Question $1$

Consider a camera which is located at $(0,0,0)$ in an arbitrary coordinate system and it is facing in the direction $(0,0,1)$; it captures an image I$1$ of the scene. Now consider that the camera position has been translated but its orientation remains the same. In its new position, the camera takes an image I$2$ of the scene. The camera translation is given by $(5,0,0).$

$($a$)$ Explain why points closer to the camera appear to move faster than those further away.

$($b$)$ Sketch the epipolar lines in I$1$ that correspond to features in I$2$ and label the location of the epipole in I$1.$

$($c$)$ Explain what is the projective interpretation of $\backslash$times $,$ the cross product of the epipole on the right camera and a point $$ on the image plane of the right camera.

$($d$)$ Describe how the structure of the scene determines the epipolar geometry.