Differences
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research:hflow:start [2015/08/13 11:21] aneufeld |
research:hflow:start [2015/08/14 13:40] aneufeld |
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| Given rotation $R \in \text{SO}(3)$, translation $t \in S(2)$ and 3D point $X$, the point $X'$ relative to the second camera is given by $X' = R^\top (X - t)$. The translation is restricted to the unit sphere, since the translation norm cannot be estimated without additional information. | Given rotation $R \in \text{SO}(3)$, translation $t \in S(2)$ and 3D point $X$, the point $X'$ relative to the second camera is given by $X' = R^\top (X - t)$. The translation is restricted to the unit sphere, since the translation norm cannot be estimated without additional information. | ||
| Let $\pi$ denote the projection onto the image plane, | Let $\pi$ denote the projection onto the image plane, | ||
| - | $$ \pi\begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \frac{1}{x_3} \begin{pmatrix} x_1 \\ x_2 \end{pmatrix}. $$ | + | $$ \pi\begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \frac{1}{x_3} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix}. $$ |
| Let $z(x)$ denote the depth of pixel $x$ in the image plane, $X = z(x) x$. Depth can be calculated from the plane parameters, $z(x,v) = (v^\top x)^{-1}$. | Let $z(x)$ denote the depth of pixel $x$ in the image plane, $X = z(x) x$. Depth can be calculated from the plane parameters, $z(x,v) = (v^\top x)^{-1}$. | ||
| Optical flow is given by | Optical flow is given by | ||