这里写目录标题

平滑（低通）空间滤波器

平滑（也称平均）空间滤波器用于降低灰度的急剧过渡

在图像重取样之前平滑图像以减少混淆用于减少图像中无关细节平滑因灰度级数量不足导致的图像中的伪轮廓平滑核与一幅图像的卷积会模糊图像

盒式滤波器核

盒式核是最简单的可分离低通滤波器，其系数的值相同（通常为1）

m×nm\times{n}m×n的盒式滤波器为1的一个m×nm\times{n}m×n的阵列，其前面有一个归一化的常数，通过是1除以系数值之和（通过是1/mn1/mn1/mn）

def box_filter(image, kernel):""":param image: input image:param kernel: input kernel:return: image after convolution"""img_h = image.shape[0]img_w = image.shape[1]m = kernel.shape[0]n = kernel.shape[1]# paddingpadding_h = int((m -1)/2)padding_w = int((n -1)/2)image_pad = np.zeros((image.shape[0]+padding_h*2, image.shape[1]+padding_w*2), np.uint8)image_pad[padding_h:padding_h+img_h, padding_w:padding_w+img_w] = imageimage_convol = image.copy()for i in range(padding_h, img_h + padding_h):for j in range(padding_w, img_w + padding_w):temp = np.sum(image_pad[i-padding_h:i+padding_h+1, j-padding_w:j+padding_w+1] * kernel)image_convol[i - padding_h][j - padding_w] = temp # 1/(m * n) * tempreturn image_convol

# 盒式滤波器核img = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH03/Fig0333(a)(test_pattern_blurring_orig).tif', 0)kernel_size = [3, 11, 21]fig = plt.figure(figsize=(10, 10))for i in range(len(kernel_size) + 1):ax = fig.add_subplot(2, 2, i+1)if i == 0:ax.imshow(img, cmap='gray', vmin=0, vmax=255), ax.set_xticks([]), ax.set_yticks([])ax.set_title('Original')else:kernel = np.ones([kernel_size[i-1], kernel_size[i-1]])kernel = kernel / kernel.sizeimg_dst = box_filter(img, kernel)ax.imshow(img_dst, cmap='gray', vmin=0, vmax=255), ax.set_xticks([]), ax.set_yticks([])ax.set_title(f'kernel size {kernel_size[i-1]}')plt.tight_layout()plt.show()

# 盒式滤波器核 可分离核的效果img = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH03/Fig0333(a)(test_pattern_blurring_orig).tif', 0)kernel_size = [3, 11, 21]fig = plt.figure(figsize=(10, 10))for i in range(len(kernel_size) + 1):ax = fig.add_subplot(2, 2, i+1)if i == 0:ax.imshow(img, cmap='gray', vmin=0, vmax=255), ax.set_xticks([]), ax.set_yticks([])ax.set_title('Original')else:kernel = np.ones([kernel_size[i-1], kernel_size[i-1]])kernel = kernel / kernel.sizeimg_dst = separate_kernel_conv2D(img, kernel)img_dst = normalize(img_dst) * 255ax.imshow(img_dst, cmap='gray', vmin=0, vmax=255), ax.set_xticks([]), ax.set_yticks([])ax.set_title(f'kernel size {kernel_size[i-1]}')plt.tight_layout()plt.show()