Sobel operator is one of the most important operators in pixel image edge detection, and plays a pivotal role in machine learning, digital media, computer vision and other information technology fields. Technically, it is a discrete first-order
difference
operator that computes an approximation of the first-order gradient of the image brightness function. Using this operator at any point in the image will generate the gradient vector or its normal vector corresponding to that point.
[1]
The operator consists of two sets of 3x3
matrices
, which are horizontal and vertical, respectively.
Convolve
, and then the approximation of the horizontal and vertical luminance
difference .
If A represents the original image, Gx and Gy
represent
the image detected by the horizontal and vertical edges, respectively, the formula is as follows:
The horizontal and vertical gradient approximations of each pixel of the image can be combined with the following formulas to calculate the magnitude of the gradient.
The gradient direction can be calculated using the following formula.
In the above example, if the above angle Θ is equal to zero, it means that the image has a vertical edge there, and the left side is darker than the right side.
Gaussian blur ( https://en.wikipedia.org/wiki/Gaussian_blur ), also known as Gaussian smoothing, is a processing effect widely used in image processing software such as Adobe Photoshop , GIMP and Paint.NET , usually used to reduce images noise and reduced level of detail.
import
matplotlib.pyplot
as
plt
import
matplotlib.image
as
mpimg
import
cv2
import
numpy
as
np
image
=
cv2.imread(
"./imgs/9.jpg"
)
gray
=
cv2.cvtColor(image,cv2.COLOR_BGR2GRAY)
gray_blur
=
cv2.GaussianBlur(gray,(
9
,
9
),
5
)
f
=
np.fft.fft2(gray
/
225.0
)
f_shift
=
np.fft.fftshift(f)
grayfft
=
10* np.log(np.abs(f_shift))
core_sobelx
=
np.array([[
-
1
,
0
,
1
],[
-
2
,
0
,
2
],[
-
1
,
0
,
1
]])
core_sobely
=
np.array([[
-
1
,
0
,
1
],[
-
2
,
0
,
2
],[
-
1
,
0
,
1
]])
gray_blur_sobelx
=
cv2.filter2D(gray_blur,
2
,core_sobelx)
gray_blur_sobely
=
cv2.filter2D(gray_blur,
2
,core_sobely)
gray_blur
=
cv2.filter2D(gray,
2
,core_sobelx)
f,(a0,a1,a2,a3,a4,a5)
=
plt.subplots(
1
,
6
,
figsize
=
(
30
,
30
))
a5.set_title(
"fft gray"
)
a5.imshow(grayfft,
cmap
=
'gray'
)
a0.set_title(
"oraginal gray"
)
a0.imshow(gray,
cmap
=
'gray'
)
a1.set_title(
"oraginal gray filter"
)
a1.imshow(gray_blur,
cmap
=
'gray'
)
a2.set_title(
"blur gray"
)
a2.imshow(gray_blur,
cmap
=
'gray'
)
a3.set_title(
"blur gray with sobel x"
)
a3.imshow(gray_blur_sobelx,
cmap
=
'gray'
)
a4.set_title(
"blur gray with sobel y"
)
a4.imshow(gray_blur_sobely,
cmap
=
'gray'
)
retval,binary_image
=
cv2.threshold(gray_blur_sobelx,
100
,
225
,cv2.THRESH_BINARY)
plt.figure()
plt.imshow(binary_image,
cmap
=
'gray'
)
plt.show()
