diff --git a/mr/ub6/UB6.pdf b/mr/ub6/UB6.pdf index 27f9c10..4836ac6 100644 --- a/mr/ub6/UB6.pdf +++ b/mr/ub6/UB6.pdf Binary files differ diff --git a/mr/ub6/UB6.tex b/mr/ub6/UB6.tex index 9d6f652..c4f58e3 100644 --- a/mr/ub6/UB6.tex +++ b/mr/ub6/UB6.tex @@ -207,26 +207,26 @@ \end{enumerate} \Aufgabe{Stereo Vision}{8} - \begin{enumerate} - \item As higher $d_{max}$ gets as smaller $z_b$ can be. It has no influnce on the highest observable $z_b$\\ - $z_{p,min}=\frac{f\cdot b}{d_{max}}=\frac{512px\cdot10cm}{64px}=80cm$ + \begin{enumerate}[(a)] + \item As $d_{max}$ increases $z_b$ decreases. So $d_{max}$ sets a lower bound. For $d$ appoaching 0 $z_b$ goes to infinity, so there is no upper bound set by setting $d_{max}$\\ + $z_{p,min}=\frac{f\cdot b}{d_{max}}=\frac{512px\cdot10cm}{64px}=\frac{2^9}{2^6}\cdot10cm=80cm$ \item $ d \sim N(d_{true},\sigma_d)$\\ $z_{p}(d)=\frac{f\cdot b}{d}$\\ TaylorApprox:\\$z_p(d)=z(d_{true})+z'(d_{true})(d-d_{true})=\frac{f\cdot b}{d_{true}}- \frac{f\cdot b}{d_{true}^2}(d-d_{true})= \frac{2f\cdot b}{d_{true}}-\frac{f\cdot b}{d_{true}^2}\cdot d\\ - \sigma_z= a\cdot\sigma_d\cdot a = a^2\cdot \sigma_d = - \frac{f^2\cdot b^2\cdot \sigma_d}{d_{true}^4}= - \frac{f^2\cdot b^2\cdot \sigma_d}{\frac{f^4\cdot b^4}{z_p^4}}= \frac{z_p^4}{f^2\cdot b^2}\sigma_d \\ - $schneller: $\sigma = f'(a)^2\cdot \sigma_{alt} + \sigma_z= |A|\cdot \sigma_d = \frac{f\cdot b}{d_{true}^2}\cdot \sigma_d= \frac{f\cdot b}{\frac{f^2\cdot b^2}{z_p^2}}\cdot \sigma_d= \frac{z_p^2}{f\cdot b}\sigma_d \\ + $schneller: $\sigma = |f'(a)|\cdot \sigma_{alt} $ - \item siehe b) + \item see b) \item $f=512px \\ b=5cm\\ - o_d=0.5cm\\ - z_p=5m\\ - \sigma_z= \frac{5^4}{512^2\cdot5^2}\cdot 0.5=\frac{5^2}{512^2\cdot 2}=0.0000477=4.77*10^{-5}cm + \sigma_d=0.5px\\ + z_p=500cm\\ + \sigma_z= \frac{500^2}{512\cdot5}\cdot 0.5=\frac{500^2}{512\cdot 2}\approx 244.1cm $ - \item $o_{z}=5\\ - b=\sqrt{\frac{z_p^4}{f^2\cdot o_z}\sigma_d} = \sqrt{\dfrac{5^3}{512^2\cdot2}}= 0.0154 cm - $ + \item $\sigma_{z}=5cm\\ + b=\frac{z_p^2}{f\cdot o_z}\sigma_d= \frac{500^2}{512\cdot5}\cdot \sigma_d= 97.65625\frac{cm}{px}\cdot\sigma_d$\\ + for $\sigma_d=0.5px:\ b=97.65625\frac{cm}{px}\cdot 0.5px=48.828125cm$ \end{enumerate} \end{document}