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---
title: Planar Scenes
categories: session
---
**Briefing** [Planar Lecture]()
# Exercises
This exercise builds on the [Synthetic Experiment]() last week.
This exercise builds on the previous exercises on
the [Eight-point algorithm]().
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]().
the [Eight-point algorithm]().
## 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?
## Extra exercise
+ Exercise 5.14
