""" 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 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 4 GLCMs using 1-pixel distance and 4 different angles. For example, an angle of 0 radians refers to the neighboring pixel to the right; pi/4 radians to the top-right diagonal neighbor; pi/2 radians to the pixel above, and so forth. >>> 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 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] - 'mean': :math:`\\sum_{i=0}^{levels-1} i*P_{i}` - 'variance': :math:`\\sum_{i=0}^{levels-1} P_{i}*(i-mean)^2` - 'std': :math:`\\sqrt{variance}` - 'entropy': :math:`\\sum_{i,j=0}^{levels-1} -P_{i,j}*log(P_{i,j})` 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', 'mean', 'variance', 'std', 'entropy'}, 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 ]]) """ def glcm_mean(): I = np.arange(num_level).reshape((num_level, 1, 1, 1)) mean = np.sum(I * P, axis=(0, 1)) return I, mean 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', 'entropy', 'variance', 'mean', 'std']: 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 == 'mean': _, results = glcm_mean() elif prop == 'variance': I, mean = glcm_mean() results = np.sum(P * ((I - mean) ** 2), axis=(0, 1)) elif prop == 'std': I, mean = glcm_mean() var = np.sum(P * ((I - mean) ** 2), axis=(0, 1)) results = np.sqrt(var) elif prop == 'entropy': ln = -np.log(P, where=(P != 0), out=np.zeros_like(P)) results = np.sum(P * ln, 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 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 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 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