COMP322/S2000/L211 Relationship between part, camera, and robot For any object (part) on a robot pick up table, any point on the part can be given in three forms: l w.r.t. the robot base, P base (3D) l w.r.t. the camera, P camera, (3D) l image of P, P image,(2D) Objective is to relate P base, P camera, and P image. Consider P camera and P image first: (Diagrams are given in class) Let f be the focal length of the camera; P image is a projection of P camera through the lens of the camera, By similar triangles, we can relate

COMP322/S2000/L212 Relationship between part, and camera or

COMP322/S2000/L213 Relationship between part, and camera Note: l Negative sign indicates image is inverted l Object is in front of the camera, i.e. l Another point Q camera lying on the line joining P image, P camera will have the same image => P camera to P image is a many-to-one mapping l P camera to P image is a non-linear transformation, i.e. perspective transform about the z-axis,

COMP322/S2000/L214 Relationship between part, and camera One can show that

COMP322/S2000/L215 Relationship between part, and camera Usually, by image processing techniques, P image can be computed. Need to know P camera or P base for the robot to pick up the part. We have we need but does not exist.

COMP322/S2000/L216 Relationship between part, and camera Inverse Perspective Transformation, Geometrically, ==> andcan be computed; f is known, ==> is the determining factor.

COMP322/S2000/L217 Relationship between part, and camera Another point Q camera producing the same image can also be computed by ==> againis the determining factor. Let denoteand,i.e. The distance along the z- axis of the part from the camera.

COMP322/S2000/L218 Relationship between part, and camera It has been found that Verification:

COMP322/S2000/L219 Relationship between part, camera, and robot Recall: And in this case, An example is given in class.