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research:hflow:start [2015/08/12 16:46] aneufeld |
research:hflow:start [2015/10/08 14:00] aneufeld [Estimating Vehicle Ego-Motion and Piecewise Planar Scene Structure from Optical Flow in a Continuous Framework] |
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- | ====== Monocular 3D Reconstruction of Traffic Scenes from Optical Flow ====== | + | ====== Estimating Vehicle Ego-Motion and Piecewise Planar Scene Structure from Optical Flow in a Continuous Framework ====== |
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+ | {{:research:hflow:neufeld_gcpr2015.pdf|GCPR 2015 slides}} | ||
We estimate a 3D scene structure and the vehicle egomotion given the forward and backward optical flow fields between two consecutive frames. | We estimate a 3D scene structure and the vehicle egomotion given the forward and backward optical flow fields between two consecutive frames. | ||
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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 | ||
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| {{ :research:hflow:000027_10.png?direct&200 |}} {{ :research:hflow:depth_000027.png?direct&200 |}} {{ :research:hflow:normals_lab_000027.png?direct&200 |}} {{ :research:hflow:err_000027.png?direct&200 |}} | {{ :research:hflow:000028_10.png?direct&200 |}} {{ :research:hflow:depth_000028.png?direct&200 |}} {{ :research:hflow:normals_lab_000028.png?direct&200 |}} {{ :research:hflow:err_000028.png?direct&200 |}} | {{ :research:hflow:000029_10.png?direct&200 |}} {{ :research:hflow:depth_000029.png?direct&200 |}} {{ :research:hflow:normals_lab_000029.png?direct&200 |}} {{ :research:hflow:err_000029.png?direct&200 |}} | | | {{ :research:hflow:000027_10.png?direct&200 |}} {{ :research:hflow:depth_000027.png?direct&200 |}} {{ :research:hflow:normals_lab_000027.png?direct&200 |}} {{ :research:hflow:err_000027.png?direct&200 |}} | {{ :research:hflow:000028_10.png?direct&200 |}} {{ :research:hflow:depth_000028.png?direct&200 |}} {{ :research:hflow:normals_lab_000028.png?direct&200 |}} {{ :research:hflow:err_000028.png?direct&200 |}} | {{ :research:hflow:000029_10.png?direct&200 |}} {{ :research:hflow:depth_000029.png?direct&200 |}} {{ :research:hflow:normals_lab_000029.png?direct&200 |}} {{ :research:hflow:err_000029.png?direct&200 |}} | | ||
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===== References ===== | ===== References ===== |