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Finding 3D coordinate when all 3 coordinates can vary in the object coordinate system

I have the 3D coordinates of 4 coplanar points of my target in the object coordinate system.I also have their the 2D coordinates in every frame of a video.I have also calculated the intrinsic parameters (M) for the camera, the R (rotation) and t (translation) matrices between the object coordinate system and the camera coordinate system using solvepnp(). I have read from here the complete process,which is very clear.It is also similar to the process I followed.Therefore I wanted to use the same equation

s [u v 1]T = M ( R [X Y Z]T + t)

for calculating my 3D coordinates but I have no constant as the link explains for calculating s.My target rotates about the x axis in the OpenCV coordinate system.My questions are -

  1. Can anyone suggest me a way to find s? Is it definitely mandatory for this calculation or can i use s=1?
  2. Is there any other methods for calculating the 3d point with what parameters I have?
click to hide/show revision 2
retagged

updated 2014-02-26 01:52:40 -0500

berak gravatar image

Finding 3D coordinate when all 3 coordinates can vary in the object coordinate system

I have the 3D coordinates of 4 coplanar points of my target in the object coordinate system.I also have their the 2D coordinates in every frame of a video.I have also calculated the intrinsic parameters (M) for the camera, the R (rotation) and t (translation) matrices between the object coordinate system and the camera coordinate system using solvepnp(). I have read from here the complete process,which is very clear.It is also similar to the process I followed.Therefore I wanted to use the same equation

s [u v 1]T = M ( R [X Y Z]T + t)

for calculating my 3D coordinates but I have no constant as the link explains for calculating s.My target rotates about the x axis in the OpenCV coordinate system.My questions are -

  1. Can anyone suggest me a way to find s? Is it definitely mandatory for this calculation or can i use s=1?
  2. Is there any other methods for calculating the 3d point with what parameters I have?
click to hide/show revision 3
retagged

updated 2014-02-26 01:53:33 -0500

berak gravatar image

Finding 3D coordinate when all 3 coordinates can vary in the object coordinate system

I have the 3D coordinates of 4 coplanar points of my target in the object coordinate system.I also have their the 2D coordinates in every frame of a video.I have also calculated the intrinsic parameters (M) for the camera, the R (rotation) and t (translation) matrices between the object coordinate system and the camera coordinate system using solvepnp(). I have read from here the complete process,which is very clear.It is also similar to the process I followed.Therefore I wanted to use the same equation

s [u v 1]T = M ( R [X Y Z]T + t)

for calculating my 3D coordinates but I have no constant as the link explains for calculating s.My target rotates about the x axis in the OpenCV coordinate system.My questions are -

  1. Can anyone suggest me a way to find s? Is it definitely mandatory for this calculation or can i use s=1?
  2. Is there any other methods for calculating the 3d point with what parameters I have?
click to hide/show revision 4
added the link which i referred

Finding 3D coordinate when all 3 coordinates can vary in the object coordinate system

I have the 3D coordinates of 4 coplanar points of my target in the object coordinate system.I also have their the 2D coordinates in every frame of a video.I have also calculated the intrinsic parameters (M) for the camera, the R (rotation) and t (translation) matrices between the object coordinate system and the camera coordinate system using solvepnp(). I have read from here here the complete process,which is very clear.It is also similar to the process I followed.Therefore I wanted to use the same equation

s [u v 1]T = M ( R [X Y Z]T + t)

for calculating my 3D coordinates but I have no constant as the link explains for calculating s.My target rotates about the x axis in the OpenCV coordinate system.My questions are -

  1. Can anyone suggest me a way to find s? Is it definitely mandatory for this calculation or can i use s=1?
  2. Is there any other methods for calculating the 3d point with what parameters I have?