ShapeMatch
1. Image Moments Calculation
1.1. raw moments
1.2. central moments
the central moments are
translation invariant, no matter where the blob is in the image, if the shape is the same, the moment will be the same.
1.3. Normalized central moments
both
translation and scale invariant.
2. Hu Moments
Hu Moments are a set of 7 numbers calculated using central moments that are invariant to image transformations, the first 6 moments have been proved to be invariant to translation,scale and rotation and reflection, while the 7th moments’s sign changes for image reflection.
2.1 calculation using Opencv
# Read image as grayscale image
im=cv2.imread(filename,cv2.IMREAD_GRAYSCALE)
_,im=cv2.threshold(im,128,255,cv2.THRESH_BINARY)
#calculate Moments
mements=cv2.moments(im)
# calculate Hu Moments
huMoments=cv2.HuMoments(moments)
# log scale hu moments
for i in range(0,7):
huMoments[i]=-1*copysign(1.0,huMoments[i])*log10(abs(huMoments[i]))
#shape matching using Hu Moments
d1=cv2.matchShapes(im1,im2,cv2.CONTOURS_MATCH_I1,0)
d2=cv2.matchShapes(im1,im2,cv2.CONTOURS_MATCH_I2,0)
d3=cv2.matchShapes(im1,im2,cv2.CONTOURS_MATCH_I3,0)
The Hu Moments obtained in the previous step have a large range. For example, the 7 Hu Moments of K ( K0.png ) shown above.
h[0] = 0.00162663 h[1] = 3.11619e-07 h[2] = 3.61005e-10 h[3] = 1.44485e-10 h[4] = -2.55279e-20 h[5] = -7.57625e-14 h[6] = 2.09098e-20
Note that hu[0] is not comparable in magnitude as hu[6]. We can use use a log transform given below to bring them in the same range
using log transform to translate date to the same range.
opencv provides an easy to use a utility function called matchShapes that takes in two images(or contours) and finds the distance between them using Hu Moments,
3. Blob
a blob is a group of connected pixels in an image that shares some commn property(eg. grayscale value).
To find the center of the blob, we will perform the following steps:-
-
Convert the Image to grayscale.
-
Perform Binarization on the Image.
-
Find the center of the image after calculating the moments.
3.1. Center of a single blob
# convert image to grayscale image
gray_image = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
# convert the grayscale image to binary image
ret,thresh = cv2.threshold(gray_image,127,255,0)
# calculate moments of binary image
M = cv2.moments(thresh)
# calculate x,y coordinate of center
cX = int(M["m10"] / M["m00"])
cY = int(M["m01"] / M["m00"])
# put text and highlight the center
cv2.circle(img, (cX, cY), 5, (255, 255, 255), -1)
cv2.putText(img, "centroid", (cX - 25, cY - 25),cv2.FONT_HERSHEY_SIMPLEX, 0.5, (255, 255, 255), 2)
# display the image
cv2.imshow("Image", img)
cv2.waitKey(0)
3.2. Center of Multiple blobs
# read image through command line
img = cv2.imread(args["ipimage"])
# convert the image to grayscale
gray_image = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
# convert the grayscale image to binary image
ret,thresh = cv2.threshold(gray_image,127,255,0)
# find contours in the binary image
im2, contours, hierarchy = cv2.findContours(thresh,cv2.RETR_TREE,cv2.CHAIN_APPROX_SIMPLE)
for c in contours:
# calculate moments for each contour
M = cv2.moments(c)
if M["m00"] != 0:
cX = int(M["m10"] / M["m00"])
cY = int(M["m01"] / M["m00"])
else:
cX, cY = 0, 0
# calculate x,y coordinate of center
cv2.circle(img, (cX, cY), 5, (255, 255, 255), -1)
cv2.putText(img, "centroid", (cX - 25, cY - 25),cv2.FONT_HERSHEY_SIMPLEX, 0.5, (255, 255, 255), 2)
# display the image
cv2.imshow("Image", img)
cv2.waitKey(0)
4. matchShape methods
