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
image-processing
asked Jan 14 at 19:09
Moon LeeMoon Lee
212
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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 Jan 14 at 19:09
Moon LeeMoon Lee
212
$endgroup$
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 Jan 14 at 19:09
Moon LeeMoon Lee
212
$endgroup$
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 Jan 14 at 19:09
Moon LeeMoon Lee
212
asked Jan 14 at 19:09
Moon LeeMoon Lee
212
asked Jan 14 at 19:09
Moon LeeMoon Lee
212
asked Jan 14 at 19:09
Moon LeeMoon Lee
212
asked Jan 14 at 19:09
Moon LeeMoon Lee
212
212
add a comment |
add a comment |
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 Jan 14 at 19:25
Peter K.♦Peter K.
17.3k83162
$endgroup$
$begingroup$
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/…
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– Moon Lee
Jan 14 at 19:39
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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.♦
Jan 14 at 19:51
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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
Jan 14 at 19:58
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
Jan 14 at 20:03
$begingroup$
Thanks. I understood it. However, what term in the formula (2) shows the curve distance? It is not so clear
$endgroup$
– Moon Lee
Jan 16 at 15:02
|
show 2 more comments
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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 Jan 14 at 19:25
Peter K.♦Peter K.
17.3k83162
$endgroup$
$begingroup$
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
Jan 14 at 19:39
$begingroup$
@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.♦
Jan 14 at 19:51
$begingroup$
K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
$endgroup$
– Moon Lee
Jan 14 at 19:58
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
Jan 14 at 20:03
$begingroup$
Thanks. I understood it. However, what term in the formula (2) shows the curve distance? It is not so clear
$endgroup$
– Moon Lee
Jan 16 at 15:02
|
show 2 more comments
$begingroup$
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 Jan 14 at 19:25
Peter K.♦Peter K.
17.3k83162
$endgroup$
$begingroup$
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
Jan 14 at 19:39
$begingroup$
@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.♦
Jan 14 at 19:51
$begingroup$
K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
$endgroup$
– Moon Lee
Jan 14 at 19:58
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
Jan 14 at 20:03
$begingroup$
Thanks. I understood it. However, what term in the formula (2) shows the curve distance? It is not so clear
$endgroup$
– Moon Lee
Jan 16 at 15:02
|
show 2 more comments
$begingroup$
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 Jan 14 at 19:25
Peter K.♦Peter K.
17.3k83162
$endgroup$
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 Jan 14 at 19:25
Peter K.♦Peter K.
17.3k83162
edited Jan 14 at 19:38
answered Jan 14 at 19:25
Peter K.♦Peter K.
17.3k83162
answered Jan 14 at 19:25
Peter K.♦Peter K.
17.3k83162
answered Jan 14 at 19:25
Peter K.♦Peter K.
17.3k83162
17.3k83162
$begingroup$
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
Jan 14 at 19:39
$begingroup$
@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.♦
Jan 14 at 19:51
$begingroup$
K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
$endgroup$
– Moon Lee
Jan 14 at 19:58
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
Jan 14 at 20:03
$begingroup$
Thanks. I understood it. However, what term in the formula (2) shows the curve distance? It is not so clear
$endgroup$
– Moon Lee
Jan 16 at 15:02
|
show 2 more comments
$begingroup$
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
Jan 14 at 19:39
$begingroup$
@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.♦
Jan 14 at 19:51
$begingroup$
K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
$endgroup$
– Moon Lee
Jan 14 at 19:58
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
Jan 14 at 20:03
$begingroup$
Thanks. I understood it. However, what term in the formula (2) shows the curve distance? It is not so clear
$endgroup$
– Moon Lee
Jan 16 at 15:02
$begingroup$
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
Jan 14 at 19:39
$begingroup$
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
Jan 14 at 19:39
$begingroup$
@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.♦
Jan 14 at 19:51
$begingroup$
@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.♦
Jan 14 at 19:51
$begingroup$
K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
$endgroup$
– Moon Lee
Jan 14 at 19:58
$begingroup$
K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
$endgroup$
– Moon Lee
Jan 14 at 19:58
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
Jan 14 at 20:03
$begingroup$
@MoonLee: See this answer on SO for some information about how to implement it.
$endgroup$
– Peter K.♦
Jan 14 at 20:03
$begingroup$
Thanks. I understood it. However, what term in the formula (2) shows the curve distance? It is not so clear
$endgroup$
– Moon Lee
Jan 16 at 15:02
$begingroup$
Thanks. I understood it. However, what term in the formula (2) shows the curve distance? It is not so clear
$endgroup$
– Moon Lee
Jan 16 at 15:02
|
show 2 more comments
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