标题
线性位置不变退化估计退化函数采用观察法估计退化函数采用试验法估计退化函数采用建模法估计退化函数运动模糊函数OpenCV Motion Blur在这一节中，得到的结果，有些不是很好，我需要再努力多找资料，重新完成学习，如果大佬有相关资料推荐，不胜感激。
线性位置不变退化
# 巴特沃斯带阻陷波滤波器 BNRFimg_temp = np.zeros([512, 512])BNF_1 = butterworth_notch_resistant_filter(img_temp, radius=20, uk=-80, vk=60)BNF_2 = butterworth_notch_resistant_filter(img_temp, radius=10, uk=30, vk=80)BNF_3 = butterworth_notch_resistant_filter(img_temp, radius=10, uk=-30, vk=80)plt.figure(figsize=(16, 16))plt.subplot(221), plt.imshow(BNF_1, 'gray'), plt.title('BNF_1')plt.subplot(222), plt.imshow(BNF_2, 'gray'), plt.title('BNF_2')plt.subplot(223), plt.imshow(BNF_3, 'gray'), plt.title('BNF_3')BNF_dst = BNF_1 * BNF_2 * BNF_3plt.subplot(224), plt.imshow(BNF_dst, 'gray'), plt.title('BNF_dst')plt.tight_layout()plt.show()
估计退化函数
In this section, I think I still got some problem have to sort out, when I have some more time or some more reading.
采用观察法估计退化函数
选择一个信号内容很强的区域（如一个高对比度区域）表示为g(x,y)g(x, y)g(x,y)，令f^(x,y)\hat{f}(x, y)f^(x,y)表示为处理后的子图像，则有：
Hs(u,v)=Gs(u,v)F^s(u,v)(5.66)H_{s}(u, v) = \frac{G_{s}(u, v)}{\hat{F}_{s}(u, v)} \tag{5.66}Hs(u,v)=F^s(u,v)Gs(u,v)(5.66)
根据位置不变的假设来推断完整的退化函数H(u,v)H(u, v)H(u,v)
采用试验法估计退化函数
一个冲激由一个亮点来模拟，这个点应亮到能降低噪声对可忽略值的影响。一个冲激的傅里叶变换是一个常量：
H(u,v)=G(u,v)A(5.67)H(u, v) = \frac{G(u, v)}{A} \tag{5.67}H(u,v)=AG(u,v)(5.67)
# 试验法估计退化函数img_impulse = cv2.imread("DIP_Figures/DIP3E_Original_Images_CH05/Fig0524(a)(impulse).tif", 0)img_blurred = cv2.imread("DIP_Figures/DIP3E_Original_Images_CH05/Fig0524(b)(blurred-impulse).tif", 0)fig = plt.figure(figsize=(10, 5))plt.subplot(1, 2, 1), plt.imshow(img_impulse, cmap='gray'), plt.xticks([]), plt.yticks([])plt.subplot(1, 2, 2), plt.imshow(img_blurred, cmap='gray'), plt.xticks([]), plt.yticks([])plt.tight_layout()plt.show()
下面两个例子，你会看到傅立叶变换后，频谱图像的美。把频谱图像上了颜色后，更是美极啦
# 傅里叶变换fp_impulse = pad_image(img_impulse)impluse_cen = centralized_2d(fp_impulse)fft_impulse = np.fft.fft2(impluse_cen)impulse_spectrume = np.log(1 + spectrum_fft(fft_impulse))fp_blurred = pad_image(img_blurred)blurred_cen = centralized_2d(fp_blurred)fft_blurred = np.fft.fft2(blurred_cen)blurred_spectrum = np.log(1 + spectrum_fft(fft_blurred))H = fft_blurred / fft_impulseh_spectrum = np.log(1 + spectrum_fft(H))h_spectrum = h_spectrum / h_spectrum.max()fig = plt.figure(figsize=(15, 5))plt.subplot(1, 3, 1), plt.imshow(impulse_spectrume, cmap='gray'), plt.xticks([]), plt.yticks([])plt.subplot(1, 3, 2), plt.imshow(blurred_spectrum, cmap='gray'), plt.xticks([]), plt.yticks([])plt.subplot(1, 3, 3), plt.imshow(h_spectrum, cmap='gray'), plt.xticks([]), plt.yticks([])plt.tight_layout()plt.show()
# 一些傅里叶变换img_temp = np.zeros([256, 256])# H = butterworth_low_pass_filter(img_temp, 10, 500)H = 1 - butterworth_band_resistant_filter(img_temp, img_temp.shape, radius=50, w=5, n=5)fp_blurred = pad_image(H)blurred_cen = centralized_2d(fp_blurred)fft_blurred = np.fft.fft2(blurred_cen)blurred_spectrum = np.log(1 + spectrum_fft(fft_blurred))fig = plt.figure(figsize=(15, 15))plt.imshow(blurred_spectrum, cmap='PiYG'), plt.xticks([]), plt.yticks([])# plt.savefig("bbrf_4.png", dpi=300, quality=100)# plt.subplot(1, 3, 1), plt.imshow(impulse_spectrume, cmap='gray'), plt.xticks([]), plt.yticks([])# plt.subplot(1, 3, 2), plt.imshow(blurred_spectrum, cmap='gray'), plt.xticks([]), plt.yticks([])# # plt.subplot(1, 3, 3), plt.imshow(h_spectrum, cmap='gray'), plt.xticks([]), plt.yticks([])plt.tight_layout()plt.show()
采用建模法估计退化函数
H(u,v)=e−k(u2+v2)56(5.68)H(u,v) = e^{-k(u^2 + v^2)^{\frac{5}{6}}} \tag{5.68}H(u,v)=e−k(u2+v2)65(5.68)
关于频率矩形的中心，可用如下函数
H(u,v)=e−k((u−P/2)2+(v−Q/2)2)56H(u, v) = e^{-k((u - P/2)^2 + (v - Q/2)^2 \ \ )^{\frac{5}{6}}}H(u,v)=e−k((u−P/2)2+(v−Q/2)2)65
参加书上P247页，运动导的图像模糊的退化过程，是否用错？
这个问题已经得到解决啦，解决方案如下。
def modeling_degrade(img, k=1):"""modeling degradation fuction, math: $$H(u,v) = e^{-k(u^2 +v^2)^{\frac{5}{6}}}$$param: img: input imgparam: k: """N, M = img.shape[:2]u = np.arange(M)v = np.arange(N)u, v = np.meshgrid(u, v)temp = (u - M//2)**2 + (v - N//2)**2kernel = np.exp(-k * np.power(temp, 5/6))return kernel
# 不填充，结果与书上一致啦def get_degenerate_image(img, img_deg):"""不填充图像做傅里叶变换后与退化函数做乘积，再反傅里叶变换"""# FFT--------------------------------------------fft = np.fft.fft2(img)# FFT * H(u, v)----------------------------------fft_huv = fft * img_deg# IFFT-------------------------------------------ifft = np.fft.ifft2(fft_huv)return ifftimg_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH05/Fig0525(a)(aerial_view_no_turb).tif', 0)# k = [1, 0.1, 0.01, 0.001, 0.0025, 0.00025]k = [0.0025, 0.001, 0.00025]fp_cen = centralized_2d(img_ori)fig = plt.figure(figsize=(12, 12))for i in range(len(k) + 1):ax = fig.add_subplot(2, 2, i+1, xticks=[], yticks=[])if i == 0:ax.imshow(img_ori, 'gray'), ax.set_title(f"Original")else:img_deg = modeling_degrade(fp_cen, k=k[i-1])ifft = get_degenerate_image(fp_cen, img_deg)img_new = centralized_2d(ifft.real)img_new = np.clip(img_new, 0, img_new.max())img_new = np.uint8(normalize(img_new) * 255)ax.imshow(img_new, 'gray')ax.set_title(f"k = {k[i-1]}")plt.tight_layout()plt.show()
运动模糊函数
H(u,v)=Tπ(ua+vb)sin[π(ua+vb)]e−jπ(ua+vb)H(u,v) =\frac{T}{\pi(ua + vb)}sin[\pi(ua+vb)]e^{-j\pi(ua+vb)}H(u,v)=π(ua+vb)Tsin[π(ua+vb)]e−jπ(ua+vb)
下面的代码可能比较混乱，因为实验过程，而得出的结果不太好，还没有整理。需要继续学习后，再完成整理。
img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH05/Fig0526(a)(original_DIP).tif', 0)
def motion_huv(img, a, b, T):eps = 1e-8M, N = img.shape[1], img.shape[0]u = np.arange(1, M+1)v = np.arange(1, N+1)u, v = np.meshgrid(u, v)temp = np.pi * (u * a + v * b)kernel = (T * np.sin(temp) * np.exp(-temp*1j) /(temp + eps))return kernel
# 对图片进行运动模糊def make_blurred(img, PSF, eps):#=====================#fft = np.fft.fft2(img)# #fft_shift = np.fft.fftshift(fft)#fft_psf = fft * PSF#ifft = np.fft.ifft2(fft_psf)# #ifft_shift = np.fft.ifftshift(ifft)#blurred = abs(ifft.real)#=========================M, N = img.shape[:2]fp = pad_image(img, mode='constant')fp_cen = centralized_2d(fp)img_fft = np.fft.fft2(fp_cen)img_fft_psf = img_fft * PSFifft = np.fft.ifft2(img_fft_psf)blurred = centralized_2d(ifft.real)[:N, :M]# #blurred = ifft.real[:N, :M]return blurred
def get_motion_dsf(image_size, motion_angle, motion_dis):PSF = np.zeros(image_size) # 点扩散函数x_center = (image_size[0] - 1) / 2y_center = (image_size[1] - 1) / 2sin_val = np.sin(motion_angle * np.pi / 180)cos_val = np.cos(motion_angle * np.pi / 180)# 将对应角度上motion_dis个点置成1for i in range(motion_dis):x_offset = round(sin_val * i)y_offset = round(cos_val * i)PSF[int(x_center - x_offset), int(y_center + y_offset)] = 1return PSF / PSF.sum() # 归一化
img_motion = get_motion_dsf((480, 480), 70, 200)plt.figure(figsize=(10, 8))plt.subplot(121), plt.imshow(img_motion,'gray'), plt.title('img_motion')plt.show()
OpenCV Motion Blur
def motion_blur(image, degree=12, angle=45):"""create motion blur using opencvparam: image: input imageparam: degree: the size of the blurryparam: angle: blur anglereturn uint8 image"""image = np.array(image)# 这里生成任意角度的运动模糊kernel的矩阵， degree越大，模糊程度越高M = cv2.getRotationMatrix2D((degree / 2, degree / 2), angle, 1)motion_blur_kernel = np.diag(np.ones(degree))motion_blur_kernel = cv2.warpAffine(motion_blur_kernel, M, (degree, degree))motion_blur_kernel = motion_blur_kernel / degreeblurred = cv2.filter2D(image, -1, motion_blur_kernel)# convert to uint8cv2.normalize(blurred, blurred, 0, 255, cv2.NORM_MINMAX)blurred = np.array(blurred, dtype=np.uint8)return blurred
# 运动模糊图像img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH05/Fig0526(a)(original_DIP).tif', 0)img_blur = motion_blur(img_ori, degree=75, angle=15)plt.figure(figsize=(12, 8))plt.subplot(121), plt.imshow(img_ori,'gray'), plt.title('img_deg')plt.subplot(122), plt.imshow(img_blur,'gray'), plt.title('high_pass')plt.show()
第5章 Python 数字图像处理(DIP) - 图像复原与重建13 - 空间滤波 - 线性位置不变退化 - 退化函数估计 运动模糊函数
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