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calibrateCamera

I followed the example in this tutorial: http://www.aishack.in/2010/07/calibrating-undistorting-with-opencv-in-c-oh-yeah/ ...and I got these results... image description ...where the middle image shows successful 3x7 corner detection but the corrected image on the right doesn't 'flatten' the image as expected.

One deviation from the tutorial: I only sampled the checker board once instead of multiple time. The image sampled is the image on the left. A post I found online suggested that too-few samples would result in calibration problems. I can, of course, post my values in the matrices updated by the calibrateCamera() call - I wanted to start with a short post.

Will a single sample work with calibrateCamera()?

A follow-on question: Could I do a similar remap using remap() with just a 3x7 matrix of points? The examples I found that use remap() appear to specify a matrix for ALL pixels to be remapped. I'd like to try a remap by specifying where I want the 3x7 matrix of points to appear. This would allow me to skip the calibrateCamera() call and use a more arbitrary remapping.