部分 IV
OpenCV 中的图像处理
19 Canny 边缘检测
目标
• 了解 Canny 边缘检测的概念
• 学习函数 cv2.Canny()
19.1 原理
Canny 边缘检测是一种非常流行的边缘检测算法,是 John F.Canny 在1986 年提出的。它是一个有很多步构成的算法,我们接下来会逐步介绍。
19.1.1 噪声去除
由于边缘检测很容易受到噪声影响,所以第一步是使用 5x5 的高斯滤波器去除噪声,这个前面我们已经学过了。
19.1.2 计算图像梯度
对平滑后的图像使用 Sobel 算子计算水平方向和竖直方向的一阶导数(图像梯度)(Gx 和 Gy)。根据得到的这两幅梯度图(Gx 和 Gy)找到边界的梯度和方向,公式如下:
梯度的方向一般总是与边界垂直。梯度方向被归为四类:垂直,水平,和两个对角线。
19.1.3 非极大值抑制
在获得梯度的方向和大小之后,应该对整幅图像做一个扫描,去除那些非边界上的点。对每一个像素进行检查,看这个点的梯度是不是周围具有相同梯度方向的点中最大的。如下图所示:
现在你得到的是一个包含“窄边界”的二值图像。
19.1.4 滞后阈值
现在要确定那些边界才是真正的边界。这时我们需要设置两个阈值:minVal 和 maxVal。当图像的灰度梯度高于 maxVal 时被认为是真的边界,那些低于 minVal 的边界会被抛弃。如果介于两者之间的话,就要看这个点是否与某个被确定为真正的边界点相连,如果是就认为它也是边界点,如果不是就抛弃。如下图:
A 高于阈值 maxVal 所以是真正的边界点,C 虽然低于 maxVal 但高于minVal 并且与 A 相连,所以也被认为是真正的边界点。而 B 就会被抛弃,因为他不仅低于 maxVal 而且不与真正的边界点相连。所以选择合适的 maxVal和 minVal 对于能否得到好的结果非常重要。
在这一步一些小的噪声点也会被除去,因为我们假设边界都是一些长的线段。
19.2 OpenCV 中的 Canny 边界检测
在 OpenCV 中只需要一个函数:cv2.Canny(),就可以完成以上几步。
让我们看如何使用这个函数。这个函数的第一个参数是输入图像。第二和第三个分别是 minVal 和 maxVal。第三个参数设置用来计算图像梯度的 Sobel卷积核的大小,默认值为 3。最后一个参数是 L2gradient,它可以用来设定求梯度大小的方程。如果设为 True,就会使用我们上面提到过的方程,否则使用方程:. 代替,默认值为 False。
import cv2
import numpy as np
from matplotlib import pyplot as plt img = cv2.imread('messi5.jpg',0)
edges = cv2.Canny(img,100,200) plt.subplot(121),plt.imshow(img,cmap = 'gray')
plt.title('Original Image'), plt.xticks([]), plt.yticks([])
plt.subplot(122),plt.imshow(edges,cmap = 'gray')
plt.title('Edge Image'), plt.xticks([]), plt.yticks([]) plt.show()
结果:
我的结果
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" alt="" width="448" height="161" />
官方结果
更多资源
1. Canny edge detector at Wikipedia
2. Canny Edge Detection Tutorial by Bill Green, 2002.
练习
1. 写一个小程序,可以通过调节滑动条来设置阈值 minVal 和 maxVal 进而来进行 Canny 边界检测。这样你就会理解阈值的重要性了。
20 图像金字塔
目标
• 学习图像金字塔
• 使用图像创建一个新水果:“橘子苹果”
• 将要学习的函数有:cv2.pyrUp(),cv2.pyrDown()。
20.1 原理
一般情况下,我们要处理是一副具有固定分辨率的图像。但是有些情况下,我们需要对同一图像的不同分辨率的子图像进行处理。比如,我们要在一幅图像中查找某个目标,比如脸,我们不知道目标在图像中的尺寸大小。这种情况下,我们需要创建创建一组图像,这些图像是具有不同分辨率的原始图像。我们把这组图像叫做图像金字塔(简单来说就是同一图像的不同分辨率的子图集合)。如果我们把最大的图像放在底部,最小的放在顶部,看起来像一座金字塔,故而得名图像金字塔。
有两类图像金字塔:高斯金字塔和拉普拉斯金字塔。
高斯金字塔的顶部是通过将底部图像中的连续的行和列去除得到的。顶部图像中的每个像素值等于下一层图像中 5 个像素的高斯加权平均值。这样操作一次一个 MxN 的图像就变成了一个 M/2xN/2 的图像。所以这幅图像的面积就变为原来图像面积的四分之一。这被称为 Octave。连续进行这样的操作我们就会得到一个分辨率不断下降的图像金字塔。我们可以使用函数cv2.pyrDown() 和 cv2.pyrUp() 构建图像金字塔。
函数 cv2.pyrDown() 从一个高分辨率大尺寸的图像向上构建一个金子塔(尺寸变小,分辨率降低)。
img = cv2.imread('messi5.jpg')
lower_reso = cv2.pyrDown(higher_reso)
下图是一个四层的图像金字塔。
函数 cv2.pyrUp() 从一个低分辨率小尺寸的图像向下构建一个金子塔(尺寸变大,但分辨率不会增加)。
higher_reso2 = cv2.pyrUp(lower_reso)
你要记住的是是 higher_reso2 和 higher_reso 是不同的。因为一旦使用 cv2.pyrDown(),图像的分辨率就会降低,信息就会被丢失。下图就是从 cv2.pyrDown() 产生的图像金字塔的(由下到上)第三层图像使用函数cv2.pyrUp() 得到的图像,与原图像相比分辨率差了很多。
拉普拉斯金字塔可以有高斯金字塔计算得来,公式如下:
拉普拉金字塔的图像看起来就像边界图,其中很多像素都是 0。他们经常被用在图像压缩中。下图就是一个三层的拉普拉斯金字塔:
20.2 使用金字塔进行图像融合
图像金字塔的一个应用是图像融合。例如,在图像缝合中,你需要将两幅图叠在一起,但是由于连接区域图像像素的不连续性,整幅图的效果看起来会很差。这时图像金字塔就可以排上用场了,他可以帮你实现无缝连接。这里的一个经典案例就是将两个水果融合成一个,看看下图也许你就明白我在讲什么了。
你可以通过阅读后边的更多资源来了解更多关于图像融合,拉普拉斯金字塔的细节。
实现上述效果的步骤如下:
1. 读入两幅图像,苹果和句子
2. 构建苹果和橘子的高斯金字塔(6 层)
3. 根据高斯金字塔计算拉普拉斯金字塔
4. 在拉普拉斯的每一层进行图像融合(苹果的左边与橘子的右边融合)
5. 根据融合后的图像金字塔重建原始图像。
下图是摘自《学习 OpenCV》展示了金子塔的构建,以及如何从金字塔重建原始图像的过程。
整个过程的代码如下。(为了简单,每一步都是独立完成的,这回消耗更多、的内存,如果你愿意的话可以对他进行优化)
import cv2
import numpy as np,sys A = cv2.imread('apple.jpg')
B = cv2.imread('orange.jpg') # generate Gaussian pyramid for A
G = A.copy()
gpA = [G]
for i in xrange(6):
G = cv2.pyrDown(G)
gpA.append(G) # generate Gaussian pyramid for B
G = B.copy()
gpB = [G]
for i in xrange(6):
G = cv2.pyrDown(G)
gpB.append(G) # generate Laplacian Pyramid for A
lpA = [gpA[5]]
for i in xrange(5,0,-1):
GE = cv2.pyrUp(gpA[i])
L = cv2.subtract(gpA[i-1],GE)
lpA.append(L) # generate Laplacian Pyramid for B
lpB = [gpB[5]]
for i in xrange(5,0,-1):
GE = cv2.pyrUp(gpB[i])
L = cv2.subtract(gpB[i-1],GE)
lpB.append(L) # Now add left and right halves of images in each level
LS = []
for la,lb in zip(lpA,lpB):
rows,cols,dpt = la.shape
ls = np.hstack((la[:,0:cols/2], lb[:,cols/2:]))
LS.append(ls) # now reconstruct
ls_ = LS[0]
for i in xrange(1,6):
ls_ = cv2.pyrUp(ls_)
ls_ = cv2.add(ls_, LS[i]) # image with direct connecting each half
real = np.hstack((A[:,:cols/2],B[:,cols/2:])) cv2.imwrite('Pyramid_blending2.jpg',ls_)
cv2.imwrite('Direct_blending.jpg',real)