import numpy as np
from scipy import ndimage as ndi
from scipy.ndimage import binary_erosion, convolve
from .._shared.utils import _supported_float_type, check_nD
from ..restoration.uft import laplacian
from ..util.dtype import img_as_float
# n-dimensional filter weights
SOBEL_EDGE = np.array([1, 0, -1])
SOBEL_SMOOTH = np.array([1, 2, 1]) / 4
HSOBEL_WEIGHTS = SOBEL_EDGE.reshape((3, 1)) * SOBEL_SMOOTH.reshape((1, 3))
VSOBEL_WEIGHTS = HSOBEL_WEIGHTS.T
SCHARR_EDGE = np.array([1, 0, -1])
SCHARR_SMOOTH = np.array([3, 10, 3]) / 16
HSCHARR_WEIGHTS = SCHARR_EDGE.reshape((3, 1)) * SCHARR_SMOOTH.reshape((1, 3))
VSCHARR_WEIGHTS = HSCHARR_WEIGHTS.T
PREWITT_EDGE = np.array([1, 0, -1])
PREWITT_SMOOTH = np.full((3,), 1 / 3)
HPREWITT_WEIGHTS = PREWITT_EDGE.reshape((3, 1)) * PREWITT_SMOOTH.reshape((1, 3))
VPREWITT_WEIGHTS = HPREWITT_WEIGHTS.T
# 2D-only filter weights
ROBERTS_PD_WEIGHTS = np.array([[1, 0], [0, -1]], dtype=np.float64)
ROBERTS_ND_WEIGHTS = np.array([[0, 1], [-1, 0]], dtype=np.float64)
# These filter weights can be found in Farid & Simoncelli (2004),
# Table 1 (3rd and 4th row). Additional decimal places were computed
# using the code found at https://www.cs.dartmouth.edu/farid/
farid_smooth = np.array(
[
[
0.0376593171958126,
0.249153396177344,
0.426374573253687,
0.249153396177344,
0.0376593171958126,
]
]
)
farid_edge = np.array(
[[0.109603762960254, 0.276690988455557, 0, -0.276690988455557, -0.109603762960254]]
)
HFARID_WEIGHTS = farid_edge.T * farid_smooth
VFARID_WEIGHTS = np.copy(HFARID_WEIGHTS.T)
def _mask_filter_result(result, mask):
"""Return result after masking.
Input masks are eroded so that mask areas in the original image don't
affect values in the result.
"""
if mask is not None:
erosion_footprint = ndi.generate_binary_structure(mask.ndim, mask.ndim)
mask = binary_erosion(mask, erosion_footprint, border_value=0)
result *= mask
return result
def _kernel_shape(ndim, dim):
"""Return list of `ndim` 1s except at position `dim`, where value is -1.
Parameters
----------
ndim : int
The number of dimensions of the kernel shape.
dim : int
The axis of the kernel to expand to shape -1.
Returns
-------
shape : list of int
The requested shape.
Examples
--------
>>> _kernel_shape(2, 0)
[-1, 1]
>>> _kernel_shape(3, 1)
[1, -1, 1]
>>> _kernel_shape(4, -1)
[1, 1, 1, -1]
"""
shape = [
1,
] * ndim
shape[dim] = -1
return shape
def _reshape_nd(arr, ndim, dim):
"""Reshape a 1D array to have n dimensions, all singletons but one.
Parameters
----------
arr : array, shape (N,)
Input array
ndim : int
Number of desired dimensions of reshaped array.
dim : int
Which dimension/axis will not be singleton-sized.
Returns
-------
arr_reshaped : array, shape ([1, ...], N, [1,...])
View of `arr` reshaped to the desired shape.
Examples
--------
>>> rng = np.random.default_rng()
>>> arr = rng.random(7)
>>> _reshape_nd(arr, 2, 0).shape
(7, 1)
>>> _reshape_nd(arr, 3, 1).shape
(1, 7, 1)
>>> _reshape_nd(arr, 4, -1).shape
(1, 1, 1, 7)
"""
kernel_shape = _kernel_shape(ndim, dim)
return np.reshape(arr, kernel_shape)
def _generic_edge_filter(
image,
*,
smooth_weights,
edge_weights=[1, 0, -1],
axis=None,
mode='reflect',
cval=0.0,
mask=None,
):
"""Apply a generic, n-dimensional edge filter.
The filter is computed by applying the edge weights along one dimension
and the smoothing weights along all other dimensions. If no axis is given,
or a tuple of axes is given the filter is computed along all axes in turn,
and the magnitude is computed as the square root of the average square
magnitude of all the axes.
Parameters
----------
image : array
The input image.
smooth_weights : array of float
The smoothing weights for the filter. These are applied to dimensions
orthogonal to the edge axis.
edge_weights : 1D array of float, optional
The weights to compute the edge along the chosen axes.
axis : int or sequence of int, optional
Compute the edge filter along this axis. If not provided, the edge
magnitude is computed. This is defined as::
edge_mag = np.sqrt(sum([_generic_edge_filter(image, ..., axis=i)**2
for i in range(image.ndim)]) / image.ndim)
The magnitude is also computed if axis is a sequence.
mode : str or sequence of str, optional
The boundary mode for the convolution. See `scipy.ndimage.convolve`
for a description of the modes. This can be either a single boundary
mode or one boundary mode per axis.
cval : float, optional
When `mode` is ``'constant'``, this is the constant used in values
outside the boundary of the image data.
"""
ndim = image.ndim
if axis is None:
axes = list(range(ndim))
elif np.isscalar(axis):
axes = [axis]
else:
axes = axis
return_magnitude = len(axes) > 1
if image.dtype.kind == 'f':
float_dtype = _supported_float_type(image.dtype)
image = image.astype(float_dtype, copy=False)
else:
image = img_as_float(image)
output = np.zeros(image.shape, dtype=image.dtype)
for edge_dim in axes:
kernel = _reshape_nd(edge_weights, ndim, edge_dim)
smooth_axes = list(set(range(ndim)) - {edge_dim})
for smooth_dim in smooth_axes:
kernel = kernel * _reshape_nd(smooth_weights, ndim, smooth_dim)
ax_output = ndi.convolve(image, kernel, mode=mode)
if return_magnitude:
ax_output *= ax_output
output += ax_output
if return_magnitude:
output = np.sqrt(output) / np.sqrt(ndim, dtype=output.dtype)
return output
[文档]
def sobel(image, mask=None, *, axis=None, mode='reflect', cval=0.0):
"""Find edges in an image using the Sobel filter.
Parameters
----------
image : array
The input image.
mask : array of bool, optional
Clip the output image to this mask. (Values where mask=0 will be set
to 0.)
axis : int or sequence of int, optional
Compute the edge filter along this axis. If not provided, the edge
magnitude is computed. This is defined as::
sobel_mag = np.sqrt(sum([sobel(image, axis=i)**2
for i in range(image.ndim)]) / image.ndim)
The magnitude is also computed if axis is a sequence.
mode : str or sequence of str, optional
The boundary mode for the convolution. See `scipy.ndimage.convolve`
for a description of the modes. This can be either a single boundary
mode or one boundary mode per axis.
cval : float, optional
When `mode` is ``'constant'``, this is the constant used in values
outside the boundary of the image data.
Returns
-------
output : array of float
The Sobel edge map.
See also
--------
sobel_h, sobel_v : horizontal and vertical edge detection.
scharr, prewitt, farid, skimage.feature.canny
References
----------
.. [1] D. Kroon, 2009, Short Paper University Twente, Numerical
Optimization of Kernel Based Image Derivatives.
.. [2] https://en.wikipedia.org/wiki/Sobel_operator
Examples
--------
>>> from skimage import data
>>> from skimage import filters
>>> camera = data.camera()
>>> edges = filters.sobel(camera)
"""
output = _generic_edge_filter(
image, smooth_weights=SOBEL_SMOOTH, axis=axis, mode=mode, cval=cval
)
output = _mask_filter_result(output, mask)
return output
[文档]
def sobel_h(image, mask=None):
"""Find the horizontal edges of an image using the Sobel transform.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Sobel edge map.
Notes
-----
We use the following kernel::
1 2 1
0 0 0
-1 -2 -1
"""
check_nD(image, 2)
return sobel(image, mask=mask, axis=0)
[文档]
def sobel_v(image, mask=None):
"""Find the vertical edges of an image using the Sobel transform.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Sobel edge map.
Notes
-----
We use the following kernel::
1 0 -1
2 0 -2
1 0 -1
"""
check_nD(image, 2)
return sobel(image, mask=mask, axis=1)
[文档]
def scharr(image, mask=None, *, axis=None, mode='reflect', cval=0.0):
"""Find the edge magnitude using the Scharr transform.
Parameters
----------
image : array
The input image.
mask : array of bool, optional
Clip the output image to this mask. (Values where mask=0 will be set
to 0.)
axis : int or sequence of int, optional
Compute the edge filter along this axis. If not provided, the edge
magnitude is computed. This is defined as::
sch_mag = np.sqrt(sum([scharr(image, axis=i)**2
for i in range(image.ndim)]) / image.ndim)
The magnitude is also computed if axis is a sequence.
mode : str or sequence of str, optional
The boundary mode for the convolution. See `scipy.ndimage.convolve`
for a description of the modes. This can be either a single boundary
mode or one boundary mode per axis.
cval : float, optional
When `mode` is ``'constant'``, this is the constant used in values
outside the boundary of the image data.
Returns
-------
output : array of float
The Scharr edge map.
See also
--------
scharr_h, scharr_v : horizontal and vertical edge detection.
sobel, prewitt, farid, skimage.feature.canny
Notes
-----
The Scharr operator has a better rotation invariance than
other edge filters such as the Sobel or the Prewitt operators.
References
----------
.. [1] D. Kroon, 2009, Short Paper University Twente, Numerical
Optimization of Kernel Based Image Derivatives.
.. [2] https://en.wikipedia.org/wiki/Sobel_operator#Alternative_operators
Examples
--------
>>> from skimage import data
>>> from skimage import filters
>>> camera = data.camera()
>>> edges = filters.scharr(camera)
"""
output = _generic_edge_filter(
image, smooth_weights=SCHARR_SMOOTH, axis=axis, mode=mode, cval=cval
)
output = _mask_filter_result(output, mask)
return output
[文档]
def scharr_h(image, mask=None):
"""Find the horizontal edges of an image using the Scharr transform.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Scharr edge map.
Notes
-----
We use the following kernel::
3 10 3
0 0 0
-3 -10 -3
References
----------
.. [1] D. Kroon, 2009, Short Paper University Twente, Numerical
Optimization of Kernel Based Image Derivatives.
"""
check_nD(image, 2)
return scharr(image, mask=mask, axis=0)
[文档]
def scharr_v(image, mask=None):
"""Find the vertical edges of an image using the Scharr transform.
Parameters
----------
image : 2-D array
Image to process
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Scharr edge map.
Notes
-----
We use the following kernel::
3 0 -3
10 0 -10
3 0 -3
References
----------
.. [1] D. Kroon, 2009, Short Paper University Twente, Numerical
Optimization of Kernel Based Image Derivatives.
"""
check_nD(image, 2)
return scharr(image, mask=mask, axis=1)
[文档]
def prewitt(image, mask=None, *, axis=None, mode='reflect', cval=0.0):
"""Find the edge magnitude using the Prewitt transform.
Parameters
----------
image : array
The input image.
mask : array of bool, optional
Clip the output image to this mask. (Values where mask=0 will be set
to 0.)
axis : int or sequence of int, optional
Compute the edge filter along this axis. If not provided, the edge
magnitude is computed. This is defined as::
prw_mag = np.sqrt(sum([prewitt(image, axis=i)**2
for i in range(image.ndim)]) / image.ndim)
The magnitude is also computed if axis is a sequence.
mode : str or sequence of str, optional
The boundary mode for the convolution. See `scipy.ndimage.convolve`
for a description of the modes. This can be either a single boundary
mode or one boundary mode per axis.
cval : float, optional
When `mode` is ``'constant'``, this is the constant used in values
outside the boundary of the image data.
Returns
-------
output : array of float
The Prewitt edge map.
See also
--------
prewitt_h, prewitt_v : horizontal and vertical edge detection.
sobel, scharr, farid, skimage.feature.canny
Notes
-----
The edge magnitude depends slightly on edge directions, since the
approximation of the gradient operator by the Prewitt operator is not
completely rotation invariant. For a better rotation invariance, the Scharr
operator should be used. The Sobel operator has a better rotation
invariance than the Prewitt operator, but a worse rotation invariance than
the Scharr operator.
Examples
--------
>>> from skimage import data
>>> from skimage import filters
>>> camera = data.camera()
>>> edges = filters.prewitt(camera)
"""
output = _generic_edge_filter(
image, smooth_weights=PREWITT_SMOOTH, axis=axis, mode=mode, cval=cval
)
output = _mask_filter_result(output, mask)
return output
[文档]
def prewitt_h(image, mask=None):
"""Find the horizontal edges of an image using the Prewitt transform.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Prewitt edge map.
Notes
-----
We use the following kernel::
1/3 1/3 1/3
0 0 0
-1/3 -1/3 -1/3
"""
check_nD(image, 2)
return prewitt(image, mask=mask, axis=0)
[文档]
def prewitt_v(image, mask=None):
"""Find the vertical edges of an image using the Prewitt transform.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Prewitt edge map.
Notes
-----
We use the following kernel::
1/3 0 -1/3
1/3 0 -1/3
1/3 0 -1/3
"""
check_nD(image, 2)
return prewitt(image, mask=mask, axis=1)
[文档]
def roberts(image, mask=None):
"""Find the edge magnitude using Roberts' cross operator.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Roberts' Cross edge map.
See also
--------
roberts_pos_diag, roberts_neg_diag : diagonal edge detection.
sobel, scharr, prewitt, skimage.feature.canny
Examples
--------
>>> from skimage import data
>>> camera = data.camera()
>>> from skimage import filters
>>> edges = filters.roberts(camera)
"""
check_nD(image, 2)
out = np.sqrt(
roberts_pos_diag(image, mask) ** 2 + roberts_neg_diag(image, mask) ** 2
)
out /= np.sqrt(2)
return out
[文档]
def roberts_pos_diag(image, mask=None):
"""Find the cross edges of an image using Roberts' cross operator.
The kernel is applied to the input image to produce separate measurements
of the gradient component one orientation.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Robert's edge map.
Notes
-----
We use the following kernel::
1 0
0 -1
"""
check_nD(image, 2)
if image.dtype.kind == 'f':
float_dtype = _supported_float_type(image.dtype)
image = image.astype(float_dtype, copy=False)
else:
image = img_as_float(image)
result = convolve(image, ROBERTS_PD_WEIGHTS)
return _mask_filter_result(result, mask)
[文档]
def roberts_neg_diag(image, mask=None):
"""Find the cross edges of an image using the Roberts' Cross operator.
The kernel is applied to the input image to produce separate measurements
of the gradient component one orientation.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Robert's edge map.
Notes
-----
We use the following kernel::
0 1
-1 0
"""
check_nD(image, 2)
if image.dtype.kind == 'f':
float_dtype = _supported_float_type(image.dtype)
image = image.astype(float_dtype, copy=False)
else:
image = img_as_float(image)
result = convolve(image, ROBERTS_ND_WEIGHTS)
return _mask_filter_result(result, mask)
[文档]
def laplace(image, ksize=3, mask=None):
"""Find the edges of an image using the Laplace operator.
Parameters
----------
image : ndarray
Image to process.
ksize : int, optional
Define the size of the discrete Laplacian operator such that it
will have a size of (ksize,) * image.ndim.
mask : ndarray, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : ndarray
The Laplace edge map.
Notes
-----
The Laplacian operator is generated using the function
skimage.restoration.uft.laplacian().
"""
if image.dtype.kind == 'f':
float_dtype = _supported_float_type(image.dtype)
image = image.astype(float_dtype, copy=False)
else:
image = img_as_float(image)
# Create the discrete Laplacian operator - We keep only the real part of
# the filter
_, laplace_op = laplacian(image.ndim, (ksize,) * image.ndim)
result = convolve(image, laplace_op)
return _mask_filter_result(result, mask)
[文档]
def farid(image, mask=None, *, axis=None, mode='reflect', cval=0.0):
"""Find the edge magnitude using the Farid transform.
Parameters
----------
image : array
The input image.
mask : array of bool, optional
Clip the output image to this mask. (Values where mask=0 will be set
to 0.)
axis : int or sequence of int, optional
Compute the edge filter along this axis. If not provided, the edge
magnitude is computed. This is defined as::
farid_mag = np.sqrt(sum([farid(image, axis=i)**2
for i in range(image.ndim)]) / image.ndim)
The magnitude is also computed if axis is a sequence.
mode : str or sequence of str, optional
The boundary mode for the convolution. See `scipy.ndimage.convolve`
for a description of the modes. This can be either a single boundary
mode or one boundary mode per axis.
cval : float, optional
When `mode` is ``'constant'``, this is the constant used in values
outside the boundary of the image data.
Returns
-------
output : array of float
The Farid edge map.
See also
--------
farid_h, farid_v : horizontal and vertical edge detection.
scharr, sobel, prewitt, skimage.feature.canny
Notes
-----
Take the square root of the sum of the squares of the horizontal and
vertical derivatives to get a magnitude that is somewhat insensitive to
direction. Similar to the Scharr operator, this operator is designed with
a rotation invariance constraint.
References
----------
.. [1] Farid, H. and Simoncelli, E. P., "Differentiation of discrete
multidimensional signals", IEEE Transactions on Image Processing
13(4): 496-508, 2004. :DOI:`10.1109/TIP.2004.823819`
.. [2] Wikipedia, "Farid and Simoncelli Derivatives." Available at:
<https://en.wikipedia.org/wiki/Image_derivatives#Farid_and_Simoncelli_Derivatives>
Examples
--------
>>> from skimage import data
>>> camera = data.camera()
>>> from skimage import filters
>>> edges = filters.farid(camera)
"""
output = _generic_edge_filter(
image,
smooth_weights=farid_smooth,
edge_weights=farid_edge,
axis=axis,
mode=mode,
cval=cval,
)
output = _mask_filter_result(output, mask)
return output
[文档]
def farid_h(image, *, mask=None):
"""Find the horizontal edges of an image using the Farid transform.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Farid edge map.
Notes
-----
The kernel was constructed using the 5-tap weights from [1].
References
----------
.. [1] Farid, H. and Simoncelli, E. P., "Differentiation of discrete
multidimensional signals", IEEE Transactions on Image Processing
13(4): 496-508, 2004. :DOI:`10.1109/TIP.2004.823819`
.. [2] Farid, H. and Simoncelli, E. P. "Optimally rotation-equivariant
directional derivative kernels", In: 7th International Conference on
Computer Analysis of Images and Patterns, Kiel, Germany. Sep, 1997.
"""
check_nD(image, 2)
if image.dtype.kind == 'f':
float_dtype = _supported_float_type(image.dtype)
image = image.astype(float_dtype, copy=False)
else:
image = img_as_float(image)
result = convolve(image, HFARID_WEIGHTS)
return _mask_filter_result(result, mask)
[文档]
def farid_v(image, *, mask=None):
"""Find the vertical edges of an image using the Farid transform.
Parameters
----------
image : 2-D array
Image to process.
mask : 2-D array, optional
An optional mask to limit the application to a certain area.
Note that pixels surrounding masked regions are also masked to
prevent masked regions from affecting the result.
Returns
-------
output : 2-D array
The Farid edge map.
Notes
-----
The kernel was constructed using the 5-tap weights from [1].
References
----------
.. [1] Farid, H. and Simoncelli, E. P., "Differentiation of discrete
multidimensional signals", IEEE Transactions on Image Processing
13(4): 496-508, 2004. :DOI:`10.1109/TIP.2004.823819`
"""
check_nD(image, 2)
if image.dtype.kind == 'f':
float_dtype = _supported_float_type(image.dtype)
image = image.astype(float_dtype, copy=False)
else:
image = img_as_float(image)
result = convolve(image, VFARID_WEIGHTS)
return _mask_filter_result(result, mask)
