mode="reflect", cval=0.0, origin=0):
|
|
"""
|
|
Calculate a greyscale erosion, using either a structuring element,
|
|
or a footprint corresponding to a flat structuring element.
|
|
|
|
Grayscale erosion is a mathematical morphology operation. For the
|
|
simple case of a full and flat structuring element, it can be viewed
|
|
as a minimum filter over a sliding window.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Array over which the grayscale erosion is to be computed.
|
|
size : tuple of ints
|
|
Shape of a flat and full structuring element used for the grayscale
|
|
erosion. Optional if `footprint` or `structure` is provided.
|
|
footprint : array of ints, optional
|
|
Positions of non-infinite elements of a flat structuring element
|
|
used for the grayscale erosion. Non-zero values give the set of
|
|
neighbors of the center over which the minimum is chosen.
|
|
structure : array of ints, optional
|
|
Structuring element used for the grayscale erosion. `structure`
|
|
may be a non-flat structuring element.
|
|
output : array, optional
|
|
An array used for storing the output of the erosion may be provided.
|
|
mode : {'reflect','constant','nearest','mirror', 'wrap'}, optional
|
|
The `mode` parameter determines how the array borders are
|
|
handled, where `cval` is the value when mode is equal to
|
|
'constant'. Default is 'reflect'
|
|
cval : scalar, optional
|
|
Value to fill past edges of input if `mode` is 'constant'. Default
|
|
is 0.0.
|
|
origin : scalar, optional
|
|
The `origin` parameter controls the placement of the filter.
|
|
Default 0
|
|
|
|
Returns
|
|
-------
|
|
output : ndarray
|
|
Grayscale erosion of `input`.
|
|
|
|
See also
|
|
--------
|
|
binary_erosion, grey_dilation, grey_opening, grey_closing
|
|
generate_binary_structure, minimum_filter
|
|
|
|
Notes
|
|
-----
|
|
The grayscale erosion of an image input by a structuring element s defined
|
|
over a domain E is given by:
|
|
|
|
(input+s)(x) = min {input(y) - s(x-y), for y in E}
|
|
|
|
In particular, for structuring elements defined as
|
|
s(y) = 0 for y in E, the grayscale erosion computes the minimum of the
|
|
input image inside a sliding window defined by E.
|
|
|
|
Grayscale erosion [1]_ is a *mathematical morphology* operation [2]_.
|
|
|
|
References
|
|
----------
|
|
.. [1] https://en.wikipedia.org/wiki/Erosion_%28morphology%29
|
|
.. [2] https://en.wikipedia.org/wiki/Mathematical_morphology
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy import ndimage
|
|
>>> a = np.zeros((7,7), dtype=int)
|
|
>>> a[1:6, 1:6] = 3
|
|
>>> a[4,4] = 2; a[2,3] = 1
|
|
>>> a
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 3, 3, 3, 3, 3, 0],
|
|
[0, 3, 3, 1, 3, 3, 0],
|
|
[0, 3, 3, 3, 3, 3, 0],
|
|
[0, 3, 3, 3, 2, 3, 0],
|
|
[0, 3, 3, 3, 3, 3, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> ndimage.grey_erosion(a, size=(3,3))
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 3, 2, 2, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> footprint = ndimage.generate_binary_structure(2, 1)
|
|
>>> footprint
|
|
array([[False, True, False],
|
|
[ True, True, True],
|
|
[False, True, False]], dtype=bool)
|
|
>>> # Diagonally-connected elements are not considered neighbors
|
|
>>> ndimage.grey_erosion(a, size=(3,3), footprint=footprint)
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 3, 1, 2, 0, 0],
|
|
[0, 0, 3, 2, 2, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
|
|
"""
|
|
if size is None and footprint is None and structure is None:
|
|
raise ValueError("size, footprint or structure must be specified")
|
|
|
|
return filters._min_or_max_filter(input, size, footprint, structure,
|
|
output, mode, cval, origin, 1)
|
|
|
|
|
|
def grey_dilation(input, size=None, footprint=None, structure=None,
|
|
output=None, mode="reflect", cval=0.0, origin=0):
|
|
"""
|
|
Calculate a greyscale dilation, using either a structuring element,
|
|
or a footprint corresponding to a flat structuring element.
|
|
|
|
Grayscale dilation is a mathematical morphology operation. For the
|
|
simple case of a full and flat structuring element, it can be viewed
|
|
as a maximum filter over a sliding window.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Array over which the grayscale dilation is to be computed.
|
|
size : tuple of ints
|
|
Shape of a flat and full structuring element used for the grayscale
|
|
dilation. Optional if `footprint` or `structure` is provided.
|
|
footprint : array of ints, optional
|
|
Positions of non-infinite elements of a flat structuring element
|
|
used for the grayscale dilation. Non-zero values give the set of
|
|
neighbors of the center over which the maximum is chosen.
|
|
structure : array of ints, optional
|
|
Structuring element used for the grayscale dilation. `structure`
|
|
may be a non-flat structuring element.
|
|
output : array, optional
|
|
An array used for storing the output of the dilation may be provided.
|
|
mode : {'reflect','constant','nearest','mirror', 'wrap'}, optional
|
|
The `mode` parameter determines how the array borders are
|
|
handled, where `cval` is the value when mode is equal to
|
|
'constant'. Default is 'reflect'
|
|
cval : scalar, optional
|
|
Value to fill past edges of input if `mode` is 'constant'. Default
|
|
is 0.0.
|
|
origin : scalar, optional
|
|
The `origin` parameter controls the placement of the filter.
|
|
Default 0
|
|
|
|
Returns
|
|
-------
|
|
grey_dilation : ndarray
|
|
Grayscale dilation of `input`.
|
|
|
|
See also
|
|
--------
|
|
binary_dilation, grey_erosion, grey_closing, grey_opening
|
|
generate_binary_structure, maximum_filter
|
|
|
|
Notes
|
|
-----
|
|
The grayscale dilation of an image input by a structuring element s defined
|
|
over a domain E is given by:
|
|
|
|
(input+s)(x) = max {input(y) + s(x-y), for y in E}
|
|
|
|
In particular, for structuring elements defined as
|
|
s(y) = 0 for y in E, the grayscale dilation computes the maximum of the
|
|
input image inside a sliding window defined by E.
|
|
|
|
Grayscale dilation [1]_ is a *mathematical morphology* operation [2]_.
|
|
|
|
References
|
|
----------
|
|
.. [1] https://en.wikipedia.org/wiki/Dilation_%28morphology%29
|
|
.. [2] https://en.wikipedia.org/wiki/Mathematical_morphology
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy import ndimage
|
|
>>> a = np.zeros((7,7), dtype=int)
|
|
>>> a[2:5, 2:5] = 1
|
|
>>> a[4,4] = 2; a[2,3] = 3
|
|
>>> a
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 3, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 1, 1, 2, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> ndimage.grey_dilation(a, size=(3,3))
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 1, 3, 3, 3, 1, 0],
|
|
[0, 1, 3, 3, 3, 1, 0],
|
|
[0, 1, 3, 3, 3, 2, 0],
|
|
[0, 1, 1, 2, 2, 2, 0],
|
|
[0, 1, 1, 2, 2, 2, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> ndimage.grey_dilation(a, footprint=np.ones((3,3)))
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 1, 3, 3, 3, 1, 0],
|
|
[0, 1, 3, 3, 3, 1, 0],
|
|
[0, 1, 3, 3, 3, 2, 0],
|
|
[0, 1, 1, 2, 2, 2, 0],
|
|
[0, 1, 1, 2, 2, 2, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> s = ndimage.generate_binary_structure(2,1)
|
|
>>> s
|
|
array([[False, True, False],
|
|
[ True, True, True],
|
|
[False, True, False]], dtype=bool)
|
|
>>> ndimage.grey_dilation(a, footprint=s)
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 3, 1, 0, 0],
|
|
[0, 1, 3, 3, 3, 1, 0],
|
|
[0, 1, 1, 3, 2, 1, 0],
|
|
[0, 1, 1, 2, 2, 2, 0],
|
|
[0, 0, 1, 1, 2, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> ndimage.grey_dilation(a, size=(3,3), structure=np.ones((3,3)))
|
|
array([[1, 1, 1, 1, 1, 1, 1],
|
|
[1, 2, 4, 4, 4, 2, 1],
|
|
[1, 2, 4, 4, 4, 2, 1],
|
|
[1, 2, 4, 4, 4, 3, 1],
|
|
[1, 2, 2, 3, 3, 3, 1],
|
|
[1, 2, 2, 3, 3, 3, 1],
|
|
[1, 1, 1, 1, 1, 1, 1]])
|
|
|
|
"""
|
|
if size is None and footprint is None and structure is None:
|
|
raise ValueError("size, footprint or structure must be specified")
|
|
if structure is not None:
|
|
structure = numpy.asarray(structure)
|
|
structure = structure[tuple([slice(None, None, -1)] *
|
|
structure.ndim)]
|
|
if footprint is not None:
|
|
footprint = numpy.asarray(footprint)
|
|
footprint = footprint[tuple([slice(None, None, -1)] *
|
|
footprint.ndim)]
|
|
|
|
input = numpy.asarray(input)
|
|
origin = _ni_support._normalize_sequence(origin, input.ndim)
|
|
for ii in range(len(origin)):
|
|
origin[ii] = -origin[ii]
|
|
if footprint is not None:
|
|
sz = footprint.shape[ii]
|
|
elif structure is not None:
|
|
sz = structure.shape[ii]
|
|
elif numpy.isscalar(size):
|
|
sz = size
|
|
else:
|
|
sz = size[ii]
|
|
if not sz & 1:
|
|
origin[ii] -= 1
|
|
|
|
return filters._min_or_max_filter(input, size, footprint, structure,
|
|
output, mode, cval, origin, 0)
|
|
|
|
|
|
def grey_opening(input, size=None, footprint=None, structure=None,
|
|
output=None, mode="reflect", cval=0.0, origin=0):
|
|
"""
|
|
Multi-dimensional greyscale opening.
|
|
|
|
A greyscale opening consists in the succession of a greyscale erosion,
|
|
and a greyscale dilation.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Array over which the grayscale opening is to be computed.
|
|
size : tuple of ints
|
|
Shape of a flat and full structuring element used for the grayscale
|
|
opening. Optional if `footprint` or `structure` is provided.
|
|
footprint : array of ints, optional
|
|
Positions of non-infinite elements of a flat structuring element
|
|
used for the grayscale opening.
|
|
structure : array of ints, optional
|
|
Structuring element used for the grayscale opening. `structure`
|
|
may be a non-flat structuring element.
|
|
output : array, optional
|
|
An array used for storing the output of the opening may be provided.
|
|
mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
|
|
The `mode` parameter determines how the array borders are
|
|
handled, where `cval` is the value when mode is equal to
|
|
'constant'. Default is 'reflect'
|
|
cval : scalar, optional
|
|
Value to fill past edges of input if `mode` is 'constant'. Default
|
|
is 0.0.
|
|
origin : scalar, optional
|
|
The `origin` parameter controls the placement of the filter.
|
|
Default 0
|
|
|
|
Returns
|
|
-------
|
|
grey_opening : ndarray
|
|
Result of the grayscale opening of `input` with `structure`.
|
|
|
|
See also
|
|
--------
|
|
binary_opening, grey_dilation, grey_erosion, grey_closing
|
|
generate_binary_structure
|
|
|
|
Notes
|
|
-----
|
|
The action of a grayscale opening with a flat structuring element amounts
|
|
to smoothen high local maxima, whereas binary opening erases small objects.
|
|
|
|
References
|
|
----------
|
|
.. [1] https://en.wikipedia.org/wiki/Mathematical_morphology
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy import ndimage
|
|
>>> a = np.arange(36).reshape((6,6))
|
|
>>> a[3, 3] = 50
|
|
>>> a
|
|
array([[ 0, 1, 2, 3, 4, 5],
|
|
[ 6, 7, 8, 9, 10, 11],
|
|
[12, 13, 14, 15, 16, 17],
|
|
[18, 19, 20, 50, 22, 23],
|
|
[24, 25, 26, 27, 28, 29],
|
|
[30, 31, 32, 33, 34, 35]])
|
|
>>> ndimage.grey_opening(a, size=(3,3))
|
|
array([[ 0, 1, 2, 3, 4, 4],
|
|
[ 6, 7, 8, 9, 10, 10],
|
|
[12, 13, 14, 15, 16, 16],
|
|
[18, 19, 20, 22, 22, 22],
|
|
[24, 25, 26, 27, 28, 28],
|
|
[24, 25, 26, 27, 28, 28]])
|
|
>>> # Note that the local maximum a[3,3] has disappeared
|
|
|
|
"""
|
|
if (size is not None) and (footprint is not None):
|
|
warnings.warn("ignoring size because footprint is set", UserWarning, stacklevel=2)
|
|
tmp = grey_erosion(input, size, footprint, structure, None, mode,
|
|
cval, origin)
|
|
return grey_dilation(tmp, size, footprint, structure, output, mode,
|
|
cval, origin)
|
|
|
|
|
|
def grey_closing(input, size=None, footprint=None, structure=None,
|
|
output=None, mode="reflect", cval=0.0, origin=0):
|
|
"""
|
|
Multi-dimensional greyscale closing.
|
|
|
|
A greyscale closing consists in the succession of a greyscale dilation,
|
|
and a greyscale erosion.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Array over which the grayscale closing is to be computed.
|
|
size : tuple of ints
|
|
Shape of a flat and full structuring element used for the grayscale
|
|
closing. Optional if `footprint` or `structure` is provided.
|
|
footprint : array of ints, optional
|
|
Positions of non-infinite elements of a flat structuring element
|
|
used for the grayscale closing.
|
|
structure : array of ints, optional
|
|
Structuring element used for the grayscale closing. `structure`
|
|
may be a non-flat structuring element.
|
|
output : array, optional
|
|
An array used for storing the output of the closing may be provided.
|
|
mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
|
|
The `mode` parameter determines how the array borders are
|
|
handled, where `cval` is the value when mode is equal to
|
|
'constant'. Default is 'reflect'
|
|
cval : scalar, optional
|
|
Value to fill past edges of input if `mode` is 'constant'. Default
|
|
is 0.0.
|
|
origin : scalar, optional
|
|
The `origin` parameter controls the placement of the filter.
|
|
Default 0
|
|
|
|
Returns
|
|
-------
|
|
grey_closing : ndarray
|
|
Result of the grayscale closing of `input` with `structure`.
|
|
|
|
See also
|
|
--------
|
|
binary_closing, grey_dilation, grey_erosion, grey_opening,
|
|
generate_binary_structure
|
|
|
|
Notes
|
|
-----
|
|
The action of a grayscale closing with a flat structuring element amounts
|
|
to smoothen deep local minima, whereas binary closing fills small holes.
|
|
|
|
References
|
|
----------
|
|
.. [1] https://en.wikipedia.org/wiki/Mathematical_morphology
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy import ndimage
|
|
>>> a = np.arange(36).reshape((6,6))
|
|
>>> a[3,3] = 0
|
|
>>> a
|
|
array([[ 0, 1, 2, 3, 4, 5],
|
|
[ 6, 7, 8, 9, 10, 11],
|
|
[12, 13, 14, 15, 16, 17],
|
|
[18, 19, 20, 0, 22, 23],
|
|
[24, 25, 26, 27, 28, 29],
|
|
[30, 31, 32, 33, 34, 35]])
|
|
>>> ndimage.grey_closing(a, size=(3,3))
|
|
array([[ 7, 7, 8, 9, 10, 11],
|
|
[ 7, 7, 8, 9, 10, 11],
|
|
[13, 13, 14, 15, 16, 17],
|
|
[19, 19, 20, 20, 22, 23],
|
|
[25, 25, 26, 27, 28, 29],
|
|
[31, 31, 32, 33, 34, 35]])
|
|
>>> # Note that the local minimum a[3,3] has disappeared
|
|
|
|
"""
|
|
if (size is not None) and (footprint is not None):
|
|
warnings.warn("ignoring size because footprint is set", UserWarning, stacklevel=2)
|
|
tmp = grey_dilation(input, size, footprint, structure, None, mode,
|
|
cval, origin)
|
|
return grey_erosion(tmp, size, footprint, structure, output, mode,
|
|
cval, origin)
|
|
|
|
|
|
def morphological_gradient(input, size=None, footprint=None, structure=None,
|
|
output=None, mode="reflect", cval=0.0, origin=0):
|
|
"""
|
|
Multi-dimensional morphological gradient.
|
|
|
|
The morphological gradient is calculated as the difference between a
|
|
dilation and an erosion of the input with a given structuring element.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Array over which to compute the morphlogical gradient.
|
|
size : tuple of ints
|
|
Shape of a flat and full structuring element used for the mathematical
|
|
morphology operations. Optional if `footprint` or `structure` is
|
|
provided. A larger `size` yields a more blurred gradient.
|
|
footprint : array of ints, optional
|
|
Positions of non-infinite elements of a flat structuring element
|
|
used for the morphology operations. Larger footprints
|
|
give a more blurred morphological gradient.
|
|
structure : array of ints, optional
|
|
Structuring element used for the morphology operations.
|
|
`structure` may be a non-flat structuring element.
|
|
output : array, optional
|
|
An array used for storing the output of the morphological gradient
|
|
may be provided.
|
|
mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
|
|
The `mode` parameter determines how the array borders are
|
|
handled, where `cval` is the value when mode is equal to
|
|
'constant'. Default is 'reflect'
|
|
cval : scalar, optional
|
|
Value to fill past edges of input if `mode` is 'constant'. Default
|
|
is 0.0.
|
|
origin : scalar, optional
|
|
The `origin` parameter controls the placement of the filter.
|
|
Default 0
|
|
|
|
Returns
|
|
-------
|
|
morphological_gradient : ndarray
|
|
Morphological gradient of `input`.
|
|
|
|
See also
|
|
--------
|
|
grey_dilation, grey_erosion, gaussian_gradient_magnitude
|
|
|
|
Notes
|
|
-----
|
|
For a flat structuring element, the morphological gradient
|
|
computed at a given point corresponds to the maximal difference
|
|
between elements of the input among the elements covered by the
|
|
structuring element centered on the point.
|
|
|
|
References
|
|
----------
|
|
.. [1] https://en.wikipedia.org/wiki/Mathematical_morphology
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy import ndimage
|
|
>>> a = np.zeros((7,7), dtype=int)
|
|
>>> a[2:5, 2:5] = 1
|
|
>>> ndimage.morphological_gradient(a, size=(3,3))
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 1, 1, 0],
|
|
[0, 1, 1, 0, 1, 1, 0],
|
|
[0, 1, 1, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 1, 1, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> # The morphological gradient is computed as the difference
|
|
>>> # between a dilation and an erosion
|
|
>>> ndimage.grey_dilation(a, size=(3,3)) -\\
|
|
... ndimage.grey_erosion(a, size=(3,3))
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 1, 1, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 1, 1, 0],
|
|
[0, 1, 1, 0, 1, 1, 0],
|
|
[0, 1, 1, 1, 1, 1, 0],
|
|
[0, 1, 1, 1, 1, 1, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> a = np.zeros((7,7), dtype=int)
|
|
>>> a[2:5, 2:5] = 1
|
|
>>> a[4,4] = 2; a[2,3] = 3
|
|
>>> a
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 3, 1, 0, 0],
|
|
[0, 0, 1, 1, 1, 0, 0],
|
|
[0, 0, 1, 1, 2, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
>>> ndimage.morphological_gradient(a, size=(3,3))
|
|
array([[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 1, 3, 3, 3, 1, 0],
|
|
[0, 1, 3, 3, 3, 1, 0],
|
|
[0, 1, 3, 2, 3, 2, 0],
|
|
[0, 1, 1, 2, 2, 2, 0],
|
|
[0, 1, 1, 2, 2, 2, 0],
|
|
[0, 0, 0, 0, 0, 0, 0]])
|
|
|
|
"""
|
|
tmp = grey_dilation(input, size, footprint, structure, None, mode,
|
|
cval, origin)
|
|
if isinstance(output, numpy.ndarray):
|
|
grey_erosion(input, size, footprint, structure, output, mode,
|
|
cval, origin)
|
|
return numpy.subtract(tmp, output, output)
|
|
else:
|
|
return (tmp - grey_erosion(input, size, footprint, structure,
|
|
None, mode, cval, origin))
|
|
|
|
|
|
def morphological_laplace(input, size=None, footprint=None,
|
|
structure=None, output=None,
|
|
mode="reflect", cval=0.0, origin=0):
|
|
"""
|
|
Multi-dimensional morphological laplace.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Input.
|
|
size : int or sequence of ints, optional
|
|
See `structure`.
|
|
footprint : bool or ndarray, optional
|
|
See `structure`.
|
|
structure : structure, optional
|
|
Either `size`, `footprint`, or the `structure` must be provided.
|
|
output : ndarray, optional
|
|
An output array can optionally be provided.
|
|
mode : {'reflect','constant','nearest','mirror', 'wrap'}, optional
|
|
The mode parameter determines how the array borders are handled.
|
|
For 'constant' mode, values beyond borders are set to be `cval`.
|
|
Default is 'reflect'.
|
|
cval : scalar, optional
|
|
Value to fill past edges of input if mode is 'constant'.
|
|
Default is 0.0
|
|
origin : origin, optional
|
|
The origin parameter controls the placement of the filter.
|
|
|
|
Returns
|
|
-------
|
|
morphological_laplace : ndarray
|
|
Output
|
|
|
|
"""
|
|
tmp1 = grey_dilation(input, size, footprint, structure, None, mode,
|
|
cval, origin)
|
|
if isinstance(output, numpy.ndarray):
|
|
grey_erosion(input, size, footprint, structure, output, mode,
|
|
cval, origin)
|
|
numpy.add(tmp1, output, output)
|
|
numpy.subtract(output, input, output)
|
|
return numpy.subtract(output, input, output)
|
|
else:
|
|
tmp2 = grey_erosion(input, size, footprint, structure, None, mode,
|
|
cval, origin)
|
|
numpy.add(tmp1, tmp2, tmp2)
|
|
numpy.subtract(tmp2, input, tmp2)
|
|
numpy.subtract(tmp2, input, tmp2)
|
|
return tmp2
|
|
|
|
|
|
def white_tophat(input, size=None, footprint=None, structure=None,
|
|
output=None, mode="reflect", cval=0.0, origin=0):
|
|
"""
|
|
Multi-dimensional white tophat filter.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Input.
|
|
size : tuple of ints
|
|
Shape of a flat and full structuring element used for the filter.
|
|
Optional if `footprint` or `structure` is provided.
|
|
footprint : array of ints, optional
|
|
Positions of elements of a flat structuring element
|
|
used for the white tophat filter.
|
|
structure : array of ints, optional
|
|
Structuring element used for the filter. `structure`
|
|
may be a non-flat structuring element.
|
|
output : array, optional
|
|
An array used for storing the output of the filter may be provided.
|
|
mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
|
|
The `mode` parameter determines how the array borders are
|
|
handled, where `cval` is the value when mode is equal to
|
|
'constant'. Default is 'reflect'
|
|
cval : scalar, optional
|
|
Value to fill past edges of input if `mode` is 'constant'.
|
|
Default is 0.0.
|
|
origin : scalar, optional
|
|
The `origin` parameter controls the placement of the filter.
|
|
Default is 0.
|
|
|
|
Returns
|
|
-------
|
|
output : ndarray
|
|
Result of the filter of `input` with `structure`.
|
|
|
|
See also
|
|
--------
|
|
black_tophat
|
|
|
|
"""
|
|
if (size is not None) and (footprint is not None):
|
|
warnings.warn("ignoring size because footprint is set", UserWarning, stacklevel=2)
|
|
tmp = grey_erosion(input, size, footprint, structure, None, mode,
|
|
cval, origin)
|
|
tmp = grey_dilation(tmp, size, footprint, structure, output, mode,
|
|
cval, origin)
|
|
if tmp is None:
|
|
tmp = output
|
|
|
|
if input.dtype == numpy.bool_ and tmp.dtype == numpy.bool_:
|
|
numpy.bitwise_xor(input, tmp, out=tmp)
|
|
else:
|
|
numpy.subtract(input, tmp, out=tmp)
|
|
return tmp
|
|
|
|
|
|
def black_tophat(input, size=None, footprint=None,
|
|
structure=None, output=None, mode="reflect",
|
|
cval=0.0, origin=0):
|
|
"""
|
|
Multi-dimensional black tophat filter.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Input.
|
|
size : tuple of ints, optional
|
|
Shape of a flat and full structuring element used for the filter.
|
|
Optional if `footprint` or `structure` is provided.
|
|
footprint : array of ints, optional
|
|
Positions of non-infinite elements of a flat structuring element
|
|
used for the black tophat filter.
|
|
structure : array of ints, optional
|
|
Structuring element used for the filter. `structure`
|
|
may be a non-flat structuring element.
|
|
output : array, optional
|
|
An array used for storing the output of the filter may be provided.
|
|
mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
|
|
The `mode` parameter determines how the array borders are
|
|
handled, where `cval` is the value when mode is equal to
|
|
'constant'. Default is 'reflect'
|
|
cval : scalar, optional
|
|
Value to fill past edges of input if `mode` is 'constant'. Default
|
|
is 0.0.
|
|
origin : scalar, optional
|
|
The `origin` parameter controls the placement of the filter.
|
|
Default 0
|
|
|
|
Returns
|
|
-------
|
|
black_tophat : ndarray
|
|
Result of the filter of `input` with `structure`.
|
|
|
|
See also
|
|
--------
|
|
white_tophat, grey_opening, grey_closing
|
|
|
|
"""
|
|
if (size is not None) and (footprint is not None):
|
|
warnings.warn("ignoring size because footprint is set", UserWarning, stacklevel=2)
|
|
tmp = grey_dilation(input, size, footprint, structure, None, mode,
|
|
cval, origin)
|
|
tmp = grey_erosion(tmp, size, footprint, structure, output, mode,
|
|
cval, origin)
|
|
if tmp is None:
|
|
tmp = output
|
|
|
|
if input.dtype == numpy.bool_ and tmp.dtype == numpy.bool_:
|
|
numpy.bitwise_xor(tmp, input, out=tmp)
|
|
else:
|
|
numpy.subtract(tmp, input, out=tmp)
|
|
return tmp
|
|
|
|
|
|
def distance_transform_bf(input, metric="euclidean", sampling=None,
|
|
return_distances=True, return_indices=False,
|
|
distances=None, indices=None):
|
|
"""
|
|
Distance transform function by a brute force algorithm.
|
|
|
|
This function calculates the distance transform of the `input`, by
|
|
replacing each foreground (non-zero) element, with its
|
|
shortest distance to the background (any zero-valued element).
|
|
|
|
In addition to the distance transform, the feature transform can
|
|
be calculated. In this case the index of the closest background
|
|
element is returned along the first axis of the result.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Input
|
|
metric : str, optional
|
|
Three types of distance metric are supported: 'euclidean', 'taxicab'
|
|
and 'chessboard'.
|
|
sampling : {int, sequence of ints}, optional
|
|
This parameter is only used in the case of the euclidean `metric`
|
|
distance transform.
|
|
|
|
The sampling along each axis can be given by the `sampling` parameter
|
|
which should be a sequence of length equal to the input rank, or a
|
|
single number in which the `sampling` is assumed to be equal along all
|
|
axes.
|
|
return_distances : bool, optional
|
|
The `return_distances` flag can be used to indicate if the distance
|
|
transform is returned.
|
|
|
|
The default is True.
|
|
return_indices : bool, optional
|
|
The `return_indices` flags can be used to indicate if the feature
|
|
transform is returned.
|
|
|
|
The default is False.
|
|
distances : float64 ndarray, optional
|
|
Optional output array to hold distances (if `return_distances` is
|
|
True).
|
|
indices : int64 ndarray, optional
|
|
Optional output array to hold indices (if `return_indices` is True).
|
|
|
|
Returns
|
|
-------
|
|
distances : ndarray
|
|
Distance array if `return_distances` is True.
|
|
indices : ndarray
|
|
Indices array if `return_indices` is True.
|
|
|
|
Notes
|
|
-----
|
|
This function employs a slow brute force algorithm, see also the
|
|
function distance_transform_cdt for more efficient taxicab and
|
|
chessboard algorithms.
|
|
|
|
"""
|
|
if (not return_distances) and (not return_indices):
|
|
msg = 'at least one of distances/indices must be specified'
|
|
raise RuntimeError(msg)
|
|
|
|
tmp1 = numpy.asarray(input) != 0
|
|
struct = generate_binary_structure(tmp1.ndim, tmp1.ndim)
|
|
tmp2 = binary_dilation(tmp1, struct)
|
|
tmp2 = numpy.logical_xor(tmp1, tmp2)
|
|
tmp1 = tmp1.astype(numpy.int8) - tmp2.astype(numpy.int8)
|
|
metric = metric.lower()
|
|
if metric == 'euclidean':
|
|
metric = 1
|
|
elif metric in ['taxicab', 'cityblock', 'manhattan']:
|
|
metric = 2
|
|
elif metric == 'chessboard':
|
|
metric = 3
|
|
else:
|
|
raise RuntimeError('distance metric not supported')
|
|
if sampling is not None:
|
|
sampling = _ni_support._normalize_sequence(sampling, tmp1.ndim)
|
|
sampling = numpy.asarray(sampling, dtype=numpy.float64)
|
|
if not sampling.flags.contiguous:
|
|
sampling = sampling.copy()
|
|
if return_indices:
|
|
ft = numpy.zeros(tmp1.shape, dtype=numpy.int32)
|
|
else:
|
|
ft = None
|
|
if return_distances:
|
|
if distances is None:
|
|
if metric == 1:
|
|
dt = numpy.zeros(tmp1.shape, dtype=numpy.float64)
|
|
else:
|
|
dt = numpy.zeros(tmp1.shape, dtype=numpy.uint32)
|
|
else:
|
|
if distances.shape != tmp1.shape:
|
|
raise RuntimeError('distances array has wrong shape')
|
|
if metric == 1:
|
|
if distances.dtype.type != numpy.float64:
|
|
raise RuntimeError('distances array must be float64')
|
|
else:
|
|
if distances.dtype.type != numpy.uint32:
|
|
raise RuntimeError('distances array must be uint32')
|
|
dt = distances
|
|
else:
|
|
dt = None
|
|
|
|
_nd_image.distance_transform_bf(tmp1, metric, sampling, dt, ft)
|
|
if return_indices:
|
|
if isinstance(indices, numpy.ndarray):
|
|
if indices.dtype.type != numpy.int32:
|
|
raise RuntimeError('indices must of int32 type')
|
|
if indices.shape != (tmp1.ndim,) + tmp1.shape:
|
|
raise RuntimeError('indices has wrong shape')
|
|
tmp2 = indices
|
|
else:
|
|
tmp2 = numpy.indices(tmp1.shape, dtype=numpy.int32)
|
|
ft = numpy.ravel(ft)
|
|
for ii in range(tmp2.shape[0]):
|
|
rtmp = numpy.ravel(tmp2[ii, ...])[ft]
|
|
rtmp.shape = tmp1.shape
|
|
tmp2[ii, ...] = rtmp
|
|
ft = tmp2
|
|
|
|
# construct and return the result
|
|
result = []
|
|
if return_distances and not isinstance(distances, numpy.ndarray):
|
|
result.append(dt)
|
|
if return_indices and not isinstance(indices, numpy.ndarray):
|
|
result.append(ft)
|
|
|
|
if len(result) == 2:
|
|
return tuple(result)
|
|
elif len(result) == 1:
|
|
return result[0]
|
|
else:
|
|
return None
|
|
|
|
|
|
def distance_transform_cdt(input, metric='chessboard', return_distances=True,
|
|
return_indices=False, distances=None, indices=None):
|
|
"""
|
|
Distance transform for chamfer type of transforms.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Input
|
|
metric : {'chessboard', 'taxicab'}, optional
|
|
The `metric` determines the type of chamfering that is done. If the
|
|
`metric` is equal to 'taxicab' a structure is generated using
|
|
generate_binary_structure with a squared distance equal to 1. If
|
|
the `metric` is equal to 'chessboard', a `metric` is generated
|
|
using generate_binary_structure with a squared distance equal to
|
|
the dimensionality of the array. These choices correspond to the
|
|
common interpretations of the 'taxicab' and the 'chessboard'
|
|
distance metrics in two dimensions.
|
|
|
|
The default for `metric` is 'chessboard'.
|
|
return_distances, return_indices : bool, optional
|
|
The `return_distances`, and `return_indices` flags can be used to
|
|
indicate if the distance transform, the feature transform, or both
|
|
must be returned.
|
|
|
|
If the feature transform is returned (``return_indices=True``),
|
|
the index of the closest background element is returned along
|
|
the first axis of the result.
|
|
|
|
The `return_distances` default is True, and the
|
|
`return_indices` default is False.
|
|
distances, indices : ndarrays of int32, optional
|
|
The `distances` and `indices` arguments can be used to give optional
|
|
output arrays that must be the same shape as `input`.
|
|
|
|
"""
|
|
if (not return_distances) and (not return_indices):
|
|
msg = 'at least one of distances/indices must be specified'
|
|
raise RuntimeError(msg)
|
|
|
|
ft_inplace = isinstance(indices, numpy.ndarray)
|
|
dt_inplace = isinstance(distances, numpy.ndarray)
|
|
input = numpy.asarray(input)
|
|
if metric in ['taxicab', 'cityblock', 'manhattan']:
|
|
rank = input.ndim
|
|
metric = generate_binary_structure(rank, 1)
|
|
elif metric == 'chessboard':
|
|
rank = input.ndim
|
|
metric = generate_binary_structure(rank, rank)
|
|
else:
|
|
try:
|
|
metric = numpy.asarray(metric)
|
|
except Exception:
|
|
raise RuntimeError('invalid metric provided')
|
|
for s in metric.shape:
|
|
if s != 3:
|
|
raise RuntimeError('metric sizes must be equal to 3')
|
|
|
|
if not metric.flags.contiguous:
|
|
metric = metric.copy()
|
|
if dt_inplace:
|
|
if distances.dtype.type != numpy.int32:
|
|
raise RuntimeError('distances must be of int32 type')
|
|
if distances.shape != input.shape:
|
|
raise RuntimeError('distances has wrong shape')
|
|
dt = distances
|
|
dt[...] = numpy.where(input, -1, 0).astype(numpy.int32)
|
|
else:
|
|
dt = numpy.where(input, -1, 0).astype(numpy.int32)
|
|
|
|
rank = dt.ndim
|
|
if return_indices:
|
|
sz = numpy.prod(dt.shape, axis=0)
|
|
ft = numpy.arange(sz, dtype=numpy.int32)
|
|
ft.shape = dt.shape
|
|
else:
|
|
ft = None
|
|
|
|
_nd_image.distance_transform_op(metric, dt, ft)
|
|
dt = dt[tuple([slice(None, None, -1)] * rank)]
|
|
if return_indices:
|
|
ft = ft[tuple([slice(None, None, -1)] * rank)]
|
|
_nd_image.distance_transform_op(metric, dt, ft)
|
|
dt = dt[tuple([slice(None, None, -1)] * rank)]
|
|
if return_indices:
|
|
ft = ft[tuple([slice(None, None, -1)] * rank)]
|
|
ft = numpy.ravel(ft)
|
|
if ft_inplace:
|
|
if indices.dtype.type != numpy.int32:
|
|
raise RuntimeError('indices must of int32 type')
|
|
if indices.shape != (dt.ndim,) + dt.shape:
|
|
raise RuntimeError('indices has wrong shape')
|
|
tmp = indices
|
|
else:
|
|
tmp = numpy.indices(dt.shape, dtype=numpy.int32)
|
|
for ii in range(tmp.shape[0]):
|
|
rtmp = numpy.ravel(tmp[ii, ...])[ft]
|
|
rtmp.shape = dt.shape
|
|
tmp[ii, ...] = rtmp
|
|
ft = tmp
|
|
|
|
# construct and return the result
|
|
result = []
|
|
if return_distances and not dt_inplace:
|
|
result.append(dt)
|
|
if return_indices and not ft_inplace:
|
|
result.append(ft)
|
|
|
|
if len(result) == 2:
|
|
return tuple(result)
|
|
elif len(result) == 1:
|
|
return result[0]
|
|
else:
|
|
return None
|
|
|
|
|
|
def distance_transform_edt(input, sampling=None, return_distances=True,
|
|
return_indices=False, distances=None, indices=None):
|
|
"""
|
|
Exact euclidean distance transform.
|
|
|
|
In addition to the distance transform, the feature transform can
|
|
be calculated. In this case the index of the closest background
|
|
element is returned along the first axis of the result.
|
|
|
|
Parameters
|
|
----------
|
|
input : array_like
|
|
Input data to transform. Can be any type but will be converted
|
|
into binary: 1 wherever input equates to True, 0 elsewhere.
|
|
sampling : float or int, or sequence of same, optional
|
|
Spacing of elements along each dimension. If a sequence, must be of
|
|
length equal to the input rank; if a single number, this is used for
|
|
all axes. If not specified, a grid spacing of unity is implied.
|
|
return_distances : bool, optional
|
|
Whether to return distance matrix. At least one of
|
|
return_distances/return_indices must be True. Default is True.
|
|
return_indices : bool, optional
|
|
Whether to return indices matrix. Default is False.
|
|
distances : ndarray, optional
|
|
Used for output of distance array, must be of type float64.
|
|
indices : ndarray, optional
|
|
Used for output of indices, must be of type int32.
|
|
|
|
Returns
|
|
-------
|
|
distance_transform_edt : ndarray or list of ndarrays
|
|
Either distance matrix, index matrix, or a list of the two,
|
|
depending on `return_x` flags and `distance` and `indices`
|
|
input parameters.
|
|
|
|
Notes
|
|
-----
|
|
The euclidean distance transform gives values of the euclidean
|
|
distance::
|
|
|
|
n
|
|
y_i = sqrt(sum (x[i]-b[i])**2)
|
|
i
|
|
|
|
where b[i] is the background point (value 0) with the smallest
|
|
Euclidean distance to input points x[i], and n is the
|
|
number of dimensions.
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy import ndimage
|
|
>>> a = np.array(([0,1,1,1,1],
|
|
... [0,0,1,1,1],
|
|
... [0,1,1,1,1],
|
|
... [0,1,1,1,0],
|
|
... [0,1,1,0,0]))
|
|
>>> ndimage.distance_transform_edt(a)
|
|
array([[ 0. , 1. , 1.4142, 2.2361, 3. ],
|
|
[ 0. , 0. , 1. , 2. , 2. ],
|
|
[ 0. , 1. , 1.4142, 1.4142, 1. ],
|
|
[ 0. , 1. , 1.4142, 1. , 0. ],
|
|
[ 0. , 1. , 1. , 0. , 0. ]])
|
|
|
|
With a sampling of 2 units along x, 1 along y:
|
|
|
|
>>> ndimage.distance_transform_edt(a, sampling=[2,1])
|
|
array([[ 0. , 1. , 2. , 2.8284, 3.6056],
|
|
[ 0. , 0. , 1. , 2. , 3. ],
|
|
[ 0. , 1. , 2. , 2.2361, 2. ],
|
|
[ 0. , 1. , 2. , 1. , 0. ],
|
|
[ 0. , 1. , 1. , 0. , 0. ]])
|
|
|
|
Asking for indices as well:
|
|
|
|
>>> edt, inds = ndimage.distance_transform_edt(a, return_indices=True)
|
|
>>> inds
|
|
array([[[0, 0, 1, 1, 3],
|
|
[1, 1, 1, 1, 3],
|
|
[2, 2, 1, 3, 3],
|
|
[3, 3, 4, 4, 3],
|
|
[4, 4, 4, 4, 4]],
|
|
[[0, 0, 1, 1, 4],
|
|
[0, 1, 1, 1, 4],
|
|
[0, 0, 1, 4, 4],
|
|
[0, 0, 3, 3, 4],
|
|
[0, 0, 3, 3, 4]]])
|
|
|
|
With arrays provided for inplace outputs:
|
|
|
|
>>> indices = np.zeros(((np.ndim(a),) + a.shape), dtype=np.int32)
|
|
>>> ndimage.distance_transform_edt(a, return_indices=True, indices=indices)
|
|
array([[ 0. , 1. , 1.4142, 2.2361, 3. ],
|
|
[ 0. , 0. , 1. , 2. , 2. ],
|
|
[ 0. , 1. , 1.4142, 1.4142, 1. ],
|
|
[ 0. , 1. , 1.4142, 1. , 0. ],
|
|
[ 0. , 1. , 1. , 0. , 0. ]])
|
|
>>> indices
|
|
array([[[0, 0, 1, 1, 3],
|
|
[1, 1, 1, 1, 3],
|
|
[2, 2, 1, 3, 3],
|
|
[3, 3, 4, 4, 3],
|
|
[4, 4, 4, 4, 4]],
|
|
[[0, 0, 1, 1, 4],
|
|
[0, 1, 1, 1, 4],
|
|
[0, 0, 1, 4, 4],
|
|
[0, 0, 3, 3, 4],
|
|
[0, 0, 3, 3, 4]]])
|
|
|
|
"""
|
|
if (not return_distances) and (not return_indices):
|
|
msg = 'at least one of distances/indices must be specified'
|
|
raise RuntimeError(msg)
|
|
|
|
ft_inplace = isinstance(indices, numpy.ndarray)
|
|
dt_inplace = isinstance(distances, numpy.ndarray)
|
|
# calculate the feature transform
|
|
input = numpy.atleast_1d(numpy.where(input, 1, 0).astype(numpy.int8))
|
|
if sampling is not None:
|
|
sampling = _ni_support._normalize_sequence(sampling, input.ndim)
|
|
sampling = numpy.asarray(sampling, dtype=numpy.float64)
|
|
if not sampling.flags.contiguous:
|
|
sampling = sampling.copy()
|
|
|
|
if ft_inplace:
|
|
ft = indices
|
|
if ft.shape != (input.ndim,) + input.shape:
|
|
raise RuntimeError('indices has wrong shape')
|
|
if ft.dtype.type != numpy.int32:
|
|
raise RuntimeError('indices must be of int32 type')
|
|
else:
|
|
ft = numpy.zeros((input.ndim,) + input.shape, dtype=numpy.int32)
|
|
|
|
_nd_image.euclidean_feature_transform(input, sampling, ft)
|
|
# if requested, calculate the distance transform
|
|
if return_distances:
|
|
dt = ft - numpy.indices(input.shape, dtype=ft.dtype)
|
|
dt = dt.astype(numpy.float64)
|
|
if sampling is not None:
|
|
for ii in range(len(sampling)):
|
|
dt[ii, ...] *= sampling[ii]
|
|
numpy.multiply(dt, dt, dt)
|
|
if dt_inplace:
|
|
dt = numpy.add.reduce(dt, axis=0)
|
|
if distances.shape != dt.shape:
|
|
raise RuntimeError('indices has wrong shape')
|
|
if distances.dtype.type != numpy.float64:
|
|
raise RuntimeError('indices must be of float64 type')
|
|
numpy.sqrt(dt, distances)
|
|
else:
|
|
dt = numpy.add.reduce(dt, axis=0)
|
|
dt = numpy.sqrt(dt)
|
|
|
|
# construct and return the result
|
|
result = []
|
|
if return_distances and not dt_inplace:
|
|
result.append(dt)
|
|
if return_indices and not ft_inplace:
|
|
result.append(ft)
|
|
|
|
if len(result) == 2:
|
|
return tuple(result)
|
|
elif len(result) == 1:
|
|
return result[0]
|
|
else:
|
|
return None
|