[Solved] EECE5639 Computer Vision I Homework 4 Homographies

1. (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?
2. A template g is matched against an image f, both shown below:

f =g=

• Find the SSD between f and g .
• Find the Correlation between f and g .
• Find the Normalized Correlation between f and g

1