如何使用MATLAB将2D（x，y）坐标转换为3D（x，y，z）坐标？

Question

I am trying to automate an robotic arm using MATLAB. So the thing is, camera will be mounted on the base of robotic arm. It will capture the snapshots of the camera frames and do image processing on it and it will detect the target(object) and find the pixel coordinate for it. After it is done, this pixel coordinates should be mapped to real world xyz metric coordinates? and this real world coordinates(x,y,z) would serve as parameters for inverse kinematics function which would give the value of theta so that servos can move.

I'm stuck here, this pixel coordinates should be mapped to real world xyz metric coordinates? i dont know how to do it. nor getting any ideas, how to proceed it? Anyone having any lead, please share it!!

PS anyone of you guyz thinks that for automation of robotic arm should i use MATLAB or something else?. Coz this all code would be uploaded on raspberry pi 3 using ROS environment.

BEST REGARDS

hitesh kumar

Answer 1

To calculate 3D world point for the given pixel in an image, you need depth information (should use 3D camera like Kinect ..etc). One you have depth information and camera intrinsics and extrinsics you can convert 2D pixels to 3D world coordinates and vice versa.

Below equation for calcualting X,Y,Z in world coordinates.

Technically Perspective projection is what camera does in converting 3D world to 2D and below equation represents this projection.

Above image is from here