Robustly fitting a linear model from outlier-contaminated data is an important and basic task in many scientific fields, and it is often tackled by consensus set maximization. We develop a globally optimal algorithm aiming at consensus set maximization to solve robust linear model fitting problem with the unit-norm constraint, which is based on the branch-and-bound optimization framework. The use of unit-norm constraint can eliminate the scale ambiguity of the model parameters and avoid the user-specified initial searching space. We propose a compact representation of the unit-bounded searching domain to avoid introducing additional non-linearity that is intractable for many other globally optimal methods. The compact representation leads to a geometrically derived bound, which accelerates the calculation and enables the method to handle the problems with large number of observations.
Linear model with unit-norm constraint:
- Synthetic linear model.
- Plane fitting.
- Translation estimation.
- Affine fundamental matrix estimation.
- Clone this repository.
- Run function "demo()" in MATLAB.
Email: [email protected]