#### Haralick Descriptors

p
```"""
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 = 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 convolution
# to not go out of bounds of the original the image
transformed = np.zeros(image.shape, dtype=np.uint8)

for x in range(center_x, padded.shape[0] - center_x):
for y in range(center_y, padded.shape[1] - center_y):
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 = 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 = 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)

image_gray: np.ndarray, image_map: np.ndarray
) -> tuple[np.ndarray, np.ndarray]:
"""
Apply binary mask, or thresholding based

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)
(array([[1, 1],
[1, 1]], dtype=uint8), array([[158,  97],
[ 56, 200]], dtype=uint8))
"""

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)
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-occurrence input matrix.
All descriptors are as follows:
Maximum probability, Inverse Difference, Homogeneity, Entropy,
Energy, Dissimilarity, Contrast and Correlation

Args:
matrix: Co-occurrence 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)
>>> 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)
array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
"""
descriptors = np.array(
)

# 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(
...               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.
gray = grayscale(image)
threshold = binarize(gray, parameters["threshold"])

morphological = (
opening_filter(threshold)
if parameters["format"] == 1
else closing_filter(threshold)
)