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Texture analysis using Haralick Descriptors for Computer Vision tasks (#8004)

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No! What if the Kernel is empty?
Example:

>>> kernel = np.zeros((1))
>>> kernel or np.ones((3, 3))
array([[1., 1., 1.],
          [1., 1., 1.],
          [1., 1., 1.]])

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---------

Co-authored-by: Rafael Zimmer <rzimmerdev@monmo.localdomain>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
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"""
https://en.wikipedia.org/wiki/Image_texture
https://en.wikipedia.org/wiki/Co-occurrence_matrix#Application_to_image_analysis
"""
import imageio.v2 as imageio
import numpy as np
def root_mean_square_error(original: np.ndarray, reference: np.ndarray) -> float:
"""Simple implementation of Root Mean Squared Error
for two N dimensional numpy arrays.
Examples:
>>> root_mean_square_error(np.array([1, 2, 3]), np.array([1, 2, 3]))
0.0
>>> root_mean_square_error(np.array([1, 2, 3]), np.array([2, 2, 2]))
0.816496580927726
>>> root_mean_square_error(np.array([1, 2, 3]), np.array([6, 4, 2]))
3.1622776601683795
"""
return np.sqrt(((original - reference) ** 2).mean())
def normalize_image(
image: np.ndarray, cap: float = 255.0, data_type: np.dtype = np.uint8
) -> np.ndarray:
"""
Normalizes image in Numpy 2D array format, between ranges 0-cap,
as to fit uint8 type.
Args:
image: 2D numpy array representing image as matrix, with values in any range
cap: Maximum cap amount for normalization
data_type: numpy data type to set output variable to
Returns:
return 2D numpy array of type uint8, corresponding to limited range matrix
Examples:
>>> normalize_image(np.array([[1, 2, 3], [4, 5, 10]]),
... cap=1.0, data_type=np.float64)
array([[0. , 0.11111111, 0.22222222],
[0.33333333, 0.44444444, 1. ]])
>>> normalize_image(np.array([[4, 4, 3], [1, 7, 2]]))
array([[127, 127, 85],
[ 0, 255, 42]], dtype=uint8)
"""
normalized = (image - np.min(image)) / (np.max(image) - np.min(image)) * cap
return normalized.astype(data_type)
def normalize_array(array: np.ndarray, cap: float = 1) -> np.ndarray:
"""Normalizes a 1D array, between ranges 0-cap.
Args:
array: List containing values to be normalized between cap range.
cap: Maximum cap amount for normalization.
Returns:
return 1D numpy array, corresponding to limited range array
Examples:
>>> normalize_array(np.array([2, 3, 5, 7]))
array([0. , 0.2, 0.6, 1. ])
>>> normalize_array(np.array([[5], [7], [11], [13]]))
array([[0. ],
[0.25],
[0.75],
[1. ]])
"""
diff = np.max(array) - np.min(array)
return (array - np.min(array)) / (1 if diff == 0 else diff) * cap
def grayscale(image: np.ndarray) -> np.ndarray:
"""
Uses luminance weights to transform RGB channel to greyscale, by
taking the dot product between the channel and the weights.
Example:
>>> grayscale(np.array([[[108, 201, 72], [255, 11, 127]],
... [[56, 56, 56], [128, 255, 107]]]))
array([[158, 97],
[ 56, 200]], dtype=uint8)
"""
return np.dot(image[:, :, 0:3], [0.299, 0.587, 0.114]).astype(np.uint8)
def binarize(image: np.ndarray, threshold: float = 127.0) -> np.ndarray:
"""
Binarizes a grayscale image based on a given threshold value,
setting values to 1 or 0 accordingly.
Examples:
>>> binarize(np.array([[128, 255], [101, 156]]))
array([[1, 1],
[0, 1]])
>>> binarize(np.array([[0.07, 1], [0.51, 0.3]]), threshold=0.5)
array([[0, 1],
[1, 0]])
"""
return np.where(image > threshold, 1, 0)
def transform(image: np.ndarray, kind: str, kernel: np.ndarray = None) -> np.ndarray:
"""
Simple image transformation using one of two available filter functions:
Erosion and Dilation.
Args:
image: binarized input image, onto which to apply transformation
kind: Can be either 'erosion', in which case the :func:np.max
function is called, or 'dilation', when :func:np.min is used instead.
kernel: n x n kernel with shape < :attr:image.shape,
to be used when applying convolution to original image
Returns:
returns a numpy array with same shape as input image,
corresponding to applied binary transformation.
Examples:
>>> img = np.array([[1, 0.5], [0.2, 0.7]])
>>> img = binarize(img, threshold=0.5)
>>> transform(img, 'erosion')
array([[1, 1],
[1, 1]], dtype=uint8)
>>> transform(img, 'dilation')
array([[0, 0],
[0, 0]], dtype=uint8)
"""
if kernel is None:
kernel = np.ones((3, 3))
if kind == "erosion":
constant = 1
apply = np.max
else:
constant = 0
apply = np.min
center_x, center_y = (x // 2 for x in kernel.shape)
# Use padded image when applying convolotion
# to not go out of bounds of the original the image
transformed = np.zeros(image.shape, dtype=np.uint8)
padded = np.pad(image, 1, "constant", constant_values=constant)
for x in range(center_x, padded.shape[0] - center_x):
for y in range(center_y, padded.shape[1] - center_y):
center = padded[
x - center_x : x + center_x + 1, y - center_y : y + center_y + 1
]
# Apply transformation method to the centered section of the image
transformed[x - center_x, y - center_y] = apply(center[kernel == 1])
return transformed
def opening_filter(image: np.ndarray, kernel: np.ndarray = None) -> np.ndarray:
"""
Opening filter, defined as the sequence of
erosion and then a dilation filter on the same image.
Examples:
>>> img = np.array([[1, 0.5], [0.2, 0.7]])
>>> img = binarize(img, threshold=0.5)
>>> opening_filter(img)
array([[1, 1],
[1, 1]], dtype=uint8)
"""
if kernel is None:
np.ones((3, 3))
return transform(transform(image, "dilation", kernel), "erosion", kernel)
def closing_filter(image: np.ndarray, kernel: np.ndarray = None) -> np.ndarray:
"""
Opening filter, defined as the sequence of
dilation and then erosion filter on the same image.
Examples:
>>> img = np.array([[1, 0.5], [0.2, 0.7]])
>>> img = binarize(img, threshold=0.5)
>>> closing_filter(img)
array([[0, 0],
[0, 0]], dtype=uint8)
"""
if kernel is None:
kernel = np.ones((3, 3))
return transform(transform(image, "erosion", kernel), "dilation", kernel)
def binary_mask(
image_gray: np.ndarray, image_map: np.ndarray
) -> tuple[np.ndarray, np.ndarray]:
"""
Apply binary mask, or thresholding based
on bit mask value (mapping mask is binary).
Returns the mapped true value mask and its complementary false value mask.
Example:
>>> img = np.array([[[108, 201, 72], [255, 11, 127]],
... [[56, 56, 56], [128, 255, 107]]])
>>> gray = grayscale(img)
>>> binary = binarize(gray)
>>> morphological = opening_filter(binary)
>>> binary_mask(gray, morphological)
(array([[1, 1],
[1, 1]], dtype=uint8), array([[158, 97],
[ 56, 200]], dtype=uint8))
"""
true_mask, false_mask = image_gray.copy(), image_gray.copy()
true_mask[image_map == 1] = 1
false_mask[image_map == 0] = 0
return true_mask, false_mask
def matrix_concurrency(image: np.ndarray, coordinate: tuple[int, int]) -> np.ndarray:
"""
Calculate sample co-occurrence matrix based on input image
as well as selected coordinates on image.
Implementation is made using basic iteration,
as function to be performed (np.max) is non-linear and therefore
not callable on the frequency domain.
Example:
>>> img = np.array([[[108, 201, 72], [255, 11, 127]],
... [[56, 56, 56], [128, 255, 107]]])
>>> gray = grayscale(img)
>>> binary = binarize(gray)
>>> morphological = opening_filter(binary)
>>> mask_1 = binary_mask(gray, morphological)[0]
>>> matrix_concurrency(mask_1, (0, 1))
array([[0., 0.],
[0., 0.]])
"""
matrix = np.zeros([np.max(image) + 1, np.max(image) + 1])
offset_x, offset_y = coordinate
for x in range(1, image.shape[0] - 1):
for y in range(1, image.shape[1] - 1):
base_pixel = image[x, y]
offset_pixel = image[x + offset_x, y + offset_y]
matrix[base_pixel, offset_pixel] += 1
matrix_sum = np.sum(matrix)
return matrix / (1 if matrix_sum == 0 else matrix_sum)
def haralick_descriptors(matrix: np.ndarray) -> list[float]:
"""Calculates all 8 Haralick descriptors based on co-occurence input matrix.
All descriptors are as follows:
Maximum probability, Inverse Difference, Homogeneity, Entropy,
Energy, Dissimilarity, Contrast and Correlation
Args:
matrix: Co-occurence matrix to use as base for calculating descriptors.
Returns:
Reverse ordered list of resulting descriptors
Example:
>>> img = np.array([[[108, 201, 72], [255, 11, 127]],
... [[56, 56, 56], [128, 255, 107]]])
>>> gray = grayscale(img)
>>> binary = binarize(gray)
>>> morphological = opening_filter(binary)
>>> mask_1 = binary_mask(gray, morphological)[0]
>>> concurrency = matrix_concurrency(mask_1, (0, 1))
>>> haralick_descriptors(concurrency)
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
"""
# Function np.indices could be used for bigger input types,
# but np.ogrid works just fine
i, j = np.ogrid[0 : matrix.shape[0], 0 : matrix.shape[1]] # np.indices()
# Pre-calculate frequent multiplication and subtraction
prod = np.multiply(i, j)
sub = np.subtract(i, j)
# Calculate numerical value of Maximum Probability
maximum_prob = np.max(matrix)
# Using the definition for each descriptor individually to calculate its matrix
correlation = prod * matrix
energy = np.power(matrix, 2)
contrast = matrix * np.power(sub, 2)
dissimilarity = matrix * np.abs(sub)
inverse_difference = matrix / (1 + np.abs(sub))
homogeneity = matrix / (1 + np.power(sub, 2))
entropy = -(matrix[matrix > 0] * np.log(matrix[matrix > 0]))
# Sum values for descriptors ranging from the first one to the last,
# as all are their respective origin matrix and not the resulting value yet.
return [
maximum_prob,
correlation.sum(),
energy.sum(),
contrast.sum(),
dissimilarity.sum(),
inverse_difference.sum(),
homogeneity.sum(),
entropy.sum(),
]
def get_descriptors(
masks: tuple[np.ndarray, np.ndarray], coordinate: tuple[int, int]
) -> np.ndarray:
"""
Calculate all Haralick descriptors for a sequence of
different co-occurrence matrices, given input masks and coordinates.
Example:
>>> img = np.array([[[108, 201, 72], [255, 11, 127]],
... [[56, 56, 56], [128, 255, 107]]])
>>> gray = grayscale(img)
>>> binary = binarize(gray)
>>> morphological = opening_filter(binary)
>>> get_descriptors(binary_mask(gray, morphological), (0, 1))
array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
"""
descriptors = np.array(
[haralick_descriptors(matrix_concurrency(mask, coordinate)) for mask in masks]
)
# Concatenate each individual descriptor into
# one single list containing sequence of descriptors
return np.concatenate(descriptors, axis=None)
def euclidean(point_1: np.ndarray, point_2: np.ndarray) -> np.float32:
"""
Simple method for calculating the euclidean distance between two points,
with type np.ndarray.
Example:
>>> a = np.array([1, 0, -2])
>>> b = np.array([2, -1, 1])
>>> euclidean(a, b)
3.3166247903554
"""
return np.sqrt(np.sum(np.square(point_1 - point_2)))
def get_distances(descriptors: np.ndarray, base: int) -> list[tuple[int, float]]:
"""
Calculate all Euclidean distances between a selected base descriptor
and all other Haralick descriptors
The resulting comparison is return in decreasing order,
showing which descriptor is the most similar to the selected base.
Args:
descriptors: Haralick descriptors to compare with base index
base: Haralick descriptor index to use as base when calculating respective
euclidean distance to other descriptors.
Returns:
Ordered distances between descriptors
Example:
>>> index = 1
>>> img = np.array([[[108, 201, 72], [255, 11, 127]],
... [[56, 56, 56], [128, 255, 107]]])
>>> gray = grayscale(img)
>>> binary = binarize(gray)
>>> morphological = opening_filter(binary)
>>> get_distances(get_descriptors(
... binary_mask(gray, morphological), (0, 1)),
... index)
[(0, 0.0), (1, 0.0), (2, 0.0), (3, 0.0), (4, 0.0), (5, 0.0), \
(6, 0.0), (7, 0.0), (8, 0.0), (9, 0.0), (10, 0.0), (11, 0.0), (12, 0.0), \
(13, 0.0), (14, 0.0), (15, 0.0)]
"""
distances = np.array(
[euclidean(descriptor, descriptors[base]) for descriptor in descriptors]
)
# Normalize distances between range [0, 1]
normalized_distances: list[float] = normalize_array(distances, 1).tolist()
enum_distances = list(enumerate(normalized_distances))
enum_distances.sort(key=lambda tup: tup[1], reverse=True)
return enum_distances
if __name__ == "__main__":
# Index to compare haralick descriptors to
index = int(input())
q_value_list = [int(value) for value in input().split()]
q_value = (q_value_list[0], q_value_list[1])
# Format is the respective filter to apply,
# can be either 1 for the opening filter or else for the closing
parameters = {"format": int(input()), "threshold": int(input())}
# Number of images to perform methods on
b_number = int(input())
files, descriptors = [], []
for _ in range(b_number):
file = input().rstrip()
files.append(file)
# Open given image and calculate morphological filter,
# respective masks and correspondent Harralick Descriptors.
image = imageio.imread(file).astype(np.float32)
gray = grayscale(image)
threshold = binarize(gray, parameters["threshold"])
morphological = (
opening_filter(threshold)
if parameters["format"] == 1
else closing_filter(threshold)
)
masks = binary_mask(gray, morphological)
descriptors.append(get_descriptors(masks, q_value))
# Transform ordered distances array into a sequence of indexes
# corresponding to original file position
distances = get_distances(np.array(descriptors), index)
indexed_distances = np.array(distances).astype(np.uint8)[:, 0]
# Finally, print distances considering the Haralick descriptions from the base
# file to all other images using the morphology method of choice.
print(f"Query: {files[index]}")
print("Ranking:")
for idx, file_idx in enumerate(indexed_distances):
print(f"({idx}) {files[file_idx]}", end="\n")

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requirements.txt
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beautifulsoup4
fake_useragent
imageio
keras
lxml
matplotlib