Planar Scenes

Briefing Planar Lecture


This exercise builds on the Synthetic Experiment last week. You should complete that exercise first. When you have a working implementation of the Eight-Point Algorithm, you can continue with the Four-Point Algorithm for planar scenes.

Step 1.

Select four points situated in the same plane in 3D. For instance, consider \[(10,10,30),(-10,10,30),(10,-10,30),(-10,-10,30)\] Choose two camera frames and generate the four image points in each frame, as you did in the Synthetic Experiment.

Step 2.

Implement the four-point algorithm (Ma 2004:139:Alg 5.2), and recover the transformation \((R,T)\). Does this match the transformation you chose in Step 1? Remember that there are scalar factors that cannot be determined.

Step 3.

Using the transformation from Step 3 and the image point, reconstruct the 3D points.
Is your result consistent with the points chosen in Step 1?