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research:hflow:start [2015/08/12 16:44] aneufeld |
research:hflow:start [2021/03/02 13:28] (current) |
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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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| ===== Results ===== | ===== Results ===== | ||
| - | We demonstrate the output of our algorithms on a few examples here, the paper contains a quantitative evaluation. From top to bottom, each example shows the reference frame, estimated depth and normals and the flow error as measured in the paper. Depth and depth error (in pixels) are encoded as follows, the scale is derived from ground truth data. | + | We demonstrate the output of our algorithms on a few examples here, the paper contains a quantitative evaluation. From top to bottom, each example shows the reference frame, estimated depth and normals and the flow error as measured in the paper (click for a full size view). Depth and depth error (in pixels) are encoded as follows, the scale is derived from ground truth data. |
| {{ :research:hflow:depth2.png?nolink&200 |}} | {{ :research:hflow:depth2.png?nolink&200 |}} | ||
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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 ===== | ||