【8】python-opencv3教程：边缘检测（Roberts算子边缘检测，Prewitt算子边缘检测，Sobel算子边缘检测）

亦凉 2022-03-14 18:08 469阅读 0赞

# 第八节：边缘检测 #

>          边缘检测：边缘检测指的是灰度值发生急剧变化的位置，边缘检测的目的是制作一个线图，在不会损害理解图像内容的情况下， 有大大减少了图像的数据量，提供了对图像数据的合适概述。

### 一：Roberts算子 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 1][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 2][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 3][]

***代码实现：***

import cv2
    import numpy as np
    from scipy import signal
    
    
    def roberts(I, _boundary='fill', _fillvalue=0):
    
        # 图像的高，宽
        H1, W1 = I.shape[0:2]
    
        # 卷积核的尺寸
        H2, W2 = 2, 2
    
        # 卷积核1 和 锚点的位置
        R1 = np.array([[1, 0], [0, -1]], np.float32)
        kr1, kc1 = 0, 0
    
        # 计算full卷积
        IconR1 = signal.convolve2d(I, R1, mode='full', boundary=_boundary, fillvalue=_fillvalue)
        IconR1 = IconR1[H2-kr1-1:H1+H2-kr1-1, W2-kc1-1:W1+W2-kc1-1]
    
        # 卷积核2 和 锚点的位置
        R2 = np.array([[0, 1], [-1, 0]], np.float32)
        kr2, kc2 = 0, 1
        # 再计算full卷积
        IconR2 = signal.convolve2d(I, R2, mode='full', boundary=_boundary, fillvalue=_fillvalue)
        IconR2 = IconR2[H2-kr2-1:H1+H2-kr2-1, W2-kc2-1:W1+W2-kc2-1]
    
        return (IconR1, IconR2)
    
    if __name__ == '__main__':
    
        I = cv2.imread('img3.png', cv2.IMREAD_GRAYSCALE)
        # 显示原图
        cv2.imshow('origin', I)
        # 卷积，注意边界一般扩充采用的symm
        IconR1, IconR2 = roberts(I, 'symm')
    
        # 45度方向上的边缘强度的灰度级显示
        IconR1 = np.abs(IconR1)
        edge45 = IconR1.astype(np.uint8)
        cv2.imshow('edge45', edge45)
    
        # 135度方向上的边缘强度的灰度级显示
        IconR2 = np.abs(IconR2)
        edge135 = IconR2.astype(np.uint8)
        cv2.imshow('edge135', edge135)
    
        # 用平方和的开方来衡量最后输出的边缘
        edge = np.sqrt(np.power(IconR1, 2.0) + np.power(IconR2, 2.0))
        edge = np.round(edge)
        edge[edge > 255] = 255
        edge = edge.astype(np.uint8)
    
        # 显示边缘
        cv2.imshow('edge', edge)
        cv2.waitKey(0)
        cv2.destroyAllWindows()

***输出结果：***

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 4][]

### 二： Prewitt边缘检测 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 5][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 6][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 7][]

***代码实现：***

import cv2
    import numpy as np
    from scipy import signal
    
    
    def prewitt(I, _boundary = 'symm', ):
    
        # prewitt算子是可分离的。 根据卷积运算的结合律，分两次小卷积核运算
    
        # 算子分为两部分，这是对第一部分操作
        # 1: 垂直方向上的均值平滑
        ones_y = np.array([[1], [1], [1]], np.float32)
        i_conv_pre_x = signal.convolve2d(I, ones_y, mode='same', boundary=_boundary)
        # 2: 水平方向上的差分
        diff_x = np.array([[1, 0, -1]], np.float32)
        i_conv_pre_x = signal.convolve2d(i_conv_pre_x, diff_x, mode='same', boundary=_boundary)
    
        # 算子分为两部分，这是对第二部分操作
        # 1: 水平方向上的均值平滑
        ones_x = np.array([[1, 1, 1]], np.float32)
        i_conv_pre_y = signal.convolve2d(I, ones_x, mode='same', boundary=_boundary)
        # 2: 垂直方向上的差分
        diff_y = np.array([[1], [0], [-1]], np.float32)
        i_conv_pre_y = signal.convolve2d(i_conv_pre_y, diff_y, mode='same', boundary=_boundary)
    
        return (i_conv_pre_x, i_conv_pre_y)
    
    if __name__ == '__main__':
    
        I = cv2.imread('img7.jpg', cv2.IMREAD_GRAYSCALE)
        cv2.imshow('origin', I)
    
        i_conv_pre_x, i_conv_pre_y = prewitt(I)
    
        # 取绝对值，分别得到水平方向和垂直方向的边缘强度
        abs_i_conv_pre_x = np.abs(i_conv_pre_x)
        abs_i_conv_pre_y = np.abs(i_conv_pre_y)
    
        # 水平方向和垂直方向上的边缘强度的灰度级显示
        edge_x = abs_i_conv_pre_x.copy()
        edge_y = abs_i_conv_pre_y.copy()
    
        # 将大于255的值截断为255
        edge_x[edge_x > 255] = 255
        edge_y[edge_y > 255] = 255
    
        # 数据类型转换
        edge_x = edge_x.astype(np.uint8)
        edge_y = edge_y.astype(np.uint8)
    
        # 显示
        cv2.imshow('edge_x', edge_x)
        cv2.imshow('edge_y', edge_y)
    
        # 利用abs_i_conv_pre_x 和 abs_i_conv_pre_y 求最终的边缘强度
        # 求边缘强度有多重方法, 这里使用的是插值法
        edge = 0.5 * abs_i_conv_pre_x + 0.5 * abs_i_conv_pre_y
    
        # 边缘强度灰度级显示
        edge[edge > 255] = 255
        edge = edge.astype(np.uint8)
        cv2.imshow('edge', edge)
        cv2.waitKey(0)
        cv2.destroyAllWindows()

***输出结果：***

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 8][]

### 三：Sobel边缘检测 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 9][]

![201903081601490.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 10][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 11][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 12][]

***代码实现：***

import math
    import cv2
    import numpy as np
    from scipy import signal
    
    def pascalSmooth(n):
        # 返回n阶的非归一化的高斯平滑算子
        pascalSmooth = np.zeros([1, n], np.float32)
        for i in  range(n):
            pascalSmooth[0][i] = math.factorial(n - 1) / (math.factorial(i) * math.factorial(n-1-i))
        return pascalSmooth
    
    def pascalDiff(n):      # 在一半之前是逐差法。。后半部分的值和前半部分对应
        # 返回n阶差分算子
        pascalDiff = np.zeros([1, n], np.float32)
        pascalSmooth_previous = pascalSmooth(n - 1)
        for i in range(n):
            if i == 0:
                # 恒等于1
                pascalDiff[0][i] = pascalSmooth_previous[0][i]
            elif i == n-1:
                pascalDiff[0][i] = pascalSmooth_previous[0][i-1]
            else:
                pascalDiff[0][i] = pascalSmooth_previous[0][i] - pascalSmooth_previous[0][i-1]
        return pascalDiff
    
    def getSmoothKernel(n):
        # 返回两个sobel算子
        pascalSmoothKernel = pascalSmooth(n)
        pascalDiffKernel = pascalDiff(n)
    
        # 水平方向上的卷积核
        sobelKernel_x = signal.convolve2d(pascalSmoothKernel.transpose(), pascalDiffKernel, mode='full')
        # 垂直方向上的卷积核
        sobelKernel_y = signal.convolve2d(pascalSmoothKernel, pascalDiffKernel.transpose(), mode='full')
        return (sobelKernel_x, sobelKernel_y)
    
    def sobel(image, n):
    
        rows, cols = image.shape
        # 得到平滑算子
        pascalSmoothKernel = pascalSmooth(n)
        # 得到差分算子
        pascalDiffKernel = pascalDiff(n)
    
        # 与水平方向的sobel核卷积
        # 先进行垂直方向的平滑
        image_sobel_x = signal.convolve2d(image, pascalSmoothKernel.transpose(), mode='same')
        # 再进行水平方向的差分
        image_sobel_x = signal.convolve2d(image_sobel_x, pascalDiffKernel, mode='same')
    
        # 与垂直方向的sobel核卷积
        # 先进行水平方向的平滑
        image_sobel_y = signal.convolve2d(image, pascalSmoothKernel, mode='same')
        image_sobel_y = signal.convolve2d(image_sobel_y, pascalDiffKernel.transpose(), mode='same')
    
        return (image_sobel_x, image_sobel_y)
    
    if __name__ == '__main__':
        I = cv2.imread('img7.jpg', cv2.IMREAD_GRAYSCALE)
        cv2.imshow('origin', I)
    
        # 卷积
        image_sobel_x, image_sobel_y = sobel(I, 7)
    
        # cv2.imshow('image_sobel_x', image_sobel_x)
        # cv2.imshow('image_sobel_y', image_sobel_y)
    
        # 平方和的方式展开
        edge = np.sqrt(np.power(image_sobel_x, 2.0) + np.power(image_sobel_y, 2.0))
        # 边缘强度的灰度级显示
        edge = edge / np.max(edge)
        edge = np.power(edge, 1)
        edge = edge * 255
        edge = edge.astype(np.uint8)
        cv2.imshow('edge', edge)
        cv2.waitKey(0)
        cv2.destroyAllWindows()

***输出结果：***

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 13][]

### *    后面出一节，狂调API。。。无需实现这些算法，只需知道在opencv中怎么调用。*  ###

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70]: /images/20220311/cee60b8e144f4d4b9b4411f30593c93c.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 1]: /images/20220311/c26199d2068c4d62a5d7a9ff7bc6e305.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 2]: /images/20220311/5219344ecb3148a39855cb69947aadf5.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 3]: /images/20220311/34c1d92ea974403eb52af8d50f85e30a.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 4]: /images/20220311/13c31133567741b6a3d66b1d37d926bd.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 5]: /images/20220311/a2953ea063e6446ba19d2b27be3e8033.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 6]: /images/20220311/bec62d800fce42399554380b7f783647.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 7]: /images/20220311/41a7a21b56be4db2814638d86e626723.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 8]: /images/20220311/96dc29c79e134c8c8c4cd2d57601c300.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 9]: /images/20220311/d28a7dc728f74244aa973325084e1154.png
[201903081601490.png]: /images/20220311/b4d93f4515df4c0b83018857bf44e46f.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 10]: /images/20220311/8e23e7ac23f0409387a1b03c1eb9227c.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 11]: /images/20220311/9c283a7c0d0a4c8d9cdd61a8ca645204.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 12]: /images/20220311/c6e7d9cfd3104c46a26cef951b18a79f.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoYXdyb2FkODg_size_16_color_FFFFFF_t_70 13]: /images/20220311/185eb3a5658a435a8504ab905005d6f8.png