- (Old exam problem) The planar facade of a building is captured in an image taken by a camera. Assume this pane corresponds to the world coordinate frames Z = 0 plane, and scene point (X,Y ) on the building projects to image pixel coordinates (u,v).
- What is the planar projective transformation that describes the relationship between (X,Y ) and (u,v)? Give your answer using homogeneous coordinates.
- How many degrees of freedom does this transformation have?
- How many point correspondences are required to determine this transformation?
- Would having more correspondences that your answer above be helpful in any way? If no, brieflyexplain why not. If yes, explain how they could be used.
- Give one invariant of a planar projective transformation.
- Give one invariant of a planar affine transformation that is not an invariant for a planar projectivetransformation.
- If the building has sets of lines on it running parallel to both the X and Y axes, how could we use the corresponding lines in the image to determine if the building plane is parallel to the image plane?
- A template g is matched against an image f, both shown below:
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 2 | 4 | 2 | 0 | 0 | 0 | 0 |
| 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 0 | 0 | 0 | 2 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 |
| 1 | 2 | 1 | 0 | 0 | 2 | 4 | 2 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 2 | 1 |
| 0 | 1 | 0 |
| 0 | 1 | 0 |
f =g=
- Find the SSD between f and g .
- Find the Correlation between f and g .
- Find the Normalized Correlation between f and g
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