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Fix up docstrings

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Summary:
One of the docstrings is a disaster see https://pytorch3d.readthedocs.io/en/latest/modules/ops.html

Also some minor fixes I encountered when browsing the code

Reviewed By: bottler

Differential Revision: D38581595

fbshipit-source-id: 3b6ca97788af380a44df9144a6a4cac782c6eab8
This commit is contained in:
Krzysztof Chalupka
2022-08-23 14:58:49 -07:00
committed by Facebook GitHub Bot
parent c4545a7cbc
commit 6653f4400b
3 changed files with 29 additions and 28 deletions
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29
pytorch3d/ops/cameras_alignment.py
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@@ -39,20 +39,20 @@ def corresponding_cameras_alignment(
such that the following holds:
Under the change of coordinates using a similarity transform
(R_A, T_A, s_A) a 3D point X' is mapped to X with:
```
(R_A, T_A, s_A) a 3D point X' is mapped to X with: ::
X = (X' R_A + T_A) / s_A
```
Then, for all cameras `i`, we assume that the following holds:
```
Then, for all cameras `i`, we assume that the following holds: ::
X R_i + T_i = s' (X' R_i' + T_i'),
```
i.e. an adjusted point X' is mapped by a camera (R_i', T_i')
to the same point as imaged from camera (R_i, T_i) after resolving
the scale ambiguity with a global scalar factor s'.
Substituting for X above gives rise to the following:
```
Substituting for X above gives rise to the following: ::
(X' R_A + T_A) / s_A R_i + T_i = s' (X' R_i' + T_i') // · s_A
(X' R_A + T_A) R_i + T_i s_A = (s' s_A) (X' R_i' + T_i')
s' := 1 / s_A # without loss of generality
@@ -60,10 +60,11 @@ def corresponding_cameras_alignment(
X' R_A R_i + T_A R_i + T_i s_A = X' R_i' + T_i'
^^^^^^^ ^^^^^^^^^^^^^^^^^
~= R_i' ~= T_i'
```
i.e. after estimating R_A, T_A, s_A, the aligned source cameras have
extrinsics:
`cameras_src_align = (R_A R_i, T_A R_i + T_i s_A) ~= (R_i', T_i')`
extrinsics: ::
cameras_src_align = (R_A R_i, T_A R_i + T_i s_A) ~= (R_i', T_i')
We support two ways `R_A, T_A, s_A` can be estimated:
1) `mode=='centers'`
@@ -73,12 +74,12 @@ def corresponding_cameras_alignment(
2) `mode=='extrinsics'`
Defines the alignment problem as a system
of the following equations:
```
of the following equations: ::
for all i:
[ R_A 0 ] x [ R_i 0 ] = [ R_i' 0 ]
[ T_A^T 1 ] [ (s_A T_i^T) 1 ] [ T_i' 1 ]
```
`R_A, T_A` and `s_A` are then obtained by solving the
system in the least squares sense.