(一)频域低通滤波
(二)频域高通滤波
import numpy as np
from PIL import Image
import matplotlib.pyplot as plt
"""
(一)频域低通滤波
产生如图所示图象 f1(x,y)(64×64 大小,中间亮条宽16,高 40,居中,暗处=0,亮处=255)
产生实验四中的白条图像。
设计不同截止频率的理想低通滤波器、Butterworth低通滤波器,对其进行频域增强。
观察频域滤波效果,并解释之。
"""
def pro_11():
def ideal_low_filter(lr, cr, cc, img):
tmp = np.zeros((img.shape[0], img.shape[1]))
for i in range(img.shape[0]):
for j in range(img.shape[1]):
tmp[i, j] = (1 if np.sqrt((i - cr) ** 2 + (j - cc) ** 2) <= lr else 0)
return tmp
# 产生白条图像
im_arr = np.zeros((640, 640))
for i in range(im_arr.shape[0]):
for j in range(im_arr.shape[1]):
if 120 < i < 520 and 240 < j < 400:
im_arr[i, j] = 255
im_ft2 = np.fft.fft2(np.array(im_arr)) # 白条图二维傅里叶变换矩阵
im_ft2_shift = np.fft.fftshift(im_ft2)
r, c = im_arr.shape[0], im_arr.shape[1]
cr, cc = r // 2, c // 2 # 频谱中心
# 理想滤波器
ideal_filter1 = ideal_low_filter(10, cr, cc, im_ft2_shift)
ideal_filter2 = ideal_low_filter(30, cr, cc, im_ft2_shift)
# 求经理想低通滤波器后的图像
tmp = im_ft2_shift * ideal_filter1
irreversed_im_ft2 = np.fft.ifft2(tmp)
tmp2 = im_ft2_shift * ideal_filter2
irreversed_im_ft22 = np.fft.ifft2(tmp2)
plt.figure(figsize=(13, 13))
plt.subplot(221)
plt.imshow(Image.fromarray(np.abs(im_arr)))
plt.subplot(223)
plt.imshow(Image.fromarray(np.abs(im_ft2_shift)))
plt.subplot(222)
plt.title("lr=10")
plt.imshow(Image.fromarray(np.abs(irreversed_im_ft2)))
plt.subplot(224)
plt.title("lr=30")
plt.imshow(Image.fromarray(np.abs(irreversed_im_ft22)))
plt.show()
def pro_12():
def butterworth(lr, cr, cc, n, img):
tmp = np.zeros((img.shape[0], img.shape[1]))
for i in range(img.shape[0]):
for j in range(img.shape[1]):
tmp[i, j] = 1 / (1 + np.sqrt((i - cr) ** 2 + (j - cc) ** 2) / lr) ** (2 * n)
return tmp
# 产生白条图像
im_arr = np.zeros((640, 640))
for i in range(im_arr.shape[0]):
for j in range(im_arr.shape[1]):
if 120 < i < 520 and 240 < j < 400:
im_arr[i, j] = 255
im_ft2 = np.fft.fft2(np.array(im_arr)) # 白条图二维傅里叶变换矩阵
im_ft2_shift = np.fft.fftshift(im_ft2)
r, c = im_arr.shape[0], im_arr.shape[1]
cr, cc = r // 2, c // 2 # 频谱中心
# 理想滤波器
butterworth1 = butterworth(10, cr, cc, 2, im_arr)
butterworth2 = butterworth(30, cr, cc, 2, im_arr)
# 求经理想低通滤波器后的图像
tmp = im_ft2_shift * butterworth1
irreversed_im_ft2 = np.fft.ifft2(tmp)
tmp2 = im_ft2_shift * butterworth2
irreversed_im_ft22 = np.fft.ifft2(tmp2)
plt.figure(figsize=(13, 13))
plt.subplot(221)
plt.imshow(Image.fromarray(np.abs(im_arr)))
plt.subplot(223)
plt.imshow(Image.fromarray(np.abs(im_ft2_shift)))
plt.subplot(222)
plt.title("lr=10")
plt.imshow(Image.fromarray(np.abs(irreversed_im_ft2)))
plt.subplot(224)
plt.title("lr=30")
plt.imshow(Image.fromarray(np.abs(irreversed_im_ft22)))
plt.show()
def pro_12():
def ideal_low_filter(lr, cr, cc, img):
tmp = np.zeros((img.shape[0], img.shape[1]))
for i in range(img.shape[0]):
for j in range(img.shape[1]):
tmp[i, j] = (1 if np.sqrt((i - cr) ** 2 + (j - cc) ** 2) <= lr else 0)
return tmp
def butterworth(lr, cr, cc, n, img):
tmp = np.zeros((img.shape[0], img.shape[1]))
for i in range(img.shape[0]):
for j in range(img.shape[1]):
tmp[i, j] = 1 / (1 + np.sqrt((i - cr) ** 2 + (j - cc) ** 2) / lr) ** (2 * n)
return tmp
def gauss_noise(img, sigma):
temp_img = np.float64(np.copy(img))
h = temp_img.shape[0]
w = temp_img.shape[1]
noise = np.random.randn(h, w) * sigma
noisy_img = np.zeros(temp_img.shape, np.float64)
if len(temp_img.shape) == 2:
noisy_img = temp_img + noise
else:
noisy_img[:, :, 0] = temp_img[:, :, 0] + noise
noisy_img[:, :, 1] = temp_img[:, :, 1] + noise
noisy_img[:, :, 2] = temp_img[:, :, 2] + noise
# noisy_img = noisy_img.astype(np.uint8)
return noisy_img
lena = np.array(Image.open("lena_gray_512.tif"))
noise_lena = gauss_noise(lena, 25)
noise_lena_fft2 = np.fft.fft2(noise_lena)
noise_lena_fft2_shift = np.fft.fftshift(noise_lena_fft2)
r, c = lena.shape[0], lena.shape[1]
cr, cc = r // 2, c // 2 # 频谱中心
butterworth1 = butterworth(30, cr, cc, 2, lena)
butterworth2 = butterworth(50, cr, cc, 2, lena)
ideal_filter1 = ideal_low_filter(10, cr, cc, noise_lena_fft2_shift)
ideal_filter2 = ideal_low_filter(30, cr, cc, noise_lena_fft2_shift)
btmp1 = noise_lena_fft2_shift * butterworth1
blena_ift21 = np.fft.ifft2(btmp1)
btmp2 = noise_lena_fft2_shift * butterworth2
blena_ift22 = np.fft.ifft2(btmp2)
itmp1 = noise_lena_fft2_shift * ideal_filter1
ilena_ift21 = np.fft.ifft2(itmp1)
itmp2 = noise_lena_fft2_shift * ideal_filter2
ilena_ift22 = np.fft.ifft2(itmp2)
plt.figure(figsize=(13, 13))
plt.subplot(221)
plt.title("Butterworth Filter: lr=30/100")
plt.imshow(Image.fromarray(np.abs(blena_ift21)))
plt.subplot(223)
plt.imshow(Image.fromarray(np.abs(blena_ift22)))
plt.subplot(222)
plt.title("Ideal Filter: lr=10/30")
plt.imshow(Image.fromarray(np.abs(ilena_ift21)))
plt.subplot(224)
plt.imshow(Image.fromarray(np.abs(ilena_ift22)))
plt.show()
"""
(二)频域高通滤波
1. 设计不同截止频率的理想高通滤波器、Butterworth高通滤波器,对上述白条图像进行频域增强。观察频域滤波效果,并解释之。
2. 设计不同截止频率的理想高通滤波器、Butterworth高通滤波器,对含高斯噪声的lena图像进行频域增强。观察频域滤波效果,并解释之。
"""
def pro_2():
def ideal_high_filter(lr, cr, cc, img):
tmp = np.zeros((img.shape[0], img.shape[1]))
for i in range(img.shape[0]):
for j in range(img.shape[1]):
tmp[i, j] = (0 if np.sqrt((i - cr) ** 2 + (j - cc) ** 2) <= lr else 1)
return tmp
def butterworth_high(lr, cr, cc, n, img):
tmp = np.zeros((img.shape[0], img.shape[1]))
for i in range(img.shape[0]):
for j in range(img.shape[1]):
tmp[i, j] = 1 / (1 + lr / np.sqrt((i - cr) ** 2 + (j - cc) ** 2)) ** (2 * n)
return tmp
def gauss_noise(img, sigma):
temp_img = np.float64(np.copy(img))
h = temp_img.shape[0]
w = temp_img.shape[1]
noise = np.random.randn(h, w) * sigma
noisy_img = np.zeros(temp_img.shape, np.float64)
if len(temp_img.shape) == 2:
noisy_img = temp_img + noise
else:
noisy_img[:, :, 0] = temp_img[:, :, 0] + noise
noisy_img[:, :, 1] = temp_img[:, :, 1] + noise
noisy_img[:, :, 2] = temp_img[:, :, 2] + noise
# noisy_img = noisy_img.astype(np.uint8)
return noisy_img
def lena_proceed():
lena = np.array(Image.open("lena_gray_512.tif"))
noise_lena = gauss_noise(lena, 25)
noise_lena_fft2 = np.fft.fft2(noise_lena)
noise_lena_fft2_shift = np.fft.fftshift(noise_lena_fft2)
r, c = lena.shape[0], lena.shape[1]
cr, cc = r // 2, c // 2 # 频谱中心
butterworth1 = butterworth_high(10, cr, cc, 1, lena)
butterworth2 = butterworth_high(5, cr, cc, 1, lena)
ideal_filter1 = ideal_high_filter(10, cr, cc, noise_lena_fft2_shift)
ideal_filter2 = ideal_high_filter(30, cr, cc, noise_lena_fft2_shift)
btmp1 = noise_lena_fft2_shift * butterworth1
blena_ift21 = np.fft.ifft2(btmp1)
btmp2 = noise_lena_fft2_shift * butterworth2
blena_ift22 = np.fft.ifft2(btmp2)
itmp1 = noise_lena_fft2_shift * ideal_filter1
ilena_ift21 = np.fft.ifft2(itmp1)
itmp2 = noise_lena_fft2_shift * ideal_filter2
ilena_ift22 = np.fft.ifft2(itmp2)
plt.figure(figsize=(13, 13))
plt.subplot(221)
plt.title("Butterworth Filter: lr=30/5")
plt.imshow(Image.fromarray(np.abs(blena_ift21)))
plt.subplot(223)
plt.imshow(Image.fromarray(np.abs(blena_ift22)))
plt.subplot(222)
plt.title("Ideal Filter: lr=10/30")
plt.imshow(Image.fromarray(np.abs(ilena_ift21)))
plt.subplot(224)
plt.imshow(Image.fromarray(np.abs(ilena_ift22)))
plt.show()
def white_bar_proceed():
# 产生白条图像
im_arr = np.zeros((640, 640))
for i in range(im_arr.shape[0]):
for j in range(im_arr.shape[1]):
if 120 < i < 520 and 240 < j < 400:
im_arr[i, j] = 255
im_ft2 = np.fft.fft2(np.array(im_arr)) # 白条图二维傅里叶变换矩阵
im_ft2_shift = np.fft.fftshift(im_ft2)
r, c = im_arr.shape[0], im_arr.shape[1]
cr, cc = r // 2, c // 2 # 频谱中心
butterworth1 = butterworth_high(30, cr, cc, 1, im_arr)
butterworth2 = butterworth_high(5, cr, cc, 1, im_arr)
ideal_filter1 = ideal_high_filter(10, cr, cc, im_ft2_shift)
ideal_filter2 = ideal_high_filter(30, cr, cc, im_ft2_shift)
btmp1 = im_ft2_shift * butterworth1
blena_ift21 = np.fft.ifft2(btmp1)
btmp2 = im_ft2_shift * butterworth2
blena_ift22 = np.fft.ifft2(btmp2)
itmp1 = im_ft2_shift * ideal_filter1
ilena_ift21 = np.fft.ifft2(itmp1)
itmp2 = im_ft2_shift * ideal_filter2
ilena_ift22 = np.fft.ifft2(itmp2)
plt.figure(figsize=(13, 13))
plt.subplot(221)
plt.title("Butterworth Filter: lr=30/5")
plt.imshow(Image.fromarray(np.abs(blena_ift21)))
plt.subplot(223)
plt.imshow(Image.fromarray(np.abs(blena_ift22)))
plt.subplot(222)
plt.title("Ideal Filter: lr=10/30")
plt.imshow(Image.fromarray(np.abs(ilena_ift21)))
plt.subplot(224)
plt.imshow(Image.fromarray(np.abs(ilena_ift22)))
plt.show()
lena_proceed()
white_bar_proceed()
if __name__ == '__main__':
pro_11()
pro_12()
pro_2()