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I gone through some similar post for this problem like this,

@RafazZ

OpenCV unproject 2D points to 3D with known depth `Z`

2D Coordinate to 3D world coordinate

as doing 2d to 3d conversion in camera_frame they have removed R,T matrix from calculation and only using like this,

x = (u-cx)/fx
y= (v-cy)/fy

actual (X,Y,Z)
X= x * depth.at(u,v)
Y= y * depth.at(u,v)
Z = depth.at(u,v)

so, I want to understand why we can remove R,t from calculation like this when doing 2d-->3d in camera_frame?

user22120
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    As you mentioned this calculation in camera frame. This position relative to camera. If you wanna move to world coordinate space, you need to multiply by R and do offset by t. – Gralex Jul 11 '19 at 10:26
  • @Gralex my camera is attached to robot arm. I know transformation to camera_frame to tool_frame and then to robot base using URDF in ROS. so I can give this X,Y,Z value to tool for moving at that position without R,t. is this correct? also camera looking at that point from any angle without being parallel to object(where point is) plane? – user22120 Jul 11 '19 at 11:12
  • @Gralex will it work regardless of camera orientation, I mean camera looking to that point at any angles? – user22120 Jul 16 '19 at 09:41
  • This point will be relative to camera. So if your robot require position relative to camera it's ok. But if relative to robot base, you will need multiply this point to transform matrix from camera to robot base. – Gralex Jul 16 '19 at 11:23
  • @Gralex I can transfer this point to robot base using URDF in ROS. but I still have confusion why people are talking about using R,t matrix(in above equation) when getting 2d->3d w.r.t camera? – user22120 Jul 16 '19 at 11:30
  • To calculate position relative to some origin. – Gralex Jul 16 '19 at 11:31
  • so, I am getting this 3d coordinate w.r.t camera and with R,t we can transfer this information to any point in space (in my case origin is robot base)? – user22120 Jul 16 '19 at 11:37
  • Yes, you are right – Gralex Jul 16 '19 at 12:02

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