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← 16-02 Image Formation

Unit 16 02 Image Formation.mp4

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Showing Revision 1 created 11/28/2012 by Amara Bot.

  1. [Thrun] The science of how images are created using cameras is called image formation,
  2. where formation just means the way an image is being captured.
  3. Perhaps the easiest model of a camera is called a pinhole camera.
  4. In a pinhole camera, the light from within the world
  5. goes through a various small hole--ideally it's a really, really small hole--
  6. to project into a camera chip that sits somewhere in the background.
  7. So for example, if you had an object that was a person over here,
  8. then this person would be projected as follows.
  9. The feet would be projected to over here and the head to over here,
  10. which gives us this inverted person on the projection plane or the camera chip.
  11. There is some very basic math that governs the geometry of a pinhole camera.
  12. If we call X the physical height of the object and small x the height of the projection,
  13. which I'll call -x because it points in the opposite direction as the original object,
  14. then we can also talk about other values
  15. such as the distance of the object to the camera plane
  16. and f, which is the focal distance of the camera,
  17. which is the distance between the pinhole and the projection plane over here.
  18. There's a simple piece of math that relates all of those 4 variables over here,
  19. and it's easily obtained by what's called equal triangles.
  20. In particular, it turns out if I map this triangle over here to right over here--
  21. so these are the same triangles, just flipped, where x is over here and f is over here--
  22. we get that the ratio of upper caps X to Z is the same as lower caps x to f.
  23. So I write this as follows.
  24. This is a result of equal triangles.
  25. So as you take a triangle of a certain shape,
  26. when you scale it up to larger triangles, those proportions are retained,
  27. so therefore, upper caps X divided by Z is the same as lower caps x divided by f.
  28. If we now transform this, I find that the projection of lower caps x,
  29. which I might care about, is upper caps X, the physical size of the object itself,
  30. times the quotient of the focal length over the distance.
  31. That's an interesting equation.
  32. The further an object is away, the smaller it appears.
  33. The larger the focal length of the camera, the larger the object in its projection.
  34. And of course the size of the object itself directly influences
  35. how big its image of the object really is.
  36. So let's see if you can practice that equation using a quiz.