Mimas Camera Calibration
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\vec{h_i}^\top=\begin{pmatrix}h_{i1}&h_{i2}&h_{i3}\end{pmatrix},\ i\in\{1,2,3\} | \vec{h_i}^\top=\begin{pmatrix}h_{i1}&h_{i2}&h_{i3}\end{pmatrix},\ i\in\{1,2,3\} | ||
</math> | </math> | ||
| + | |||
| + | <math>\lambda</math> is Eigenvalue of <math>\mathcal{A}</math> with Eigenvector | ||
| + | <math>\vec{x}</math><math>:\Leftrightarrow</math><math>\mathcal{A}\,\vec{x}=\lambda\vec{x}</math> | ||
<math> | <math> | ||
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\vec{\epsilon_i} | \vec{\epsilon_i} | ||
</math> | </math> | ||
| + | |||
| + | Other symbols: | ||
| + | <math> | ||
| + | \vec{0}, \neq, ||\mathcal{A}||, \mathcal{A}\in\mathbb{C}^{3\times 3}, i\in\mathbb{N}_0,0\approx 1, \begin{pmatrix}1-\lambda&0\\0&1-\lambda\end{pmatrix}, \mathbb{R}^3, i\in\{1,2,\ldots,n\}</math> | ||
| + | |||
| + | <math> | ||
| + | \begin{pmatrix}1-\lambda&0&\cdots&\cdots&0\\0&1-\lambda&\ddots&&\vdots\end{pmatrix},V^*,a*b, \sigma, \Sigma, \lambda, \Lambda</math> | ||
| + | |||
| + | <math> | ||
| + | \sum_{i=1}^n p^i, \prod_{i=1}^{+\infty}a_i, \cos(\omega), \widehat{i}=\mathrm{argmax}_{i\in\mathbb{N}}f(i) | ||
| + | </math> | ||
| + | |||
| + | <!-- \backsimeq \usepackage{amssymb}, \begin{qmatrix}1-\lambda&0\\0&1-\lambda\end{qmatrix} \displaystyle --> | ||
=See Also= | =See Also= | ||
Revision as of 20:12, 22 June 2006
Calibration
Under construction ... <math> \lambda\,\begin{pmatrix}\widehat{m}_{i1}\\\widehat{m}_{i2}\\\widehat{m}_{i3}\end{pmatrix}= \begin{pmatrix}h_{11}&h_{12}&h_{13}\\h_{21}&h_{22}&h_{23}\\h_{31}&h_{32}&h_{33}\end{pmatrix}\, \begin{pmatrix}m_{i1}\\m_{i2}\\m_{i3}\end{pmatrix} </math>
<math> \vec{h_i}^\top=\begin{pmatrix}h_{i1}&h_{i2}&h_{i3}\end{pmatrix},\ i\in\{1,2,3\} </math>
<math>\lambda</math> is Eigenvalue of <math>\mathcal{A}</math> with Eigenvector <math>\vec{x}</math><math>:\Leftrightarrow</math><math>\mathcal{A}\,\vec{x}=\lambda\vec{x}</math>
<math> \begin{pmatrix}\widehat{m}_{i1}\\\widehat{m}_{i2}\end{pmatrix}= \cfrac{1}{\vec{h_3}^\top\cdot\vec{m}_i}\, \begin{pmatrix}\vec{h_1}^\top\\\vec{h_2}^\top\end{pmatrix}\, \begin{pmatrix}m_{i1}\\m_{i2}\\m_{i3}\end{pmatrix}+ \vec{\epsilon_i} </math>
Other symbols: <math> \vec{0}, \neq, ||\mathcal{A}||, \mathcal{A}\in\mathbb{C}^{3\times 3}, i\in\mathbb{N}_0,0\approx 1, \begin{pmatrix}1-\lambda&0\\0&1-\lambda\end{pmatrix}, \mathbb{R}^3, i\in\{1,2,\ldots,n\}</math>
<math> \begin{pmatrix}1-\lambda&0&\cdots&\cdots&0\\0&1-\lambda&\ddots&&\vdots\end{pmatrix},V^*,a*b, \sigma, \Sigma, \lambda, \Lambda</math>
<math> \sum_{i=1}^n p^i, \prod_{i=1}^{+\infty}a_i, \cos(\omega), \widehat{i}=\mathrm{argmax}_{i\in\mathbb{N}}f(i) </math>
