501 lines
17 KiB
Python
501 lines
17 KiB
Python
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import numpy as np
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import cv2 as cv2
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from matplotlib import pyplot as plt
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from PIL import Image
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from typing import Union
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import numpy.typing as npt
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import enum
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class ImageType(enum.Enum):
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uint8 = 0
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float64 = 1
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class DistanceMeasure(enum.Enum):
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euclidian_distance = 0
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chi_square_distance = 1
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intersection_distance = 2
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hellinger_distance = 3
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def imread(path: str, type: ImageType) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
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"""
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Reads an image in RGB order. Image type is transformed from uint8 to float, and
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range of values is reduced from [0, 255] to [0, 1].
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"""
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I = Image.open(path).convert('RGB') # PIL image.
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I = np.asarray(I) # Converting to Numpy array.
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if type == ImageType.float64:
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I = I.astype(np.float64) / 255
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return I
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elif type == ImageType.uint8:
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return I
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raise Exception(f"Unrecognized image format! {type}")
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def imread_gray(path: str, type: ImageType) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
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"""
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Reads an image in gray. Image type is transformed from uint8 to float, and
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range of values is reduced from [0, 255] to [0, 1].
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"""
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I = Image.open(path).convert('L') # PIL image opening and converting to gray.
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I = np.asarray(I) # Converting to Numpy array.
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if type == ImageType.float64:
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I = I.astype(np.float64) / 255
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return I
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elif type == ImageType.uint8:
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return I
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raise Exception("Unrecognized image format!")
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def signal_show(*signals):
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"""
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Plots all given 1D signals in the same plot.
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Signals can be Python lists or 1D numpy array.
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"""
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for s in signals:
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if type(s) == np.ndarray:
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s = s.squeeze()
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plt.plot(s)
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plt.show()
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def convolve(I: np.ndarray, *ks):
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"""
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Convolves input image I with all given kernels.
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:param I: Image, should be of type float64 and scaled from 0 to 1.
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:param ks: 2D Kernels
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:return: Image convolved with all kernels.
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"""
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for k in ks:
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k = np.flip(k) # filter2D performs correlation, so flipping is necessary
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I = cv2.filter2D(I, cv2.CV_64F, k)
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return I
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def transform_coloured_image_to_grayscale(image: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
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"""
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Accepts float64 picture with three colour channels and returns float64 grayscale image
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with one channel.
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"""
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grayscale_image = np.zeros(image.shape[:2])
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for i in range(image.shape[0]):
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for j in range(image.shape[1]):
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grayscale_image[i, j] = (image[i, j, 0] + image[i,j, 1] + image[i, j, 2]) / 3
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return grayscale_image
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def invert_coloured_image_part(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], startx: int, endx: int, starty: int, endy: int) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
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"""
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Accepts image, starting position end end position for axes x & y. Returns whole image with inverted part.
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"""
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inverted_image = image.copy()
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if image.dtype.type == np.float64:
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for i in range(startx, endx):
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for j in range(starty, endy):
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inverted_image[i, j, 0] = 1 - image[i, j, 0]
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inverted_image[i, j, 1] = 1 - image[i, j, 1]
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inverted_image[i, j, 2] = 1 - image[i, j, 2]
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return inverted_image
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elif image.dtype.type == np.uint8:
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for i in range(startx, endx):
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for j in range(starty, endy):
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inverted_image[i, j, 0] = 255 - image[i, j, 0]
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inverted_image[i, j, 1] = 255 - image[i, j, 1]
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inverted_image[i, j, 2] = 255 - image[i, j, 2]
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return inverted_image
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raise Exception("Unrecognized image format!")
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def invert_coloured_image(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
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"""
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Accepts image and inverts it
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"""
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return invert_coloured_image_part(image, 0, image.shape[0], 0, image.shape[1])
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def calculate_best_treshold_using_otsu_method(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]) -> int:
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"""
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Accepts image and returns best treshold using otsu method
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"""
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if image.dtype.type == np.float64:
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im = image.copy()
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im = im * (255.0/im.max())
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elif image.dtype.type == np.uint8:
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im = image.copy()
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else:
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raise Exception("Unrecognized image format!")
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treshold_range = np.arange(np.max(im) + 1)
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criterias = []
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for treshold in treshold_range:
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# create the thresholded image
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thresholded_im = np.zeros(im.shape)
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thresholded_im[im >= treshold] = 1
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# compute weights
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nb_pixels = im.size
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nb_pixels1 = np.count_nonzero(thresholded_im)
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weight1 = nb_pixels1 / nb_pixels
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weight0 = 1 - weight1
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# if one the classes is empty, eg all pixels are below or above the threshold, that threshold will not be considered
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# in the search for the best threshold
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if weight1 == 0 or weight0 == 0:
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continue
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# find all pixels belonging to each class
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val_pixels1 = im[thresholded_im == 1]
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val_pixels0 = im[thresholded_im == 0]
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# compute variance of these classes
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var0 = np.var(val_pixels0) if len(val_pixels0) > 0 else 0
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var1 = np.var(val_pixels1) if len(val_pixels1) > 0 else 0
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criterias.append( weight0 * var0 + weight1 * var1)
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best_threshold = treshold_range[np.argmin(criterias)]
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return best_threshold
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def get_image_bins_for_loop(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], number_of_bins: int) -> npt.NDArray[np.float64]:
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"""
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Accepts image in the float64 format or uint8, returns normailzed
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image bins, histogram
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"""
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if image.dtype.type == np.float64 or image.dtype.type == np.uint8:
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bin_restrictions = np.linspace(np.min(image), np.max(image), num=number_of_bins)
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else:
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raise Exception("Unrecognized image format!")
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bins = np.zeros(number_of_bins).astype(np.float64)
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for pixel in image.reshape(-1):
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# https://stackoverflow.com/a/16244044
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bins[np.argmax(bin_restrictions > pixel)] += 1
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return bins / np.sum(bins)
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# Much faster implementation than for loop
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def get_image_bins(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], number_of_bins: int) -> npt.NDArray[np.float64]:
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"""
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Accepts image in the float64 format or uint8, returns normailzed
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image bins, histogram
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"""
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if image.dtype.type == np.float64 or image.dtype.type == np.uint8:
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bins = np.linspace(np.min(image), np.max(image), num=number_of_bins)
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else:
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raise Exception("Unrecognized image format!")
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# Put pixels into classes
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# ex. binsize = 10 then 0.4 would map into 4
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binarray = np.digitize(image.reshape(-1), bins).astype(np.uint8)
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# Now count those values
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binarray = np.unique(binarray, return_counts=True)
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counts = binarray[1].astype(np.float64) # Get the counts out of tuple
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# Check if there is any empty bin
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empty_bins = []
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bins = binarray[0]
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for i in range(1, number_of_bins + 1):
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if i not in bins:
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empty_bins.append(i)
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# Add empty bins with zeros
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if empty_bins != []:
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for i in empty_bins:
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counts = np.insert(counts, i - 1, 0)
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return counts
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def get_image_bins_ND(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], number_of_bins: int) -> npt.NDArray[np.float64]:
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"""
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Accepts image in the float64 format or uint8 and number of bins
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Returns normailzed image histogram bins
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"""
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bs = []
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hist = np.zeros((number_of_bins, number_of_bins, number_of_bins))
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bins = np.linspace(np.min(image), np.max(image), num=number_of_bins)
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for i in range(image.shape[2]):
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v = image[:, :, i].reshape(-1)
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bs.append(np.digitize(v, bins).astype(np.uint32))
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for i in range(len(bs[0])):
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hist[bs[2][i] -1, bs[1][i] -1, bs[0][i] - 1] += 1
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return hist / np.sum(hist)
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def compare_two_histograms(h1: npt.NDArray[np.float64], h2: npt.NDArray[np.float64], method: DistanceMeasure) -> float:
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"""
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Accepts two histograms and method of comparison
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Returns distance between them
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"""
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if method == DistanceMeasure.euclidian_distance:
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d = np.sqrt(np.sum(np.square(h1 - h2)))
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elif method == DistanceMeasure.chi_square_distance:
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d = 0.5 * np.sum(np.square(h1 - h2) / (h1 + h2 + np.finfo(float).eps))
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elif method == DistanceMeasure.intersection_distance:
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d = 1 - np.sum(np.minimum(h1, h2))
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elif method == DistanceMeasure.hellinger_distance:
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d = np.sqrt(0.5 * np.sum(np.square(np.sqrt(h1) - np.sqrt(h2))))
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else:
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raise Exception('Unsuported method chosen!')
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return d.astype(float)
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def apply_mask_on_image(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], mask: npt.NDArray[np.uint8]) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
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"""
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Accepts image and applys mask to image
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"""
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image = image.copy()
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mask = np.expand_dims(mask, axis=2)
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image = mask * image
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return image
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def simple_convolution(signal: npt.NDArray[np.float64], kernel: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
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"""
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Accepts: signal & kernel
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Returns: convolved signal with a kernel
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"""
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N = int(np.ceil(len(kernel) / 2 - 1))
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n_conv = signal.size - kernel.size + 1
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print(N, signal.size -N, n_conv)
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convolved_signal = np.zeros(len(signal))
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rev_kernel = kernel[::-1].copy()
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for i in range(n_conv):
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convolved_signal[i] = np.dot(signal[i: i+kernel.size], rev_kernel) # Well if you would add i+N then you wuold shift this
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return convolved_signal
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def simple_convolution_improved(signal: npt.NDArray[np.float64], kernel: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
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"""
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Accepts: signal & kernel
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Returns: convolved signal with a kernel
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Improved method replicates edges of an signal
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"""
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signal_len = signal.size
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kernel_len = kernel.size
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signal = signal.copy()
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# Calculate which values to fill in and range
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EDGE_FRONT = signal[0]
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EDGE_BACK = signal[-1]
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EXTEND_RANGE = int(np.floor(kernel.size / 2))
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# Append end insert edges
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front = [ EDGE_FRONT for _ in range(EXTEND_RANGE)]
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back = [ EDGE_BACK for _ in range(EXTEND_RANGE)]
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signal = np.insert(signal, 1, front, axis=0)
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signal = np.append(signal, back, axis=0)
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convolved_signal = np.zeros(signal_len)
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rev_kernel = kernel[::-1].copy()
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n_conv = signal_len - kernel_len + 1
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for i in range(n_conv):
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convolved_signal[i] = np.dot(signal[i: i+kernel.size], rev_kernel)
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return convolved_signal
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def get_gaussian_kernel(sigma: float) -> npt.NDArray[np.float64]:
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"""
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Accepts sigma
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Returns gaussian kernel
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"""
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# https://github.com/mikepound/convolve/blob/master/run.gaussian.py
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kernel_size = int(2 * np.ceil(3*sigma) + 1)
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k_min_max = np.ceil(3*sigma)
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k_interval = np.arange(-k_min_max, k_min_max + 1.)
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result = (1. / (np.sqrt(2. * np.pi )* sigma)) * np.exp(- (np.square(k_interval)) / (2.*np.square(sigma)))
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assert(kernel_size == len(result))
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return result / np.sum(result)
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def sharpen_image(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], sharpen_factor=1.0) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
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"""
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Accepts: image & sharpen factor
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Returns: sharpened image
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https://blog.demofox.org/2022/02/26/image-sharpening-convolution-kernels/ <-- sharpening kernel, but also on slides
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good explanation
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"""
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sharpened_image = image.copy()
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KERNEL = np.array([[-1, -1, -1],
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[-1, 17, -1],
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[-1, -1,-1]]) * 1./9. * sharpen_factor
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if image.dtype.type == np.float64:
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sharpened_image = cv2.filter2D(sharpened_image, cv2.CV_64F, KERNEL)
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elif image.dtype.type == np.uint8:
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sharpened_image = cv2.filter2D(sharpened_image, cv2.CV_8U, KERNEL)
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return sharpened_image
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def gaussfilter2D(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], sigma: float) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
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"""
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Accepts: image, sigma
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Applies gaussian noise on image
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returns: filtered_image
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"""
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filtered_image = image.copy()
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kernel = np.array([get_gaussian_kernel(sigma)])
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filtered_image = cv2.filter2D(filtered_image, cv2.CV_64F, kernel)
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filtered_image = cv2.filter2D(filtered_image, cv2.CV_64F, kernel.T)
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return filtered_image
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def gaussdx(sigma: float) -> npt.NDArray[np.float64]:
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"""
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Accepts sigma
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Returns gaussian kernel
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"""
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kernel_size = int(2 * np.ceil(3*sigma) + 1)
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k_min_max = np.ceil(3*sigma)
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k_interval = np.arange(-k_min_max, k_min_max + 1.)
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result = - (1. / (np.sqrt(2. * np.pi )* np.power(sigma, 3))) * k_interval* np.exp(- (np.square(k_interval)) / (2.*np.square(sigma)))
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assert(kernel_size == len(result))
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return result / np.sum(np.abs(result))
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def simple_median(signal: npt.NDArray[np.float64], width: int) -> npt.NDArray[np.float64]:
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"""
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Accepts: signal & width
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returns signal improved using median filter
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"""
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if width % 2 == 0:
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raise Exception('No u won\'t do that')
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signal = signal.copy()
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for i in range(len(signal) - int(np.ceil(width/2))):
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middle_element = int(i + np.floor(width/2))
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signal[middle_element] = np.median(signal[i:i+width])
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return signal
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def apply_median_method_2D(image:Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], width: int) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
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"""
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Accepts: image & filter width
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returns: image with median filter applied
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"""
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if width % 2 == 0:
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raise Exception('No u won\'t do that')
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image = image.copy()
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W_HALF = int(np.floor(width/2))
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padded_image = np.pad(image, W_HALF, mode='edge')
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IMAGE_HEIGHT = image.shape[0] # y
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IMAGE_WIDTH = image.shape[1] # x
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for x in range(W_HALF, IMAGE_WIDTH):
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for y in range(W_HALF, IMAGE_HEIGHT):
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median_filter = np.zeros(0)
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STARTX = x - W_HALF
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STARTY = y - W_HALF
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for m in range(width):
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median_filter = np.append(median_filter, padded_image[STARTY + m][STARTX: STARTX + width], axis=0)
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if image.dtype.type == np.uint8:
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image[y][x] = int(np.mean(median_filter))
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else:
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image[y][x] = np.mean(median_filter)
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return image
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def filter_laplace(image:Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], sigma: float) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
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"""
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Accepts: image & sigma
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returns: image with laplace filter applied
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"""
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# Prepare unit impulse and gauss kernel
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unit_impulse = np.zeros((1, 2 * int(np.ceil(3*sigma)) + 1))
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unit_impulse[0][int(np.ceil(unit_impulse.size /2)) - 1]= 1
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gauss_kernel = np.array([get_gaussian_kernel(sigma)])
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assert(len(gauss_kernel[0]) == len(unit_impulse[0]))
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laplacian_filter = unit_impulse - gauss_kernel[0]
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# Now apply laplacian filter
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applied_by_x = cv2.filter2D(image, -1, laplacian_filter)
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applied_by_y = cv2.filter2D(applied_by_x, -1, laplacian_filter.T)
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return applied_by_y
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def gauss_noise(I, magnitude=.1) -> npt.NDArray[np.float64]:
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"""
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Accepts: image & magnitude
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Returns: image with gaussian noise applied
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"""
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# input: image, magnitude of noise
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# output: modified image
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I = I.copy()
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return I + np.random.normal(size=I.shape) * magnitude
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def sp_noise(I, percent=.1) -> npt.NDArray[np.float64]:
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"""
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Accepts: image & percent
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Returns: image with salt and pepper noise applied
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"""
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# input: image, percent of corrupted pixels
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# output: modified image
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res = I.copy()
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res[np.random.rand(I.shape[0], I.shape[1]) < percent / 2] = 1
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res[np.random.rand(I.shape[0], I.shape[1]) < percent / 2] = 0
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return res
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def sp_noise1D(signal, percent=.1) -> npt.NDArray[np.float64]:
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"""
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Accepts: signal & percent
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Returns: signal with salt and pepper noise applied
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|
"""
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signal = signal.copy()
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signal[np.random.rand(signal.shape[0]) < percent / 2] = 2
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signal[np.random.rand(signal.shape[0]) < percent / 2] = 1
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signal[np.random.rand(signal.shape[0]) < percent / 2] = 4
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signal[np.random.rand(signal.shape[0]) < percent / 2] = 0.4
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return signal
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def sum_two_grayscale_images(image_a: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], image_b :Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]:
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"""
|
|
Accepts: image_a, image_b
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|
Returns: image_a + image_b
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|
"""
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|
# Merge image_a and image_b
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return (image_a + image_b)/ 2
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def generate_dirac_impulse(size: int) -> npt.NDArray[np.float64]:
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|
"""
|
|
Accepts: size
|
|
Returns: dirac impulse of size
|
|
"""
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|
|
|
dirac_impulse = np.zeros((size, size))
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dirac_impulse[int(size/2), int(size/2)] = 1
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|
|
|
return dirac_impulse
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