$2-$view special case: unknown yaw and horizontal translation Assume that a two$-$view config$-$

uration consists of two cameras with identical and known intrinsic parameters displaced as follows:

Xr $=$ RXl $+$ t where R $=$

$$

$$

cos $\backslash$beta $0$ sin $\backslash$beta

$010$

$$ sin $\backslash$beta $0$ cos $\backslash$beta

$$

$,$ t $=$ t cos $\backslash$alpha $0$ t sin $\backslash$alpha T $,(1)$

with t the magnitude of the translation, and Xr $,$ Xl position vectors of points wrt the right and left

camera coordinate system, respectively. Another way to think of this set$-$up is one camera moving in

the XZ$-$plane.

$1.$ Write the essential matrix E $($defined from the epipolar constraint xT

r Exl $=0)$

$2.$ How many points do I need in order to solve for the E$-$matrix using a homogeneous linear system?

$3.$ In this configuration, the two optical axes intersect the way that the human eyes converge.

Compute the coordinates $($Xl$,$ Zl$)$ of the intersection of the optical axes wrt the left coordinate

system.

$1$