# Progressive-X: Efficient, Anytime, Multi-Model Fitting Algorithm

## TL;DR

Progressive-X is an efficient, anytime algorithm for multi-model geometric fitting that progressively explores data, providing accurate results and the ability to stop at any time with meaningful outputs.

## Contribution

It introduces a novel progressive data exploration approach with a clear termination criterion and anytime capability for multi-model fitting.

## Key findings

- Outperforms state-of-the-art in accuracy on synthetic and real datasets.
- Effectively handles homography, two-view motion, and motion segmentation.
- Provides reliable results even when interrupted early.

## Abstract

The Progressive-X algorithm, Prog-X in short, is proposed for geometric multi-model fitting. The method interleaves sampling and consolidation of the current data interpretation via repetitive hypothesis proposal, fast rejection, and integration of the new hypothesis into the kept instance set by labeling energy minimization. Due to exploring the data progressively, the method has several beneficial properties compared with the state-of-the-art. First, a clear criterion, adopted from RANSAC, controls the termination and stops the algorithm when the probability of finding a new model with a reasonable number of inliers falls below a threshold. Second, Prog-X is an any-time algorithm. Thus, whenever is interrupted, e.g. due to a time limit, the returned instances cover real and, likely, the most dominant ones. The method is superior to the state-of-the-art in terms of accuracy in both synthetic experiments and on publicly available real-world datasets for homography, two-view motion, and motion segmentation.