【圖像處理】python不調包實現圖像銳化邊緣檢測算子（Robert、Sobel、Prewitt、Laplacian算子）

一、Robert算子

羅伯特梯度法(Robert Gradient), 是一種交叉差分方法。其數學表達式可近似爲：

G[f(x, y)] ≈|f(i, j)-f(i+1, j+1) |+|f(i+1, j)-f(i, j+1)|

################################################
#           Robert算子
################################################
def robert_filter(image):
    h = image.shape[0]
    w = image.shape[1]
    image_new = np.zeros(image.shape, np.uint8)
    for i in range(1, h-1):
        for j in range(1, w-1):
            image_new[i][j] = np.abs((image[i][j]-image[i+1][j+1])) + np.abs(image[i+1][j]-image[i][j+1])
    return image_new

二、Sobel算子

採用梯度微分銳化圖像，同時會使噪聲、條紋等得到增強， Sobel算子則在一定程度上克服了這個問題。Sobel算子法的基本原理是：計算3×3窗口的灰度， 將其作爲變換後圖像g(i, j)的灰度。公式如下：

################################################
#           Sobel算子
################################################
def sobel_filter(image):
    h = image.shape[0]
    w = image.shape[1]
    image_new = np.zeros(image.shape, np.uint8)

    for i in range(1, h-1):
        for j in range(1, w-1):
            sx = (image[i + 1][j - 1] + 2 * image[i + 1][j] + image[i + 1][j + 1]) - \
                 (image[i - 1][j - 1] + 2 * image[i - 1][j] + image[i - 1][j + 1])
            sy = (image[i - 1][j + 1] + 2 * image[i][j + 1] + image[i + 1][j + 1]) - \
                 (image[i - 1][j - 1] + 2 * image[i][j - 1] + image[i + 1][j - 1])
            image_new[i][j] = np.sqrt(np.square(sx) + np.square(sy))
    return image_new

三、Prewitt算子

與Sobel相比，Prewitt算子有一定的抗干擾性，圖像效果比較乾淨。

公式如下：

################################################
#           Prewitt算子
################################################
def prewitt_filter(image):
    h = image.shape[0]
    w = image.shape[1]
    image_new = np.zeros(image.shape, np.uint8)

    for i in range(1, h-1):
        for j in range(1, w-1):
            sx = (image[i - 1][j - 1] + image[i - 1][j] + image[i - 1][j + 1]) - \
                 (image[i + 1][j - 1] + image[i + 1][j] + image[i + 1][j + 1])
            sy = (image[i - 1][j - 1] + image[i][j - 1] + image[i + 1][j - 1]) - \
                 (image[i - 1][j + 1] + image[i][j + 1] + image[i + 1][j + 1])
            image_new[i][j] = np.sqrt(np.square(sx) + np.square(sy))
    return image_new

四、Laplacian算子

拉普拉斯運算是偏導數運算的線性組合運算，屬於二階微分運算。與以上三類一階微分運算相比，Laplacian算子獲得的邊界更爲細緻，包含了更多信息，

公式如下：

 

################################################
#           Laplacian算子
################################################
def laplacian_filter(image):
    h = image.shape[0]
    w = image.shape[1]
    image_new = np.zeros(image.shape, np.uint8)
    for i in range(1, h-1):
        for j in range(1, w-1):
            image_new[i][j] = image[i + 1][j] + image[i - 1][j] + image[i][j + 1] + image[i][j - 1] - 8 * image[i][j]
    return image_new

五、完整代碼

import numpy as np
import matplotlib.pyplot as plt
import random


################################################
#           Robert算子
################################################
def robert_filter(image):
    h = image.shape[0]
    w = image.shape[1]
    image_new = np.zeros(image.shape, np.uint8)
    for i in range(1, h-1):
        for j in range(1, w-1):
            image_new[i][j] = np.abs((image[i][j]-image[i+1][j+1])) + np.abs(image[i+1][j]-image[i][j+1])
    return image_new


################################################
#           Sobel算子
################################################
def sobel_filter(image):
    h = image.shape[0]
    w = image.shape[1]
    image_new = np.zeros(image.shape, np.uint8)

    for i in range(1, h-1):
        for j in range(1, w-1):
            sx = (image[i + 1][j - 1] + 2 * image[i + 1][j] + image[i + 1][j + 1]) - \
                 (image[i - 1][j - 1] + 2 * image[i - 1][j] + image[i - 1][j + 1])
            sy = (image[i - 1][j + 1] + 2 * image[i][j + 1] + image[i + 1][j + 1]) - \
                 (image[i - 1][j - 1] + 2 * image[i][j - 1] + image[i + 1][j - 1])
            image_new[i][j] = np.sqrt(np.square(sx) + np.square(sy))
    return image_new


################################################
#           Prewitt算子
################################################
def prewitt_filter(image):
    h = image.shape[0]
    w = image.shape[1]
    image_new = np.zeros(image.shape, np.uint8)

    for i in range(1, h-1):
        for j in range(1, w-1):
            sx = (image[i - 1][j - 1] + image[i - 1][j] + image[i - 1][j + 1]) - \
                 (image[i + 1][j - 1] + image[i + 1][j] + image[i + 1][j + 1])
            sy = (image[i - 1][j - 1] + image[i][j - 1] + image[i + 1][j - 1]) - \
                 (image[i - 1][j + 1] + image[i][j + 1] + image[i + 1][j + 1])
            image_new[i][j] = np.sqrt(np.square(sx) + np.square(sy))
    return image_new


################################################
#           Laplacian算子
################################################
def laplacian_filter(image):
    h = image.shape[0]
    w = image.shape[1]
    image_new = np.zeros(image.shape, np.uint8)
    for i in range(1, h-1):
        for j in range(1, w-1):
            image_new[i][j] = image[i + 1][j] + image[i - 1][j] + image[i][j + 1] + image[i][j - 1] - 8 * image[i][j]
    return image_new

#############################################################################


if __name__ == "__main__":
    img = plt.imread("1.jpg")

    rgb_weight = [0.299, 0.587, 0.114]
    img_gray = np.dot(img, rgb_weight)

################################################
#           原圖
################################################
    plt.subplot(241)
    plt.imshow(img)
    plt.xticks([])
    plt.yticks([])
    plt.title("Original")

################################################
#           灰度圖
################################################
    plt.subplot(242)
    plt.imshow(img_gray, cmap=plt.cm.gray)
    plt.xticks([])
    plt.yticks([])
    plt.title("Gray")

################################################
#           Robert算子
################################################
    img_Robert = robert_filter(img_gray)
    img_Robert = img_Robert.astype(np.float64)
    plt.subplot(245)
    plt.imshow(img_Robert, cmap=plt.cm.gray)
    plt.xticks([])
    plt.yticks([])
    plt.title("robert_filter")

################################################
#           Sobel算子
################################################
    img_Sobel = sobel_filter(img_gray)
    img_Sobel = img_Sobel.astype(np.float64)
    plt.subplot(246)
    plt.imshow(img_Sobel, cmap=plt.cm.gray)
    plt.xticks([])
    plt.yticks([])
    plt.title("sobel_filter")

################################################
#           Prewitt算子
################################################
    img_Prewitt = prewitt_filter(img_gray)
    img_Prewitt = img_Prewitt.astype(np.float64)
    plt.subplot(247)
    plt.imshow(img_Prewitt, cmap=plt.cm.gray)
    plt.xticks([])
    plt.yticks([])
    plt.title("prewitt_filter")

################################################
#           Laplacian算子
################################################
    img_Laplacian = laplacian_filter(img_gray)
    img_Laplacian = img_Laplacian.astype(np.float64)
    plt.subplot(248)
    plt.imshow(img_Laplacian, cmap=plt.cm.gray)
    plt.xticks([])
    plt.yticks([])
    plt.title("laplacian_filter")
    plt.show()

結果如下：