import numpy as np
from .._shared.utils import _supported_float_type
from ..filters._rank_order import rank_order
from ._grayreconstruct import reconstruction_loop
[文档]
def reconstruction(seed, mask, method='dilation', footprint=None, offset=None):
"""Perform a morphological reconstruction of an image.
Morphological reconstruction by dilation is similar to basic morphological
dilation: high-intensity values will replace nearby low-intensity values.
The basic dilation operator, however, uses a footprint to
determine how far a value in the input image can spread. In contrast,
reconstruction uses two images: a "seed" image, which specifies the values
that spread, and a "mask" image, which gives the maximum allowed value at
each pixel. The mask image, like the footprint, limits the spread
of high-intensity values. Reconstruction by erosion is simply the inverse:
low-intensity values spread from the seed image and are limited by the mask
image, which represents the minimum allowed value.
Alternatively, you can think of reconstruction as a way to isolate the
connected regions of an image. For dilation, reconstruction connects
regions marked by local maxima in the seed image: neighboring pixels
less-than-or-equal-to those seeds are connected to the seeded region.
Local maxima with values larger than the seed image will get truncated to
the seed value.
Parameters
----------
seed : ndarray
The seed image (a.k.a. marker image), which specifies the values that
are dilated or eroded.
mask : ndarray
The maximum (dilation) / minimum (erosion) allowed value at each pixel.
method : {'dilation'|'erosion'}, optional
Perform reconstruction by dilation or erosion. In dilation (or
erosion), the seed image is dilated (or eroded) until limited by the
mask image. For dilation, each seed value must be less than or equal
to the corresponding mask value; for erosion, the reverse is true.
Default is 'dilation'.
footprint : ndarray, optional
The neighborhood expressed as an n-D array of 1's and 0's.
Default is the n-D square of radius equal to 1 (i.e. a 3x3 square
for 2D images, a 3x3x3 cube for 3D images, etc.)
offset : ndarray, optional
The coordinates of the center of the footprint.
Default is located on the geometrical center of the footprint, in that
case footprint dimensions must be odd.
Returns
-------
reconstructed : ndarray
The result of morphological reconstruction.
Examples
--------
>>> import numpy as np
>>> from skimage.morphology import reconstruction
First, we create a sinusoidal mask image with peaks at middle and ends.
>>> x = np.linspace(0, 4 * np.pi)
>>> y_mask = np.cos(x)
Then, we create a seed image initialized to the minimum mask value (for
reconstruction by dilation, min-intensity values don't spread) and add
"seeds" to the left and right peak, but at a fraction of peak value (1).
>>> y_seed = y_mask.min() * np.ones_like(x)
>>> y_seed[0] = 0.5
>>> y_seed[-1] = 0
>>> y_rec = reconstruction(y_seed, y_mask)
The reconstructed image (or curve, in this case) is exactly the same as the
mask image, except that the peaks are truncated to 0.5 and 0. The middle
peak disappears completely: Since there were no seed values in this peak
region, its reconstructed value is truncated to the surrounding value (-1).
As a more practical example, we try to extract the bright features of an
image by subtracting a background image created by reconstruction.
>>> y, x = np.mgrid[:20:0.5, :20:0.5]
>>> bumps = np.sin(x) + np.sin(y)
To create the background image, set the mask image to the original image,
and the seed image to the original image with an intensity offset, `h`.
>>> h = 0.3
>>> seed = bumps - h
>>> background = reconstruction(seed, bumps)
The resulting reconstructed image looks exactly like the original image,
but with the peaks of the bumps cut off. Subtracting this reconstructed
image from the original image leaves just the peaks of the bumps
>>> hdome = bumps - background
This operation is known as the h-dome of the image and leaves features
of height `h` in the subtracted image.
Notes
-----
The algorithm is taken from [1]_. Applications for grayscale reconstruction
are discussed in [2]_ and [3]_.
References
----------
.. [1] Robinson, "Efficient morphological reconstruction: a downhill
filter", Pattern Recognition Letters 25 (2004) 1759-1767.
.. [2] Vincent, L., "Morphological Grayscale Reconstruction in Image
Analysis: Applications and Efficient Algorithms", IEEE Transactions
on Image Processing (1993)
.. [3] Soille, P., "Morphological Image Analysis: Principles and
Applications", Chapter 6, 2nd edition (2003), ISBN 3540429883.
"""
assert tuple(seed.shape) == tuple(mask.shape)
if method == 'dilation' and np.any(seed > mask):
raise ValueError(
"Intensity of seed image must be less than that "
"of the mask image for reconstruction by dilation."
)
elif method == 'erosion' and np.any(seed < mask):
raise ValueError(
"Intensity of seed image must be greater than that "
"of the mask image for reconstruction by erosion."
)
if footprint is None:
footprint = np.ones([3] * seed.ndim, dtype=bool)
else:
footprint = footprint.astype(bool, copy=True)
if offset is None:
if not all([d % 2 == 1 for d in footprint.shape]):
raise ValueError("Footprint dimensions must all be odd")
offset = np.array([d // 2 for d in footprint.shape])
else:
if offset.ndim != footprint.ndim:
raise ValueError("Offset and footprint ndims must be equal.")
if not all([(0 <= o < d) for o, d in zip(offset, footprint.shape)]):
raise ValueError("Offset must be included inside footprint")
# Cross out the center of the footprint
footprint[tuple(slice(d, d + 1) for d in offset)] = False
# Make padding for edges of reconstructed image so we can ignore boundaries
dims = np.zeros(seed.ndim + 1, dtype=int)
dims[1:] = np.array(seed.shape) + (np.array(footprint.shape) - 1)
dims[0] = 2
inside_slices = tuple(slice(o, o + s) for o, s in zip(offset, seed.shape))
# Set padded region to minimum image intensity and mask along first axis so
# we can interleave image and mask pixels when sorting.
if method == 'dilation':
pad_value = np.min(seed)
elif method == 'erosion':
pad_value = np.max(seed)
else:
raise ValueError(
"Reconstruction method can be one of 'erosion' "
f"or 'dilation'. Got '{method}'."
)
float_dtype = _supported_float_type(mask.dtype)
images = np.full(dims, pad_value, dtype=float_dtype)
images[(0, *inside_slices)] = seed
images[(1, *inside_slices)] = mask
# determine whether image is large enough to require 64-bit integers
isize = images.size
# use -isize so we get a signed dtype rather than an unsigned one
signed_int_dtype = np.result_type(np.min_scalar_type(-isize), np.int32)
# the corresponding unsigned type has same char, but uppercase
unsigned_int_dtype = np.dtype(signed_int_dtype.char.upper())
# Create a list of strides across the array to get the neighbors within
# a flattened array
value_stride = np.array(images.strides[1:]) // images.dtype.itemsize
image_stride = images.strides[0] // images.dtype.itemsize
footprint_mgrid = np.mgrid[
[slice(-o, d - o) for d, o in zip(footprint.shape, offset)]
]
footprint_offsets = footprint_mgrid[:, footprint].transpose()
nb_strides = np.array(
[
np.sum(value_stride * footprint_offset)
for footprint_offset in footprint_offsets
],
signed_int_dtype,
)
images = images.reshape(-1)
# Erosion goes smallest to largest; dilation goes largest to smallest.
index_sorted = np.argsort(images).astype(signed_int_dtype, copy=False)
if method == 'dilation':
index_sorted = index_sorted[::-1]
# Make a linked list of pixels sorted by value. -1 is the list terminator.
prev = np.full(isize, -1, signed_int_dtype)
next = np.full(isize, -1, signed_int_dtype)
prev[index_sorted[1:]] = index_sorted[:-1]
next[index_sorted[:-1]] = index_sorted[1:]
# Cython inner-loop compares the rank of pixel values.
if method == 'dilation':
value_rank, value_map = rank_order(images)
elif method == 'erosion':
value_rank, value_map = rank_order(-images)
value_map = -value_map
start = index_sorted[0]
value_rank = value_rank.astype(unsigned_int_dtype, copy=False)
reconstruction_loop(value_rank, prev, next, nb_strides, start, image_stride)
# Reshape reconstructed image to original image shape and remove padding.
rec_img = value_map[value_rank[:image_stride]]
rec_img.shape = np.array(seed.shape) + (np.array(footprint.shape) - 1)
return rec_img[inside_slices]
