update

src/master/paper/evm.md

@@ -30,79 +30,6 @@ First decompose the video into different spatial frequency bands. Then perform t
 
 Originally, image was a matrix of pixels (spatial domain). Through FT, it becomes a combination of frequency planes (spectrum) with different weight (frequency domain). Each plane represents a different spatial frequency. High frequency spectrum looks like dense wave.
 
-A demo of 2D Fourier transform is shown below.
-
-```python
-import numpy as np
-import matplotlib.pyplot as plt
-import cv2
-
-# 读取图像
-image = cv2.imread('cuhk.jpg', cv2.IMREAD_GRAYSCALE)
-
-# 计算傅里叶变换
-f_transform = np.fft.fft2(image)
-f_transform_shifted = np.fft.fftshift(f_transform)
-
-# 计算幅度谱
-magnitude_spectrum = np.abs(f_transform_shifted)
-
-# 找出权重最大的10个频率成分
-indices = np.unravel_index(np.argsort(magnitude_spectrum.ravel())[-10:], magnitude_spectrum.shape)
-
-# 创建一个空的复数数组，用于存储合成图像的傅里叶变换
-f_transform_combined = np.zeros_like(f_transform_shifted, dtype=complex)
-
-# 可视化原始图像和幅度谱
-plt.figure(figsize=(15, 15))
-
-# 原始图像
-plt.subplot(4, 4, 1)
-plt.imshow(image, cmap='gray')
-plt.title('Original Image')
-plt.axis('off')
-
-# 幅度谱
-plt.subplot(4, 4, 2)
-plt.imshow(20 * np.log(magnitude_spectrum + 1), cmap='gray')
-plt.title('Magnitude Spectrum')
-plt.axis('off')
-
-# 生成仅包含一个频率成分的图像并合成
-for i, (row, col) in enumerate(zip(*indices)):
-    single_freq_mask = np.zeros_like(f_transform_shifted, dtype=complex)
-    single_freq_mask[row, col] = f_transform_shifted[row, col]
-
-    # 计算仅包含一个频率成分的图像
-    f_transform_single_freq = np.fft.ifftshift(single_freq_mask)
-    image_single_freq = np.fft.ifft2(f_transform_single_freq)
-    image_single_freq = np.abs(image_single_freq)
-
-    # 将单频图像的傅里叶变换累加到合成图像的傅里叶变换中
-    f_transform_combined += single_freq_mask
-
-    # 可视化仅包含一个频率成分的图像
-    plt.subplot(4, 4, i + 3)
-    plt.imshow(image_single_freq, cmap='gray')
-    plt.title(f'Single Frequency {i + 1}')
-    plt.axis('off')
-
-# 计算合成图像
-f_transform_combined_shifted = np.fft.ifftshift(f_transform_combined)
-image_combined = np.fft.ifft2(f_transform_combined_shifted)
-image_combined = np.abs(image_combined)
-
-# 可视化合成图像
-plt.subplot(4, 4, 13)
-plt.imshow(image_combined, cmap='gray')
-plt.title('Combined Image')
-plt.axis('off')
-
-plt.show()
-```
-
-Output:
-
 ![Fourier Transform](/EVMFTdemo.png)
 
 ### What is frequency band? What information does it contain? How to get from a video file? 
@@ -116,73 +43,7 @@ Fourier transform can be used to get frequency bands.
 
 Band-pass filter can be used to isolate a specific frequency band. A demo of band-pass filter is shown below.
 
-```python
-import cv2
-import numpy as np
-import matplotlib.pyplot as plt
-
-# 读取图像
-image = cv2.imread("cuhk.jpg", cv2.IMREAD_GRAYSCALE)
-
-# 显示原始图像
-plt.figure(figsize=(10, 5))
-plt.subplot(231), plt.imshow(image, cmap='gray')
-plt.title("Original Image"), plt.xticks([]), plt.yticks([])
-
-# 对图像进行二维傅里叶变换
-f_transform = np.fft.fft2(image)
-f_transform_shifted = np.fft.fftshift(f_transform)  # 将零频率分量移到中心
-
-# 计算幅度谱并显示
-magnitude_spectrum = 20 * np.log(np.abs(f_transform_shifted))
-plt.subplot(232), plt.imshow(magnitude_spectrum, cmap='gray')
-plt.title("Magnitude Spectrum"), plt.xticks([]), plt.yticks([])
-
-# 获取图像的尺寸
-rows, cols = image.shape
-crow, ccol = rows // 2, cols // 2  # 中心点
-
-# 创建一个掩码（初始值为0）
-mask = np.zeros((rows, cols), np.uint8)
-
-# 定义带通滤波器的频率范围
-r_inner = 0  # 内半径（低频截止）
-r_outer = 60  # 外半径（高频截止）
-
-# 在掩码上创建一个环形区域（值为1）
-center = [crow, ccol]
-x, y = np.ogrid[:rows, :cols]
-mask_area = (x - center[0]) ** 2 + (y - center[1]) ** 2
-mask[(mask_area >= r_inner ** 2) & (mask_area <= r_outer ** 2)] = 1
-
-# 显示掩码
-plt.subplot(233), plt.imshow(mask, cmap='gray')
-plt.title("Band-Pass Mask"), plt.xticks([]), plt.yticks([])
-
-# 将掩码应用到傅里叶变换结果上
-f_transform_filtered = f_transform_shifted * mask
-
-# 计算滤波后的幅度谱
-magnitude_spectrum_filtered = 20 * np.log(np.abs(f_transform_filtered) + 1e-5)  # 避免log(0)
-
-# 显示滤波后的幅度谱
-plt.subplot(234), plt.imshow(magnitude_spectrum_filtered, cmap='gray')
-plt.title("Filtered Magnitude Spectrum"), plt.xticks([]), plt.yticks([])
-
-# 将滤波后的结果逆变换回空间域
-f_transform_filtered_shifted = np.fft.ifftshift(f_transform_filtered)
-image_filtered = np.fft.ifft2(f_transform_filtered_shifted)
-image_filtered = np.abs(image_filtered)
-
-# 显示滤波后的图像
-plt.subplot(235), plt.imshow(image_filtered, cmap='gray')
-plt.title("Filtered Image"), plt.xticks([]), plt.yticks([])
-plt.show()
-```
-
-Output:
-
-![Band-Pass Filter](/EVMBandpassdemo.png)
+![Band-Pass Filter](/EVMFilterdemo.png)
 
 ## What are spatial decomposition techniques?