def hsobel(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 and return the absolute value of the
result at each point::
1 2 1
0 0 0
-1 -2 -1
"""
assert_nD(image, 2)
image = img_as_float(image)
result = np.abs(convolve(image, HSOBEL_WEIGHTS))
return _mask_filter_result(result, mask)
def sobel(image, mask=None):
"""Find the edge magnitude 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
-----
Take the square root of the sum of the squares of the horizontal and
vertical Sobels to get a magnitude that's somewhat insensitive to
direction.
Note that ``scipy.ndimage.sobel`` returns a directional Sobel which
has to be further processed to perform edge detection.
"""
assert_nD(image, 2)
return np.sqrt(hsobel(image, mask)**2 + vsobel(image, mask)**2)
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 0 -1
1 0 -1
1 0 -1
"""
assert_nD(image, 2)
image = img_as_float(image)
result = convolve(image, VPREWITT_WEIGHTS)
return _mask_filter_result(result, mask)
def prewitt(image, mask=None):
"""Find the edge magnitude 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
-----
Return the square root of the sum of squares of the horizontal
and vertical Prewitt transforms.
"""
assert_nD(image, 2)
out = np.sqrt(prewitt_h(image, mask)**2 + prewitt_v(image, mask)**2)
out /= np.sqrt(2)
return out
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.
"""
assert_nD(image, 2)
image = img_as_float(image)
result = convolve(image, VSCHARR_WEIGHTS)
return _mask_filter_result(result, mask)
def _apply(func,
image,
selem,
out,
mask,
shift_x,
shift_y,
s0,
s1,
out_dtype=None):
assert_nD(image, 2)
image, selem, out, mask, max_bin = _handle_input(image, selem, out, mask,
out_dtype)
func(image,
selem,
shift_x=shift_x,
shift_y=shift_y,
mask=mask,
out=out,
max_bin=max_bin,
s0=s0,
s1=s1)
return out.reshape(out.shape[:2])
def _check_input(image, init_level_set):
"""Check that shapes of `image` and `init_level_set` match."""
assert_nD(image, [2, 3])
if len(image.shape) != len(init_level_set.shape):
raise ValueError("The dimensions of the initial level set do not "
"match the dimensions of the image.")
def roberts_negative_diagonal(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 and return the absolute value of the
result at each point::
0 1
-1 0
"""
assert_nD(image, 2)
image = img_as_float(image)
result = np.abs(convolve(image, ROBERTS_ND_WEIGHTS))
return _mask_filter_result(result, mask)
def prewitt(image, mask=None):
"""Find the edge magnitude 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
-----
Return the square root of the sum of squares of the horizontal
and vertical Prewitt transforms.
"""
assert_nD(image, 2)
out = np.sqrt(hprewitt(image, mask)**2 + vprewitt(image, mask)**2)
out /= np.sqrt(2)
return out
def forward(data, impulse_response=None, filter_params={},
predefined_filter=None):
"""Apply the given filter to data.
Parameters
----------
data : (M,N) ndarray
Input data.
impulse_response : callable `f(r, c, **filter_params)`
Impulse response of the filter. See LPIFilter2D.__init__.
filter_params : dict
Additional keyword parameters to the impulse_response function.
Other Parameters
----------------
predefined_filter : LPIFilter2D
If you need to apply the same filter multiple times over different
images, construct the LPIFilter2D and specify it here.
Examples
--------
Gaussian filter:
>>> def filt_func(r, c):
... return np.exp(-np.hypot(r, c)/1)
>>>
>>> from skimage import data
>>> filtered = forward(data.coins(), filt_func)
"""
assert_nD(data, 2, 'data')
if predefined_filter is None:
predefined_filter = LPIFilter2D(impulse_response, **filter_params)
return predefined_filter(data)
def hsobel(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 and return the absolute value of the
result at each point::
1 2 1
0 0 0
-1 -2 -1
"""
assert_nD(image, 2)
image = img_as_float(image)
result = np.abs(convolve(image, HSOBEL_WEIGHTS))
return _mask_filter_result(result, mask)
def sobel(image, mask=None):
"""Find the edge magnitude 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
-----
Take the square root of the sum of the squares of the horizontal and
vertical Sobels to get a magnitude that's somewhat insensitive to
direction.
Note that ``scipy.ndimage.sobel`` returns a directional Sobel which
has to be further processed to perform edge detection.
"""
assert_nD(image, 2)
out = np.sqrt(hsobel(image, mask)**2 + vsobel(image, mask)**2)
out /= np.sqrt(2)
return out
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
"""
assert_nD(image, 2)
image = img_as_float(image)
result = convolve(image, ROBERTS_ND_WEIGHTS)
return _mask_filter_result(result, mask)
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
--------
sobel, scharr, prewitt, feature.canny
Examples
--------
>>> from skimage import data
>>> camera = data.camera()
>>> from skimage import filters
>>> edges = filters.roberts(camera)
"""
assert_nD(image, 2)
out = np.sqrt(roberts_pos_diag(image, mask)**2 +
roberts_neg_diag(image, mask)**2)
out /= np.sqrt(2)
return out
def local_binary_pattern(image, P, R, method='default'):
"""Gray scale and rotation invariant LBP (Local Binary Patterns).
LBP is an invariant descriptor that can be used for texture classification.
Parameters
----------
image : (N, M) array
Graylevel image.
P : int
Number of circularly symmetric neighbour set points (quantization of
the angular space).
R : float
Radius of circle (spatial resolution of the operator).
method : {'default', 'ror', 'uniform', 'var'}
Method to determine the pattern.
* 'default': original local binary pattern which is gray scale but not
rotation invariant.
* 'ror': extension of default implementation which is gray scale and
rotation invariant.
* 'uniform': improved rotation invariance with uniform patterns and
finer quantization of the angular space which is gray scale and
rotation invariant.
* 'nri_uniform': non rotation-invariant uniform patterns variant
which is only gray scale invariant [2].
* 'var': rotation invariant variance measures of the contrast of local
image texture which is rotation but not gray scale invariant.
Returns
-------
output : (N, M) array
LBP image.
References
----------
.. [1] Multiresolution Gray-Scale and Rotation Invariant Texture
Classification with Local Binary Patterns.
Timo Ojala, Matti Pietikainen, Topi Maenpaa.
http://www.rafbis.it/biplab15/images/stories/docenti/Danielriccio/Articoliriferimento/LBP.pdf, 2002.
.. [2] Face recognition with local binary patterns.
Timo Ahonen, Abdenour Hadid, Matti Pietikainen,
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.6851,
2004.
"""
assert_nD(image, 2)
methods = {
'default': ord('D'),
'ror': ord('R'),
'uniform': ord('U'),
'nri_uniform': ord('N'),
'var': ord('V')
}
image = np.ascontiguousarray(image, dtype=np.double)
output = _local_binary_pattern(image, P, R, methods[method.lower()])
return output
def extract(self, image, keypoints):
"""Extract BRIEF binary descriptors for given keypoints in image.
Parameters
----------
image : 2D array
Input image.
keypoints : (N, 2) array
Keypoint coordinates as ``(row, col)``.
"""
assert_nD(image, 2)
np.random.seed(self.sample_seed)
image = _prepare_grayscale_input_2D(image)
# Gaussian low-pass filtering to alleviate noise sensitivity
image = np.ascontiguousarray(gaussian_filter(image, self.sigma))
# Sampling pairs of decision pixels in patch_size x patch_size window
desc_size = self.descriptor_size
patch_size = self.patch_size
if self.mode == 'normal':
samples = (patch_size / 5.0) * np.random.randn(desc_size * 8)
samples = np.array(samples, dtype=np.int32)
samples = samples[(samples < (patch_size // 2))
& (samples > -(patch_size - 2) // 2)]
pos1 = samples[:desc_size * 2].reshape(desc_size, 2)
pos2 = samples[desc_size * 2:desc_size * 4].reshape(desc_size, 2)
elif self.mode == 'uniform':
samples = np.random.randint(-(patch_size - 2) // 2,
(patch_size // 2) + 1,
(desc_size * 2, 2))
samples = np.array(samples, dtype=np.int32)
pos1, pos2 = np.split(samples, 2)
pos1 = np.ascontiguousarray(pos1)
pos2 = np.ascontiguousarray(pos2)
# Removing keypoints that are within (patch_size / 2) distance from the
# image border
self.mask = _mask_border_keypoints(image.shape, keypoints,
patch_size // 2)
keypoints = np.array(keypoints[self.mask, :],
dtype=np.intp,
order='C',
copy=False)
self.descriptors = np.zeros((keypoints.shape[0], desc_size),
dtype=bool,
order='C')
_brief_loop(image, self.descriptors.view(np.uint8), keypoints, pos1,
pos2)
def local_binary_pattern(image, P, R, method='default'):
"""Gray scale and rotation invariant LBP (Local Binary Patterns).
LBP is an invariant descriptor that can be used for texture classification.
Parameters
----------
image : (N, M) array
Graylevel image.
P : int
Number of circularly symmetric neighbour set points (quantization of
the angular space).
R : float
Radius of circle (spatial resolution of the operator).
method : {'default', 'ror', 'uniform', 'var'}
Method to determine the pattern.
* 'default': original local binary pattern which is gray scale but not
rotation invariant.
* 'ror': extension of default implementation which is gray scale and
rotation invariant.
* 'uniform': improved rotation invariance with uniform patterns and
finer quantization of the angular space which is gray scale and
rotation invariant.
* 'nri_uniform': non rotation-invariant uniform patterns variant
which is only gray scale invariant [2].
* 'var': rotation invariant variance measures of the contrast of local
image texture which is rotation but not gray scale invariant.
Returns
-------
output : (N, M) array
LBP image.
References
----------
.. [1] Multiresolution Gray-Scale and Rotation Invariant Texture
Classification with Local Binary Patterns.
Timo Ojala, Matti Pietikainen, Topi Maenpaa.
http://www.rafbis.it/biplab15/images/stories/docenti/Danielriccio/Articoliriferimento/LBP.pdf, 2002.
.. [2] Face recognition with local binary patterns.
Timo Ahonen, Abdenour Hadid, Matti Pietikainen,
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.6851,
2004.
"""
assert_nD(image, 2)
methods = {
'default': ord('D'),
'ror': ord('R'),
'uniform': ord('U'),
'nri_uniform': ord('N'),
'var': ord('V')
}
image = np.ascontiguousarray(image, dtype=np.double)
output = _local_binary_pattern(image, P, R, methods[method.lower()])
return output
def gabor_filter(image,
frequency,
theta=0,
bandwidth=1,
sigma_x=None,
sigma_y=None,
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.
Frequency and orientation representations of the Gabor filter are similar
to those of the human visual system. It is especially suitable for texture
classification using Gabor filter banks.
Parameters
----------
image : array
Input image.
frequency : float
Frequency of the harmonic function.
theta : float
Orientation in radians. If 0, the harmonic is in the x-direction.
bandwidth : float
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
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.
offset : float, optional
Phase offset of harmonic function in radians.
Returns
-------
real, imag : arrays
Filtered images using the real and imaginary parts of the Gabor filter
kernel.
References
----------
.. [1] http://en.wikipedia.org/wiki/Gabor_filter
.. [2] http://mplab.ucsd.edu/tutorials/gabor.pdf
"""
assert_nD(image, 2)
g = gabor_kernel(frequency, theta, bandwidth, sigma_x, sigma_y, offset)
filtered_real = ndimage.convolve(image, np.real(g), mode=mode, cval=cval)
filtered_imag = ndimage.convolve(image, np.imag(g), mode=mode, cval=cval)
return filtered_real, filtered_imag
def extract(self, image, keypoints):
"""Extract BRIEF binary descriptors for given keypoints in image.
Parameters
----------
image : 2D array
Input image.
keypoints : (N, 2) array
Keypoint coordinates as ``(row, col)``.
"""
assert_nD(image, 2)
np.random.seed(self.sample_seed)
image = _prepare_grayscale_input_2D(image)
# Gaussian low-pass filtering to alleviate noise sensitivity
image = np.ascontiguousarray(gaussian_filter(image, self.sigma))
# Sampling pairs of decision pixels in patch_size x patch_size window
desc_size = self.descriptor_size
patch_size = self.patch_size
if self.mode == 'normal':
samples = (patch_size / 5.0) * np.random.randn(desc_size * 8)
samples = np.array(samples, dtype=np.int32)
samples = samples[(samples < (patch_size // 2))
& (samples > - (patch_size - 2) // 2)]
pos1 = samples[:desc_size * 2].reshape(desc_size, 2)
pos2 = samples[desc_size * 2:desc_size * 4].reshape(desc_size, 2)
elif self.mode == 'uniform':
samples = np.random.randint(-(patch_size - 2) // 2,
(patch_size // 2) + 1,
(desc_size * 2, 2))
samples = np.array(samples, dtype=np.int32)
pos1, pos2 = np.split(samples, 2)
pos1 = np.ascontiguousarray(pos1)
pos2 = np.ascontiguousarray(pos2)
# Removing keypoints that are within (patch_size / 2) distance from the
# image border
self.mask = _mask_border_keypoints(image.shape, keypoints,
patch_size // 2)
keypoints = np.array(keypoints[self.mask, :], dtype=np.intp,
order='C', copy=False)
self.descriptors = np.zeros((keypoints.shape[0], desc_size),
dtype=bool, order='C')
_brief_loop(image, self.descriptors.view(np.uint8), keypoints,
pos1, pos2)
def _apply(func, image, selem, out, mask, shift_x, shift_y, s0, s1,
out_dtype=None):
assert_nD(image, 2)
image, selem, out, mask, max_bin = _handle_input(image, selem, out, mask,
out_dtype)
func(image, selem, shift_x=shift_x, shift_y=shift_y, mask=mask,
out=out, max_bin=max_bin, s0=s0, s1=s1)
return out.reshape(out.shape[:2])
def extract(self, image, keypoints, scales, orientations):
"""Extract rBRIEF binary descriptors for given keypoints in image.
Note that the keypoints must be extracted using the same `downscale`
and `n_scales` parameters. Additionally, if you want to extract both
keypoints and descriptors you should use the faster
`detect_and_extract`.
Parameters
----------
image : 2D array
Input image.
keypoints : (N, 2) array
Keypoint coordinates as ``(row, col)``.
scales : (N, ) array
Corresponding scales.
orientations : (N, ) array
Corresponding orientations in radians.
"""
assert_nD(image, 2)
pyramid = self._build_pyramid(image)
descriptors_list = []
mask_list = []
# Determine octaves from scales
octaves = (np.log(scales) / np.log(self.downscale)).astype(np.intp)
for octave in range(len(pyramid)):
# Mask for all keypoints in current octave
octave_mask = octaves == octave
if np.sum(octave_mask) > 0:
octave_image = np.ascontiguousarray(pyramid[octave])
octave_keypoints = keypoints[octave_mask]
octave_keypoints /= self.downscale ** octave
octave_orientations = orientations[octave_mask]
descriptors, mask = self._extract_octave(octave_image,
octave_keypoints,
octave_orientations)
descriptors_list.append(descriptors)
mask_list.append(mask)
self.descriptors = np.vstack(descriptors_list).view(np.bool)
self.mask_ = np.hstack(mask_list)
def extract(self, image, keypoints, scales, orientations):
"""Extract rBRIEF binary descriptors for given keypoints in image.
Note that the keypoints must be extracted using the same `downscale`
and `n_scales` parameters. Additionally, if you want to extract both
keypoints and descriptors you should use the faster
`detect_and_extract`.
Parameters
----------
image : 2D array
Input image.
keypoints : (N, 2) array
Keypoint coordinates as ``(row, col)``.
scales : (N, ) array
Corresponding scales.
orientations : (N, ) array
Corresponding orientations in radians.
"""
assert_nD(image, 2)
pyramid = self._build_pyramid(image)
descriptors_list = []
mask_list = []
# Determine octaves from scales
octaves = (np.log(scales) / np.log(self.downscale)).astype(np.intp)
for octave in range(len(pyramid)):
# Mask for all keypoints in current octave
octave_mask = octaves == octave
if np.sum(octave_mask) > 0:
octave_image = np.ascontiguousarray(pyramid[octave])
octave_keypoints = keypoints[octave_mask]
octave_keypoints /= self.downscale**octave
octave_orientations = orientations[octave_mask]
descriptors, mask = self._extract_octave(
octave_image, octave_keypoints, octave_orientations)
descriptors_list.append(descriptors)
mask_list.append(mask)
self.descriptors = np.vstack(descriptors_list).view(np.bool)
self.mask_ = np.hstack(mask_list)
def __call__(self, data):
"""Apply the filter to the given data.
Parameters
----------
data : (M,N) ndarray
"""
assert_nD(data, 2, 'data')
F, G = self._prepare(data)
out = np.dual.ifftn(F * G)
out = np.abs(_centre(out, data.shape))
return out
def __call__(self, data):
"""Apply the filter to the given data.
Parameters
----------
data : (M,N) ndarray
"""
assert_nD(data, 2, 'data')
F, G = self._prepare(data)
out = np.dual.ifftn(F * G)
out = np.abs(_centre(out, data.shape))
return out
def gabor_filter(image, frequency, theta=0, bandwidth=1, sigma_x=None,
sigma_y=None, 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.
Frequency and orientation representations of the Gabor filter are similar
to those of the human visual system. It is especially suitable for texture
classification using Gabor filter banks.
Parameters
----------
image : array
Input image.
frequency : float
Frequency of the harmonic function.
theta : float
Orientation in radians. If 0, the harmonic is in the x-direction.
bandwidth : float
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
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.
offset : float, optional
Phase offset of harmonic function in radians.
Returns
-------
real, imag : arrays
Filtered images using the real and imaginary parts of the Gabor filter
kernel.
References
----------
.. [1] http://en.wikipedia.org/wiki/Gabor_filter
.. [2] http://mplab.ucsd.edu/tutorials/gabor.pdf
"""
assert_nD(image, 2)
g = gabor_kernel(frequency, theta, bandwidth, sigma_x, sigma_y, offset)
filtered_real = ndimage.convolve(image, np.real(g), mode=mode, cval=cval)
filtered_imag = ndimage.convolve(image, np.imag(g), mode=mode, cval=cval)
return filtered_real, filtered_imag
def detect(self, image):
"""Detect oriented FAST keypoints along with the corresponding scale.
Parameters
----------
image : 2D array
Input image.
"""
assert_nD(image, 2)
pyramid = self._build_pyramid(image)
keypoints_list = []
orientations_list = []
scales_list = []
responses_list = []
for octave in range(len(pyramid)):
octave_image = np.ascontiguousarray(pyramid[octave])
keypoints, orientations, responses = \
self._detect_octave(octave_image)
keypoints_list.append(keypoints * self.downscale**octave)
orientations_list.append(orientations)
scales_list.append(self.downscale**octave *
np.ones(keypoints.shape[0], dtype=np.intp))
responses_list.append(responses)
keypoints = np.vstack(keypoints_list)
orientations = np.hstack(orientations_list)
scales = np.hstack(scales_list)
responses = np.hstack(responses_list)
if keypoints.shape[0] < self.n_keypoints:
self.keypoints = keypoints
self.scales = scales
self.orientations = orientations
self.responses = responses
else:
# Choose best n_keypoints according to Harris corner response
best_indices = responses.argsort()[::-1][:self.n_keypoints]
self.keypoints = keypoints[best_indices]
self.scales = scales[best_indices]
self.orientations = orientations[best_indices]
self.responses = responses[best_indices]
def sobel(image, mask=None):
"""Find the edge magnitude 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.
See also
--------
scharr, prewitt, roberts, feature.canny
Notes
-----
Take the square root of the sum of the squares of the horizontal and
vertical Sobels to get a magnitude that's somewhat insensitive to
direction.
The 3x3 convolution kernel used in the horizontal and vertical Sobels is
an approximation of the gradient of the image (with some slight blurring
since 9 pixels are used to compute the gradient at a given pixel). As an
approximation of the gradient, the Sobel operator is not completely
rotation-invariant. The Scharr operator should be used for a better
rotation invariance.
Note that ``scipy.ndimage.sobel`` returns a directional Sobel which
has to be further processed to perform edge detection.
Examples
--------
>>> from skimage import data
>>> camera = data.camera()
>>> from skimage import filters
>>> edges = filters.sobel(camera)
"""
assert_nD(image, 2)
out = np.sqrt(sobel_h(image, mask)**2 + sobel_v(image, mask)**2)
out /= np.sqrt(2)
return out
def detect(self, image):
"""Detect oriented FAST keypoints along with the corresponding scale.
Parameters
----------
image : 2D array
Input image.
"""
assert_nD(image, 2)
pyramid = self._build_pyramid(image)
keypoints_list = []
orientations_list = []
scales_list = []
responses_list = []
for octave in range(len(pyramid)):
octave_image = np.ascontiguousarray(pyramid[octave])
keypoints, orientations, responses = \
self._detect_octave(octave_image)
keypoints_list.append(keypoints * self.downscale ** octave)
orientations_list.append(orientations)
scales_list.append(self.downscale ** octave
* np.ones(keypoints.shape[0], dtype=np.intp))
responses_list.append(responses)
keypoints = np.vstack(keypoints_list)
orientations = np.hstack(orientations_list)
scales = np.hstack(scales_list)
responses = np.hstack(responses_list)
if keypoints.shape[0] < self.n_keypoints:
self.keypoints = keypoints
self.scales = scales
self.orientations = orientations
self.responses = responses
else:
# Choose best n_keypoints according to Harris corner response
best_indices = responses.argsort()[::-1][:self.n_keypoints]
self.keypoints = keypoints[best_indices]
self.scales = scales[best_indices]
self.orientations = orientations[best_indices]
self.responses = responses[best_indices]
def angular_lbp(image, P, R, method='default'):
"""Angular Difference LBP"""
assert_nD(image, 2)
methods = {
'default': ord('D'),
'ror': ord('R'),
'uniform': ord('U'),
'nri_uniform': ord('N'),
'var': ord('V'),
}
image = np.ascontiguousarray(image, dtype=np.double)
output = _lbp_ang._angular_lbp(image, P, R, methods[method.lower()])
return output
def ni_lbp(image, P, R, method='default'):
"""Neighbour Intensity LBP"""
assert_nD(image, 2)
methods = {
'default': ord('D'),
'ror': ord('R'),
'uniform': ord('U'),
'nri_uniform': ord('N'),
'var': ord('V'),
}
image = np.ascontiguousarray(image, dtype=np.double)
output = _nilbp._ni_lbp(image, P, R, methods[method.lower()])
return output
def radial_lbp(image, P, R_OUT, R_IN, method='default'):
"""Radial Difference LBP"""
assert_nD(image, 2)
methods = {
'default': ord('D'),
'ror': ord('R'),
'uniform': ord('U'),
'nri_uniform': ord('N'),
'var': ord('V'),
}
image = np.ascontiguousarray(image, dtype=np.double)
output = _lbp_rad._radial_lbp(image, P, R_OUT, R_IN,
methods[method.lower()])
return output
def wiener(data,
impulse_response=None,
filter_params={},
K=0.25,
predefined_filter=None):
"""Minimum Mean Square Error (Wiener) inverse filter.
Parameters
----------
data : (M,N) ndarray
Input data.
K : float or (M,N) ndarray
Ratio between power spectrum of noise and undegraded
image.
impulse_response : callable `f(r, c, **filter_params)`
Impulse response of the filter. See LPIFilter2D.__init__.
filter_params : dict
Additional keyword parameters to the impulse_response function.
Other Parameters
----------------
predefined_filter : LPIFilter2D
If you need to apply the same filter multiple times over different
images, construct the LPIFilter2D and specify it here.
"""
assert_nD(data, 2, 'data')
if not isinstance(K, float):
assert_nD(K, 2, 'K')
if predefined_filter is None:
filt = LPIFilter2D(impulse_response, **filter_params)
else:
filt = predefined_filter
F, G = filt._prepare(data)
_min_limit(F)
H_mag_sqr = np.abs(F)**2
F = 1 / F * H_mag_sqr / (H_mag_sqr + K)
return _centre(np.abs(ifftshift(np.dual.ifftn(G * F))), data.shape)
def prewitt(image, mask=None):
"""Find the edge magnitude 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.
See also
--------
sobel, scharr
Notes
-----
Return the square root of the sum of squares of the horizontal
and vertical Prewitt transforms. 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
>>> camera = data.camera()
>>> from skimage import filters
>>> edges = filters.prewitt(camera)
"""
assert_nD(image, 2)
out = np.sqrt(prewitt_h(image, mask)**2 + prewitt_v(image, mask)**2)
out /= np.sqrt(2)
return out
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.
"""
assert_nD(image, 2)
return np.sqrt(roberts_positive_diagonal(image, mask)**2 +
roberts_negative_diagonal(image, mask)**2)
def inverse(data,
impulse_response=None,
filter_params={},
max_gain=2,
predefined_filter=None):
"""Apply the filter in reverse to the given data.
Parameters
----------
data : (M,N) ndarray
Input data.
impulse_response : callable `f(r, c, **filter_params)`
Impulse response of the filter. See LPIFilter2D.__init__.
filter_params : dict
Additional keyword parameters to the impulse_response function.
max_gain : float
Limit the filter gain. Often, the filter contains zeros, which would
cause the inverse filter to have infinite gain. High gain causes
amplification of artefacts, so a conservative limit is recommended.
Other Parameters
----------------
predefined_filter : LPIFilter2D
If you need to apply the same filter multiple times over different
images, construct the LPIFilter2D and specify it here.
"""
assert_nD(data, 2, 'data')
if predefined_filter is None:
filt = LPIFilter2D(impulse_response, **filter_params)
else:
filt = predefined_filter
F, G = filt._prepare(data)
_min_limit(F)
F = 1 / F
mask = np.abs(F) > max_gain
F[mask] = np.sign(F[mask]) * max_gain
return _centre(np.abs(ifftshift(np.dual.ifftn(G * F))), data.shape)
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.
"""
assert_nD(image, 2)
return np.sqrt(
roberts_positive_diagonal(image, mask)**2 +
roberts_negative_diagonal(image, mask)**2)
def wiener(data, impulse_response=None, filter_params={}, K=0.25,
predefined_filter=None):
"""Minimum Mean Square Error (Wiener) inverse filter.
Parameters
----------
data : (M,N) ndarray
Input data.
K : float or (M,N) ndarray
Ratio between power spectrum of noise and undegraded
image.
impulse_response : callable `f(r, c, **filter_params)`
Impulse response of the filter. See LPIFilter2D.__init__.
filter_params : dict
Additional keyword parameters to the impulse_response function.
Other Parameters
----------------
predefined_filter : LPIFilter2D
If you need to apply the same filter multiple times over different
images, construct the LPIFilter2D and specify it here.
"""
assert_nD(data, 2, 'data')
if not isinstance(K, float):
assert_nD(K, 2, 'K')
if predefined_filter is None:
filt = LPIFilter2D(impulse_response, **filter_params)
else:
filt = predefined_filter
F, G = filt._prepare(data)
_min_limit(F)
H_mag_sqr = np.abs(F)**2
F = 1 / F * H_mag_sqr / (H_mag_sqr + K)
return _centre(np.abs(ifftshift(np.dual.ifftn(G * F))), data.shape)
def _handle_input(image, selem, out, mask, out_dtype=None, pixel_size=1):
assert_nD(image, 2)
if image.dtype not in (np.uint8, np.uint16):
image = img_as_ubyte(image)
selem = np.ascontiguousarray(img_as_ubyte(selem > 0))
image = np.ascontiguousarray(image)
if mask is None:
mask = np.ones(image.shape, dtype=np.uint8)
else:
mask = img_as_ubyte(mask)
mask = np.ascontiguousarray(mask)
if image is out:
raise NotImplementedError("Cannot perform rank operation in place.")
if out is None:
if out_dtype is None:
out_dtype = image.dtype
out = np.empty(image.shape + (pixel_size, ), dtype=out_dtype)
else:
if len(out.shape) == 2:
out = out.reshape(out.shape + (pixel_size, ))
is_8bit = image.dtype in (np.uint8, np.int8)
if is_8bit:
max_bin = 255
else:
max_bin = max(4, image.max())
bitdepth = int(np.log2(max_bin))
if bitdepth > 10:
warnings.warn("Bitdepth of %d may result in bad rank filter "
"performance due to large number of bins." % bitdepth)
return image, selem, out, mask, max_bin
def _handle_input(image, selem, out, mask, out_dtype=None, pixel_size=1):
assert_nD(image, 2)
if image.dtype not in (np.uint8, np.uint16):
image = img_as_ubyte(image)
selem = np.ascontiguousarray(img_as_ubyte(selem > 0))
image = np.ascontiguousarray(image)
if mask is None:
mask = np.ones(image.shape, dtype=np.uint8)
else:
mask = img_as_ubyte(mask)
mask = np.ascontiguousarray(mask)
if image is out:
raise NotImplementedError("Cannot perform rank operation in place.")
if out is None:
if out_dtype is None:
out_dtype = image.dtype
out = np.empty(image.shape+(pixel_size,), dtype=out_dtype)
else:
if len(out.shape) == 2:
out = out.reshape(out.shape+(pixel_size,))
is_8bit = image.dtype in (np.uint8, np.int8)
if is_8bit:
max_bin = 255
else:
max_bin = max(4, image.max())
bitdepth = int(np.log2(max_bin))
if bitdepth > 10:
warnings.warn("Bitdepth of %d may result in bad rank filter "
"performance due to large number of bins." % bitdepth)
return image, selem, out, mask, max_bin
def inverse(data, impulse_response=None, filter_params={}, max_gain=2,
predefined_filter=None):
"""Apply the filter in reverse to the given data.
Parameters
----------
data : (M,N) ndarray
Input data.
impulse_response : callable `f(r, c, **filter_params)`
Impulse response of the filter. See LPIFilter2D.__init__.
filter_params : dict
Additional keyword parameters to the impulse_response function.
max_gain : float
Limit the filter gain. Often, the filter contains zeros, which would
cause the inverse filter to have infinite gain. High gain causes
amplification of artefacts, so a conservative limit is recommended.
Other Parameters
----------------
predefined_filter : LPIFilter2D
If you need to apply the same filter multiple times over different
images, construct the LPIFilter2D and specify it here.
"""
assert_nD(data, 2, 'data')
if predefined_filter is None:
filt = LPIFilter2D(impulse_response, **filter_params)
else:
filt = predefined_filter
F, G = filt._prepare(data)
_min_limit(F)
F = 1 / F
mask = np.abs(F) > max_gain
F[mask] = np.sign(F[mask]) * max_gain
return _centre(np.abs(ifftshift(np.dual.ifftn(G * F))), data.shape)
def forward(data,
impulse_response=None,
filter_params={},
predefined_filter=None):
"""Apply the given filter to data.
Parameters
----------
data : (M,N) ndarray
Input data.
impulse_response : callable `f(r, c, **filter_params)`
Impulse response of the filter. See LPIFilter2D.__init__.
filter_params : dict
Additional keyword parameters to the impulse_response function.
Other Parameters
----------------
predefined_filter : LPIFilter2D
If you need to apply the same filter multiple times over different
images, construct the LPIFilter2D and specify it here.
Examples
--------
Gaussian filter:
>>> def filt_func(r, c):
... return np.exp(-np.hypot(r, c)/1)
>>>
>>> from skimage import data
>>> filtered = forward(data.coins(), filt_func)
"""
assert_nD(data, 2, 'data')
if predefined_filter is None:
predefined_filter = LPIFilter2D(impulse_response, **filter_params)
return predefined_filter(data)
def gabor_filter(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 : string, optional
Mode used to convolve image with a kernel, passed to `ndimage.convolve`
cval : scalar, optional
Value to fill past edges of input if `mode` of convolution is
'constant'. The parameter is passed to `ndimage.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] http://en.wikipedia.org/wiki/Gabor_filter
.. [2] http://mplab.ucsd.edu/tutorials/gabor.pdf
Examples
--------
>>> from skimage.filter import gabor_filter
>>> 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_filter(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_filter(image, frequency=0.1)
>>> plt.figure() # doctest: +SKIP
>>> io.imshow(filt_real) # doctest: +SKIP
>>> io.show() # doctest: +SKIP
"""
assert_nD(image, 2)
g = gabor_kernel(frequency, theta, bandwidth, sigma_x, sigma_y, n_stds,
offset)
filtered_real = ndimage.convolve(image, np.real(g), mode=mode, cval=cval)
filtered_imag = ndimage.convolve(image, np.imag(g), mode=mode, cval=cval)
return filtered_real, filtered_imag
def threshold_adaptive(image, block_size, method='gaussian', offset=0,
mode='reflect', param=None):
"""Applies an adaptive threshold to an array.
Also known as local or dynamic thresholding where the threshold value is
the weighted mean for the local neighborhood of a pixel subtracted by a
constant. Alternatively the threshold can be determined dynamically by a a
given function using the 'generic' method.
Parameters
----------
image : (N, M) ndarray
Input image.
block_size : int
Uneven size of pixel neighborhood which is used to calculate the
threshold value (e.g. 3, 5, 7, ..., 21, ...).
method : {'generic', 'gaussian', 'mean', 'median'}, optional
Method used to determine adaptive threshold for local neighbourhood in
weighted mean image.
* 'generic': use custom function (see `param` parameter)
* 'gaussian': apply gaussian filter (see `param` parameter for custom\
sigma value)
* 'mean': apply arithmetic mean filter
* 'median': apply median rank filter
By default the 'gaussian' method is used.
offset : float, optional
Constant subtracted from weighted mean of neighborhood to calculate
the local threshold value. Default offset is 0.
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'.
param : {int, function}, optional
Either specify sigma for 'gaussian' method or function object for
'generic' method. This functions takes the flat array of local
neighbourhood as a single argument and returns the calculated
threshold for the centre pixel.
Returns
-------
threshold : (N, M) ndarray
Thresholded binary image
References
----------
.. [1] http://docs.opencv.org/modules/imgproc/doc/miscellaneous_transformations.html?highlight=threshold#adaptivethreshold
Examples
--------
>>> from skimage.data import camera
>>> image = camera()[:50, :50]
>>> binary_image1 = threshold_adaptive(image, 15, 'mean')
>>> func = lambda arr: arr.mean()
>>> binary_image2 = threshold_adaptive(image, 15, 'generic', param=func)
"""
assert_nD(image, 2)
thresh_image = np.zeros(image.shape, 'double')
if method == 'generic':
scipy.ndimage.generic_filter(image, param, block_size,
output=thresh_image, mode=mode)
elif method == 'gaussian':
if param is None:
# automatically determine sigma which covers > 99% of distribution
sigma = (block_size - 1) / 6.0
else:
sigma = param
scipy.ndimage.gaussian_filter(image, sigma, output=thresh_image,
mode=mode)
elif method == 'mean':
mask = 1. / block_size * np.ones((block_size,))
# separation of filters to speedup convolution
scipy.ndimage.convolve1d(image, mask, axis=0, output=thresh_image,
mode=mode)
scipy.ndimage.convolve1d(thresh_image, mask, axis=1,
output=thresh_image, mode=mode)
elif method == 'median':
scipy.ndimage.median_filter(image, block_size, output=thresh_image,
mode=mode)
return image > (thresh_image - offset)
def blob_doh(image, min_sigma=1, max_sigma=30, num_sigma=10, threshold=0.01,
overlap=.5, log_scale=False):
"""Finds blobs in the given grayscale image.
Blobs are found using the Determinant of Hessian method [1]_. For each blob
found, the method returns its coordinates and the standard deviation
of the Gaussian Kernel used for the Hessian matrix whose determinant
detected the blob. Determinant of Hessians is approximated using [2]_.
Parameters
----------
image : ndarray
Input grayscale image.Blobs can either be light on dark or vice versa.
min_sigma : float, optional
The minimum standard deviation for Gaussian Kernel used to compute
Hessian matrix. Keep this low to detect smaller blobs.
max_sigma : float, optional
The maximum standard deviation for Gaussian Kernel used to compute
Hessian matrix. Keep this high to detect larger blobs.
num_sigma : int, optional
The number of intermediate values of standard deviations to consider
between `min_sigma` and `max_sigma`.
threshold : float, optional.
The absolute lower bound for scale space maxima. Local maxima smaller
than thresh are ignored. Reduce this to detect less prominent blobs.
overlap : float, optional
A value between 0 and 1. If the area of two blobs overlaps by a
fraction greater than `threshold`, the smaller blob is eliminated.
log_scale : bool, optional
If set intermediate values of standard deviations are interpolated
using a logarithmic scale to the base `10`. If not, linear
interpolation is used.
Returns
-------
A : (n, 3) ndarray
A 2d array with each row representing 3 values, ``(y,x,sigma)``
where ``(y,x)`` are coordinates of the blob and ``sigma`` is the
standard deviation of the Gaussian kernel of the Hessian Matrix whose
determinant detected the blob.
References
----------
.. [1] http://en.wikipedia.org/wiki/Blob_detection#The_determinant_of_the_Hessian
.. [2] Herbert Bay, Andreas Ess, Tinne Tuytelaars, Luc Van Gool,
"SURF: Speeded Up Robust Features"
ftp://ftp.vision.ee.ethz.ch/publications/articles/eth_biwi_00517.pdf
Examples
--------
>>> from skimage import data, feature
>>> img = data.coins()
>>> feature.blob_doh(img)
array([[121, 271, 30],
[123, 44, 23],
[123, 205, 20],
[124, 336, 20],
[126, 101, 20],
[126, 153, 20],
[156, 302, 30],
[185, 348, 30],
[192, 212, 23],
[193, 275, 23],
[195, 100, 23],
[197, 44, 20],
[197, 153, 20],
[260, 173, 30],
[262, 243, 23],
[265, 113, 23],
[270, 363, 30]])
Notes
-----
The radius of each blob is approximately `sigma`.
Computation of Determinant of Hessians is independent of the standard
deviation. Therefore detecting larger blobs won't take more time. In
methods line :py:meth:`blob_dog` and :py:meth:`blob_log` the computation
of Gaussians for larger `sigma` takes more time. The downside is that
this method can't be used for detecting blobs of radius less than `3px`
due to the box filters used in the approximation of Hessian Determinant.
"""
assert_nD(image, 2)
image = img_as_float(image)
image = integral_image(image)
if log_scale:
start, stop = log(min_sigma, 10), log(max_sigma, 10)
sigma_list = np.logspace(start, stop, num_sigma)
else:
sigma_list = np.linspace(min_sigma, max_sigma, num_sigma)
hessian_images = [_hessian_matrix_det(image, s) for s in sigma_list]
image_cube = np.dstack(hessian_images)
local_maxima = peak_local_max(image_cube, threshold_abs=threshold,
footprint=np.ones((3, 3, 3)),
threshold_rel=0.0,
exclude_border=False)
# Convert the last index to its corresponding scale value
local_maxima[:, 2] = sigma_list[local_maxima[:, 2]]
return _prune_blobs(local_maxima, overlap)
def blob_log(image, min_sigma=1, max_sigma=50, num_sigma=10, threshold=.2,
overlap=.5, log_scale=False):
"""Finds blobs in the given grayscale image.
Blobs are found using the Laplacian of Gaussian (LoG) method [1]_.
For each blob found, the method returns its coordinates and the standard
deviation of the Gaussian kernel that detected the blob.
Parameters
----------
image : ndarray
Input grayscale image, blobs are assumed to be light on dark
background (white on black).
min_sigma : float, optional
The minimum standard deviation for Gaussian Kernel. Keep this low to
detect smaller blobs.
max_sigma : float, optional
The maximum standard deviation for Gaussian Kernel. Keep this high to
detect larger blobs.
num_sigma : int, optional
The number of intermediate values of standard deviations to consider
between `min_sigma` and `max_sigma`.
threshold : float, optional.
The absolute lower bound for scale space maxima. Local maxima smaller
than thresh are ignored. Reduce this to detect blobs with less
intensities.
overlap : float, optional
A value between 0 and 1. If the area of two blobs overlaps by a
fraction greater than `threshold`, the smaller blob is eliminated.
log_scale : bool, optional
If set intermediate values of standard deviations are interpolated
using a logarithmic scale to the base `10`. If not, linear
interpolation is used.
Returns
-------
A : (n, 3) ndarray
A 2d array with each row representing 3 values, ``(y,x,sigma)``
where ``(y,x)`` are coordinates of the blob and ``sigma`` is the
standard deviation of the Gaussian kernel which detected the blob.
References
----------
.. [1] http://en.wikipedia.org/wiki/Blob_detection#The_Laplacian_of_Gaussian
Examples
--------
>>> from skimage import data, feature, exposure
>>> img = data.coins()
>>> img = exposure.equalize_hist(img) # improves detection
>>> feature.blob_log(img, threshold = .3)
array([[113, 323, 1],
[121, 272, 17],
[124, 336, 11],
[126, 46, 11],
[126, 208, 11],
[127, 102, 11],
[128, 154, 11],
[185, 344, 17],
[194, 213, 17],
[194, 276, 17],
[197, 44, 11],
[198, 103, 11],
[198, 155, 11],
[260, 174, 17],
[263, 244, 17],
[263, 302, 17],
[266, 115, 11]])
Notes
-----
The radius of each blob is approximately :math:`\sqrt{2}sigma`.
"""
assert_nD(image, 2)
image = img_as_float(image)
if log_scale:
start, stop = log(min_sigma, 10), log(max_sigma, 10)
sigma_list = np.logspace(start, stop, num_sigma)
else:
sigma_list = np.linspace(min_sigma, max_sigma, num_sigma)
# computing gaussian laplace
# s**2 provides scale invariance
gl_images = [-gaussian_laplace(image, s) * s ** 2 for s in sigma_list]
image_cube = np.dstack(gl_images)
local_maxima = peak_local_max(image_cube, threshold_abs=threshold,
footprint=np.ones((3, 3, 3)),
threshold_rel=0.0,
exclude_border=False)
# Convert the last index to its corresponding scale value
local_maxima[:, 2] = sigma_list[local_maxima[:, 2]]
return _prune_blobs(local_maxima, overlap)
def blob_dog(image, min_sigma=1, max_sigma=50, sigma_ratio=1.6, threshold=2.0,
overlap=.5,):
"""Finds blobs in the given grayscale image.
Blobs are found using the Difference of Gaussian (DoG) method [1]_.
For each blob found, the method returns its coordinates and the standard
deviation of the Gaussian kernel that detected the blob.
Parameters
----------
image : ndarray
Input grayscale image, blobs are assumed to be light on dark
background (white on black).
min_sigma : float, optional
The minimum standard deviation for Gaussian Kernel. Keep this low to
detect smaller blobs.
max_sigma : float, optional
The maximum standard deviation for Gaussian Kernel. Keep this high to
detect larger blobs.
sigma_ratio : float, optional
The ratio between the standard deviation of Gaussian Kernels used for
computing the Difference of Gaussians
threshold : float, optional.
The absolute lower bound for scale space maxima. Local maxima smaller
than thresh are ignored. Reduce this to detect blobs with less
intensities.
overlap : float, optional
A value between 0 and 1. If the area of two blobs overlaps by a
fraction greater than `threshold`, the smaller blob is eliminated.
Returns
-------
A : (n, 3) ndarray
A 2d array with each row representing 3 values, ``(y,x,sigma)``
where ``(y,x)`` are coordinates of the blob and ``sigma`` is the
standard deviation of the Gaussian kernel which detected the blob.
References
----------
.. [1] http://en.wikipedia.org/wiki/Blob_detection#The_difference_of_Gaussians_approach
Examples
--------
>>> from skimage import data, feature
>>> feature.blob_dog(data.coins(), threshold=.5, max_sigma=40)
array([[ 45, 336, 16],
[ 52, 155, 16],
[ 52, 216, 16],
[ 54, 42, 16],
[ 54, 276, 10],
[ 58, 100, 10],
[120, 272, 16],
[124, 337, 10],
[125, 45, 16],
[125, 208, 10],
[127, 102, 10],
[128, 154, 10],
[185, 347, 16],
[193, 213, 16],
[194, 277, 16],
[195, 102, 16],
[196, 43, 10],
[198, 155, 10],
[260, 46, 16],
[261, 173, 16],
[263, 245, 16],
[263, 302, 16],
[267, 115, 10],
[267, 359, 16]])
Notes
-----
The radius of each blob is approximately :math:`\sqrt{2}sigma`.
"""
assert_nD(image, 2)
image = img_as_float(image)
# k such that min_sigma*(sigma_ratio**k) > max_sigma
k = int(log(float(max_sigma) / min_sigma, sigma_ratio)) + 1
# a geometric progression of standard deviations for gaussian kernels
sigma_list = np.array([min_sigma * (sigma_ratio ** i)
for i in range(k + 1)])
gaussian_images = [gaussian_filter(image, s) for s in sigma_list]
# computing difference between two successive Gaussian blurred images
# multiplying with standard deviation provides scale invariance
dog_images = [(gaussian_images[i] - gaussian_images[i + 1])
* sigma_list[i] for i in range(k)]
image_cube = np.dstack(dog_images)
# local_maxima = get_local_maxima(image_cube, threshold)
local_maxima = peak_local_max(image_cube, threshold_abs=threshold,
footprint=np.ones((3, 3, 3)),
threshold_rel=0.0,
exclude_border=False)
# Convert the last index to its corresponding scale value
local_maxima[:, 2] = sigma_list[local_maxima[:, 2]]
return _prune_blobs(local_maxima, overlap)
def greycomatrix(image,
distances,
angles,
levels=256,
symmetric=False,
normed=False):
"""Calculate the grey-level co-occurrence matrix.
A grey level co-occurrence matrix is a histogram of co-occurring
greyscale values at a given offset over an image.
Parameters
----------
image : array_like of uint8
Integer typed input image. The image will be cast to uint8, so
the maximum value must be less than 256.
distances : array_like
List of pixel pair distance offsets.
angles : array_like
List of pixel pair angles in radians.
levels : int, optional
The input image should contain integers in [0, levels-1],
where levels indicate the number of grey-levels counted
(typically 256 for an 8-bit image). The maximum value is
256.
symmetric : bool, optional
If True, the output matrix `P[:, :, d, theta]` is symmetric. This
is accomplished by ignoring the order of value pairs, so both
(i, j) and (j, i) are accumulated when (i, j) is encountered
for a given offset. The default is False.
normed : bool, optional
If True, normalize each matrix `P[:, :, d, theta]` by dividing
by the total number of accumulated co-occurrences for the given
offset. The elements of the resulting matrix sum to 1. The
default is False.
Returns
-------
P : 4-D ndarray
The grey-level co-occurrence histogram. The value
`P[i,j,d,theta]` is the number of times that grey-level `j`
occurs at a distance `d` and at an angle `theta` from
grey-level `i`. If `normed` is `False`, the output is of
type uint32, otherwise it is float64.
References
----------
.. [1] The GLCM Tutorial Home Page,
http://www.fp.ucalgary.ca/mhallbey/tutorial.htm
.. [2] Pattern Recognition Engineering, Morton Nadler & Eric P.
Smith
.. [3] Wikipedia, http://en.wikipedia.org/wiki/Co-occurrence_matrix
Examples
--------
Compute 2 GLCMs: One for a 1-pixel offset to the right, and one
for a 1-pixel offset upwards.
>>> image = np.array([[0, 0, 1, 1],
... [0, 0, 1, 1],
... [0, 2, 2, 2],
... [2, 2, 3, 3]], dtype=np.uint8)
>>> result = greycomatrix(image, [1], [0, np.pi/4, np.pi/2, 3*np.pi/4], levels=4)
>>> result[:, :, 0, 0]
array([[2, 2, 1, 0],
[0, 2, 0, 0],
[0, 0, 3, 1],
[0, 0, 0, 1]], dtype=uint32)
>>> result[:, :, 0, 1]
array([[1, 1, 3, 0],
[0, 1, 1, 0],
[0, 0, 0, 2],
[0, 0, 0, 0]], dtype=uint32)
>>> result[:, :, 0, 2]
array([[3, 0, 2, 0],
[0, 2, 2, 0],
[0, 0, 1, 2],
[0, 0, 0, 0]], dtype=uint32)
>>> result[:, :, 0, 3]
array([[2, 0, 0, 0],
[1, 1, 2, 0],
[0, 0, 2, 1],
[0, 0, 0, 0]], dtype=uint32)
"""
assert_nD(image, 2)
assert_nD(distances, 1, 'distances')
assert_nD(angles, 1, 'angles')
assert levels <= 256
image = np.ascontiguousarray(image)
assert image.min() >= 0
assert image.max() < levels
image = image.astype(np.uint8)
distances = np.ascontiguousarray(distances, dtype=np.float64)
angles = np.ascontiguousarray(angles, dtype=np.float64)
P = np.zeros((levels, levels, len(distances), len(angles)),
dtype=np.uint32,
order='C')
# count co-occurences
_glcm_loop(image, distances, angles, levels, P)
# make each GLMC symmetric
if symmetric:
Pt = np.transpose(P, (1, 0, 2, 3))
P = P + Pt
# normalize each GLMC
if normed:
P = P.astype(np.float64)
glcm_sums = np.apply_over_axes(np.sum, P, axes=(0, 1))
glcm_sums[glcm_sums == 0] = 1
P /= glcm_sums
return P
def gabor_filter(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 : string, optional
Mode used to convolve image with a kernel, passed to `ndimage.convolve`
cval : scalar, optional
Value to fill past edges of input if `mode` of convolution is
'constant'. The parameter is passed to `ndimage.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] http://en.wikipedia.org/wiki/Gabor_filter
.. [2] http://mplab.ucsd.edu/tutorials/gabor.pdf
Examples
--------
>>> from skimage.filter import gabor_filter
>>> 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_filter(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_filter(image, frequency=0.1)
>>> plt.figure() # doctest: +SKIP
>>> io.imshow(filt_real) # doctest: +SKIP
>>> io.show() # doctest: +SKIP
"""
assert_nD(image, 2)
g = gabor_kernel(frequency, theta, bandwidth, sigma_x, sigma_y, n_stds,
offset)
filtered_real = ndimage.convolve(image, np.real(g), mode=mode, cval=cval)
filtered_imag = ndimage.convolve(image, np.imag(g), mode=mode, cval=cval)
return filtered_real, filtered_imag
def test_assert_nD():
z = np.random.random(200**2).reshape((200, 200))
x = z[10:30, 30:10]
with testing.raises(ValueError):
assert_nD(x, 2)
def greycomatrix(image, distances, angles, levels=256, symmetric=False,
normed=False):
"""Calculate the grey-level co-occurrence matrix.
A grey level co-occurence matrix is a histogram of co-occuring
greyscale values at a given offset over an image.
Parameters
----------
image : array_like of uint8
Integer typed input image. The image will be cast to uint8, so
the maximum value must be less than 256.
distances : array_like
List of pixel pair distance offsets.
angles : array_like
List of pixel pair angles in radians.
levels : int, optional
The input image should contain integers in [0, levels-1],
where levels indicate the number of grey-levels counted
(typically 256 for an 8-bit image). The maximum value is
256.
symmetric : bool, optional
If True, the output matrix `P[:, :, d, theta]` is symmetric. This
is accomplished by ignoring the order of value pairs, so both
(i, j) and (j, i) are accumulated when (i, j) is encountered
for a given offset. The default is False.
normed : bool, optional
If True, normalize each matrix `P[:, :, d, theta]` by dividing
by the total number of accumulated co-occurrences for the given
offset. The elements of the resulting matrix sum to 1. The
default is False.
Returns
-------
P : 4-D ndarray
The grey-level co-occurrence histogram. The value
`P[i,j,d,theta]` is the number of times that grey-level `j`
occurs at a distance `d` and at an angle `theta` from
grey-level `i`. If `normed` is `False`, the output is of
type uint32, otherwise it is float64.
References
----------
.. [1] The GLCM Tutorial Home Page,
http://www.fp.ucalgary.ca/mhallbey/tutorial.htm
.. [2] Pattern Recognition Engineering, Morton Nadler & Eric P.
Smith
.. [3] Wikipedia, http://en.wikipedia.org/wiki/Co-occurrence_matrix
Examples
--------
Compute 2 GLCMs: One for a 1-pixel offset to the right, and one
for a 1-pixel offset upwards.
>>> image = np.array([[0, 0, 1, 1],
... [0, 0, 1, 1],
... [0, 2, 2, 2],
... [2, 2, 3, 3]], dtype=np.uint8)
>>> result = greycomatrix(image, [1], [0, np.pi/4, np.pi/2, 3*np.pi/4], levels=4)
>>> result[:, :, 0, 0]
array([[2, 2, 1, 0],
[0, 2, 0, 0],
[0, 0, 3, 1],
[0, 0, 0, 1]], dtype=uint32)
>>> result[:, :, 0, 1]
array([[1, 1, 3, 0],
[0, 1, 1, 0],
[0, 0, 0, 2],
[0, 0, 0, 0]], dtype=uint32)
>>> result[:, :, 0, 2]
array([[3, 0, 2, 0],
[0, 2, 2, 0],
[0, 0, 1, 2],
[0, 0, 0, 0]], dtype=uint32)
>>> result[:, :, 0, 3]
array([[2, 0, 0, 0],
[1, 1, 2, 0],
[0, 0, 2, 1],
[0, 0, 0, 0]], dtype=uint32)
"""
assert_nD(image, 2)
assert_nD(distances, 1, 'distances')
assert_nD(angles, 1, 'angles')
assert levels <= 256
image = np.ascontiguousarray(image)
assert image.min() >= 0
assert image.max() < levels
image = image.astype(np.uint8)
distances = np.ascontiguousarray(distances, dtype=np.float64)
angles = np.ascontiguousarray(angles, dtype=np.float64)
P = np.zeros((levels, levels, len(distances), len(angles)),
dtype=np.uint32, order='C')
# count co-occurences
_glcm_loop(image, distances, angles, levels, P)
# make each GLMC symmetric
if symmetric:
Pt = np.transpose(P, (1, 0, 2, 3))
P = P + Pt
# normalize each GLMC
if normed:
P = P.astype(np.float64)
glcm_sums = np.apply_over_axes(np.sum, P, axes=(0, 1))
glcm_sums[glcm_sums == 0] = 1
P /= glcm_sums
return P
def detect(self, image):
"""Detect CENSURE keypoints along with the corresponding scale.
Parameters
----------
image : 2D ndarray
Input image.
"""
# (1) First we generate the required scales on the input grayscale
# image using a bi-level filter and stack them up in `filter_response`.
# (2) We then perform Non-Maximal suppression in 3 x 3 x 3 window on
# the filter_response to suppress points that are neither minima or
# maxima in 3 x 3 x 3 neighbourhood. We obtain a boolean ndarray
# `feature_mask` containing all the minimas and maximas in
# `filter_response` as True.
# (3) Then we suppress all the points in the `feature_mask` for which
# the corresponding point in the image at a particular scale has the
# ratio of principal curvatures greater than `line_threshold`.
# (4) Finally, we remove the border keypoints and return the keypoints
# along with its corresponding scale.
assert_nD(image, 2)
num_scales = self.max_scale - self.min_scale
image = np.ascontiguousarray(_prepare_grayscale_input_2D(image))
# Generating all the scales
filter_response = _filter_image(image, self.min_scale, self.max_scale,
self.mode)
# Suppressing points that are neither minima or maxima in their
# 3 x 3 x 3 neighborhood to zero
minimas = minimum_filter(filter_response, (3, 3, 3)) == filter_response
maximas = maximum_filter(filter_response, (3, 3, 3)) == filter_response
feature_mask = minimas | maximas
feature_mask[filter_response < self.non_max_threshold] = False
for i in range(1, num_scales):
# sigma = (window_size - 1) / 6.0, so the window covers > 99% of
# the kernel's distribution
# window_size = 7 + 2 * (min_scale - 1 + i)
# Hence sigma = 1 + (min_scale - 1 + i)/ 3.0
_suppress_lines(feature_mask[:, :, i], image,
(1 + (self.min_scale + i - 1) / 3.0),
self.line_threshold)
rows, cols, scales = np.nonzero(feature_mask[..., 1:num_scales])
keypoints = np.column_stack([rows, cols])
scales = scales + self.min_scale + 1
if self.mode == 'dob':
self.keypoints = keypoints
self.scales = scales
return
cumulative_mask = np.zeros(keypoints.shape[0], dtype=np.bool)
if self.mode == 'octagon':
for i in range(self.min_scale + 1, self.max_scale):
c = (OCTAGON_OUTER_SHAPE[i - 1][0] - 1) // 2 \
+ OCTAGON_OUTER_SHAPE[i - 1][1]
cumulative_mask |= (
_mask_border_keypoints(image.shape, keypoints, c)
& (scales == i))
elif self.mode == 'star':
for i in range(self.min_scale + 1, self.max_scale):
c = STAR_SHAPE[STAR_FILTER_SHAPE[i - 1][0]] \
+ STAR_SHAPE[STAR_FILTER_SHAPE[i - 1][0]] // 2
cumulative_mask |= (
_mask_border_keypoints(image.shape, keypoints, c)
& (scales == i))
self.keypoints = keypoints[cumulative_mask]
self.scales = scales[cumulative_mask]
def greycoprops(P, prop='contrast'):
"""Calculate texture properties of a GLCM.
Compute a feature of a grey level co-occurrence matrix to serve as
a compact summary of the matrix. The properties are computed as
follows:
- 'contrast': :math:`\\sum_{i,j=0}^{levels-1} P_{i,j}(i-j)^2`
- 'dissimilarity': :math:`\\sum_{i,j=0}^{levels-1}P_{i,j}|i-j|`
- 'homogeneity': :math:`\\sum_{i,j=0}^{levels-1}\\frac{P_{i,j}}{1+(i-j)^2}`
- 'ASM': :math:`\\sum_{i,j=0}^{levels-1} P_{i,j}^2`
- 'energy': :math:`\\sqrt{ASM}`
- 'correlation':
.. math:: \\sum_{i,j=0}^{levels-1} P_{i,j}\\left[\\frac{(i-\\mu_i) \\
(j-\\mu_j)}{\\sqrt{(\\sigma_i^2)(\\sigma_j^2)}}\\right]
Parameters
----------
P : ndarray
Input array. `P` is the grey-level co-occurrence histogram
for which to compute the specified property. The value
`P[i,j,d,theta]` is the number of times that grey-level j
occurs at a distance d and at an angle theta from
grey-level i.
prop : {'contrast', 'dissimilarity', 'homogeneity', 'energy', \
'correlation', 'ASM'}, optional
The property of the GLCM to compute. The default is 'contrast'.
Returns
-------
results : 2-D ndarray
2-dimensional array. `results[d, a]` is the property 'prop' for
the d'th distance and the a'th angle.
References
----------
.. [1] The GLCM Tutorial Home Page,
http://www.fp.ucalgary.ca/mhallbey/tutorial.htm
Examples
--------
Compute the contrast for GLCMs with distances [1, 2] and angles
[0 degrees, 90 degrees]
>>> image = np.array([[0, 0, 1, 1],
... [0, 0, 1, 1],
... [0, 2, 2, 2],
... [2, 2, 3, 3]], dtype=np.uint8)
>>> g = greycomatrix(image, [1, 2], [0, np.pi/2], levels=4,
... normed=True, symmetric=True)
>>> contrast = greycoprops(g, 'contrast')
>>> contrast
array([[ 0.58333333, 1. ],
[ 1.25 , 2.75 ]])
"""
assert_nD(P, 4, 'P')
(num_level, num_level2, num_dist, num_angle) = P.shape
assert num_level == num_level2
assert num_dist > 0
assert num_angle > 0
# create weights for specified property
I, J = np.ogrid[0:num_level, 0:num_level]
if prop == 'contrast':
weights = (I - J) ** 2
elif prop == 'dissimilarity':
weights = np.abs(I - J)
elif prop == 'homogeneity':
weights = 1. / (1. + (I - J) ** 2)
elif prop in ['ASM', 'energy', 'correlation']:
pass
else:
raise ValueError('%s is an invalid property' % (prop))
# compute property for each GLCM
if prop == 'energy':
asm = np.apply_over_axes(np.sum, (P ** 2), axes=(0, 1))[0, 0]
results = np.sqrt(asm)
elif prop == 'ASM':
results = np.apply_over_axes(np.sum, (P ** 2), axes=(0, 1))[0, 0]
elif prop == 'correlation':
results = np.zeros((num_dist, num_angle), dtype=np.float64)
I = np.array(range(num_level)).reshape((num_level, 1, 1, 1))
J = np.array(range(num_level)).reshape((1, num_level, 1, 1))
diff_i = I - np.apply_over_axes(np.sum, (I * P), axes=(0, 1))[0, 0]
diff_j = J - np.apply_over_axes(np.sum, (J * P), axes=(0, 1))[0, 0]
std_i = np.sqrt(np.apply_over_axes(np.sum, (P * (diff_i) ** 2),
axes=(0, 1))[0, 0])
std_j = np.sqrt(np.apply_over_axes(np.sum, (P * (diff_j) ** 2),
axes=(0, 1))[0, 0])
cov = np.apply_over_axes(np.sum, (P * (diff_i * diff_j)),
axes=(0, 1))[0, 0]
# handle the special case of standard deviations near zero
mask_0 = std_i < 1e-15
mask_0[std_j < 1e-15] = True
results[mask_0] = 1
# handle the standard case
mask_1 = mask_0 == False
results[mask_1] = cov[mask_1] / (std_i[mask_1] * std_j[mask_1])
elif prop in ['contrast', 'dissimilarity', 'homogeneity']:
weights = weights.reshape((num_level, num_level, 1, 1))
results = np.apply_over_axes(np.sum, (P * weights), axes=(0, 1))[0, 0]
return results