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camerarotational-matricespose-estimationopencv-solvepnp

pose estimation: determine whether rotation and transmation matrix are right

Recently I'm struggling with a pose estimation problem with a single camera. I have some 3D points and the corresponding 2D points on the image. Then I use solvePnP to get the rotation and translation vectors. The problem is, how can I determine whether the vectors are right results?

Now I use an indirect way to do this:
I use the rotation matrix, the translation vector and the world 3D coordinates of a certain point to obtain the coordinates of that point in Camera system. Then all I have to do is to determine whether the coordinates are reasonable. I think I know the directions of x, y and z axes of Camera system.

  • Is Camera center the origin of the Camera system?
  • Now consider the x component of that point. Is x equavalent to the distance of the camera and the point in the world space in Camera's x-axis direction (the sign can then be determined by the point is placed on which side of the camera)?

The figure below is in world space, while the axes depicted are in Camera system.

========How Camera and the point be placed in the world space=============
   |
   |              
Camera--------------------------> Z axis
   |                |} Xw?
   |                P(Xw, Yw, Zw)
   |              
   v x-axis

Picture here

My rvec and tvec results seems right and wrong. For a specified point, the z value seems reasonable, I mean, if this point is about one meter away from the camera in the z direction, then the z value is about 1. But for x and y, according to the location of the point I think x and y should be positive but they are negative. What's more, the pattern detected in the original image is like this:

pattern image using feature detection from the camera captured image

But using the points coordinates calculated in Camera system and the camera intrinsic parameters, I get an image like this:

recovered image

The target keeps its pattern. But it moved from bottom right to top left. I cannot understand why.

Solution

  • Now I know the answers.

    • Yes, the camera center is the origin of the camera coordinate system.

    • Consider that the coordinates in the camera system are calculated as (xc,yc,zc). Then xc should be the distance between the camera and the point in real world in the x direction.

    Next, how to determine whether the output matrices are right?
    1. as @eidelen points out, backprojection error is one indicative measure.
    2. Calculate the coordinates of the points according to their coordinates in the world coordinate system and the matrices.

    So why did I get a wrong result(the pattern remained but moved to a different region of the image)?
    Parameter cameraMatrix in solvePnP() is a matrix supplying the parameters of the camera's external parameters. In camera matrix, you should use width/2 and height/2 for cx and cy. While I use width and height of the image size. I think that caused the error. After I corrected that and re-calibrated the camera, everything seems fine.