---
title: Planar Scenes
categories: session
---

**Briefing** [Planar Lecture]()

# Exercises

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 [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?