import numpy as np import numpy.typing as npt from matplotlib import pyplot as plt import random import cv2 import uz_framework.image as uz_image import uz_framework.text as uz_text import os ################################################################# # EXCERCISE 1: Exercise 1: Global approach to image description # ################################################################# def ex1(): #one_a() one_b() #one_c() distances, selected_distances = one_d('./data/dataset', './data/dataset_reduced/', 10) one_e(distances, selected_distances) def one_a() -> npt.NDArray[np.float64]: """ Firstly, you will implement the function myhist3 that computes a 3-D histogram from a three channel image. The images you will use are RGB, but the function should also work on other color spaces. The resulting histogram is stored in a 3-D matrix. The size of the resulting histogram is determined by the parameter n_bins. The bin range calculation is exactly the same as in the previous assignment, except now you will get one index for each image channel. Iterate through the image pixels and increment the appropriate histogram cells. You can create an empty 3-D numpy array with H = np.zeros((n_bins,n_bins,n_bins)). Take care that you normalize the resulting histogram. """ lena = uz_image.imread('./data/images/lena.png', uz_image.ImageType.float64) lincoln = uz_image.imread('./data/images/lincoln.jpg', uz_image.ImageType.float64) lena_h = uz_image.get_image_bins_ND(lena, 128) lincoln_h = uz_image.get_image_bins_ND(lincoln, 128) print(uz_image.compare_two_histograms(lena_h, lincoln_h, uz_image.DistanceMeasure.euclidian_distance)) return lena_h def one_b() -> None: """ In order to perform image comparison using histograms, we need to implement some distance measures. These are defined for two input histograms and return a single scalar value that represents the similarity (or distance) between the two histograms. Implement a function compare_histograms that accepts two histograms and a string that identifies the distance measure you wish to calculate Implement L2 metric, chi-square distance, intersection and Hellinger distance. Function implemented in uz_framework """ return None def one_c() -> None: """ Test your function Compute a 8×8×8-bin 3-D histogram for each image. Reshape each of them into a 1-D array. Using plt.subplot(), display all three images in the same window as well as their corresponding histograms. Compute the L2 distance between histograms of object 1 and 2 as well as L2 distance between histograms of objects 1 and 3. Question: Which image (object_02_1.png or object_03_1.png) is more similar to image object_01_1.png considering the L2 distance? How about the other three distances? We can see that all three histograms contain a strongly expressed component (one bin has a much higher value than the others). Which color does this bin represent Answer: """ IM1 = uz_image.imread('./data/dataset/object_01_1.png', uz_image.ImageType.float64) IM2 = uz_image.imread('./data/dataset/object_02_1.png', uz_image.ImageType.float64) IM3 = uz_image.imread('./data/dataset/object_03_1.png', uz_image.ImageType.float64) N_BINS = 8 H1 = uz_image.get_image_bins_ND(IM1, N_BINS).reshape(-1) H2 = uz_image.get_image_bins_ND(IM2, N_BINS).reshape(-1) H3 = uz_image.get_image_bins_ND(IM3, N_BINS).reshape(-1) fig, axs = plt.subplots(2,3) fig.suptitle('Euclidian distance between three images') axs[0, 0].imshow(IM1) axs[0, 0].set(title='Image1') axs[0, 1].imshow(IM2) axs[0, 1].set(title='Image2') axs[0, 2].imshow(IM3) axs[0, 2].set(title='Image3') axs[1, 0].bar(np.arange(N_BINS**3), H1, width=3) axs[1, 0].set(title=f'L_2(h1, h1) = {np.round(uz_image.compare_two_histograms(H1, H1, uz_image.DistanceMeasure.euclidian_distance), 2)}') axs[1, 1].bar(np.arange(N_BINS**3), H2, width=3) axs[1, 1].set(title=f'L_2(h1, h2) = {np.round(uz_image.compare_two_histograms(H1, H2, uz_image.DistanceMeasure.euclidian_distance), 2)}') axs[1, 2].bar(np.arange(N_BINS**3), H3, width=3) axs[1, 2].set(title=f'L_2(h1, h3) = {np.round(uz_image.compare_two_histograms(H1, H3, uz_image.DistanceMeasure.euclidian_distance), 2)}') plt.show() def one_d(directory: str, reduced_directory: str, n_bins: int): """ You will now implement a simple image retrieval system that will use histograms. Write a function that will accept the path to the image directory and the parameter n_bins and then calculate RGB histograms for all images in the directory as well as transform them to 1-D arrays. Store the histograms in an appropriate data structure. Select some image from the directory dataset/ and compute the distance between its histogram and all the other histograms you calculated before. Sort the list according to the calculated similarity and display the reference image and the first five most similar images to it. Also display the corresponding histograms. Do this for all four distance measures that you implemented earlier. Question: Which distance is in your opinion best suited for image retrieval? How does the retrieved sequence change if you use a different number of bins? Is the execution time affected by the number of bins? """ img_names = os.listdir(reduced_directory) methods=[uz_image.DistanceMeasure.euclidian_distance, uz_image.DistanceMeasure.chi_square_distance, uz_image.DistanceMeasure.intersection_distance, uz_image.DistanceMeasure.hellinger_distance ] imgs=[] hists=[] selected_dists=[] for i in range(len(img_names)): imgs.append(uz_image.imread(f'{reduced_directory}/{img_names[i]}', uz_image.ImageType.float64)) hists.append(uz_image.get_image_bins_ND(imgs[i], n_bins).reshape(-1)) for method in methods: fig, axs = plt.subplots(2, len(imgs)) fig.suptitle(f'Comparrison between different measures, using:{method.name}') distances = [] for i in range(len(hists)): distances.append(uz_image.compare_two_histograms(hists[0], hists[i], method)) indexes = np.argsort(distances) selected_dists.append(distances) for i in range(len(imgs)): axs[0, i].imshow(imgs[indexes[i]]) axs[0, i].set(title=f'{img_names[indexes[i]]}') axs[1, i].bar(np.arange(n_bins**3), hists[indexes[i]], width=2) axs[1, i].set(title=f'd={distances[indexes[i]]}') plt.show() img_names = os.listdir(directory) h_image = uz_image.get_image_bins_ND(imgs[0], n_bins).reshape(-1) all_dists = [[] for _ in range(len(methods))] for i in range(len(img_names)): im = uz_image.imread(f'{directory}/{img_names[i]}', uz_image.ImageType.float64) h = uz_image.get_image_bins_ND(im, n_bins).reshape(-1) for j in range(len(methods)): all_dists[j].append(uz_image.compare_two_histograms(h_image, h, methods[j])) print(all_dists) return all_dists, selected_dists def one_e(distances: list, selected_dists: list): """ You can get a better sense of the differences in the distance values if you plot all of them at the same time. Use the function plt.plot() to display image indices on the x axis and distances to the reference image on the y axis. Display both the unsorted and the sorted image sequence and mark the most similar values using a circle (see pyplot documentation) """ methods=[uz_image.DistanceMeasure.euclidian_distance, uz_image.DistanceMeasure.chi_square_distance, uz_image.DistanceMeasure.intersection_distance, uz_image.DistanceMeasure.hellinger_distance ] for i in range(len(distances)): fig, axs = plt.subplots(1, 2) fig.suptitle(f'Using {methods[i].name}') indexes = np.arange(0, len(distances[i]) , 1) makevery_indexes = [] for j in range(len(distances[i])): print(distances[i][j]) if distances[i][j] in selected_dists[i]: makevery_indexes.append(j) axs[0].plot(indexes,distances[i],markevery=makevery_indexes, markerfacecolor = "none", marker = "o", markeredgecolor = "orange") axs[1].plot(indexes,np.sort(distances[i]),markevery=makevery_indexes, markerfacecolor = "none", marker = "o", markeredgecolor = "orange") plt.show() ############################ # EXCERCISE 2: Convolution # ############################ def ex2(): #two_b() #two_c() two_e() def two_b(): """ Implement the function simple_convolution that uses a 1-D signal I and a kernel k of size 2N + 1. The function should return the convolution between the two. To simplify, you only need to calculate the convolution on signal elements from i = N to i = |I| − N. The first and last N elements of the signal will not be used (this is different in practice where signal edges must be accounted for). Test your implementation by loading the signal (file signal.txt) and the kernel (file kernal.txt) using the function read_data from a2_utils.py and performing the operation. Display the signal, the kernel and the result on the same figure. You can compare your result with the result of function cv2.filter2D. Note that the shape should be generally identical, while the values at the edges of the results and the results’ offset might be different since you will not be addressing the issue of the border pixels. Question: Can you recognize the shape of the kernel? What is the sum of the elements in the kernel? How does the kernel affect the signal? """ signal = uz_text.read_data('./data/signal.txt') kernel = uz_text.read_data('./data/kernel.txt') convolved_signal = uz_image.simple_convolution(signal, kernel) cv2_convolved_signal = cv2.filter2D(signal, cv2.CV_64F, kernel) plt.plot(convolved_signal, color='tab:green', label='Result') plt.plot(cv2_convolved_signal, color='tab:red', label='cv2') plt.plot(signal, color='tab:blue', label='Original') plt.plot(kernel, color='tab:orange', label='Kernel') plt.legend() plt.show() def two_d(): """ Write a function that calculates a Gaussian kernel. Use the definition: The input to the function should be parameter σ, which defines the shape of the kernel. Because the values beyond 3σ are very small, we usually limit the kernel size to 2 ∗ d3σe + 1. Don’t forget to normalize the kernel. Generate kernels for different values of σ = 0.5, 1, 2, 3, 4 and display them on the same figure (aligned). """ sigmas = [0.5, 1, 2, 3, 4] for sigma in sigmas: kernel = uz_image.get_gaussian_kernel(sigma) k_min_max = np.ceil(3*sigma) x = np.arange(-k_min_max, k_min_max+1.) plt.plot(x, kernel, label=f'σ= {sigma}') plt.legend() plt.show() def two_e(): """ The main advantage of convolution in comparison to correlation is the associativity of operations. This allows us to pre-calculate multiple kernels that we want to use on an image. Test this property by loading the signal from signal.txt and then performing two consecutive convolutions on it. The first one will be with a Gaussian kernel k1 with σ = 2 and the second one will be with kernel k2 = [0.1, 0.6, 0.4]. Then, convolve the signal again, but switch the order of the operations. Finally, create a kernel k3 = k1 ∗k2 and perform the convolution of the original signal with it. Display all the resulting signals and comment on the effect the different order of operations has on the signal. Use the function from c) or cv2.filter2D() to take care of the edges when convolving. """ signal = uz_text.read_data('./data/signal.txt') k1 = uz_image.get_gaussian_kernel(2) k2 = np.array([0.1, 0.6, 0.4]) k2 = np.flip(k2) s1 = signal.copy() s2 = cv2.filter2D(signal, cv2.CV_64F, k1) s2 = cv2.filter2D(s2, cv2.CV_64F, k2) s3 = cv2.filter2D(signal, cv2.CV_64F, k2) s3 = cv2.filter2D(s3, cv2.CV_64F, k1) k3 = cv2.filter2D(k1, cv2.CV_64F, k2) k3 = np.flip(k3) s4 = cv2.filter2D(signal, cv2.CV_64F, k3) fig, axs = plt.subplots(1, 4) fig.suptitle('Convolution') axs[0].plot(s1) axs[0].set(title='s') axs[1].plot(s2) axs[1].set(title='(s*k1)*k2') axs[2].plot(s3) axs[2].set(title='(s*k2)*k1') axs[3].plot(s4) axs[3].set(title='s*(k1*k2)') plt.show() ################################ # EXCERCISE 3: Image Filtering # ################################ # ######## # # SOLUTION # # ######## # def main(): #ex1() ex2() if __name__ == '__main__': main()