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)
image = img_as_float(image)
result = ndi.convolve(image, cp.asarray(VFARID_WEIGHTS))
return _mask_filter_result(result, mask)
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().
"""
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 = ndi.convolve(image, laplace_op)
return _mask_filter_result(result, mask)
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)
image = img_as_float(image)
result = ndi.convolve(image, cp.asarray(HFARID_WEIGHTS))
return _mask_filter_result(result, mask)
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)
image = img_as_float(image)
result = ndi.convolve(image, cp.asarray(ROBERTS_ND_WEIGHTS))
return _mask_filter_result(result, mask)
def _interpolate_image(image, *, multichannel=False):
"""Replacing each pixel in ``image`` with the average of its neighbors.
Parameters
----------
image : ndarray
Input data to be interpolated.
multichannel : bool, optional
Whether the last axis of the image is to be interpreted as multiple
channels or another spatial dimension.
Returns
-------
interp : ndarray
Interpolated version of `image`.
"""
spatialdims = image.ndim if not multichannel else image.ndim - 1
conv_filter = ndi.generate_binary_structure(spatialdims,
1).astype(image.dtype)
conv_filter.ravel()[conv_filter.size // 2] = 0
conv_filter /= conv_filter.sum()
if multichannel:
conv_filter = conv_filter[..., np.newaxis]
interp = ndi.convolve(image, conv_filter, mode="mirror")
return interp
def test_image_shape():
"""Test that shape of output image in deconvolution is same as input.
This addresses issue #1172.
"""
point = cp.zeros((5, 5), np.float)
point[2, 2] = 1.0
psf = ndi.gaussian_filter(point, sigma=1.0)
# image shape: (45, 45), as reported in #1172
image = cp.asarray(test_img[110:155, 225:270]) # just the face
image_conv = ndi.convolve(image, psf)
deconv_sup = restoration.wiener(image_conv, psf, 1)
deconv_un = restoration.unsupervised_wiener(image_conv, psf)[0]
# test the shape
assert image.shape == deconv_sup.shape
assert image.shape == deconv_un.shape
# test the reconstruction error
sup_relative_error = cp.abs(deconv_sup - image) / image
un_relative_error = cp.abs(deconv_un - image) / image
cp.testing.assert_array_less(np.median(sup_relative_error.get()), 0.1)
cp.testing.assert_array_less(np.median(un_relative_error.get()), 0.1)
def perimeter(image, neighbourhood=4):
"""Calculate total perimeter of all objects in binary image.
Parameters
----------
image : (N, M) ndarray
2D binary image.
neighbourhood : 4 or 8, optional
Neighborhood connectivity for border pixel determination. It is used to
compute the contour. A higher neighbourhood widens the border on which
the perimeter is computed.
Returns
-------
perimeter : float
Total perimeter of all objects in binary image.
References
----------
.. [1] K. Benkrid, D. Crookes. Design and FPGA Implementation of
a Perimeter Estimator. The Queen's University of Belfast.
http://www.cs.qub.ac.uk/~d.crookes/webpubs/papers/perimeter.doc
Examples
--------
>>> from skimage import data, util
>>> from skimage.measure import label
>>> # coins image (binary)
>>> img_coins = data.coins() > 110
>>> # total perimeter of all objects in the image
>>> perimeter(img_coins, neighbourhood=4) # doctest: +ELLIPSIS
7796.867...
>>> perimeter(img_coins, neighbourhood=8) # doctest: +ELLIPSIS
8806.268...
"""
if image.ndim != 2:
raise NotImplementedError("`perimeter` supports 2D images only")
if neighbourhood == 4:
strel = STREL_4
else:
strel = STREL_8
strel = cp.asarray(strel)
image = image.astype(cp.uint8)
eroded_image = ndi.binary_erosion(image, strel, border_value=0)
border_image = image - eroded_image
perimeter_weights = cp.zeros(50, dtype=cp.double)
perimeter_weights[[5, 7, 15, 17, 25, 27]] = 1
perimeter_weights[[21, 33]] = sqrt(2)
perimeter_weights[[13, 23]] = (1 + sqrt(2)) / 2
perimeter_image = ndi.convolve(
border_image,
cp.asarray([[10, 2, 10], [2, 1, 2], [10, 2, 10]]),
mode="constant",
cval=0,
)
# You can also write
# return perimeter_weights[perimeter_image].sum()
# but that was measured as taking much longer than bincount + cp.dot (5x
# as much time)
perimeter_histogram = cp.bincount(perimeter_image.ravel(), minlength=50)
total_perimeter = perimeter_histogram @ perimeter_weights
return total_perimeter
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
output = cp.zeros(image.shape, dtype=float)
# Note: added these to cp.asarray calls not present in skimage
# may want to remove, but will probably require updating the tests.
edge_weights = cp.asarray(edge_weights)
smooth_weights = cp.asarray(smooth_weights)
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="reflect")
if return_magnitude:
ax_output *= ax_output
output += ax_output
if return_magnitude:
output /= ndim
output = cp.sqrt(output, out=output)
return output
def gabor(
image,
frequency,
theta=0,
bandwidth=1,
sigma_x=None,
sigma_y=None,
n_stds=3,
offset=0,
mode="reflect",
cval=0,
):
"""Return real and imaginary responses to Gabor filter.
The real and imaginary parts of the Gabor filter kernel are applied to the
image and the response is returned as a pair of arrays.
Gabor filter is a linear filter with a Gaussian kernel which is modulated
by a sinusoidal plane wave. Frequency and orientation representations of
the Gabor filter are similar to those of the human visual system.
Gabor filter banks are commonly used in computer vision and image
processing. They are especially suitable for edge detection and texture
classification.
Parameters
----------
image : 2-D array
Input image.
frequency : float
Spatial frequency of the harmonic function. Specified in pixels.
theta : float, optional
Orientation in radians. If 0, the harmonic is in the x-direction.
bandwidth : float, optional
The bandwidth captured by the filter. For fixed bandwidth, ``sigma_x``
and ``sigma_y`` will decrease with increasing frequency. This value is
ignored if ``sigma_x`` and ``sigma_y`` are set by the user.
sigma_x, sigma_y : float, optional
Standard deviation in x- and y-directions. These directions apply to
the kernel *before* rotation. If `theta = pi/2`, then the kernel is
rotated 90 degrees so that ``sigma_x`` controls the *vertical*
direction.
n_stds : scalar, optional
The linear size of the kernel is n_stds (3 by default) standard
deviations.
offset : float, optional
Phase offset of harmonic function in radians.
mode : {'constant', 'nearest', 'reflect', 'mirror', 'wrap'}, optional
Mode used to convolve image with a kernel, passed to `ndi.convolve`
cval : scalar, optional
Value to fill past edges of input if ``mode`` of convolution is
'constant'. The parameter is passed to `ndi.convolve`.
Returns
-------
real, imag : arrays
Filtered images using the real and imaginary parts of the Gabor filter
kernel. Images are of the same dimensions as the input one.
References
----------
.. [1] https://en.wikipedia.org/wiki/Gabor_filter
.. [2] https://web.archive.org/web/20180127125930/http://mplab.ucsd.edu/tutorials/gabor.pdf
Examples
--------
>>> from skimage.filters import gabor
>>> from skimage import data, io
>>> from matplotlib import pyplot as plt # doctest: +SKIP
>>> image = data.coins()
>>> # detecting edges in a coin image
>>> filt_real, filt_imag = gabor(image, frequency=0.6)
>>> plt.figure() # doctest: +SKIP
>>> io.imshow(filt_real) # doctest: +SKIP
>>> io.show() # doctest: +SKIP
>>> # less sensitivity to finer details with the lower frequency kernel
>>> filt_real, filt_imag = gabor(image, frequency=0.1)
>>> plt.figure() # doctest: +SKIP
>>> io.imshow(filt_real) # doctest: +SKIP
>>> io.show() # doctest: +SKIP
"""
check_nD(image, 2)
g = gabor_kernel(
frequency, theta, bandwidth, sigma_x, sigma_y, n_stds, offset
)
filtered = ndi.convolve(image, g, mode=mode, cval=cval)
return filtered.real, filtered.imag
