getting mean curvature with normal vector mapN(x,y,3)

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To be honest, it is a question for computer vision.
There is a normal vector map N(x,y,3) represents the normal vector(nx,ny,nz) on the point P(x,y). If the resolution is high enough(2448x2048), can we get the approximate mean curvature by this normal vector map?



I found a proof about the relationship between normal vector and curvature,
it says div(N)=K1+K2
http://willson.cm.utexas.edu/Research/Sub_Files/Surface_Phenomena/Spring%202000/surface_normal_proof.pdf
it is easy to get the part of x and y, but not z since there is no z coordinate.







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  • Is this a question about mathematics?
    – Taroccoesbrocco
    Aug 22 at 6:10










  • ya,it is about how to get the mean curvature
    – å®‹å²³ç©Ž
    Aug 22 at 6:56














up vote
0
down vote

favorite












To be honest, it is a question for computer vision.
There is a normal vector map N(x,y,3) represents the normal vector(nx,ny,nz) on the point P(x,y). If the resolution is high enough(2448x2048), can we get the approximate mean curvature by this normal vector map?



I found a proof about the relationship between normal vector and curvature,
it says div(N)=K1+K2
http://willson.cm.utexas.edu/Research/Sub_Files/Surface_Phenomena/Spring%202000/surface_normal_proof.pdf
it is easy to get the part of x and y, but not z since there is no z coordinate.







share|cite|improve this question




















  • Is this a question about mathematics?
    – Taroccoesbrocco
    Aug 22 at 6:10










  • ya,it is about how to get the mean curvature
    – å®‹å²³ç©Ž
    Aug 22 at 6:56












up vote
0
down vote

favorite









up vote
0
down vote

favorite











To be honest, it is a question for computer vision.
There is a normal vector map N(x,y,3) represents the normal vector(nx,ny,nz) on the point P(x,y). If the resolution is high enough(2448x2048), can we get the approximate mean curvature by this normal vector map?



I found a proof about the relationship between normal vector and curvature,
it says div(N)=K1+K2
http://willson.cm.utexas.edu/Research/Sub_Files/Surface_Phenomena/Spring%202000/surface_normal_proof.pdf
it is easy to get the part of x and y, but not z since there is no z coordinate.







share|cite|improve this question












To be honest, it is a question for computer vision.
There is a normal vector map N(x,y,3) represents the normal vector(nx,ny,nz) on the point P(x,y). If the resolution is high enough(2448x2048), can we get the approximate mean curvature by this normal vector map?



I found a proof about the relationship between normal vector and curvature,
it says div(N)=K1+K2
http://willson.cm.utexas.edu/Research/Sub_Files/Surface_Phenomena/Spring%202000/surface_normal_proof.pdf
it is easy to get the part of x and y, but not z since there is no z coordinate.









share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 22 at 5:36









宋岳穎

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  • Is this a question about mathematics?
    – Taroccoesbrocco
    Aug 22 at 6:10










  • ya,it is about how to get the mean curvature
    – å®‹å²³ç©Ž
    Aug 22 at 6:56
















  • Is this a question about mathematics?
    – Taroccoesbrocco
    Aug 22 at 6:10










  • ya,it is about how to get the mean curvature
    – å®‹å²³ç©Ž
    Aug 22 at 6:56















Is this a question about mathematics?
– Taroccoesbrocco
Aug 22 at 6:10




Is this a question about mathematics?
– Taroccoesbrocco
Aug 22 at 6:10












ya,it is about how to get the mean curvature
– å®‹å²³ç©Ž
Aug 22 at 6:56




ya,it is about how to get the mean curvature
– å®‹å²³ç©Ž
Aug 22 at 6:56















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