From 3a899115a69a79927f8c46d9e83cba140c522f3e Mon Sep 17 00:00:00 2001 From: Gasper Spagnolo Date: Sun, 13 Nov 2022 15:13:43 +0100 Subject: [PATCH] Well something is something --- assignment3/solution.py | 82 +++++ assignment3/uz_framework/__init__.py | 0 assignment3/uz_framework/image.py | 500 +++++++++++++++++++++++++++ assignment3/uz_framework/text.py | 9 + 4 files changed, 591 insertions(+) create mode 100644 assignment3/solution.py create mode 100644 assignment3/uz_framework/__init__.py create mode 100644 assignment3/uz_framework/image.py create mode 100644 assignment3/uz_framework/text.py diff --git a/assignment3/solution.py b/assignment3/solution.py new file mode 100644 index 0000000..aea38ee --- /dev/null +++ b/assignment3/solution.py @@ -0,0 +1,82 @@ +import numpy as np +import numpy.typing as npt +from matplotlib import pyplot as plt +import cv2 +import uz_framework.image as uz_image +import uz_framework.text as uz_text + +################################################################# +# EXCERCISE 1: Exercise 1: Global approach to image description # +################################################################# + +def ex1(): + #one_a() + #two_b() + two_c() + +def one_a() -> None: + """ + Follow the equations above and derive the equations used to compute first and + second derivatives with respect to y: Iy(x, y), Iyy(x, y), as well as the mixed derivative + Ixy(x, y) + """ + +def two_b() -> None: + """ + Implement a function that computes the derivative of a 1-D Gaussian kernel + Implement the function gaussdx(sigma) that works the same as function gauss + from the previous assignment. Don’t forget to normalize the kernel. Be careful as + the derivative is an odd function, so a simple sum will not do. Instead normalize the + kernel by dividing the values such that the sum of absolute values is 1. Effectively, + you have to divide each value by sum(abs(gx(x))). + """ + sigma = 1 + kernel = uz_image.gaussdx(sigma) + print(kernel) + +def two_c() -> None: + """ + The properties of the filter can be analyzed by using an impulse response function. + This is performed as a convolution of the filter with a Dirac delta function. The + discrete version of the Dirac function is constructed as a finite image that has all + elements set to 0 except the central element, which is set to a high value (e.g. 1). + Generate a 1-D Gaussian kernel G and a Gaussian derivative kernel D. + What happens if you apply the following operations to the impulse image? + (a) First convolution with G and then convolution with GT + (b) First convolution with G and then convolution with DT + (c) First convolution with D and then convolution with GT + (d) First convolution with GT and then convolution with D. + (e) First convolution with DT and then convolution with G. + Is the order of operations important? Display the images of the impulse responses + for different combinations of operations. + """ + impulse = uz_image.generate_dirac_impulse(50) + gauss = np.array([uz_image.get_gaussian_kernel(3)]) + gaussdx = np.array([uz_image.gaussdx(3)]) + + fig, axs = plt.subplots(2, 3) + + # Plot impulse only + axs[0, 0].imshow(impulse, cmap='gray') + axs[0, 0].set_title('Impulse') + + # Plot impulse after convolution with G and GT + g_gt_impulse = impulse.copy() + g_gt_impulse = cv2.filter2D(g_gt_impulse, cv2.CV_64F, gauss) + g_gt_impulse = cv2.filter2D(g_gt_impulse, cv2.CV_64F, gauss.T) + axs[0, 1].imshow(g_gt_impulse, cmap='gray') + axs[0, 1].set_title('impulse * G * GT') + + plt.show() + +# ######## # +# SOLUTION # +# ######## # + +def main(): + ex1() + #ex2() + #ex3() + +if __name__ == '__main__': + main() diff --git a/assignment3/uz_framework/__init__.py b/assignment3/uz_framework/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/assignment3/uz_framework/image.py b/assignment3/uz_framework/image.py new file mode 100644 index 0000000..8a039f7 --- /dev/null +++ b/assignment3/uz_framework/image.py @@ -0,0 +1,500 @@ + +import numpy as np +import cv2 as cv2 +from matplotlib import pyplot as plt +from PIL import Image +from typing import Union +import numpy.typing as npt +import enum + +class ImageType(enum.Enum): + uint8 = 0 + float64 = 1 + +class DistanceMeasure(enum.Enum): + euclidian_distance = 0 + chi_square_distance = 1 + intersection_distance = 2 + hellinger_distance = 3 + +def imread(path: str, type: ImageType) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]: + """ + Reads an image in RGB order. Image type is transformed from uint8 to float, and + range of values is reduced from [0, 255] to [0, 1]. + """ + I = Image.open(path).convert('RGB') # PIL image. + I = np.asarray(I) # Converting to Numpy array. + if type == ImageType.float64: + I = I.astype(np.float64) / 255 + return I + elif type == ImageType.uint8: + return I + + raise Exception(f"Unrecognized image format! {type}") + + +def imread_gray(path: str, type: ImageType) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]: + """ + Reads an image in gray. Image type is transformed from uint8 to float, and + range of values is reduced from [0, 255] to [0, 1]. + """ + + I = Image.open(path).convert('L') # PIL image opening and converting to gray. + I = np.asarray(I) # Converting to Numpy array. + + if type == ImageType.float64: + I = I.astype(np.float64) / 255 + return I + elif type == ImageType.uint8: + return I + + raise Exception("Unrecognized image format!") + +def signal_show(*signals): + """ + Plots all given 1D signals in the same plot. + Signals can be Python lists or 1D numpy array. + """ + for s in signals: + if type(s) == np.ndarray: + s = s.squeeze() + plt.plot(s) + plt.show() + + +def convolve(I: np.ndarray, *ks): + """ + Convolves input image I with all given kernels. + + :param I: Image, should be of type float64 and scaled from 0 to 1. + :param ks: 2D Kernels + :return: Image convolved with all kernels. + """ + for k in ks: + k = np.flip(k) # filter2D performs correlation, so flipping is necessary + I = cv2.filter2D(I, cv2.CV_64F, k) + return I + +def transform_coloured_image_to_grayscale(image: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]: + """ + Accepts float64 picture with three colour channels and returns float64 grayscale image + with one channel. + """ + grayscale_image = np.zeros(image.shape[:2]) + + for i in range(image.shape[0]): + for j in range(image.shape[1]): + grayscale_image[i, j] = (image[i, j, 0] + image[i,j, 1] + image[i, j, 2]) / 3 + + + return grayscale_image + +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]]: + """ + Accepts image, starting position end end position for axes x & y. Returns whole image with inverted part. + """ + inverted_image = image.copy() + + if image.dtype.type == np.float64: + for i in range(startx, endx): + for j in range(starty, endy): + inverted_image[i, j, 0] = 1 - image[i, j, 0] + inverted_image[i, j, 1] = 1 - image[i, j, 1] + inverted_image[i, j, 2] = 1 - image[i, j, 2] + return inverted_image + elif image.dtype.type == np.uint8: + for i in range(startx, endx): + for j in range(starty, endy): + inverted_image[i, j, 0] = 255 - image[i, j, 0] + inverted_image[i, j, 1] = 255 - image[i, j, 1] + inverted_image[i, j, 2] = 255 - image[i, j, 2] + return inverted_image + + raise Exception("Unrecognized image format!") + +def invert_coloured_image(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]: + """ + Accepts image and inverts it + """ + return invert_coloured_image_part(image, 0, image.shape[0], 0, image.shape[1]) + +def calculate_best_treshold_using_otsu_method(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]) -> int: + """ + Accepts image and returns best treshold using otsu method + """ + + if image.dtype.type == np.float64: + im = image.copy() + im = im * (255.0/im.max()) + elif image.dtype.type == np.uint8: + im = image.copy() + else: + raise Exception("Unrecognized image format!") + + treshold_range = np.arange(np.max(im) + 1) + criterias = [] + + for treshold in treshold_range: + # create the thresholded image + thresholded_im = np.zeros(im.shape) + + thresholded_im[im >= treshold] = 1 + + # compute weights + nb_pixels = im.size + nb_pixels1 = np.count_nonzero(thresholded_im) + weight1 = nb_pixels1 / nb_pixels + weight0 = 1 - weight1 + + # if one the classes is empty, eg all pixels are below or above the threshold, that threshold will not be considered + # in the search for the best threshold + if weight1 == 0 or weight0 == 0: + continue + + # find all pixels belonging to each class + val_pixels1 = im[thresholded_im == 1] + val_pixels0 = im[thresholded_im == 0] + + # compute variance of these classes + var0 = np.var(val_pixels0) if len(val_pixels0) > 0 else 0 + var1 = np.var(val_pixels1) if len(val_pixels1) > 0 else 0 + + criterias.append( weight0 * var0 + weight1 * var1) + + best_threshold = treshold_range[np.argmin(criterias)] + return best_threshold + + +def get_image_bins_for_loop(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], number_of_bins: int) -> npt.NDArray[np.float64]: + """ + Accepts image in the float64 format or uint8, returns normailzed + image bins, histogram + """ + if image.dtype.type == np.float64 or image.dtype.type == np.uint8: + bin_restrictions = np.linspace(np.min(image), np.max(image), num=number_of_bins) + else: + raise Exception("Unrecognized image format!") + + bins = np.zeros(number_of_bins).astype(np.float64) + + for pixel in image.reshape(-1): + # https://stackoverflow.com/a/16244044 + bins[np.argmax(bin_restrictions > pixel)] += 1 + + return bins / np.sum(bins) + + +# Much faster implementation than for loop +def get_image_bins(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], number_of_bins: int) -> npt.NDArray[np.float64]: + """ + Accepts image in the float64 format or uint8, returns normailzed + image bins, histogram + """ + if image.dtype.type == np.float64 or image.dtype.type == np.uint8: + bins = np.linspace(np.min(image), np.max(image), num=number_of_bins) + else: + raise Exception("Unrecognized image format!") + + # Put pixels into classes + # ex. binsize = 10 then 0.4 would map into 4 + binarray = np.digitize(image.reshape(-1), bins).astype(np.uint8) + + # Now count those values + binarray = np.unique(binarray, return_counts=True) + + counts = binarray[1].astype(np.float64) # Get the counts out of tuple + + # Check if there is any empty bin + empty_bins = [] + bins = binarray[0] + for i in range(1, number_of_bins + 1): + if i not in bins: + empty_bins.append(i) + + # Add empty bins with zeros + if empty_bins != []: + for i in empty_bins: + counts = np.insert(counts, i - 1, 0) + + return counts + +def get_image_bins_ND(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], number_of_bins: int) -> npt.NDArray[np.float64]: + """ + Accepts image in the float64 format or uint8 and number of bins + Returns normailzed image histogram bins + """ + bs = [] + hist = np.zeros((number_of_bins, number_of_bins, number_of_bins)) + bins = np.linspace(np.min(image), np.max(image), num=number_of_bins) + + for i in range(image.shape[2]): + v = image[:, :, i].reshape(-1) + bs.append(np.digitize(v, bins).astype(np.uint32)) + + for i in range(len(bs[0])): + hist[bs[2][i] -1, bs[1][i] -1, bs[0][i] - 1] += 1 + + return hist / np.sum(hist) + +def compare_two_histograms(h1: npt.NDArray[np.float64], h2: npt.NDArray[np.float64], method: DistanceMeasure) -> float: + """ + Accepts two histograms and method of comparison + Returns distance between them + """ + + if method == DistanceMeasure.euclidian_distance: + d = np.sqrt(np.sum(np.square(h1 - h2))) + elif method == DistanceMeasure.chi_square_distance: + d = 0.5 * np.sum(np.square(h1 - h2) / (h1 + h2 + np.finfo(float).eps)) + elif method == DistanceMeasure.intersection_distance: + d = 1 - np.sum(np.minimum(h1, h2)) + elif method == DistanceMeasure.hellinger_distance: + d = np.sqrt(0.5 * np.sum(np.square(np.sqrt(h1) - np.sqrt(h2)))) + else: + raise Exception('Unsuported method chosen!') + + return d.astype(float) + + +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]]: + """ + Accepts image and applys mask to image + """ + image = image.copy() + + mask = np.expand_dims(mask, axis=2) + image = mask * image + + return image + +def simple_convolution(signal: npt.NDArray[np.float64], kernel: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]: + """ + Accepts: signal & kernel + + Returns: convolved signal with a kernel + """ + N = int(np.ceil(len(kernel) / 2 - 1)) + n_conv = signal.size - kernel.size + 1 + print(N, signal.size -N, n_conv) + + convolved_signal = np.zeros(len(signal)) + rev_kernel = kernel[::-1].copy() + + for i in range(n_conv): + convolved_signal[i] = np.dot(signal[i: i+kernel.size], rev_kernel) # Well if you would add i+N then you wuold shift this + + return convolved_signal + +def simple_convolution_improved(signal: npt.NDArray[np.float64], kernel: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]: + """ + Accepts: signal & kernel + + Returns: convolved signal with a kernel + Improved method replicates edges of an signal + """ + signal_len = signal.size + kernel_len = kernel.size + signal = signal.copy() + + # Calculate which values to fill in and range + EDGE_FRONT = signal[0] + EDGE_BACK = signal[-1] + EXTEND_RANGE = int(np.floor(kernel.size / 2)) + + # Append end insert edges + front = [ EDGE_FRONT for _ in range(EXTEND_RANGE)] + back = [ EDGE_BACK for _ in range(EXTEND_RANGE)] + signal = np.insert(signal, 1, front, axis=0) + signal = np.append(signal, back, axis=0) + + convolved_signal = np.zeros(signal_len) + rev_kernel = kernel[::-1].copy() + n_conv = signal_len - kernel_len + 1 + + for i in range(n_conv): + convolved_signal[i] = np.dot(signal[i: i+kernel.size], rev_kernel) + + return convolved_signal + +def get_gaussian_kernel(sigma: float) -> npt.NDArray[np.float64]: + """ + Accepts sigma + Returns gaussian kernel + """ + # https://github.com/mikepound/convolve/blob/master/run.gaussian.py + kernel_size = int(2 * np.ceil(3*sigma) + 1) + k_min_max = np.ceil(3*sigma) + k_interval = np.arange(-k_min_max, k_min_max + 1.) + + result = (1. / (np.sqrt(2. * np.pi )* sigma)) * np.exp(- (np.square(k_interval)) / (2.*np.square(sigma))) + + assert(kernel_size == len(result)) + + return result / np.sum(result) + +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]]: + """ + Accepts: image & sharpen factor + + Returns: sharpened image + https://blog.demofox.org/2022/02/26/image-sharpening-convolution-kernels/ <-- sharpening kernel, but also on slides + good explanation + """ + sharpened_image = image.copy() + + KERNEL = np.array([[-1, -1, -1], + [-1, 17, -1], + [-1, -1,-1]]) * 1./9. * sharpen_factor + + if image.dtype.type == np.float64: + sharpened_image = cv2.filter2D(sharpened_image, cv2.CV_64F, KERNEL) + elif image.dtype.type == np.uint8: + sharpened_image = cv2.filter2D(sharpened_image, cv2.CV_8U, KERNEL) + + return sharpened_image + +def gaussfilter2D(image: Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], sigma: float) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]: + """ + Accepts: image, sigma + Applies gaussian noise on image + returns: filtered_image + """ + filtered_image = image.copy() + kernel = np.array([get_gaussian_kernel(sigma)]) + filtered_image = cv2.filter2D(filtered_image, cv2.CV_64F, kernel) + filtered_image = cv2.filter2D(filtered_image, cv2.CV_64F, kernel.T) + + return filtered_image + +def gaussdx(sigma: float) -> npt.NDArray[np.float64]: + """ + Accepts sigma + Returns gaussian kernel + """ + kernel_size = int(2 * np.ceil(3*sigma) + 1) + k_min_max = np.ceil(3*sigma) + k_interval = np.arange(-k_min_max, k_min_max + 1.) + + result = - (1. / (np.sqrt(2. * np.pi )* np.power(sigma, 3))) * k_interval* np.exp(- (np.square(k_interval)) / (2.*np.square(sigma))) + + assert(kernel_size == len(result)) + + return result / np.sum(np.abs(result)) + + +def simple_median(signal: npt.NDArray[np.float64], width: int) -> npt.NDArray[np.float64]: + """ + Accepts: signal & width + returns signal improved using median filter + """ + if width % 2 == 0: + raise Exception('No u won\'t do that') + + signal = signal.copy() + for i in range(len(signal) - int(np.ceil(width/2))): + middle_element = int(i + np.floor(width/2)) + signal[middle_element] = np.median(signal[i:i+width]) + return signal + +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]]: + """ + Accepts: image & filter width + returns: image with median filter applied + """ + if width % 2 == 0: + raise Exception('No u won\'t do that') + + image = image.copy() + W_HALF = int(np.floor(width/2)) + padded_image = np.pad(image, W_HALF, mode='edge') + IMAGE_HEIGHT = image.shape[0] # y + IMAGE_WIDTH = image.shape[1] # x + + for x in range(W_HALF, IMAGE_WIDTH): + for y in range(W_HALF, IMAGE_HEIGHT): + median_filter = np.zeros(0) + STARTX = x - W_HALF + STARTY = y - W_HALF + for m in range(width): + median_filter = np.append(median_filter, padded_image[STARTY + m][STARTX: STARTX + width], axis=0) + if image.dtype.type == np.uint8: + image[y][x] = int(np.mean(median_filter)) + else: + image[y][x] = np.mean(median_filter) + return image + +def filter_laplace(image:Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]], sigma: float) -> Union[npt.NDArray[np.float64], npt.NDArray[np.uint8]]: + """ + Accepts: image & sigma + returns: image with laplace filter applied + """ + # Prepare unit impulse and gauss kernel + unit_impulse = np.zeros((1, 2 * int(np.ceil(3*sigma)) + 1)) + unit_impulse[0][int(np.ceil(unit_impulse.size /2)) - 1]= 1 + gauss_kernel = np.array([get_gaussian_kernel(sigma)]) + assert(len(gauss_kernel[0]) == len(unit_impulse[0])) + + laplacian_filter = unit_impulse - gauss_kernel[0] + + # Now apply laplacian filter + applied_by_x = cv2.filter2D(image, -1, laplacian_filter) + applied_by_y = cv2.filter2D(applied_by_x, -1, laplacian_filter.T) + + return applied_by_y + +def gauss_noise(I, magnitude=.1) -> npt.NDArray[np.float64]: + """ + Accepts: image & magnitude + Returns: image with gaussian noise applied + """ + # input: image, magnitude of noise + # output: modified image + I = I.copy() + + return I + np.random.normal(size=I.shape) * magnitude + + +def sp_noise(I, percent=.1) -> npt.NDArray[np.float64]: + """ + Accepts: image & percent + Returns: image with salt and pepper noise applied + """ + # input: image, percent of corrupted pixels + # output: modified image + + res = I.copy() + res[np.random.rand(I.shape[0], I.shape[1]) < percent / 2] = 1 + res[np.random.rand(I.shape[0], I.shape[1]) < percent / 2] = 0 + + return res + +def sp_noise1D(signal, percent=.1) -> npt.NDArray[np.float64]: + """ + Accepts: signal & percent + Returns: signal with salt and pepper noise applied + """ + signal = signal.copy() + signal[np.random.rand(signal.shape[0]) < percent / 2] = 2 + signal[np.random.rand(signal.shape[0]) < percent / 2] = 1 + signal[np.random.rand(signal.shape[0]) < percent / 2] = 4 + signal[np.random.rand(signal.shape[0]) < percent / 2] = 0.4 + return signal + +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]]: + """ + Accepts: image_a, image_b + Returns: image_a + image_b + """ + # Merge image_a and image_b + return (image_a + image_b)/ 2 + +def generate_dirac_impulse(size: int) -> npt.NDArray[np.float64]: + """ + Accepts: size + Returns: dirac impulse of size + """ + + dirac_impulse = np.zeros((size, size)) + dirac_impulse[int(size/2), int(size/2)] = 1 + + return dirac_impulse diff --git a/assignment3/uz_framework/text.py b/assignment3/uz_framework/text.py new file mode 100644 index 0000000..08ad835 --- /dev/null +++ b/assignment3/uz_framework/text.py @@ -0,0 +1,9 @@ +import numpy as np + +def read_data(filename: str): + # reads a numpy array from a text file + with open(filename) as f: + s = f.read() + + return np.fromstring(s, sep=' ') +