2021-05-12 14:32:11
python實現canny邊緣檢測
canny邊緣檢測原理
canny邊緣檢測共有5部分組成,下邊我會分別來介紹。
1 高斯模糊(略)
2 計算梯度幅值和方向。
可選用的模板:soble運算元、Prewitt運算元、Roberts模板等等;
一般採用soble運算元,OpenCV也是如此,利用soble水平和垂直運算元與輸入影象折積計算dx、dy:
進一步可以得到影象梯度的幅值:
為了簡化計算,幅值也可以作如下近似:
角度為:
如下圖表示了中心點的梯度向量、方位角以及邊緣方向(任一點的邊緣與梯度向量正交) :
θ = θm = arctan(dy/dx)(邊緣方向)
α = θ + 90= arctan(dy/dx) + 90(梯度方向)
3、根據角度對幅值進行非極大值抑制
劃重點:是沿著梯度方向對幅值進行非極大值抑制,而非邊緣方向,這裡初學者容易弄混。
例如:3*3區域內,邊緣可以劃分為垂直、水平、45°、135°4個方向,同樣,梯度反向也為四個方向(與邊緣方向正交)。因此為了進行非極大值,將所有可能的方向量化為4個方向,如下圖:
即梯度方向分別為
α = 90
α = 45
α = 0
α = -45
非極大值抑制即為沿著上述4種型別的梯度方向,比較3*3鄰域內對應鄰域值的大小:
在每一點上,領域中心 x 與沿著其對應的梯度方向的兩個畫素相比,若中心畫素為最大值,則保留,否則中心置0,這樣可以抑制非極大值,保留區域性梯度最大的點,以得到細化的邊緣。
4、用雙閾值演演算法檢測和連線邊緣
1選取係數TH和TL,比率為2:1或3:1。(一般取TH=0.3或0.2,TL=0.1);
2 將小於低閾值的點拋棄,賦0;將大於高閾值的點立即標記(這些點為確定邊緣 點),賦1或255;
3將小於高閾值,大於低閾值的點使用8連通區域確定(即:只有與TH畫素連線時才會被接受,成為邊緣點,賦 1或255)
python 實現
import cv2 import numpy as np m1 = np.array([[1, 0, -1], [2, 0, -2], [1, 0, -1]]) m2 = np.array([[1, 2, 1], [0, 0, 0], [-1, -2, -1]]) from matplotlib import pyplot as plt # 第一步:完成高斯平滑濾波 img = cv2.imread("B9064CF1D57871735CE11A0F368DCF27.jpg", 0) sobel = cv2.Canny(img, 50, 100) cv2.namedWindow('5', 0) cv2.resizeWindow("5", 640, 480) cv2.imshow("5", sobel) # 角度值灰度圖 img = cv2.GaussianBlur(img, (3, 3), 2) # 第二步:完成一階有限差分計算,計算每一點的梯度幅值與方向 img1 = np.zeros(img.shape, dtype="uint8") # 與原圖大小相同 theta = np.zeros(img.shape, dtype="float") # 方向矩陣原影象大小 img = cv2.copyMakeBorder(img, 1, 1, 1, 1, borderType=cv2.BORDER_REPLICATE) rows, cols = img.shape for i in range(1, rows - 1): for j in range(1, cols - 1): Gy = [np.sum(m2 * img[i - 1:i + 2, j - 1:j + 2])] #Gy = (np.dot(np.array([1, 1, 1]), (m2 * img[i - 1:i + 2, j - 1:j + 2]))).dot(np.array([[1], [1], [1]])) Gx = [np.sum(m1 * img[i - 1:i + 2, j - 1:j + 2])] #Gx = (np.dot(np.array([1, 1, 1]), (m1 * img[i - 1:i + 2, j - 1:j + 2]))).dot(np.array([[1], [1], [1]])) if Gx[0] == 0: theta[i - 1, j - 1] = 90 continue else: temp = ((np.arctan2(Gy[0], Gx[0])) * 180 / np.pi)+90 if Gx[0] * Gy[0] > 0: if Gx[0] > 0: # 第一象線 theta[i - 1, j - 1] = np.abs(temp) else: # 第三象線 theta[i - 1, j - 1] = (np.abs(temp) - 180) if Gx[0] * Gy[0] < 0: if Gx[0] > 0: # 第四象線 theta[i - 1, j - 1] = (-1) * np.abs(temp) else: # 第二象線 theta[i - 1, j - 1] = 180 - np.abs(temp) img1[i - 1, j - 1] = (np.sqrt(Gx[0] ** 2 + Gy[0] ** 2)) for i in range(1, rows - 2): for j in range(1, cols - 2): if (((theta[i, j] >= -22.5) and (theta[i, j] < 22.5)) or ((theta[i, j] <= -157.5) and (theta[i, j] >= -180)) or ((theta[i, j] >= 157.5) and (theta[i, j] < 180))): theta[i, j] = 0.0 elif (((theta[i, j] >= 22.5) and (theta[i, j] < 67.5)) or ((theta[i, j] <= -112.5) and (theta[i, j] >= -157.5))): theta[i, j] = -45.0 elif (((theta[i, j] >= 67.5) and (theta[i, j] < 112.5)) or ((theta[i, j] <= -67.5) and (theta[i, j] >= -112.5))): theta[i, j] = 90.0 elif (((theta[i, j] >= 112.5) and (theta[i, j] < 157.5)) or ((theta[i, j] <= -22.5) and (theta[i, j] >= -67.5))): theta[i, j] = 45.0 ''' for i in range(1, rows - 1): for j in range(1, cols - 1): Gy = [np.sum(m2 * img[i - 1:i + 2, j - 1:j + 2])] #Gy = (np.dot(np.array([1, 1, 1]), (m2 * img[i - 1:i + 2, j - 1:j + 2]))).dot(np.array([[1], [1], [1]])) Gx = [np.sum(m1 * img[i - 1:i + 2, j - 1:j + 2])] #Gx = (np.dot(np.array([1, 1, 1]), (m1 * img[i - 1:i + 2, j - 1:j + 2]))).dot(np.array([[1], [1], [1]])) if Gx[0] == 0: theta[i - 1, j - 1] = 90 continue else: temp = (np.arctan2(Gy[0], Gx[0])) * 180 / np.pi) if Gx[0] * Gy[0] > 0: if Gx[0] > 0: # 第一象線 theta[i - 1, j - 1] = np.abs(temp) else: # 第三象線 theta[i - 1, j - 1] = (np.abs(temp) - 180) if Gx[0] * Gy[0] < 0: if Gx[0] > 0: # 第四象線 theta[i - 1, j - 1] = (-1) * np.abs(temp) else: # 第二象線 theta[i - 1, j - 1] = 180 - np.abs(temp) img1[i - 1, j - 1] = (np.sqrt(Gx[0] ** 2 + Gy[0] ** 2)) for i in range(1, rows - 2): for j in range(1, cols - 2): if (((theta[i, j] >= -22.5) and (theta[i, j] < 22.5)) or ((theta[i, j] <= -157.5) and (theta[i, j] >= -180)) or ((theta[i, j] >= 157.5) and (theta[i, j] < 180))): theta[i, j] = 90.0 elif (((theta[i, j] >= 22.5) and (theta[i, j] < 67.5)) or ((theta[i, j] <= -112.5) and (theta[i, j] >= -157.5))): theta[i, j] = 45.0 elif (((theta[i, j] >= 67.5) and (theta[i, j] < 112.5)) or ((theta[i, j] <= -67.5) and (theta[i, j] >= -112.5))): theta[i, j] = 0.0 elif (((theta[i, j] >= 112.5) and (theta[i, j] < 157.5)) or ((theta[i, j] <= -22.5) and (theta[i, j] >= -67.5))): theta[i, j] = -45.0 ''' # 第三步:進行 非極大值抑制計算 img2 = np.zeros(img1.shape) # 非極大值抑制影象矩陣 for i in range(1, img2.shape[0] - 1): for j in range(1, img2.shape[1] - 1): # 0度j不變 if (theta[i, j] == 0.0) and (img1[i, j] == np.max([img1[i, j], img1[i + 1, j], img1[i - 1, j]])): img2[i, j] = img1[i, j] if (theta[i, j] == -45.0) and img1[i, j] == np.max([img1[i, j], img1[i - 1, j - 1], img1[i + 1, j + 1]]): img2[i, j] = img1[i, j] if (theta[i, j] == 90.0) and img1[i, j] == np.max([img1[i, j], img1[i, j + 1], img1[i, j - 1]]): img2[i, j] = img1[i, j] if (theta[i, j] == 45.0) and img1[i, j] == np.max([img1[i, j], img1[i - 1, j + 1], img1[i + 1, j - 1]]): img2[i, j] = img1[i, j] # 第四步:雙閾值檢測和邊緣連線 img3 = np.zeros(img2.shape) # 定義雙閾值影象 # TL = 0.4*np.max(img2) # TH = 0.5*np.max(img2) TL = 50 TH = 100 # 關鍵在這兩個閾值的選擇 for i in range(1, img3.shape[0] - 1): for j in range(1, img3.shape[1] - 1): if img2[i, j] < TL: img3[i, j] = 0 elif img2[i, j] > TH: img3[i, j] = 255 elif ((img2[i + 1, j] < TH) or (img2[i - 1, j] < TH) or (img2[i, j + 1] < TH) or (img2[i, j - 1] < TH) or (img2[i - 1, j - 1] < TH) or (img2[i - 1, j + 1] < TH) or (img2[i + 1, j + 1] < TH) or (img2[i + 1, j - 1] < TH)): img3[i, j] = 255 cv2.namedWindow('1', 0) cv2.resizeWindow("1", 640, 480) cv2.namedWindow('2', 0) cv2.resizeWindow("2", 640, 480) cv2.namedWindow('3', 0) cv2.resizeWindow("3", 640, 480) cv2.namedWindow('4', 0) cv2.resizeWindow("4", 640, 480) cv2.imshow("1", img) # 原始影象 cv2.imshow("2", img1) # 梯度幅值圖 cv2.imshow("3", img2) # 非極大值抑制灰度圖 cv2.imshow("4", img3) # 最終效果圖 cv2.waitKey(0)
執行結果如下
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