---
title: 3D Reconstruction (continuing Eight-point algorithm)
categories: session
---

**Briefing** [Eight-point algorithm Lecture]()

**Additional Reading**
Chapter 9 in  *OpenCV 3 Computer Vision with Python Cookbook* by
Alexey Spizhevoy (author).
Search for it in [Oria](https://oria.no/).
There is an e-book available.

**Learning Outcome**
See how the eight-point algorithm can be fitted into a complete
system to do 3D reconstruction from a real stereo view.

# Exercises

In this exercise, we shall try to determine the relative pose
of two cameras, using the eight-point algorithm (or a variant thereof).

## Step 1.  Make a Data Set

1.  Take two images of the same scene, using different camera poses.
    - the difference between the poses should be significant,
      but small enough to recognise the same feature points.
    - i.e. two consecutive frames from a video will probably be too similar.
2.  Use SIFT (or similar) to find and match at least eight feature pairs
    in the two images
    - if you do not find eight, you need to use more similar poses.

**Note 1**
It may be useful to calibrate the camera(s) and undistort the
images before starting.  It is ok to try without calibration first,
for the sake of simplicity.

**Note 2**
you should validate the feature matching visually first,
to make sure that an error here does not spoil the continuation.

## Step 2.  Eight-Point Algorithm

Use the [Eight-point algorithm]() from the previous exercise (Part 2)
to recover the relative pose $(R,T)$ between the cameras.

Does the transformation $(R,T)$ seem reasonable?  
What does it mean in terms of rotation and translation in the
real world space?

## Step 3.  3D Reconstruction

Calculate 3D co-ordinates in the global frame for each of the features
from Step 1.  Do the co-ordinates seem reasonable?

## Step 4.  (Optional)  Visualisation

Visualise the reconstructed points in 3D, using for instance
`matplotlib` in python.

## Step 5.  (Optional)  Automatic Matching

Extend your system to use SIFT to automatically match features
in Step 1.

# Debrief

This example is under construction, and there is a problem
with the recovery of the relative pose.  It does, however,
exemplify the broad structure of a solution;

+ [Jupyter Notebook](Python/Triangulation.ipynb) which depends
  on two images: [Python/frame1glasses1.png]() and
  [Python/frame2glasses1.png]()