Gravity-aligned Rotation Averaging with Circular Regression

Project page | Paper | Supp.

About

This project aims at solving the rotation averaging problem with gravity prior. To achieve this, circular regression is leveraged.

If you use this project for your research, please cite

@inproceedings{pan2024ra1dof,
    author={Pan, Linfei and Pollefeys, Marc and Barath, Daniel},
    title={{Gravity-aligned Rotation Averaging with Circular Regression}},
    booktitle={European Conference on Computer Vision (ECCV)},
    year={2024},
}

Getting Started

Install GLOMAP as instrcucted in README. Then, call the rotation averager (3 degree-of-freedom) via

glomap rotation_averager --relpose_path RELPOSE_PATH --output_path OUTPUT_PATH

If gravity directions are available, call the rotation averager (1 degree-of-freedom) via

glomap rotation_averager \
    --relpose_path RELPOSE_PATH \
    --output_path OUTPUT_PATH \
    --gravity_path GRAVTIY PATH 

It is recommended to set --use_stratified=1 if only a subset of images have gravity direction. If gravity measurements are subject to i.i.d. noise, they can be refined by setting --refine_gravity=1.

File Formats

Relative Pose

The relative pose file is expected to be of the following format

IMAGE_NAME_1 IMAGE_NAME_2 QW QX QY QZ TX TY TZ

Only images contained in at least one relative pose will be included in the following procedure. The relative pose should be ₂R₁ x₁ + ₂t₁ = x₂.

Gravity Direction

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 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

The estimated global rotation will be in the following format

IMAGE_NAME QW QX QY QZ

Any images that are not within the largest connected component of the view-graph formed by the relative pose will be ignored.