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| title | tags | ||
|---|---|---|---|
| 10-3d-Cameras |
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CAMERAS AND PROJECTIONS
- Cameras project the 3D world onto a 2D image
- Input is 3D points: (𝑥, 𝑦, 𝑧)
- Output is 2D points: (𝑢, 𝑣)
- What form should P have?
[!INFO] need to apply a transformation to convert 3d coords to 2d coords P should be a 3 row and 4 column matrix
WHICH CUBE LOOKS RIGHT?
[!INFO] each cube is a projection of 3d points onto 2d space. middle cube is perspective transformation left is isometric right is orthographic
ORTHOGRAPHIC PROJECTION
- Simple way to go from 3D to 2D
- Delete one dimension!
- Deleting X projects to the X -Y plane
- This is not how our eyes work
[!INFO] z coordinate is removed since the third column is zero
PERSPECTIVE PROJECTION
- Our view of the world:
- Distant objects looks smaller
- Parallel lines in 3D converge in 2D
- The pinhole camera
- A simple, but useful, model
- There is a central point of projection (the pinhole, often a lens in reality)
- Light travels from the world, through the pinhole, to the image plane
[!INFO] need a hole that is big enough to get enough light but small enough to create a sharp image light goes through the hole to the image plane pin hole is also the "lens"
THE PINHOLE CAMERA MODEL
[!INFO] use negative of f as it is behind the pinhole find U using similar triangles rule
[!INFO] now we can project a point from 3d to 2d z is multiplies by 1 in the matrix so that the 3rd point of the homogenous coord becomes the z value
- We can put the image plane in front of the pinhole
- Removes the sign change
- Not practical for real cameras
- The maths works out just fine
[!INFO] cant really convert from 2d back to 3d without knowing focal length and z coord of every point
TRANSFORMING CAMERAS
INTRINSICS AND EXTRINSICS
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Often break this down into
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Most simple case:
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: camera calibration or intrinsics
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: camera pose or extrinsics