How to find the convolution matrix?
A isthe kernel and B is an image. How do you find a convolution matrix out of this equation?
A(x,y) = B(x,y) + 4B(x+1,y-1) + 2B(x,y+1) + 5B(x-1,y)
And directions are as below
(x-1,y-1) (x-1,y) (x-1,y+1)
(x,y-1) (x,y) (x,y+1)
(x+1,y-1) (x+1,y) (x+1,y+1)
is the matrix below?
0 5 0
0 1 2
4 0 0
image-processing matrix convolution
edited Nov 10 '18 at 13:33
Frank Puffer
6,64011035
asked Nov 9 '18 at 16:58
ThunfischeThunfische
1171313
add a comment |
A isthe kernel and B is an image. How do you find a convolution matrix out of this equation?
A(x,y) = B(x,y) + 4B(x+1,y-1) + 2B(x,y+1) + 5B(x-1,y)
And directions are as below
(x-1,y-1) (x-1,y) (x-1,y+1)
(x,y-1) (x,y) (x,y+1)
(x+1,y-1) (x+1,y) (x+1,y+1)
is the matrix below?
0 5 0
0 1 2
4 0 0
image-processing matrix convolution
edited Nov 10 '18 at 13:33
Frank Puffer
6,64011035
asked Nov 9 '18 at 16:58
ThunfischeThunfische
1171313
add a comment |
A isthe kernel and B is an image. How do you find a convolution matrix out of this equation?
A(x,y) = B(x,y) + 4B(x+1,y-1) + 2B(x,y+1) + 5B(x-1,y)
And directions are as below
(x-1,y-1) (x-1,y) (x-1,y+1)
(x,y-1) (x,y) (x,y+1)
(x+1,y-1) (x+1,y) (x+1,y+1)
is the matrix below?
0 5 0
0 1 2
4 0 0
image-processing matrix convolution
edited Nov 10 '18 at 13:33
Frank Puffer
6,64011035
asked Nov 9 '18 at 16:58
ThunfischeThunfische
1171313
A isthe kernel and B is an image. How do you find a convolution matrix out of this equation?
A(x,y) = B(x,y) + 4B(x+1,y-1) + 2B(x,y+1) + 5B(x-1,y)
And directions are as below
(x-1,y-1) (x-1,y) (x-1,y+1)
(x,y-1) (x,y) (x,y+1)
(x+1,y-1) (x+1,y) (x+1,y+1)
is the matrix below?
0 5 0
0 1 2
4 0 0
image-processing matrix convolution
image-processing matrix convolution
edited Nov 10 '18 at 13:33
Frank Puffer
6,64011035
asked Nov 9 '18 at 16:58
ThunfischeThunfische
1171313
edited Nov 10 '18 at 13:33
Frank Puffer
6,64011035
asked Nov 9 '18 at 16:58
ThunfischeThunfische
1171313
edited Nov 10 '18 at 13:33
Frank Puffer
6,64011035
edited Nov 10 '18 at 13:33
Frank Puffer
6,64011035
edited Nov 10 '18 at 13:33
Frank Puffer
6,64011035
6,64011035
asked Nov 9 '18 at 16:58
ThunfischeThunfische
1171313
asked Nov 9 '18 at 16:58
ThunfischeThunfische
1171313
asked Nov 9 '18 at 16:58
ThunfischeThunfische
1171313
1171313
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
It depends on how you define your pixel coordinates. If the origin is at the right (!) bottom of the image, x runs from bottom to top and y from right to left, your matrix is correct. However this is quite an uncommon choice.
If your origin is at the bottom left, x runs from left to right and y runs from bottom to top, the matrix would be:
4 0 0
0 1 5
0 2 0
Note that the directions are inverted: For example, the matrix coefficient on the right of the center is applied to the picel on the left.
By the way, it is not correct that A is the kernel for arbitrary B. This is only the case for B[0,0] == 1 and B[x,y] == 0 for all other values of x and y.
Update:
So your x runs from top to bottom and your y from left to right. Then the convolution matrix is:
0 0 4
2 1 0
0 5 0
answered Nov 9 '18 at 17:50
Frank PufferFrank Puffer
6,64011035
Origin is at the center of the image
– Thunfische
Nov 10 '18 at 0:14
Actually the origin position is not important. It's the directions that matter.
– Frank Puffer
Nov 10 '18 at 7:25
Updated the question
– Thunfische
Nov 10 '18 at 12:55
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
It depends on how you define your pixel coordinates. If the origin is at the right (!) bottom of the image, x runs from bottom to top and y from right to left, your matrix is correct. However this is quite an uncommon choice.
If your origin is at the bottom left, x runs from left to right and y runs from bottom to top, the matrix would be:
4 0 0
0 1 5
0 2 0
Note that the directions are inverted: For example, the matrix coefficient on the right of the center is applied to the picel on the left.
By the way, it is not correct that A is the kernel for arbitrary B. This is only the case for B[0,0] == 1 and B[x,y] == 0 for all other values of x and y.
Update:
So your x runs from top to bottom and your y from left to right. Then the convolution matrix is:
0 0 4
2 1 0
0 5 0
answered Nov 9 '18 at 17:50
Frank PufferFrank Puffer
6,64011035
Origin is at the center of the image
– Thunfische
Nov 10 '18 at 0:14
Actually the origin position is not important. It's the directions that matter.
– Frank Puffer
Nov 10 '18 at 7:25
Updated the question
– Thunfische
Nov 10 '18 at 12:55
add a comment |
It depends on how you define your pixel coordinates. If the origin is at the right (!) bottom of the image, x runs from bottom to top and y from right to left, your matrix is correct. However this is quite an uncommon choice.
If your origin is at the bottom left, x runs from left to right and y runs from bottom to top, the matrix would be:
4 0 0
0 1 5
0 2 0
Note that the directions are inverted: For example, the matrix coefficient on the right of the center is applied to the picel on the left.
By the way, it is not correct that A is the kernel for arbitrary B. This is only the case for B[0,0] == 1 and B[x,y] == 0 for all other values of x and y.
Update:
So your x runs from top to bottom and your y from left to right. Then the convolution matrix is:
0 0 4
2 1 0
0 5 0
answered Nov 9 '18 at 17:50
Frank PufferFrank Puffer
6,64011035
Origin is at the center of the image
– Thunfische
Nov 10 '18 at 0:14
Actually the origin position is not important. It's the directions that matter.
– Frank Puffer
Nov 10 '18 at 7:25
Updated the question
– Thunfische
Nov 10 '18 at 12:55
add a comment |
It depends on how you define your pixel coordinates. If the origin is at the right (!) bottom of the image, x runs from bottom to top and y from right to left, your matrix is correct. However this is quite an uncommon choice.
If your origin is at the bottom left, x runs from left to right and y runs from bottom to top, the matrix would be:
4 0 0
0 1 5
0 2 0
Note that the directions are inverted: For example, the matrix coefficient on the right of the center is applied to the picel on the left.
By the way, it is not correct that A is the kernel for arbitrary B. This is only the case for B[0,0] == 1 and B[x,y] == 0 for all other values of x and y.
Update:
So your x runs from top to bottom and your y from left to right. Then the convolution matrix is:
0 0 4
2 1 0
0 5 0
answered Nov 9 '18 at 17:50
Frank PufferFrank Puffer
6,64011035
It depends on how you define your pixel coordinates. If the origin is at the right (!) bottom of the image, x runs from bottom to top and y from right to left, your matrix is correct. However this is quite an uncommon choice.
If your origin is at the bottom left, x runs from left to right and y runs from bottom to top, the matrix would be:
4 0 0
0 1 5
0 2 0
Note that the directions are inverted: For example, the matrix coefficient on the right of the center is applied to the picel on the left.
By the way, it is not correct that A is the kernel for arbitrary B. This is only the case for B[0,0] == 1 and B[x,y] == 0 for all other values of x and y.
Update:
So your x runs from top to bottom and your y from left to right. Then the convolution matrix is:
0 0 4
2 1 0
0 5 0
answered Nov 9 '18 at 17:50
Frank PufferFrank Puffer
6,64011035
edited Nov 10 '18 at 13:41
answered Nov 9 '18 at 17:50
Frank PufferFrank Puffer
6,64011035
answered Nov 9 '18 at 17:50
Frank PufferFrank Puffer
6,64011035
answered Nov 9 '18 at 17:50
Frank PufferFrank Puffer
6,64011035
6,64011035
Origin is at the center of the image
– Thunfische
Nov 10 '18 at 0:14
Actually the origin position is not important. It's the directions that matter.
– Frank Puffer
Nov 10 '18 at 7:25
Updated the question
– Thunfische
Nov 10 '18 at 12:55
add a comment |
Origin is at the center of the image
– Thunfische
Nov 10 '18 at 0:14
Actually the origin position is not important. It's the directions that matter.
– Frank Puffer
Nov 10 '18 at 7:25
Updated the question
– Thunfische
Nov 10 '18 at 12:55
Origin is at the center of the image
– Thunfische
Nov 10 '18 at 0:14
Origin is at the center of the image
– Thunfische
Nov 10 '18 at 0:14
Actually the origin position is not important. It's the directions that matter.
– Frank Puffer
Nov 10 '18 at 7:25
Actually the origin position is not important. It's the directions that matter.
– Frank Puffer
Nov 10 '18 at 7:25
Updated the question
– Thunfische
Nov 10 '18 at 12:55
Updated the question
– Thunfische
Nov 10 '18 at 12:55
add a comment |
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