Briefing Distorted Lecture

Additional Reading 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

An Example of a Distorted spaceo

Step 1. Preliminaries.

1. Consider a triangle in the object space, formed by the three vertices, \(A=(0,0,10)\), \(B=(20,0,10)\), and \((20,10,10)\).
   Let
   • \(\alpha\) be the angle between the vectors \(\widevec{AB}\) and \(\widevec{AC}\).
   • \(\beta\) be the angle between the vectors \(\widevec{BA}\) and \(\widevec{BC}\). Draw a figure to show this information.
2. Calculate the angle \(\alpha\).
3. Consider an ideal perspective camera, posed such that the camera frame matches the world frame. Calculate the image points corresponding to \(A\), \(B\), and \(C\). Draw an image to display this projection.
4. Calculate the angles in the images of \(\alpha\) and \(\beta\). Do they match the original angles?
5. Calculate the lengths of the edges of the triangles in the image.
6. Make a new drawing to display the quantities calculated in 4 and 5. Keep it for later reference.

Step 2. Distortion.

7. Suppose the camera is not idea, but instead has calibration matrix \[K = \begin{bmatrix} 2 & \frac1{\sqrt{3}} & 4 \\ 0 & 1 & 4 \\ 0 & 0 & 1 \end{bmatrix}\]
8. Calculate the image points corresponding to \(A\), \(B\), and \(C\), using the camera calibration matrix \(K\). Draw the resulting image to scale.
9. Calculate the lengths of the edges of the image of the triangle.
10. Let \(\alpha'\) and \(\beta'\) be the images of the angles \(\alpha\) and \(\beta\). Calculate these to image angles and add the information to you figure.
11. Compare your distorted image to the original image from Step 1.

Step 3. The Distorted Inner Product Space

From the Textbook

• Exercise 6.4

Debrief