图像极坐标变换——计算齿轮的圆心位置和齿轮所有参数

 1 import cv2
 2 import numpy as np
 3 import matplotlib.pyplot as plt
 4 
 5 plt.rcParams[‘font.sans-serif‘]=[‘SimHei‘]
 6 plt.rcParams[‘axes.unicode_minus‘]=False
 7 
 8 gears = cv2.imread(‘gears.bmp‘,0)
 9 ‘‘‘对图像进行阈值分割‘‘‘
10 thres, Out1 = cv2.threshold(gears, 0, 255, cv2.THRESH_OTSU) #大津阈值分割
11 cv2.imwrite(f‘gears_binary(阈值={thres}).bmp‘, Out1)
12 plt.subplot(111), plt.imshow(Out1,‘gray‘), plt.title(f‘阈值 = {thres}‘), plt.show()

 1 def get_center():
 2     ‘‘‘得到齿轮圆的中心‘‘‘
 3     def true_line(polar_img):
 4         ‘‘‘判断纵向是否为一条直线‘‘‘
 5         lengths = []
 6         for row in range(50, 300): 
 7             line = polar_img[row, ...]
 8             len2first_255 = list(line).index(255)
 9             lengths.append(len2first_255)
10         d_value = np.ptp(lengths)   
11         print(d_value)
12         if d_value < 4: #设置阈值4
13             return True
14         else:
15             return False    
16 
17     centers = [] #记录圆心位置
18     ‘‘‘在给定的大致区域内扫描‘‘‘
19     for rows in range(225, 230):
20         for cols in range(190, 195):
21             result = cv2.logPolar(Out1, (cols, rows), 110, cv2.WARP_FILL_OUTLIERS)
22             if true_line(result):
23                 centers.append((rows,cols)) # col = x, row = y
24     for rows in range(225, 230):
25         for cols in  range(468, 473):
26             result = cv2.logPolar(Out1, (cols, rows), 70, cv2.WARP_FILL_OUTLIERS)
27             if true_line(result):
28                 centers.append((rows,cols))            
29     
30     return centers
31 
32 center = get_center()  #得到大齿轮圆心为(col=191, row=228), 小齿轮圆心(470, 226)

‘‘‘以大齿轮圆心为中心做极坐标变换‘‘‘
Polar_img = cv2.logPolar(Out1, (191, 228), 110, cv2.WARP_FILL_OUTLIERS)  #参数110影响水平轴ρ与原图像宽度col单位的比值
cv2.imwrite(‘gears_Polar.bmp‘, Polar_img)
plt.subplot(111), plt.imshow(Polar_img, ‘gray‘), plt.show()

 1 ‘‘‘取变换后图像齿形中间连续部分片段，通过傅里叶变换得到频率‘‘‘
 2 def get_curve(polar_img):
 3     ‘‘‘取齿形‘‘‘
 4     lengths = []
 5     for row in range(150, 300): # 截取长度为150的齿形
 6         for col in range(polar_img.shape[1]-1, 300, -1):
 7             if polar_img[row, col] == 255:
 8                 lengths.append(col)
 9                 break
10     return lengths
11 
12 def get_Frequence(polar_img):
13     ‘‘‘计算频率‘‘‘
14     y = get_curve(polar_img)
15     y = y - np.mean(y)
16     Fourier = np.fft.fft(y)
17     A = np.abs(Fourier)
18     x = [i for i in range(0, 75) ]
19     plt.plot(x, A[:75]), plt.savefig(‘傅里叶幅值图‘)
20     return list(A[:75]).index(max(A[:75]))/150
21 
22 Fs = get_Frequence(Polar_img)
23 print(f‘齿形的频率为：{Fs}‘)
24 gear_num = Fs * Polar_img.shape[0] #根据频率计算齿数
25 print(f‘大齿轮齿数为：{gear_num}‘) 

 1 def get_D():
 2     ‘‘‘求大齿轮齿顶圆直径‘‘‘
 3     def get_maxR(out1_img, row_range):
 4         ‘‘‘计算给定齿形片段到圆心的最大距离‘‘‘
 5         distances = []
 6         for row in range(row_range[0], row_range[1]): 
 7             for col in range(70):
 8                 if out1_img[row, col] == 255:
 9                     distance = np.sqrt( (228-row)**2 + (191-col)**2 )
10                     distances.append(distance)
11                     break
12         return max(distances)
13     R1 = get_maxR(Out1, (150, 200))
14     R2 = get_maxR(Out1, (200, 250))
15     R3 = get_maxR(Out1, (250, 300))
16     R_1 = (R1+R2+R3)/3  #取三个最大距离的平均值  
17     return R_1 * 2
18 
19 Da = get_D()  # 得到大齿轮齿顶圆直径为 351.324
20 print(f‘大齿轮齿顶圆直径为：{Df}‘)
21 mod_num = Da/(gear_num + 2) #计算模数
22 print(f‘模数 = {mod_num}‘)
23 D = gear_num * mod_num
24 print(f‘大齿轮分度圆直径 = {D}‘)
25 Dj = D * np.cos(np.deg2rad(20))
26 print(f‘大齿轮基圆直径 = {Dj}‘)

 1 center_distance = np.sqrt((470-191)**2 + (226-228)**2) # 计算中心距
 2 print(f‘中心距 = {center_distance}‘)
 3 
 4 D2 = (center_distance - D/2) * 2
 5 gear2_num = round(gear_num * D2/D)
 6 Dj2 = D2 * np.cos(np.deg2rad(20))
 7 print(f‘小齿轮齿数 = {gear2_num}，分度圆直径 = {D2}，基圆直径 = {Dj2}‘)
 8 
 9 gear_d = np.pi * mod_num
10 print(f‘齿距 = {gear_d}，齿厚 = 齿槽距 = {gear_d/2}‘)
11 ha = 1 * mod_num
12 hf = 1.25 * mod_num
13 h = ha + hf
14 print(f‘齿顶高 = {ha}，齿根高 = {hf}，齿高 = {h}‘)