How to measure the central angle with Python cv2 package

Question

Our team set up a vision system with a camera, a microscope and a tunable lens to look at the internal surface of a cone.

Visually speaking, the camera takes 12 image for one cone with each image covering 30 degrees.

Now we've collected many sample images and want to make sure each "fan"(as shown below) is at least 30 degree.

Is there any way in Python, with cv2 or other packages, to measure this central angle. Thanks.

Answer 1

Here is one way to do that in Python/OpenCV.

• Read the image
• Convert to gray
• Threshold
• Use morphology open and close to smooth and fill out the boundary
• Apply Canny edge extraction
• Separate the image into top edge and bottom edge by blackening the opposite side to each edge
• Fit lines to the top and bottom edges
• Compute the angle of each edge
• Compute the difference between the two angles
• Draw the lines on the input
• Save the results

Input:

import cv2
import numpy as np
import math

# read image
img = cv2.imread('cone_shape.jpg')

# convert to grayscale
gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)

# threshold
thresh = cv2.threshold(gray,11,255,cv2.THRESH_BINARY)[1]

# apply open then close to smooth boundary
kernel = cv2.getStructuringElement(cv2.MORPH_ELLIPSE, (13,13))
morph = cv2.morphologyEx(thresh, cv2.MORPH_OPEN, kernel)
kernel = np.ones((33,33), np.uint8)
morph = cv2.morphologyEx(morph, cv2.MORPH_CLOSE, kernel)

# apply canny edge detection
edges = cv2.Canny(morph, 150, 200)
hh, ww = edges.shape
hh2 = hh // 2

# split edge image in half vertically and blacken opposite half
top_edge = edges.copy()
top_edge[hh2:hh, 0:ww] = 0
bottom_edge = edges.copy()
bottom_edge[0:hh2, 0:ww] = 0

# get coordinates of white pixels in top and bottom
# note: need to transpose y,x in numpy to x,y for opencv
top_white_pts = np.argwhere(top_edge.transpose()==255)
bottom_white_pts = np.argwhere(bottom_edge.transpose()==255)

# fit lines to white pixels
# (x,y) is point on line, (vx,vy) is unit vector along line
(vx1,vy1,x1,y1) = cv2.fitLine(top_white_pts, cv2.DIST_L2, 0, 0.01, 0.01)
(vx2,vy2,x2,y2) = cv2.fitLine(bottom_white_pts, cv2.DIST_L2, 0, 0.01, 0.01)

# compute angle for vectors vx,vy
top_angle = (180/math.pi)*math.atan(vy1/vx1)
bottom_angle = (180/math.pi)*math.atan(vy2/vx2)
print(top_angle, bottom_angle)

# cone angle is the difference
cone_angle = math.fabs(top_angle - bottom_angle)
print(cone_angle)

# draw lines on input
lines = img.copy()
p1x1 = int(x1-1000*vx1)
p1y1 = int(y1-1000*vy1)
p1x2 = int(x1+1000*vx1)
p1y2 = int(y1+1000*vy1)
cv2.line(lines, (p1x1,p1y1), (p1x2,p1y2), (0, 0, 255), 1)
p2x1 = int(x2-1000*vx2)
p2y1 = int(y2-1000*vy2)
p2x2 = int(x2+1000*vx2)
p2y2 = int(y2+1000*vy2)
cv2.line(lines, (p2x1,p2y1), (p2x2,p2y2), (0, 0, 255), 1)

# save resulting images
cv2.imwrite('cone_shape_thresh.jpg',thresh)
cv2.imwrite('cone_shape_morph.jpg',morph)
cv2.imwrite('cone_shape_edges.jpg',edges)
cv2.imwrite('cone_shape_lines.jpg',lines)

# show thresh and result    
cv2.imshow("thresh", thresh)
cv2.imshow("morph", morph)
cv2.imshow("edges", edges)
cv2.imshow("top edge", top_edge)
cv2.imshow("bottom edge", bottom_edge)
cv2.imshow("lines", lines)
cv2.waitKey(0)
cv2.destroyAllWindows()

Thresholded image:

Morphology processed image:

Edge Image:

Lines on input:

Cone Angle (in degrees):

42.03975696357633