数字图像处理——拉普拉斯算子【像素级别处理】（python）
文章目录
数字图像处理——拉普拉斯算子【像素级别处理】（python） 简介： 代码实现
简介：
拉普拉斯算子是一种微分算子常在图像处理中强调灰度值的突变，不强调灰度变换缓慢的地方，得到的图层与原图像叠加在一起可以得到锐化的效果
一个二维图像的拉普拉斯算子可以定义为 ∇ 2 f = ∂ 2 f ∂ x 2 + ∂ 2 f ∂ y 2 \nabla^{2}f=\frac{\partial^2 f}{\partial x^2}+\frac{\partial^2 f}{\partial y^2} ∇2f=∂x2∂2f+∂y2∂2f
所以: 在X方向上存在 ∂ 2 f ∂ x = f ( x + 1 , y ) + f ( x − 1 , y ) − 2 f ( x , y ) \frac{\partial^2 f}{\partial x}=f(x+1,y)+f(x-1,y)-2f(x,y) ∂x∂2f=f(x+1,y)+f(x−1,y)−2f(x,y)
在Y方向上存在 ∂ 2 f ∂ y = f ( x , y + 1 ) + f ( x , y − 1 ) − 2 f ( x , y ) \frac{\partial^2 f}{\partial y}=f(x,y+1)+f(x,y-1)-2f(x,y) ∂y∂2f=f(x,y+1)+f(x,y−1)−2f(x,y)
可得： ∇ 2 f = f ( x + 1 , y ) + f ( x − 1 , y ) + f ( x , y + 1 ) + f ( x , y − 1 ) − 4 f ( x , y ) \nabla^2f=f(x+1,y)+f(x-1,y)+f(x,y+1)+f(x,y-1)-4f(x,y) ∇2f=f(x+1,y)+f(x−1,y)+f(x,y+1)+f(x,y−1)−4f(x,y)
扩展至对角线： ∇ 2 f = f ( x + 1 , y ) + f ( x − 1 , y ) + f ( x , y + 1 ) + f ( x , y − 1 ) + f ( x − 1 , y − 1 ) + f ( x − 1 , y + 1 ) + f ( x + 1 , y − 1 ) + f ( x + 1 , y + 1 ) − 8 f ( x , y ) \nabla^2f=f(x+1,y)+f(x-1,y)+f(x,y+1)+f(x,y-1)+f(x-1,y-1)+f(x-1,y+1)+f(x+1,y-1)+f(x+1,y+1)-8f(x,y) ∇2f=f(x+1,y)+f(x−1,y)+f(x,y+1)+f(x,y−1)+f(x−1,y−1)+f(x−1,y+1)+f(x+1,y−1)+f(x+1,y+1)−8f(x,y)
代码实现
import cv2import numpy as npimport matplotlib.pyplot as plt
img = cv2.imread('Fig0338.tif') # 测试图片H = img.shape[0]W = img.shape[1]pixa = np.zeros((H, W), np.int32)mImgae = np.zeros((H, W, 3), np.uint8) # 标定(scale)前的滤波图像smImga = np.zeros((H, W, 3), np.uint8) # 标定(scale)后的滤波图像pixb = np.zeros((H, W), np.int32)mImgbe = np.zeros((H, W, 3), np.uint8) # 标定前的滤波图像smImgb = np.zeros((H, W, 3), np.uint8) # 标定后的滤波图像imga = np.zeros((H, W, 3), np.uint8) # xy方向模板滤波后图像imgb = np.zeros((H, W, 3), np.uint8) # 加上对角方向模板滤波后图像# a用到的算子是 b用到的算子是# 0 1 0 1 1 1# 1 -4 1 1 -8 1# 0 1 0 1 1 1# 先绘制标定滤波图像# 标定指的是最小值设置为0，最大值设置为255的进行归一化的结果for i in range(1, H - 1):for j in range(1, W - 1):pixa[i, j] = int(img[i - 1, j, 0]) + img[i + 1, j, 0] + img[i, j - 1, 0] + img[i, j + 1, 0] - 4 * int(img[i, j, 0])pixb[i, j] = int(img[i - 1, j - 1, 0]) + img[i - 1, j, 0] + img[i - 1, j + 1, 0] + img[i, j - 1, 0] + img[i, j + 1, 0] + img[i + 1, j - 1, 0] + img[i + 1, j, 0] + img[i + 1, j + 1, 0] - 8 * int(img[i, j, 0])maxa = 0maxb = 0mina = 255minb = 255for i in range(H):for j in range(W):# 求出像素最大值和最小值，以利于scaleif pixa[i, j] > maxa:maxa = pixa[i, j]if pixa[i, j] < mina:mina = pixa[i, j]if pixb[i, j] > maxb:maxb = pixb[i, j]if pixb[i, j] < minb:minb = pixb[i, j]if pixa[i, j] < 0:mImgae[i, j] = [0, 0, 0]else:mImgae[i, j, 0] = pixa[i, j]mImgae[i, j, 1] = pixa[i, j]mImgae[i, j, 2] = pixa[i, j]if pixb[i, j] < 0:mImgbe[i, j] = [0, 0, 0]else:mImgbe[i, j, 0] = pixb[i, j]mImgbe[i, j, 1] = pixb[i, j]mImgbe[i, j, 2] = pixb[i, j]ka = 0kb = 0if maxa > mina:ka = 255 / (maxa - mina)if maxb > minb:kb = 255 / (maxb - minb)# scale处理for i in range(H):for j in range(W):smImga[i, j, 0] = (pixa[i, j] - mina) * ka
smImga[i, j, 1] = smImga[i, j, 0]smImga[i, j, 2] = smImga[i, j, 0]smImgb[i, j, 0] = (pixb[i, j] - minb) * kb
smImgb[i, j, 1] = smImgb[i, j, 0]smImgb[i, j, 2] = smImgb[i, j, 0]# 加上拉普拉斯算子# pixa和pixb里面就是两个算子的结果# lapa和lapb是原图加算子的结果，用来裁剪或者scale的原始数据lapa = np.zeros((H, W), np.int32)lapb = np.zeros((H, W), np.int32)# 缩放处理# maxa = 0# maxb = 0# mina = 255# minb = 255for i in range(H):for j in range(W):lapa[i, j] = img[i, j, 0] - pixa[i, j]lapb[i, j] = img[i, j, 0] - pixb[i, j]# 裁剪处理if lapa[i, j] > 255:lapa[i, j] = 255if lapa[i, j] < 0:lapa[i, j] = 0if lapb[i, j] > 255:lapb[i, j] = 255if lapb[i, j] < 0:lapb[i, j] = 0# 缩放处理# if lapa[i, j] > maxa:# maxa = lapa[i, j]# if lapa[i, j] < mina:# mina = lapa[i, j]# if lapb[i, j] > maxb:# maxb = lapb[i, j]# if lapb[i, j] < minb:# minb = lapb[i, j]# 缩放处理# ka = 0# kb = 0# if maxa > mina:# ka = 255 / maxa# if maxb > minb:# kb = 255 / maxb# scale处理for i in range(H):for j in range(W):# 裁剪处理imga[i, j, 0] = lapa[i, j]imga[i, j, 1] = lapa[i, j]imga[i, j, 2] = lapa[i, j]imgb[i, j, 0] = lapb[i, j]imgb[i, j, 1] = lapb[i, j]imgb[i, j, 2] = lapb[i, j]# 缩放处理# if lapa[i, j] > 0:# imga[i, j, 0] = lapa[i, j] * ka# else:# imga[i, j, 0] = 0# imga[i, j, 1] = imga[i, j, 0]# imga[i, j, 2] = imga[i, j, 0]# if lapb[i, j] > 0:# imgb[i, j, 0] = lapb[i, j] * kb# else:# imgb[i, j, 0] = 0# imgb[i, j, 1] = imgb[i, j, 0]# imgb[i, j, 2] = imgb[i, j, 0]# 原图plt.subplot(1, 4, 1)plt.axis('off')plt.title('Original image')plt.imshow(img)# 图3.37a的模板plt.subplot(2, 4, 2)plt.axis('off')plt.title('Before sale a')plt.imshow(mImgae)# scale后图3.37a的模板plt.subplot(2, 4, 3)plt.axis('off')plt.title('After sale a')plt.imshow(smImga)# 图3.37a的模板锐化后的图像plt.subplot(2, 4, 4)plt.axis('off')plt.title('Sharpened Image a')plt.imshow(imga)# 图3.37b的模板plt.subplot(2, 4, 6)plt.axis('off')plt.title('Before sale b')plt.imshow(mImgbe)# scale后图3.37b的模板plt.subplot(2, 4, 7)plt.axis('off')plt.title('After sale b')plt.imshow(smImgb)# 图3.37b的模板锐化后的图像plt.subplot(2, 4, 8)plt.axis('off')plt.title('Sharpened Image b')plt.imshow(imgb)plt.show()
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