Questions:

1.  Show that, in the pinhole camera model,  three collinear points in 3D space are imaged into three collinear points on the image plane.

2.  Use the perspective projection equations to explain why, in a picture of a face taken frontally and from a very small distance, the nose appears much larger than the rest of the face.  Can this effect be reduced by acting on the focal length?

3.  Given the equation of a straight line in 3D, write the equation of its image (it is a straight line).

4.  Given two parallel lines in 3D, e.g., sides of a road, determine the intersection of their straight line images.