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435 lines
15 KiB
Python
435 lines
15 KiB
Python
"""
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https://en.wikipedia.org/wiki/Image_texture
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https://en.wikipedia.org/wiki/Co-occurrence_matrix#Application_to_image_analysis
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"""
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import imageio.v2 as imageio
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import numpy as np
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def root_mean_square_error(original: np.ndarray, reference: np.ndarray) -> float:
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"""Simple implementation of Root Mean Squared Error
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for two N dimensional numpy arrays.
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Examples:
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>>> root_mean_square_error(np.array([1, 2, 3]), np.array([1, 2, 3]))
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0.0
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>>> root_mean_square_error(np.array([1, 2, 3]), np.array([2, 2, 2]))
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0.816496580927726
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>>> root_mean_square_error(np.array([1, 2, 3]), np.array([6, 4, 2]))
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3.1622776601683795
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"""
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return float(np.sqrt(((original - reference) ** 2).mean()))
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def normalize_image(
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image: np.ndarray, cap: float = 255.0, data_type: np.dtype = np.uint8
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) -> np.ndarray:
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"""
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Normalizes image in Numpy 2D array format, between ranges 0-cap,
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as to fit uint8 type.
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Args:
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image: 2D numpy array representing image as matrix, with values in any range
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cap: Maximum cap amount for normalization
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data_type: numpy data type to set output variable to
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Returns:
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return 2D numpy array of type uint8, corresponding to limited range matrix
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Examples:
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>>> normalize_image(np.array([[1, 2, 3], [4, 5, 10]]),
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... cap=1.0, data_type=np.float64)
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array([[0. , 0.11111111, 0.22222222],
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[0.33333333, 0.44444444, 1. ]])
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>>> normalize_image(np.array([[4, 4, 3], [1, 7, 2]]))
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array([[127, 127, 85],
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[ 0, 255, 42]], dtype=uint8)
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"""
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normalized = (image - np.min(image)) / (np.max(image) - np.min(image)) * cap
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return normalized.astype(data_type)
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def normalize_array(array: np.ndarray, cap: float = 1) -> np.ndarray:
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"""Normalizes a 1D array, between ranges 0-cap.
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Args:
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array: List containing values to be normalized between cap range.
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cap: Maximum cap amount for normalization.
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Returns:
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return 1D numpy array, corresponding to limited range array
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Examples:
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>>> normalize_array(np.array([2, 3, 5, 7]))
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array([0. , 0.2, 0.6, 1. ])
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>>> normalize_array(np.array([[5], [7], [11], [13]]))
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array([[0. ],
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[0.25],
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[0.75],
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[1. ]])
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"""
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diff = np.max(array) - np.min(array)
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return (array - np.min(array)) / (1 if diff == 0 else diff) * cap
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def grayscale(image: np.ndarray) -> np.ndarray:
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"""
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Uses luminance weights to transform RGB channel to greyscale, by
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taking the dot product between the channel and the weights.
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Example:
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>>> grayscale(np.array([[[108, 201, 72], [255, 11, 127]],
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... [[56, 56, 56], [128, 255, 107]]]))
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array([[158, 97],
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[ 56, 200]], dtype=uint8)
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"""
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return np.dot(image[:, :, 0:3], [0.299, 0.587, 0.114]).astype(np.uint8)
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def binarize(image: np.ndarray, threshold: float = 127.0) -> np.ndarray:
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"""
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Binarizes a grayscale image based on a given threshold value,
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setting values to 1 or 0 accordingly.
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Examples:
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>>> binarize(np.array([[128, 255], [101, 156]]))
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array([[1, 1],
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[0, 1]])
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>>> binarize(np.array([[0.07, 1], [0.51, 0.3]]), threshold=0.5)
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array([[0, 1],
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[1, 0]])
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"""
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return np.where(image > threshold, 1, 0)
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def transform(
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image: np.ndarray, kind: str, kernel: np.ndarray | None = None
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) -> np.ndarray:
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"""
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Simple image transformation using one of two available filter functions:
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Erosion and Dilation.
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Args:
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image: binarized input image, onto which to apply transformation
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kind: Can be either 'erosion', in which case the :func:np.max
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function is called, or 'dilation', when :func:np.min is used instead.
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kernel: n x n kernel with shape < :attr:image.shape,
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to be used when applying convolution to original image
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Returns:
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returns a numpy array with same shape as input image,
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corresponding to applied binary transformation.
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Examples:
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>>> img = np.array([[1, 0.5], [0.2, 0.7]])
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>>> img = binarize(img, threshold=0.5)
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>>> transform(img, 'erosion')
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array([[1, 1],
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[1, 1]], dtype=uint8)
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>>> transform(img, 'dilation')
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array([[0, 0],
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[0, 0]], dtype=uint8)
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"""
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if kernel is None:
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kernel = np.ones((3, 3))
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if kind == "erosion":
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constant = 1
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apply = np.max
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else:
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constant = 0
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apply = np.min
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center_x, center_y = (x // 2 for x in kernel.shape)
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# Use padded image when applying convolution
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# to not go out of bounds of the original the image
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transformed = np.zeros(image.shape, dtype=np.uint8)
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padded = np.pad(image, 1, "constant", constant_values=constant)
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for x in range(center_x, padded.shape[0] - center_x):
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for y in range(center_y, padded.shape[1] - center_y):
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center = padded[
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x - center_x : x + center_x + 1, y - center_y : y + center_y + 1
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]
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# Apply transformation method to the centered section of the image
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transformed[x - center_x, y - center_y] = apply(center[kernel == 1])
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return transformed
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def opening_filter(image: np.ndarray, kernel: np.ndarray | None = None) -> np.ndarray:
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"""
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Opening filter, defined as the sequence of
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erosion and then a dilation filter on the same image.
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Examples:
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>>> img = np.array([[1, 0.5], [0.2, 0.7]])
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>>> img = binarize(img, threshold=0.5)
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>>> opening_filter(img)
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array([[1, 1],
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[1, 1]], dtype=uint8)
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"""
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if kernel is None:
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np.ones((3, 3))
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return transform(transform(image, "dilation", kernel), "erosion", kernel)
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def closing_filter(image: np.ndarray, kernel: np.ndarray | None = None) -> np.ndarray:
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"""
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Opening filter, defined as the sequence of
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dilation and then erosion filter on the same image.
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Examples:
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>>> img = np.array([[1, 0.5], [0.2, 0.7]])
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>>> img = binarize(img, threshold=0.5)
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>>> closing_filter(img)
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array([[0, 0],
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[0, 0]], dtype=uint8)
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"""
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if kernel is None:
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kernel = np.ones((3, 3))
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return transform(transform(image, "erosion", kernel), "dilation", kernel)
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def binary_mask(
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image_gray: np.ndarray, image_map: np.ndarray
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) -> tuple[np.ndarray, np.ndarray]:
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"""
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Apply binary mask, or thresholding based
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on bit mask value (mapping mask is binary).
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Returns the mapped true value mask and its complementary false value mask.
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Example:
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>>> img = np.array([[[108, 201, 72], [255, 11, 127]],
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... [[56, 56, 56], [128, 255, 107]]])
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>>> gray = grayscale(img)
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>>> binary = binarize(gray)
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>>> morphological = opening_filter(binary)
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>>> binary_mask(gray, morphological)
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(array([[1, 1],
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[1, 1]], dtype=uint8), array([[158, 97],
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[ 56, 200]], dtype=uint8))
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"""
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true_mask, false_mask = image_gray.copy(), image_gray.copy()
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true_mask[image_map == 1] = 1
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false_mask[image_map == 0] = 0
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return true_mask, false_mask
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def matrix_concurrency(image: np.ndarray, coordinate: tuple[int, int]) -> np.ndarray:
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"""
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Calculate sample co-occurrence matrix based on input image
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as well as selected coordinates on image.
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Implementation is made using basic iteration,
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as function to be performed (np.max) is non-linear and therefore
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not callable on the frequency domain.
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Example:
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>>> img = np.array([[[108, 201, 72], [255, 11, 127]],
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... [[56, 56, 56], [128, 255, 107]]])
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>>> gray = grayscale(img)
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>>> binary = binarize(gray)
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>>> morphological = opening_filter(binary)
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>>> mask_1 = binary_mask(gray, morphological)[0]
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>>> matrix_concurrency(mask_1, (0, 1))
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array([[0., 0.],
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[0., 0.]])
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"""
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matrix = np.zeros([np.max(image) + 1, np.max(image) + 1])
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offset_x, offset_y = coordinate
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for x in range(1, image.shape[0] - 1):
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for y in range(1, image.shape[1] - 1):
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base_pixel = image[x, y]
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offset_pixel = image[x + offset_x, y + offset_y]
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matrix[base_pixel, offset_pixel] += 1
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matrix_sum = np.sum(matrix)
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return matrix / (1 if matrix_sum == 0 else matrix_sum)
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def haralick_descriptors(matrix: np.ndarray) -> list[float]:
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"""Calculates all 8 Haralick descriptors based on co-occurrence input matrix.
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All descriptors are as follows:
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Maximum probability, Inverse Difference, Homogeneity, Entropy,
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Energy, Dissimilarity, Contrast and Correlation
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Args:
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matrix: Co-occurrence matrix to use as base for calculating descriptors.
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Returns:
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Reverse ordered list of resulting descriptors
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Example:
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>>> img = np.array([[[108, 201, 72], [255, 11, 127]],
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... [[56, 56, 56], [128, 255, 107]]])
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>>> gray = grayscale(img)
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>>> binary = binarize(gray)
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>>> morphological = opening_filter(binary)
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>>> mask_1 = binary_mask(gray, morphological)[0]
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>>> concurrency = matrix_concurrency(mask_1, (0, 1))
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>>> [float(f) for f in haralick_descriptors(concurrency)]
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[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
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"""
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# Function np.indices could be used for bigger input types,
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# but np.ogrid works just fine
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i, j = np.ogrid[0 : matrix.shape[0], 0 : matrix.shape[1]] # np.indices()
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# Pre-calculate frequent multiplication and subtraction
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prod = np.multiply(i, j)
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sub = np.subtract(i, j)
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# Calculate numerical value of Maximum Probability
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maximum_prob = np.max(matrix)
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# Using the definition for each descriptor individually to calculate its matrix
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correlation = prod * matrix
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energy = np.power(matrix, 2)
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contrast = matrix * np.power(sub, 2)
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dissimilarity = matrix * np.abs(sub)
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inverse_difference = matrix / (1 + np.abs(sub))
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homogeneity = matrix / (1 + np.power(sub, 2))
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entropy = -(matrix[matrix > 0] * np.log(matrix[matrix > 0]))
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# Sum values for descriptors ranging from the first one to the last,
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# as all are their respective origin matrix and not the resulting value yet.
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return [
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maximum_prob,
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correlation.sum(),
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energy.sum(),
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contrast.sum(),
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dissimilarity.sum(),
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inverse_difference.sum(),
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homogeneity.sum(),
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entropy.sum(),
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]
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def get_descriptors(
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masks: tuple[np.ndarray, np.ndarray], coordinate: tuple[int, int]
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) -> np.ndarray:
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"""
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Calculate all Haralick descriptors for a sequence of
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different co-occurrence matrices, given input masks and coordinates.
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Example:
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>>> img = np.array([[[108, 201, 72], [255, 11, 127]],
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... [[56, 56, 56], [128, 255, 107]]])
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>>> gray = grayscale(img)
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>>> binary = binarize(gray)
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>>> morphological = opening_filter(binary)
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>>> get_descriptors(binary_mask(gray, morphological), (0, 1))
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array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
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"""
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descriptors = np.array(
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[haralick_descriptors(matrix_concurrency(mask, coordinate)) for mask in masks]
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)
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# Concatenate each individual descriptor into
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# one single list containing sequence of descriptors
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return np.concatenate(descriptors, axis=None)
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def euclidean(point_1: np.ndarray, point_2: np.ndarray) -> float:
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"""
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Simple method for calculating the euclidean distance between two points,
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with type np.ndarray.
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Example:
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>>> a = np.array([1, 0, -2])
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>>> b = np.array([2, -1, 1])
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>>> euclidean(a, b)
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3.3166247903554
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"""
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return float(np.sqrt(np.sum(np.square(point_1 - point_2))))
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def get_distances(descriptors: np.ndarray, base: int) -> list[tuple[int, float]]:
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"""
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Calculate all Euclidean distances between a selected base descriptor
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and all other Haralick descriptors
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The resulting comparison is return in decreasing order,
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showing which descriptor is the most similar to the selected base.
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Args:
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descriptors: Haralick descriptors to compare with base index
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base: Haralick descriptor index to use as base when calculating respective
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euclidean distance to other descriptors.
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Returns:
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Ordered distances between descriptors
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Example:
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>>> index = 1
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>>> img = np.array([[[108, 201, 72], [255, 11, 127]],
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... [[56, 56, 56], [128, 255, 107]]])
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>>> gray = grayscale(img)
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>>> binary = binarize(gray)
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>>> morphological = opening_filter(binary)
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>>> get_distances(get_descriptors(
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... binary_mask(gray, morphological), (0, 1)),
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... index)
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[(0, 0.0), (1, 0.0), (2, 0.0), (3, 0.0), (4, 0.0), (5, 0.0), \
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(6, 0.0), (7, 0.0), (8, 0.0), (9, 0.0), (10, 0.0), (11, 0.0), (12, 0.0), \
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(13, 0.0), (14, 0.0), (15, 0.0)]
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"""
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distances = np.array(
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[euclidean(descriptor, descriptors[base]) for descriptor in descriptors]
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)
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# Normalize distances between range [0, 1]
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normalized_distances: list[float] = normalize_array(distances, 1).tolist()
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enum_distances = list(enumerate(normalized_distances))
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enum_distances.sort(key=lambda tup: tup[1], reverse=True)
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return enum_distances
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if __name__ == "__main__":
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# Index to compare haralick descriptors to
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index = int(input())
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q_value_list = [int(value) for value in input().split()]
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q_value = (q_value_list[0], q_value_list[1])
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# Format is the respective filter to apply,
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# can be either 1 for the opening filter or else for the closing
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parameters = {"format": int(input()), "threshold": int(input())}
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# Number of images to perform methods on
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b_number = int(input())
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files, descriptors = [], []
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for _ in range(b_number):
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file = input().rstrip()
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files.append(file)
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# Open given image and calculate morphological filter,
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# respective masks and correspondent Harralick Descriptors.
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image = imageio.imread(file).astype(np.float32)
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gray = grayscale(image)
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threshold = binarize(gray, parameters["threshold"])
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morphological = (
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opening_filter(threshold)
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if parameters["format"] == 1
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else closing_filter(threshold)
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)
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masks = binary_mask(gray, morphological)
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descriptors.append(get_descriptors(masks, q_value))
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# Transform ordered distances array into a sequence of indexes
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# corresponding to original file position
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distances = get_distances(np.array(descriptors), index)
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indexed_distances = np.array(distances).astype(np.uint8)[:, 0]
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# Finally, print distances considering the Haralick descriptions from the base
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# file to all other images using the morphology method of choice.
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print(f"Query: {files[index]}")
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print("Ranking:")
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for idx, file_idx in enumerate(indexed_distances):
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print(f"({idx}) {files[file_idx]}", end="\n")
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