# Planar Scenes

**Briefing** Planar Lecture

# Exercises

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?