What is different between Euclidean distance and the Geodesic distance?
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We have two kinds of distance in image: Euclidean distance and the Geodesic distance. What is different between them? Could you show mathematic formula or visualization to make it clear? The reference said
Difference between the Euclidean distance and the Geodesic distance calculated with the Fast Marching Method. The Geodesic distance is the distance of the minimum length inside the figure path and the Euclidean distance is the straight line distance
This is example
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Moon LeeMoon Lee
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We have two kinds of distance in image: Euclidean distance and the Geodesic distance. What is different between them? Could you show mathematic formula or visualization to make it clear? The reference said
Difference between the Euclidean distance and the Geodesic distance calculated with the Fast Marching Method. The Geodesic distance is the distance of the minimum length inside the figure path and the Euclidean distance is the straight line distance
This is example
image-processing
asked 7 hours ago
Moon LeeMoon Lee
112
New contributor
Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment |
$begingroup$
We have two kinds of distance in image: Euclidean distance and the Geodesic distance. What is different between them? Could you show mathematic formula or visualization to make it clear? The reference said
Difference between the Euclidean distance and the Geodesic distance calculated with the Fast Marching Method. The Geodesic distance is the distance of the minimum length inside the figure path and the Euclidean distance is the straight line distance
This is example
image-processing
asked 7 hours ago
Moon LeeMoon Lee
112
New contributor
Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
We have two kinds of distance in image: Euclidean distance and the Geodesic distance. What is different between them? Could you show mathematic formula or visualization to make it clear? The reference said
Difference between the Euclidean distance and the Geodesic distance calculated with the Fast Marching Method. The Geodesic distance is the distance of the minimum length inside the figure path and the Euclidean distance is the straight line distance
This is example
image-processing
image-processing
asked 7 hours ago
Moon LeeMoon Lee
112
New contributor
Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 7 hours ago
Moon LeeMoon Lee
112
New contributor
Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 7 hours ago
Moon LeeMoon Lee
112
New contributor
Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 7 hours ago
Moon LeeMoon Lee
112
asked 7 hours ago
Moon LeeMoon Lee
112
112
New contributor
Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
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1 Answer
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Simple: the Euclidean distance completely ignores the shape when finding a path from the start point to the end point while, for the geodesic distance, the path is constrained to be within the given shape.
That's why the distances at the bottom left of the figure are so different.
answered 7 hours ago
Peter K.♦Peter K.
17k83060
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$begingroup$
Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
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– Moon Lee
7 hours ago
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@MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
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– Peter K.♦
7 hours ago
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K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
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– Moon Lee
6 hours ago
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
6 hours ago
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
$begingroup$
Simple: the Euclidean distance completely ignores the shape when finding a path from the start point to the end point while, for the geodesic distance, the path is constrained to be within the given shape.
That's why the distances at the bottom left of the figure are so different.
answered 7 hours ago
Peter K.♦Peter K.
17k83060
$endgroup$
$begingroup$
Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
$endgroup$
– Moon Lee
7 hours ago
$begingroup$
@MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
$endgroup$
– Peter K.♦
7 hours ago
$begingroup$
K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
$endgroup$
– Moon Lee
6 hours ago
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
6 hours ago
add a comment |
$begingroup$
Simple: the Euclidean distance completely ignores the shape when finding a path from the start point to the end point while, for the geodesic distance, the path is constrained to be within the given shape.
That's why the distances at the bottom left of the figure are so different.
answered 7 hours ago
Peter K.♦Peter K.
17k83060
$endgroup$
$begingroup$
Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
$endgroup$
– Moon Lee
7 hours ago
$begingroup$
@MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
$endgroup$
– Peter K.♦
7 hours ago
$begingroup$
K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
$endgroup$
– Moon Lee
6 hours ago
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
6 hours ago
add a comment |
$begingroup$
Simple: the Euclidean distance completely ignores the shape when finding a path from the start point to the end point while, for the geodesic distance, the path is constrained to be within the given shape.
That's why the distances at the bottom left of the figure are so different.
answered 7 hours ago
Peter K.♦Peter K.
17k83060
$endgroup$
Simple: the Euclidean distance completely ignores the shape when finding a path from the start point to the end point while, for the geodesic distance, the path is constrained to be within the given shape.
That's why the distances at the bottom left of the figure are so different.
answered 7 hours ago
Peter K.♦Peter K.
17k83060
edited 7 hours ago
answered 7 hours ago
Peter K.♦Peter K.
17k83060
answered 7 hours ago
Peter K.♦Peter K.
17k83060
answered 7 hours ago
Peter K.♦Peter K.
17k83060
17k83060
$begingroup$
Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
$endgroup$
– Moon Lee
7 hours ago
$begingroup$
@MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
$endgroup$
– Peter K.♦
7 hours ago
$begingroup$
K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
$endgroup$
– Moon Lee
6 hours ago
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
6 hours ago
add a comment |
$begingroup$
Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
$endgroup$
– Moon Lee
7 hours ago
$begingroup$
@MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
$endgroup$
– Peter K.♦
7 hours ago
$begingroup$
K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
$endgroup$
– Moon Lee
6 hours ago
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
6 hours ago
$begingroup$
Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
$endgroup$
– Moon Lee
7 hours ago
$begingroup$
Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
$endgroup$
– Moon Lee
7 hours ago
$begingroup$
@MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
$endgroup$
– Peter K.♦
7 hours ago
$begingroup$
@MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
$endgroup$
– Peter K.♦
7 hours ago
$begingroup$
K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
$endgroup$
– Moon Lee
6 hours ago
$begingroup$
K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
$endgroup$
– Moon Lee
6 hours ago
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
6 hours ago
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
6 hours ago
add a comment |
Moon Lee is a new contributor. Be nice, and check out our Code of Conduct.
Moon Lee is a new contributor. Be nice, and check out our Code of Conduct.
Moon Lee is a new contributor. Be nice, and check out our Code of Conduct.
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