"""
Methods to characterize image textures.
"""
import warnings
import numpy as np
from .._shared.utils import check_nD
from ..color import gray2rgb
from ..util import img_as_float
from ._texture import _glcm_loop, _local_binary_pattern, _multiblock_lbp
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def graycomatrix(image, distances, angles, levels=None, symmetric=False, normed=False):
"""Calculate the gray-level co-occurrence matrix.
A gray level co-occurrence matrix is a histogram of co-occurring
grayscale values at a given offset over an image.
.. versionchanged:: 0.19
`greymatrix` was renamed to `graymatrix` in 0.19.
Parameters
----------
image : array_like
Integer typed input image. Only positive valued images are supported.
If type is other than uint8, the argument `levels` needs to be set.
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 gray-levels counted
(typically 256 for an 8-bit image). This argument is required for
16-bit images or higher and is typically the maximum of the image.
As the output matrix is at least `levels` x `levels`, it might
be preferable to use binning of the input image rather than
large values for `levels`.
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 gray-level co-occurrence histogram. The value
`P[i,j,d,theta]` is the number of times that gray-level `j`
occurs at a distance `d` and at an angle `theta` from
gray-level `i`. If `normed` is `False`, the output is of
type uint32, otherwise it is float64. The dimensions are:
levels x levels x number of distances x number of angles.
References
----------
.. [1] M. Hall-Beyer, 2007. GLCM Texture: A Tutorial
https://prism.ucalgary.ca/handle/1880/51900
DOI:`10.11575/PRISM/33280`
.. [2] R.M. Haralick, K. Shanmugam, and I. Dinstein, "Textural features for
image classification", IEEE Transactions on Systems, Man, and
Cybernetics, vol. SMC-3, no. 6, pp. 610-621, Nov. 1973.
:DOI:`10.1109/TSMC.1973.4309314`
.. [3] M. Nadler and E.P. Smith, Pattern Recognition Engineering,
Wiley-Interscience, 1993.
.. [4] Wikipedia, https://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 = graycomatrix(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)
"""
check_nD(image, 2)
check_nD(distances, 1, 'distances')
check_nD(angles, 1, 'angles')
image = np.ascontiguousarray(image)
image_max = image.max()
if np.issubdtype(image.dtype, np.floating):
raise ValueError(
"Float images are not supported by graycomatrix. "
"Convert the image to an unsigned integer type."
)
# for image type > 8bit, levels must be set.
if image.dtype not in (np.uint8, np.int8) and levels is None:
raise ValueError(
"The levels argument is required for data types "
"other than uint8. The resulting matrix will be at "
"least levels ** 2 in size."
)
if np.issubdtype(image.dtype, np.signedinteger) and np.any(image < 0):
raise ValueError("Negative-valued images are not supported.")
if levels is None:
levels = 256
if image_max >= levels:
raise ValueError(
"The maximum grayscale value in the image should be "
"smaller than the number of levels."
)
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 GLCM
if normed:
P = P.astype(np.float64)
glcm_sums = np.sum(P, axis=(0, 1), keepdims=True)
glcm_sums[glcm_sums == 0] = 1
P /= glcm_sums
return P
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def graycoprops(P, prop='contrast'):
"""Calculate texture properties of a GLCM.
Compute a feature of a gray 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]
Each GLCM is normalized to have a sum of 1 before the computation of
texture properties.
.. versionchanged:: 0.19
`greycoprops` was renamed to `graycoprops` in 0.19.
Parameters
----------
P : ndarray
Input array. `P` is the gray-level co-occurrence histogram
for which to compute the specified property. The value
`P[i,j,d,theta]` is the number of times that gray-level j
occurs at a distance d and at an angle theta from
gray-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] M. Hall-Beyer, 2007. GLCM Texture: A Tutorial v. 1.0 through 3.0.
The GLCM Tutorial Home Page,
https://prism.ucalgary.ca/handle/1880/51900
DOI:`10.11575/PRISM/33280`
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 = graycomatrix(image, [1, 2], [0, np.pi/2], levels=4,
... normed=True, symmetric=True)
>>> contrast = graycoprops(g, 'contrast')
>>> contrast
array([[0.58333333, 1. ],
[1.25 , 2.75 ]])
"""
check_nD(P, 4, 'P')
(num_level, num_level2, num_dist, num_angle) = P.shape
if num_level != num_level2:
raise ValueError('num_level and num_level2 must be equal.')
if num_dist <= 0:
raise ValueError('num_dist must be positive.')
if num_angle <= 0:
raise ValueError('num_angle must be positive.')
# normalize each GLCM
P = P.astype(np.float64)
glcm_sums = np.sum(P, axis=(0, 1), keepdims=True)
glcm_sums[glcm_sums == 0] = 1
P /= glcm_sums
# 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 = 1.0 / (1.0 + (I - J) ** 2)
elif prop in ['ASM', 'energy', 'correlation']:
pass
else:
raise ValueError(f'{prop} is an invalid property')
# compute property for each GLCM
if prop == 'energy':
asm = np.sum(P**2, axis=(0, 1))
results = np.sqrt(asm)
elif prop == 'ASM':
results = np.sum(P**2, axis=(0, 1))
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.sum(I * P, axis=(0, 1))
diff_j = J - np.sum(J * P, axis=(0, 1))
std_i = np.sqrt(np.sum(P * (diff_i) ** 2, axis=(0, 1)))
std_j = np.sqrt(np.sum(P * (diff_j) ** 2, axis=(0, 1)))
cov = np.sum(P * (diff_i * diff_j), axis=(0, 1))
# 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
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.sum(P * weights, axis=(0, 1))
return results
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def local_binary_pattern(image, P, R, method='default'):
"""Compute the local binary patterns (LBP) of an image.
LBP is a visual descriptor often used in texture classification.
Parameters
----------
image : (M, N) array
2D grayscale image.
P : int
Number of circularly symmetric neighbor set points (quantization of
the angular space).
R : float
Radius of circle (spatial resolution of the operator).
method : str {'default', 'ror', 'uniform', 'nri_uniform', 'var'}, optional
Method to determine the pattern:
``default``
Original local binary pattern which is grayscale invariant but not
rotation invariant.
``ror``
Extension of default pattern which is grayscale invariant and
rotation invariant.
``uniform``
Uniform pattern which is grayscale invariant and rotation
invariant, offering finer quantization of the angular space.
For details, see [1]_.
``nri_uniform``
Variant of uniform pattern which is grayscale invariant but not
rotation invariant. For details, see [2]_ and [3]_.
``var``
Variance of local image texture (related to contrast)
which is rotation invariant but not grayscale invariant.
Returns
-------
output : (M, N) array
LBP image.
References
----------
.. [1] T. Ojala, M. Pietikainen, T. Maenpaa, "Multiresolution gray-scale
and rotation invariant texture classification with local binary
patterns", IEEE Transactions on Pattern Analysis and Machine
Intelligence, vol. 24, no. 7, pp. 971-987, July 2002
:DOI:`10.1109/TPAMI.2002.1017623`
.. [2] T. Ahonen, A. Hadid and M. Pietikainen. "Face recognition with
local binary patterns", in Proc. Eighth European Conf. Computer
Vision, Prague, Czech Republic, May 11-14, 2004, pp. 469-481, 2004.
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.6851
:DOI:`10.1007/978-3-540-24670-1_36`
.. [3] T. Ahonen, A. Hadid and M. Pietikainen, "Face Description with
Local Binary Patterns: Application to Face Recognition",
IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. 28, no. 12, pp. 2037-2041, Dec. 2006
:DOI:`10.1109/TPAMI.2006.244`
"""
check_nD(image, 2)
methods = {
'default': ord('D'),
'ror': ord('R'),
'uniform': ord('U'),
'nri_uniform': ord('N'),
'var': ord('V'),
}
if np.issubdtype(image.dtype, np.floating):
warnings.warn(
"Applying `local_binary_pattern` to floating-point images may "
"give unexpected results when small numerical differences between "
"adjacent pixels are present. It is recommended to use this "
"function with images of integer dtype."
)
image = np.ascontiguousarray(image, dtype=np.float64)
output = _local_binary_pattern(image, P, R, methods[method.lower()])
return output
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def multiblock_lbp(int_image, r, c, width, height):
"""Multi-block local binary pattern (MB-LBP).
The features are calculated similarly to local binary patterns (LBPs),
(See :py:meth:`local_binary_pattern`) except that summed blocks are
used instead of individual pixel values.
MB-LBP is an extension of LBP that can be computed on multiple scales
in constant time using the integral image. Nine equally-sized rectangles
are used to compute a feature. For each rectangle, the sum of the pixel
intensities is computed. Comparisons of these sums to that of the central
rectangle determine the feature, similarly to LBP.
Parameters
----------
int_image : (N, M) array
Integral image.
r : int
Row-coordinate of top left corner of a rectangle containing feature.
c : int
Column-coordinate of top left corner of a rectangle containing feature.
width : int
Width of one of the 9 equal rectangles that will be used to compute
a feature.
height : int
Height of one of the 9 equal rectangles that will be used to compute
a feature.
Returns
-------
output : int
8-bit MB-LBP feature descriptor.
References
----------
.. [1] L. Zhang, R. Chu, S. Xiang, S. Liao, S.Z. Li. "Face Detection Based
on Multi-Block LBP Representation", In Proceedings: Advances in
Biometrics, International Conference, ICB 2007, Seoul, Korea.
http://www.cbsr.ia.ac.cn/users/scliao/papers/Zhang-ICB07-MBLBP.pdf
:DOI:`10.1007/978-3-540-74549-5_2`
"""
int_image = np.ascontiguousarray(int_image, dtype=np.float32)
lbp_code = _multiblock_lbp(int_image, r, c, width, height)
return lbp_code
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def draw_multiblock_lbp(
image,
r,
c,
width,
height,
lbp_code=0,
color_greater_block=(1, 1, 1),
color_less_block=(0, 0.69, 0.96),
alpha=0.5,
):
"""Multi-block local binary pattern visualization.
Blocks with higher sums are colored with alpha-blended white rectangles,
whereas blocks with lower sums are colored alpha-blended cyan. Colors
and the `alpha` parameter can be changed.
Parameters
----------
image : ndarray of float or uint
Image on which to visualize the pattern.
r : int
Row-coordinate of top left corner of a rectangle containing feature.
c : int
Column-coordinate of top left corner of a rectangle containing feature.
width : int
Width of one of 9 equal rectangles that will be used to compute
a feature.
height : int
Height of one of 9 equal rectangles that will be used to compute
a feature.
lbp_code : int
The descriptor of feature to visualize. If not provided, the
descriptor with 0 value will be used.
color_greater_block : tuple of 3 floats
Floats specifying the color for the block that has greater
intensity value. They should be in the range [0, 1].
Corresponding values define (R, G, B) values. Default value
is white (1, 1, 1).
color_greater_block : tuple of 3 floats
Floats specifying the color for the block that has greater intensity
value. They should be in the range [0, 1]. Corresponding values define
(R, G, B) values. Default value is cyan (0, 0.69, 0.96).
alpha : float
Value in the range [0, 1] that specifies opacity of visualization.
1 - fully transparent, 0 - opaque.
Returns
-------
output : ndarray of float
Image with MB-LBP visualization.
References
----------
.. [1] L. Zhang, R. Chu, S. Xiang, S. Liao, S.Z. Li. "Face Detection Based
on Multi-Block LBP Representation", In Proceedings: Advances in
Biometrics, International Conference, ICB 2007, Seoul, Korea.
http://www.cbsr.ia.ac.cn/users/scliao/papers/Zhang-ICB07-MBLBP.pdf
:DOI:`10.1007/978-3-540-74549-5_2`
"""
# Default colors for regions.
# White is for the blocks that are brighter.
# Cyan is for the blocks that has less intensity.
color_greater_block = np.asarray(color_greater_block, dtype=np.float64)
color_less_block = np.asarray(color_less_block, dtype=np.float64)
# Copy array to avoid the changes to the original one.
output = np.copy(image)
# As the visualization uses RGB color we need 3 bands.
if len(image.shape) < 3:
output = gray2rgb(image)
# Colors are specified in floats.
output = img_as_float(output)
# Offsets of neighbor rectangles relative to central one.
# It has order starting from top left and going clockwise.
neighbor_rect_offsets = (
(-1, -1),
(-1, 0),
(-1, 1),
(0, 1),
(1, 1),
(1, 0),
(1, -1),
(0, -1),
)
# Pre-multiply the offsets with width and height.
neighbor_rect_offsets = np.array(neighbor_rect_offsets)
neighbor_rect_offsets[:, 0] *= height
neighbor_rect_offsets[:, 1] *= width
# Top-left coordinates of central rectangle.
central_rect_r = r + height
central_rect_c = c + width
for element_num, offset in enumerate(neighbor_rect_offsets):
offset_r, offset_c = offset
curr_r = central_rect_r + offset_r
curr_c = central_rect_c + offset_c
has_greater_value = lbp_code & (1 << (7 - element_num))
# Mix-in the visualization colors.
if has_greater_value:
new_value = (1 - alpha) * output[
curr_r : curr_r + height, curr_c : curr_c + width
] + alpha * color_greater_block
output[curr_r : curr_r + height, curr_c : curr_c + width] = new_value
else:
new_value = (1 - alpha) * output[
curr_r : curr_r + height, curr_c : curr_c + width
] + alpha * color_less_block
output[curr_r : curr_r + height, curr_c : curr_c + width] = new_value
return output
