1. User Interface Engineering Exercise Class 2 Camera Calibration, Undistortion, and Image Dilation.
Instructor: Otmar Hilliges
TA’s: Tobias Nageli, Liu Zhiyong, Karthik Sheshadri
Broken down table process into 4 hws, this deals with image formation. Allows obtain clean signal.

2. Overview Perspective projection based on the pinhole model
Camera Calibration
Lens Distortion and Correction
Morphological Operations (Erosion & Dilation)

3. Image Formation
Basic image model, pinhole camera, simplify the problem into two rays at extremes.

4. Perspective Projection: The Pinhole Model
The image plane π in an actual camera is at a distance of f behind the center of projection and the projected image is inverted. However we can assume that the image plane is in front of the center of projection to avoid this inversion
he line through the center of projection (i.e., optical center) c
o and perpendicular to the image plane π is the optical axis. The 3D point c
x is projected onto n
x through the optical center c
(Perspective Division)

5. Image Formation: Optics can cause issues

6. Image Formation
1 𝑓 = 1 𝑧 + 1 𝑒

7. Image Formation

8. Lens Distortion
Assume Staright lines in real world project to straight lines in image. Most lenses radial distortion, manifests as a curvature in the projection of straight lines.

9. Perspective Projection: The Pinhole Model
The Pinhole Model equations in homogeneous co-ordinates
Say that this eqn is a projection from the 3D world cords to image plane and uses the focal length of the camera .

10. Perspective Projection: The Pinhole Model
The displacements from the optical center need to be put in pixel co-ordinates.

11. Perspective Projection: The Pinhole Model
Xp -> normalized 0 to 1 space

12. Perspective Projection: The Pinhole Model
(Camera Intrinsics)

13. Perspective Projection: The Pinhole Model
(Camera Extrinsics)

14. Perspective Projection: The Pinhole Model

15. Perspective Projection: The Pinhole Model

16. Lens Distortion

17. Lens Distortion 𝑢 𝑑 𝑣 𝑑 = 1+ 𝑘 1 𝑟 2 𝑢− 𝑢 0 𝑣− 𝑣 0 + 𝑢 0 𝑣 0 ,
𝑢 𝑑 𝑣 𝑑 = 1+ 𝑘 1 𝑟 2 𝑢− 𝑢 0 𝑣− 𝑣 𝑢 0 𝑣 0 ,
With 𝑟 2 = 𝑢− 𝑢 𝑣− 𝑣 0 2

18. OpenCV Tutorial
Online tutorial: mera_calibration.html

19. Calibration procedure
Practical tips and tricks
Place your camera such that most of the image is covered by the checkerboard
Use varying orientations and distances for the views
Screenshots

20. Deliverables Send your calibration intrinsics
Send in the estimated distortion coefficients
Record a video of your undistorted images
Engineering/

21. Morphological Operations
Size of s determines extent of ero/dil .
Ero -> keep

22. Morphological Operations
Absolute Image Differences for Motion Segmentation

23. Morphological Operations

24. Morphological Operations