Python 低通 高通 理想滤波器 巴特沃斯 数字图像处理 频域滤波 图像增强

问题

（一）频域低通滤波

1. 产生白条图像 f1(x,y)（640×640 大小，中间亮条宽160，高 400，居中，暗处=0，亮处=255）
2. 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。

（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。

代码

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()

结果