95 lines
2.9 KiB
Python
95 lines
2.9 KiB
Python
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import numpy as np
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import matplotlib.pyplot as plt
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from skimage import data
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from skimage.color import rgb2gray
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from skimage import img_as_ubyte, img_as_float
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from ipywidgets import interact, interactive, interact_manual
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from numpy.linalg import svd
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import ipywidgets as widgets
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gray_images = {
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"cat": rgb2gray(img_as_float(data.chelsea())),
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"astro": rgb2gray(img_as_float(data.astronaut())),
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"camera": data.camera(),
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"coin": data.coins(),
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"clock": data.clock(),
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"blobs": data.binary_blobs(),
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"coffee": rgb2gray(img_as_float(data.coffee()))
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}
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def mc_pi(ntrials):
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"""
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calculate the value of pi using montecarlo method and visualize the process
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"""
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x = np.random.random(ntrials)
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y = np.random.random(ntrials)
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# masking
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inside_circle = x ** 2 + y ** 2 < 1
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unit_circle_x = np.linspace(0, 1, 100)
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unit_circle = [unit_circle_x, np.sqrt(1.0 - unit_circle_x ** 2)]
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plt.plot(*unit_circle, color='black')
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plt.scatter(x[inside_circle], y[inside_circle], marker='.', color='blue', s=1)
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plt.scatter(x[~inside_circle], y[~inside_circle], marker='.', color='red', s=1)
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plt.title("value of $\pi$=" + str(4.0 * np.sum(inside_circle) / float(ntrials)))
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def compress_svd(image, k):
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"""
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Perform svd decomposition and truncated (using k singular values/vectors) reconstruction
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returns
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--------
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reconstructed matrix reconst_matrix, array of singular values s
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"""
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U, s, V = svd(image, full_matrices=False)
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reconst_matrix = np.dot(U[:, :k], np.dot(np.diag(s[:k]), V[:k, :]))
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return reconst_matrix, s
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def compress_show_gray_images(img_name, k):
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"""
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compresses gray scale images and display the reconstructed image.
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Also displays a plot of singular values
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"""
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image = gray_images[img_name]
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original_shape = image.shape
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reconst_img, s = compress_svd(image, k)
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fig, axes = plt.subplots(1, 2, figsize=(8, 5))
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axes[0].plot(s)
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compression_ratio = 100.0 * (k * (original_shape[0] + original_shape[1]) + k) / (
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original_shape[0] * original_shape[1])
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axes[1].set_title("compression ratio={:.2f}".format(compression_ratio) + "%")
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axes[1].imshow(reconst_img, cmap='gray')
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axes[1].axis('off')
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fig.tight_layout()
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def compute_k_max(img_name):
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"""
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utility function for calculating max value of the slider range
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"""
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img = gray_images[img_name]
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m, n = img.shape
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return m * n / (m + n + 1)
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# set up the widgets
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list_widget = widgets.Dropdown(options=list(gray_images.keys()))
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int_slider_widget = widgets.IntSlider(min=1, max=compute_k_max('cat'))
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def update_k_max(*args):
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img_name = list_widget.value
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int_slider_widget.max = compute_k_max(img_name)
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list_widget.observe(update_k_max, 'value')
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interact(compress_show_gray_images, img_name=list_widget, k=int_slider_widget)
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mc_widget = interactive(mc_pi, ntrials=(1, 100000, 10))
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mc_widget
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