diff --git a/ea/Ub5/A1.png b/ea/Ub5/A1.png new file mode 100644 index 0000000..1e346b9 --- /dev/null +++ b/ea/Ub5/A1.png Binary files differ diff --git a/ea/Ub5/A1c.png.png b/ea/Ub5/A1c.png.png new file mode 100644 index 0000000..b43eef6 --- /dev/null +++ b/ea/Ub5/A1c.png.png Binary files differ diff --git a/mr/Ub5/UB5.pdf b/mr/Ub5/UB5.pdf index 5e26d6f..2401275 100644 --- a/mr/Ub5/UB5.pdf +++ b/mr/Ub5/UB5.pdf Binary files differ diff --git a/mr/Ub5/UB5.tex b/mr/Ub5/UB5.tex index a056126..afe7d7f 100644 --- a/mr/Ub5/UB5.tex +++ b/mr/Ub5/UB5.tex @@ -96,8 +96,39 @@ \item Principle point: 304.55702, 336.54883 \item distortion: -0.19833, 0.30243, 0.01975, -0.00276, 0.00000 \item Pixel error: 0.95118, 0.87892 + \item The pixel error ist the standard deviation of the reprojection error in x- and y-Direction \end{itemize} - \item The pixel error ist the standard deviation of the reprojection error in x- and y-Direction + %TODO \end{enumerate} + \Aufgabe{}{10} + \begin{enumerate}[(a)] + \item $n=\begin{pmatrix} + \frac{u-u_0}{k_u}\\ + \frac{v-v_0}{k_v}\\ + 1 + \end{pmatrix}$ + \item $n_c\approx\begin{pmatrix} + 0.236\\0.255\\1 + \end{pmatrix},\ n_b\approx\begin{pmatrix} + 0.245\\0.258\\1 + \end{pmatrix}$ + \item $\alpha =\tan^{-1}\left(d(n_c,n_b)\right)\approx\tan^{-1}\left(\sqrt{\left(0.236-0.245\right)^2+\left(0.255-0.258\right)^2}\right)\approx 0.00980$ + \item $Z_C=\frac{20mm }{d(n_c,n_b)}=\frac{20mm}{ \sqrt{\left(0.236-0.245\right)^2+\left(0.255-0.258\right)^2}}\approx \frac{20mm}{0.00949}\approx 2107mm$ + \item $Z_C\cdot n=N\Rightarrow P_C=\begin{pmatrix} + Z_C\cdot 0.236\\Z_C\cdot 0.255\\ Z_C + \end{pmatrix}\approx \begin{pmatrix} + 497.2\\537.3\\ 2107 + \end{pmatrix}mm$ + \item Depending on how many distortion parameters we want to know, the system of linear equations may be of high dimension. In addition we can't sepeate by coordinate because the solutions for $x$ and $y$ depend on each other. Even for only computing radial distortion only up to the second degree we have to\\ + solve $\begin{pmatrix} + x_d\\y_d + \end{pmatrix}=\begin{pmatrix} + x\\y + \end{pmatrix}+k_1\left|\left|\begin{pmatrix} + x\\y + \end{pmatrix}\right|\right|_2^2+k_2\left|\left|\begin{pmatrix} + x\\y + \end{pmatrix}\right|\right|_2^4$ for $x$ and $y$. + \end{enumerate} \end{document}