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# Real World Reconstruction

**Briefing** Real World Lecture

**Additional Reading** [Cookbook] Chapter 9 in *OpenCV 3 Computer Vision with Python Cookbook* by Alexey Spizhevoy (author). Search for it in Oria. There is an e-book available.

# Exercises

To goal for the last exercise is to test a more complete system for 3D reconstruction, using OpenCV.

The Cookbook by Alexey Spizhevoy is a useful starting point, using selected recipes from Chapter 9.

You can choose if you want to record you own data, using external webcams, or use the dataset from the cookbook. If you want to use external cameras, you may have to collaborate and share, but then group work is a good idea in any event.

## Using the cookbook

- Many recipes load image data, which are available on github
- Many recipes load data saved in previous recipes
- the save instruction is not shown in the book
- included in the complete code on github

- When you use the recipe, you should always ask yourself,
*what does the code do?* - If there is code you do not understand, you should ask.

## Stereo Calibration.

Recipe p 240ff in the cookbook: *Stereo rig calibration*

Many features of this recipe should be known from our previous Camera Calibration exercise.

- Test the recipe with your choice of data.
- What do the various output mean?
- Match the calculations in the recipe to the textbook theory.

## The Fundamental Matrix.

Recipe p 257ff in the cookbook: *Epipolar Geometry*

Note that this recipe does not solve the general problem of recovering the fundamental and/or essential matrices. It actually depends on the calibration matrix from *Stereo rig calibration* (above), and it chessboard points, making the problem planar.

- Test the recipe with your choice of data.
- We already had the fundamental and essential matrices from
*Stereo rig calibration*(above). Do the new calculations match the previous ones?

## Recovering Rotation and Translation

Recipe p 259ff in the cookbook: *Essential matrix decomposition*

- Test the recipe with your choice of data.
- Find the axis and angle of rotation for each of the two candidate rotation matrices. You can use the logarithm as described in Theorem 2.8 in the text book.
- Which of the two rotation matrices is correct? Try to answer this by visual inspection of the images.

## Triangulation

Recipe p 250f in the cookbook: *Restoring a 3D point*

Note that the recipe uses synthetic data.

- Test the recipe with your choice of data.
- How is the relative pose of the cameras defined in the recipe?

## Triangulation of Real Data

There seems not be be a recipe for triangulation in real data, but we can try to make one based on all the recipes tested so far.

### Step 1. Dataset

- Make a stereo camera, i.e. a fixed positioning of two cameras. Make sure to keep it fixed throughout data collection.
- Use a chessboard to make a set of images for calibration.
- Find some objects with a lot of corners and take images of each one with your stereo setup.

It is a good idea to take more images than you think you need, as it may be difficult to keep the camera setup fixed as you fiddle with the programming.

### Step 2. Relative Pose

Obtain the relative pose \((R,T)\) of the two cameras by repeating the recipes up until the recovery of rotation and translation.

### Step 3. Corner Detection

Use the Harris Corner Detector to find corners in the the object images. (You can do it in the chessboard images, but that is less interesting.)

If you have time, you can use SIFT to match image pairs. If you don’t, please match them manually.

### Step 4. 3D Reconstruction

Here, we use the `cv2.triangulatePoints`

as in the previous triangulation recipe. The challenge is to define the projection matrices, `P1`

and `P2`

, for our specific stereo camera.

- Recall that the projection is typically given as \(\Pi=K\Pi_0g\), where
- \(K\) is the intrinsic camera matrix
- \(\Pi_0\) is the basic projection, constructed with the
`np.eye`

function - \(g=[R,T]\) is the relative pose of the cameras.

- In the
*Stereo Calibration*, you have found \(K\) for each camera, i.e.`Kl`

and`Kr`

- If we select the first camera frame as world frame,
- the first camera has \(g={I,0]\)
- the first camera has \(g=[R,T]\) given by the relative pose of the cameras, as calculated in the previous recipe

Constructing the two \(\Pi\) matrices, you can recover the 3D points as in the previous Triangulation recipe.

### Step 5. Visualisation

Take all the 3D points from the previous step and plot them using matplotlib. Does it look correct?

Note that we have not had time to use edge information to reconstruct the 3D scene, and this makes the reconstruction rather rudimentary. It is a good start, though.

### Step 6. Reflection and Summary

Review this last exercise, and discuss,

- What assumption have been necessary in the work?
- What data do you require to do 3D reconstruction in this way?
- To what extent is the recipe relevant to real life?
- i.e. what kind of problems can and can’t you solve this way?