Application of topology in image processing
2
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I've been reading through "topological vector spaces" lately. I've realized some of the notation usually used resemble the definition of some morphological operators usually defined in image analysis.
Apart from stuff related to graph theory is there any application where actual concept of topology are used in image analysis?
general-topology soft-question image-processing
asked Jan 15 at 9:42
user8469759user8469759
1,5681618
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add a comment |
2
$begingroup$
I've been reading through "topological vector spaces" lately. I've realized some of the notation usually used resemble the definition of some morphological operators usually defined in image analysis.
Apart from stuff related to graph theory is there any application where actual concept of topology are used in image analysis?
general-topology soft-question image-processing
asked Jan 15 at 9:42
user8469759user8469759
1,5681618
$endgroup$
add a comment |
2
2
2
1
$begingroup$
I've been reading through "topological vector spaces" lately. I've realized some of the notation usually used resemble the definition of some morphological operators usually defined in image analysis.
Apart from stuff related to graph theory is there any application where actual concept of topology are used in image analysis?
general-topology soft-question image-processing
asked Jan 15 at 9:42
user8469759user8469759
1,5681618
$endgroup$
I've been reading through "topological vector spaces" lately. I've realized some of the notation usually used resemble the definition of some morphological operators usually defined in image analysis.
Apart from stuff related to graph theory is there any application where actual concept of topology are used in image analysis?
general-topology soft-question image-processing
general-topology soft-question image-processing
asked Jan 15 at 9:42
user8469759user8469759
1,5681618
asked Jan 15 at 9:42
user8469759user8469759
1,5681618
asked Jan 15 at 9:42
user8469759user8469759
1,5681618
asked Jan 15 at 9:42
user8469759user8469759
1,5681618
asked Jan 15 at 9:42
user8469759user8469759
1,5681618
1,5681618
add a comment |
add a comment |
1 Answer
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Mean-curvature motion may modify the topology in 3D but not in 2D.
answered Jan 15 at 10:14
lightxbulblightxbulb
1,150311
$endgroup$
$begingroup$
What topology concepts are used here? How is the algorithm formulated? Also, please point out the references.
$endgroup$
– user8469759
Jan 15 at 10:16
$begingroup$
It's not really that concepts are used, it's more about the topological properties of the method (topologically connected objects remain such under MCM in 2D, not so in 3D). As far as the algorithm goes, you basically solve $partial_t u = |nabla u|div(frac{nabla u}{|nabla u|})$, for more details search mean curvature motion in image processing and refer to some of the papers. There's similarly continuous-scale morphology once again described by PDEs which obviously has some connection to topology.
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– lightxbulb
Jan 15 at 10:47
$begingroup$
That's not exactly what I had in mind. But I've just learned something new, thx.
$endgroup$
– user8469759
Jan 15 at 10:53
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
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active
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votes
1
$begingroup$
Mean-curvature motion may modify the topology in 3D but not in 2D.
answered Jan 15 at 10:14
lightxbulblightxbulb
1,150311
$endgroup$
$begingroup$
What topology concepts are used here? How is the algorithm formulated? Also, please point out the references.
$endgroup$
– user8469759
Jan 15 at 10:16
$begingroup$
It's not really that concepts are used, it's more about the topological properties of the method (topologically connected objects remain such under MCM in 2D, not so in 3D). As far as the algorithm goes, you basically solve $partial_t u = |nabla u|div(frac{nabla u}{|nabla u|})$, for more details search mean curvature motion in image processing and refer to some of the papers. There's similarly continuous-scale morphology once again described by PDEs which obviously has some connection to topology.
$endgroup$
– lightxbulb
Jan 15 at 10:47
$begingroup$
That's not exactly what I had in mind. But I've just learned something new, thx.
$endgroup$
– user8469759
Jan 15 at 10:53
add a comment |
1
$begingroup$
Mean-curvature motion may modify the topology in 3D but not in 2D.
answered Jan 15 at 10:14
lightxbulblightxbulb
1,150311
$endgroup$
$begingroup$
What topology concepts are used here? How is the algorithm formulated? Also, please point out the references.
$endgroup$
– user8469759
Jan 15 at 10:16
$begingroup$
It's not really that concepts are used, it's more about the topological properties of the method (topologically connected objects remain such under MCM in 2D, not so in 3D). As far as the algorithm goes, you basically solve $partial_t u = |nabla u|div(frac{nabla u}{|nabla u|})$, for more details search mean curvature motion in image processing and refer to some of the papers. There's similarly continuous-scale morphology once again described by PDEs which obviously has some connection to topology.
$endgroup$
– lightxbulb
Jan 15 at 10:47
$begingroup$
That's not exactly what I had in mind. But I've just learned something new, thx.
$endgroup$
– user8469759
Jan 15 at 10:53
add a comment |
1
1
1
$begingroup$
Mean-curvature motion may modify the topology in 3D but not in 2D.
answered Jan 15 at 10:14
lightxbulblightxbulb
1,150311
$endgroup$
Mean-curvature motion may modify the topology in 3D but not in 2D.
answered Jan 15 at 10:14
lightxbulblightxbulb
1,150311
answered Jan 15 at 10:14
lightxbulblightxbulb
1,150311
answered Jan 15 at 10:14
lightxbulblightxbulb
1,150311
answered Jan 15 at 10:14
lightxbulblightxbulb
1,150311
1,150311
$begingroup$
What topology concepts are used here? How is the algorithm formulated? Also, please point out the references.
$endgroup$
– user8469759
Jan 15 at 10:16
$begingroup$
It's not really that concepts are used, it's more about the topological properties of the method (topologically connected objects remain such under MCM in 2D, not so in 3D). As far as the algorithm goes, you basically solve $partial_t u = |nabla u|div(frac{nabla u}{|nabla u|})$, for more details search mean curvature motion in image processing and refer to some of the papers. There's similarly continuous-scale morphology once again described by PDEs which obviously has some connection to topology.
$endgroup$
– lightxbulb
Jan 15 at 10:47
$begingroup$
That's not exactly what I had in mind. But I've just learned something new, thx.
$endgroup$
– user8469759
Jan 15 at 10:53
add a comment |
$begingroup$
What topology concepts are used here? How is the algorithm formulated? Also, please point out the references.
$endgroup$
– user8469759
Jan 15 at 10:16
$begingroup$
It's not really that concepts are used, it's more about the topological properties of the method (topologically connected objects remain such under MCM in 2D, not so in 3D). As far as the algorithm goes, you basically solve $partial_t u = |nabla u|div(frac{nabla u}{|nabla u|})$, for more details search mean curvature motion in image processing and refer to some of the papers. There's similarly continuous-scale morphology once again described by PDEs which obviously has some connection to topology.
$endgroup$
– lightxbulb
Jan 15 at 10:47
$begingroup$
That's not exactly what I had in mind. But I've just learned something new, thx.
$endgroup$
– user8469759
Jan 15 at 10:53
$begingroup$
What topology concepts are used here? How is the algorithm formulated? Also, please point out the references.
$endgroup$
– user8469759
Jan 15 at 10:16
$begingroup$
What topology concepts are used here? How is the algorithm formulated? Also, please point out the references.
$endgroup$
– user8469759
Jan 15 at 10:16
$begingroup$
It's not really that concepts are used, it's more about the topological properties of the method (topologically connected objects remain such under MCM in 2D, not so in 3D). As far as the algorithm goes, you basically solve $partial_t u = |nabla u|div(frac{nabla u}{|nabla u|})$, for more details search mean curvature motion in image processing and refer to some of the papers. There's similarly continuous-scale morphology once again described by PDEs which obviously has some connection to topology.
$endgroup$
– lightxbulb
Jan 15 at 10:47
$begingroup$
It's not really that concepts are used, it's more about the topological properties of the method (topologically connected objects remain such under MCM in 2D, not so in 3D). As far as the algorithm goes, you basically solve $partial_t u = |nabla u|div(frac{nabla u}{|nabla u|})$, for more details search mean curvature motion in image processing and refer to some of the papers. There's similarly continuous-scale morphology once again described by PDEs which obviously has some connection to topology.
$endgroup$
– lightxbulb
Jan 15 at 10:47
$begingroup$
That's not exactly what I had in mind. But I've just learned something new, thx.
$endgroup$
– user8469759
Jan 15 at 10:53
$begingroup$
That's not exactly what I had in mind. But I've just learned something new, thx.
$endgroup$
– user8469759
Jan 15 at 10:53
add a comment |
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