improved readme (#194)

* improved readme

* Update docs/rotation_averager.md

Co-authored-by: Copilot <[email protected]>

* Update docs/getting_started.md

Co-authored-by: Copilot <[email protected]>

* Update docs/rotation_averager.md

Co-authored-by: Copilot <[email protected]>

* Update docs/getting_started.md

Co-authored-by: Johannes Schönberger <[email protected]>

* Update docs/getting_started.md

Co-authored-by: Johannes Schönberger <[email protected]>

---------

Co-authored-by: Copilot <[email protected]>
Co-authored-by: Johannes Schönberger <[email protected]>

Author: 3 people

README.md

@@ -41,7 +41,7 @@ glomap mapper --database_path DATABASE_PATH --output_path OUTPUT_PATH --image_pa
 ```
 For more details on the command line interface, one can type `glomap -h` or `glomap mapper -h` for help.
 
-We also provide a guide on improving the obtained reconstruction, which can be found [here](docs/getting_started.md)
+We also provide a guide on improving the obtained reconstruction, which can be found [here](docs/getting_started.md).
 
 Note:
 - GLOMAP depends on two external libraries - [COLMAP](https://github.com/colmap/colmap) and [PoseLib](https://github.com/PoseLib/PoseLib).

docs/getting_started.md

@@ -44,3 +44,9 @@ retriangulation should already been performed.
 The number of global positioning and bundle adjustment iterations can be limited
 using the `--GlobalPositioning.max_num_iterations` and
 `--BundleAdjustment.max_num_iterations` options. 
+
+#### Enable GPU-based solver
+
+If Ceres 2.3 or above is installed and cuDSS is installed, GLOMAP supports GPU
+accelerated optimization. The process can be largely sped up with flags
+`--GlobalPositioning.use_gpu 1 --BundleAdjustment.use_gpu`.

docs/rotation_averager.md

@@ -50,8 +50,15 @@ The gravity direction file is expected to be of the following format
 ```
 IMAGE_NAME GX GY GZ
 ```
-The gravity direction $g$ should $[0, 1, 0]$ if the image is parallel to the ground plane, and the estimated rotation would have the property that $R_i \cdot [0, 1, 0]^\top = g$.
-If is acceptable if only a subset of all images have gravity direciton.
+The gravity direction $g$ should $[0, 1, 0]$ if the image is orthogonal to the ground plane, and the estimated rotation would have the property that $R_i \cdot [0, 1, 0]^\top = g$.
+More explicitly, suppose we can transpose a 3D point from the world coordinate to the image coordinate by RX + t = x. Here:
+- `R` is a 3x3 rotation matrix that aligns the world coordinate system with the image coordinate system.
+- `X` is a 3D point in the world coordinate system.
+- `t` is a 3x1 translation vector that shifts the world coordinate system to the image coordinate system.
+- `x` is the corresponding 3D point in the image coordinate system.
+The gravity direction should be the second column of the rotation matrix `R`.
+
+It is acceptable if only a subset of all images have gravity direction.
 If the specified image name does not match any known image name from relative pose, it is ignored.
 
 ### Output