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2015-08-18 10:36:21 -0600	answered a question	Can i get 2d world coordinates from a single image ([u,v] coords)? Thanks for the answer! Very helpuful. Sorry I took a long time to post how I solved my problem. I ended up using some of your equations and an additional one. From the camera intrinsic parameters I obtained: fx, fy, cx, and cy. From previous measurements I have the [object points] and their correspondent [image points] (used in solvePnP). I obtained the [image points] with 'mouse callback' function. 'Rodrigues' function gets me the Rotation Matrix with the 'rvec' from 'solvePnP'. 'HoughCircles' gives me the [u,v] of the hole center I'm identifying. Converted the 2D image coordinate of the hole in the normalized camera frame. [x', y', 1] (above equation) I made the scale factor 's' the distance from the surface to the camera sensor. Multiply 's' by the normalize camera sensor. (equation above). Finally, I use this equation to transfom the 3D coordinate in camera frame to my world frame. 'R^T' is the transposed rotation matrix and 't' is tvec. Results where pretty accurate. I've changed some things since then and I don't remember the correct tolerance but it was better than I expected. I think a different lens might help to, mine has a fish eye distortion and even the 'undistort' function doesn't fix it completely. The edges are no good. Thanks again.
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2015-07-24 13:23:08 -0600	asked a question	Can i get 2d world coordinates from a single image ([u,v] coords)? I'm new to everything vision! I've read some similar posts but I can't get my head around it. Here's what I'm trying to do: -I have a single camera looking down on a surface (we can assume it's normal to the surface) and I want to detect a hole and obtain it's [X,Y] from a world coordinate I have determined. -I do not care about the -Z info, I know the real hole diameter. I have calibrated my camera and have the intrinsic matrix. For the extrinsic info I have taken 4 points from my image(mouse callback) and their correspondent 4-real points from the world coordinate to use 'solvePnP' and 'Rodrigues'(for the rotation matrix). I can detect the hole using HoughCircles and I have the center in [u,v] coords. Now, is there a way to obtain that [u,v] point in [X,Y] in my defined coordinate system???