mirror of
https://github.com/wassname/scikit-image.git
synced 2026-06-28 02:30:57 +08:00
Steven Silvester
294 lines
10 KiB
Python
294 lines
10 KiB
Python
"""
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Methods to characterize image textures.
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"""
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import numpy as np
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from .._shared.utils import assert_nD
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from ._texture import _glcm_loop, _local_binary_pattern
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def greycomatrix(image, distances, angles, levels=256, symmetric=False,
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normed=False):
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"""Calculate the grey-level co-occurrence matrix.
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A grey level co-occurrence matrix is a histogram of co-occurring
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greyscale values at a given offset over an image.
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Parameters
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----------
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image : array_like of uint8
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Integer typed input image. The image will be cast to uint8, so
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the maximum value must be less than 256.
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distances : array_like
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List of pixel pair distance offsets.
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angles : array_like
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List of pixel pair angles in radians.
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levels : int, optional
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The input image should contain integers in [0, levels-1],
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where levels indicate the number of grey-levels counted
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(typically 256 for an 8-bit image). The maximum value is
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256.
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symmetric : bool, optional
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If True, the output matrix `P[:, :, d, theta]` is symmetric. This
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is accomplished by ignoring the order of value pairs, so both
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(i, j) and (j, i) are accumulated when (i, j) is encountered
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for a given offset. The default is False.
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normed : bool, optional
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If True, normalize each matrix `P[:, :, d, theta]` by dividing
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by the total number of accumulated co-occurrences for the given
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offset. The elements of the resulting matrix sum to 1. The
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default is False.
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Returns
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-------
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P : 4-D ndarray
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The grey-level co-occurrence histogram. The value
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`P[i,j,d,theta]` is the number of times that grey-level `j`
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occurs at a distance `d` and at an angle `theta` from
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grey-level `i`. If `normed` is `False`, the output is of
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type uint32, otherwise it is float64.
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References
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----------
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.. [1] The GLCM Tutorial Home Page,
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http://www.fp.ucalgary.ca/mhallbey/tutorial.htm
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.. [2] Pattern Recognition Engineering, Morton Nadler & Eric P.
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Smith
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.. [3] Wikipedia, http://en.wikipedia.org/wiki/Co-occurrence_matrix
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Examples
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--------
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Compute 2 GLCMs: One for a 1-pixel offset to the right, and one
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for a 1-pixel offset upwards.
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>>> image = np.array([[0, 0, 1, 1],
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... [0, 0, 1, 1],
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... [0, 2, 2, 2],
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... [2, 2, 3, 3]], dtype=np.uint8)
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>>> result = greycomatrix(image, [1], [0, np.pi/4, np.pi/2, 3*np.pi/4], levels=4)
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>>> result[:, :, 0, 0]
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array([[2, 2, 1, 0],
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[0, 2, 0, 0],
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[0, 0, 3, 1],
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[0, 0, 0, 1]], dtype=uint32)
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>>> result[:, :, 0, 1]
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array([[1, 1, 3, 0],
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[0, 1, 1, 0],
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[0, 0, 0, 2],
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[0, 0, 0, 0]], dtype=uint32)
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>>> result[:, :, 0, 2]
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array([[3, 0, 2, 0],
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[0, 2, 2, 0],
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[0, 0, 1, 2],
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[0, 0, 0, 0]], dtype=uint32)
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>>> result[:, :, 0, 3]
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array([[2, 0, 0, 0],
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[1, 1, 2, 0],
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[0, 0, 2, 1],
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[0, 0, 0, 0]], dtype=uint32)
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"""
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assert_nD(image, 2)
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assert_nD(distances, 1, 'distances')
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assert_nD(angles, 1, 'angles')
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assert levels <= 256
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image = np.ascontiguousarray(image)
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assert image.min() >= 0
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assert image.max() < levels
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image = image.astype(np.uint8)
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distances = np.ascontiguousarray(distances, dtype=np.float64)
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angles = np.ascontiguousarray(angles, dtype=np.float64)
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P = np.zeros((levels, levels, len(distances), len(angles)),
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dtype=np.uint32, order='C')
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# count co-occurences
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_glcm_loop(image, distances, angles, levels, P)
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# make each GLMC symmetric
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if symmetric:
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Pt = np.transpose(P, (1, 0, 2, 3))
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P = P + Pt
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# normalize each GLMC
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if normed:
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P = P.astype(np.float64)
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glcm_sums = np.apply_over_axes(np.sum, P, axes=(0, 1))
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glcm_sums[glcm_sums == 0] = 1
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P /= glcm_sums
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return P
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def greycoprops(P, prop='contrast'):
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"""Calculate texture properties of a GLCM.
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Compute a feature of a grey level co-occurrence matrix to serve as
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a compact summary of the matrix. The properties are computed as
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follows:
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- 'contrast': :math:`\\sum_{i,j=0}^{levels-1} P_{i,j}(i-j)^2`
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- 'dissimilarity': :math:`\\sum_{i,j=0}^{levels-1}P_{i,j}|i-j|`
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- 'homogeneity': :math:`\\sum_{i,j=0}^{levels-1}\\frac{P_{i,j}}{1+(i-j)^2}`
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- 'ASM': :math:`\\sum_{i,j=0}^{levels-1} P_{i,j}^2`
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- 'energy': :math:`\\sqrt{ASM}`
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- 'correlation':
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.. math:: \\sum_{i,j=0}^{levels-1} P_{i,j}\\left[\\frac{(i-\\mu_i) \\
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(j-\\mu_j)}{\\sqrt{(\\sigma_i^2)(\\sigma_j^2)}}\\right]
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Parameters
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----------
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P : ndarray
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Input array. `P` is the grey-level co-occurrence histogram
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for which to compute the specified property. The value
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`P[i,j,d,theta]` is the number of times that grey-level j
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occurs at a distance d and at an angle theta from
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grey-level i.
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prop : {'contrast', 'dissimilarity', 'homogeneity', 'energy', \
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'correlation', 'ASM'}, optional
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The property of the GLCM to compute. The default is 'contrast'.
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Returns
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-------
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results : 2-D ndarray
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2-dimensional array. `results[d, a]` is the property 'prop' for
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the d'th distance and the a'th angle.
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References
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----------
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.. [1] The GLCM Tutorial Home Page,
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http://www.fp.ucalgary.ca/mhallbey/tutorial.htm
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Examples
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--------
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Compute the contrast for GLCMs with distances [1, 2] and angles
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[0 degrees, 90 degrees]
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>>> image = np.array([[0, 0, 1, 1],
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... [0, 0, 1, 1],
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... [0, 2, 2, 2],
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... [2, 2, 3, 3]], dtype=np.uint8)
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>>> g = greycomatrix(image, [1, 2], [0, np.pi/2], levels=4,
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... normed=True, symmetric=True)
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>>> contrast = greycoprops(g, 'contrast')
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>>> contrast
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array([[ 0.58333333, 1. ],
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[ 1.25 , 2.75 ]])
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"""
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assert_nD(P, 4, 'P')
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(num_level, num_level2, num_dist, num_angle) = P.shape
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assert num_level == num_level2
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assert num_dist > 0
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assert num_angle > 0
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# create weights for specified property
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I, J = np.ogrid[0:num_level, 0:num_level]
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if prop == 'contrast':
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weights = (I - J) ** 2
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elif prop == 'dissimilarity':
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weights = np.abs(I - J)
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elif prop == 'homogeneity':
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weights = 1. / (1. + (I - J) ** 2)
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elif prop in ['ASM', 'energy', 'correlation']:
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pass
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else:
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raise ValueError('%s is an invalid property' % (prop))
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# compute property for each GLCM
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if prop == 'energy':
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asm = np.apply_over_axes(np.sum, (P ** 2), axes=(0, 1))[0, 0]
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results = np.sqrt(asm)
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elif prop == 'ASM':
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results = np.apply_over_axes(np.sum, (P ** 2), axes=(0, 1))[0, 0]
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elif prop == 'correlation':
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results = np.zeros((num_dist, num_angle), dtype=np.float64)
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I = np.array(range(num_level)).reshape((num_level, 1, 1, 1))
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J = np.array(range(num_level)).reshape((1, num_level, 1, 1))
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diff_i = I - np.apply_over_axes(np.sum, (I * P), axes=(0, 1))[0, 0]
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diff_j = J - np.apply_over_axes(np.sum, (J * P), axes=(0, 1))[0, 0]
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std_i = np.sqrt(np.apply_over_axes(np.sum, (P * (diff_i) ** 2),
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axes=(0, 1))[0, 0])
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std_j = np.sqrt(np.apply_over_axes(np.sum, (P * (diff_j) ** 2),
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axes=(0, 1))[0, 0])
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cov = np.apply_over_axes(np.sum, (P * (diff_i * diff_j)),
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axes=(0, 1))[0, 0]
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# handle the special case of standard deviations near zero
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mask_0 = std_i < 1e-15
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mask_0[std_j < 1e-15] = True
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results[mask_0] = 1
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# handle the standard case
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mask_1 = mask_0 == False
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results[mask_1] = cov[mask_1] / (std_i[mask_1] * std_j[mask_1])
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elif prop in ['contrast', 'dissimilarity', 'homogeneity']:
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weights = weights.reshape((num_level, num_level, 1, 1))
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results = np.apply_over_axes(np.sum, (P * weights), axes=(0, 1))[0, 0]
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return results
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def local_binary_pattern(image, P, R, method='default'):
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"""Gray scale and rotation invariant LBP (Local Binary Patterns).
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LBP is an invariant descriptor that can be used for texture classification.
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Parameters
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----------
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image : (N, M) array
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Graylevel image.
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P : int
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Number of circularly symmetric neighbour set points (quantization of
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the angular space).
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R : float
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Radius of circle (spatial resolution of the operator).
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method : {'default', 'ror', 'uniform', 'var'}
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Method to determine the pattern.
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* 'default': original local binary pattern which is gray scale but not
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rotation invariant.
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* 'ror': extension of default implementation which is gray scale and
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rotation invariant.
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* 'uniform': improved rotation invariance with uniform patterns and
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finer quantization of the angular space which is gray scale and
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rotation invariant.
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* 'nri_uniform': non rotation-invariant uniform patterns variant
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which is only gray scale invariant [2]_.
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* 'var': rotation invariant variance measures of the contrast of local
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image texture which is rotation but not gray scale invariant.
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Returns
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-------
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output : (N, M) array
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LBP image.
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References
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----------
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.. [1] Multiresolution Gray-Scale and Rotation Invariant Texture
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Classification with Local Binary Patterns.
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Timo Ojala, Matti Pietikainen, Topi Maenpaa.
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http://www.rafbis.it/biplab15/images/stories/docenti/Danielriccio/Articoliriferimento/LBP.pdf, 2002.
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.. [2] Face recognition with local binary patterns.
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Timo Ahonen, Abdenour Hadid, Matti Pietikainen,
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.6851,
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2004.
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"""
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assert_nD(image, 2)
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methods = {
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'default': ord('D'),
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'ror': ord('R'),
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'uniform': ord('U'),
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'nri_uniform': ord('N'),
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'var': ord('V')
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}
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image = np.ascontiguousarray(image, dtype=np.double)
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output = _local_binary_pattern(image, P, R, methods[method.lower()])
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return output
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