RANSAC in SLAM
RANSAC is crucial in SLAM for robust estimation in the presence of outliers.
Key applications include:
- Loop closure detection
- Point cloud registration
- Feature matching between frames
Mathematical Model
For a set of corresponding points between two frames, RANSAC helps find the optimal transformation:
\[
T_{opt} = \arg\min_T \sum_{i \in \text{inliers}} \|p_i' - T(p_i)\|^2
\]
The RANSAC algorithm follows these steps:
- Randomly sample minimum points needed for model
- Compute transformation model
- Count inliers within threshold
- Repeat and keep best model
RANSAC in Practice
In SLAM, RANSAC is used to:
- Filter incorrect feature matches between frames
- Estimate rigid body transformations between point clouds
- Detect and validate loop closures
- Remove dynamic objects from static map building