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As mentioned, we assume that we have a fully calibrated camera, which all intrinsic and extrinsic parameters known, as well as known distances od all the points.

Assuming for a point (100,100,500), how can we calculate the position of the point if it were to have a distance of 1000?

Converting from image point to 3d world coordinate point is something I have already implemented, I am interested on how to find the image / 3d world coordinate point of point if its depth wasn't 500, but 1000, the collinear of the initial point for a specific depth.

Konstantine
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  • have a look at this: https://stackoverflow.com/questions/31265245/extracting-3d-coordinates-given-2d-image-points-depth-map-and-camera-calibratio/31266627#31266627 to compute the global coordinates you'll have to transform with camera ectrinsics, too. – Micka Nov 10 '18 at 09:29
  • I improved my question a bit. Converting from image points to 3d world coordinate point is not an issue. What I need is to find those coordinates for the collinear of the said in a different depth, in either image or 3d worlds coordinates. – Konstantine Nov 10 '18 at 10:38
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    simplest code would be to just replace the depth=500 to depth=1000 and run the "reconstruction" again. However you could instead construct the ray from camera projection center through the 3D point and parametrize this line for a unit and evaluate that line-ewuation for multiple depth values. – Micka Nov 10 '18 at 12:30
  • e.g. direction=(point3d - camera_center)/depth and then: newPoint1000 = camera_center + 1000*direction – Micka Nov 10 '18 at 12:33
  • Is the camera center actually the translation matrix? – Konstantine Nov 10 '18 at 12:39
  • I think so, but I'm not totally sure, sorry. – Micka Nov 10 '18 at 13:41
  • transforming point (0,0) (or any other point) and depth 0 should be the projection center, so should be the translation? You should verify that 3 different depths for one pixel coordinate should transform to collinear points! – Micka Nov 10 '18 at 13:51

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