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Update bundle_adjustment.ipynb (#81)

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Summary:
*: Fixed references to colors in the diagram
Pull Request resolved: https://github.com/facebookresearch/pytorch3d/pull/81

Reviewed By: bottler

Differential Revision: D20064048

Pulled By: nikhilaravi

fbshipit-source-id: a70ee446f1223ec900072a2380c75ed95fb4431d
This commit is contained in:
Tyler Barron 2020-02-24 12:12:22 -08:00 committed by Facebook Github Bot
parent dab7f61a12
commit 40be4cf78b
1 changed files with 2 additions and 2 deletions
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docs/tutorials/bundle_adjustment.ipynb
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@ -36,10 +36,10 @@
"$$,\n",
"where $d(g_i, g_j)$ is a suitable metric that compares the extrinsics of cameras $g_i$ and $g_j$. \n",
"\n",
"Visually, the problem can be described as follows. The picture below depicts the situation at the beginning of our optimization. The ground truth cameras are plotted in green while the randomly initialized estimated cameras are plotted in blue:\n",
"Visually, the problem can be described as follows. The picture below depicts the situation at the beginning of our optimization. The ground truth cameras are plotted in purple while the randomly initialized estimated cameras are plotted in orange:\n",
"![Initialization](https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/data/bundle_adjustment_initialization.png?raw=1)\n",
"\n",
"Our optimization seeks to align the estimated (blue) cameras with the ground truth (green) cameras, by minimizing the discrepancies between pairs of relative cameras. Thus, the solution to the problem should look as follows:\n",
"Our optimization seeks to align the estimated (orange) cameras with the ground truth (purple) cameras, by minimizing the discrepancies between pairs of relative cameras. Thus, the solution to the problem should look as follows:\n",
"![Solution](https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/data/bundle_adjustment_final.png?raw=1)\n",
"\n",
"In practice, the camera extrinsics $g_{ij}$ and $g_i$ are represented using objects from the `SfMPerspectiveCameras` class initialized with the corresponding rotation and translation matrices `R_absolute` and `T_absolute` that define the extrinsic parameters $g = (R, T); R \\in SO(3); T \\in \\mathbb{R}^3$. In order to ensure that `R_absolute` is a valid rotation matrix, we represent it using an exponential map (implemented with `so3_exponential_map`) of the axis-angle representation of the rotation `log_R_absolute`.\n",