TOPSAC for Fast and Accurate Geometric Estimation

Geometric estimation in computer vision often struggles with balancing speed and accuracy, especially when confronted with high outlier ratios or challenging viewpoint changes inherent in real-world data. This paper introduces TOPology consistency SAmple Consensus (TOPSAC), a novel resampling-based method designed for fast, robust, and accurate geometric estimation. By exploiting the topology consistency in two-view geometry, we design a TOP sampler that only samples one data point per trial and infers its topologically compatible local inliers accordingly, for model generation. Albeit ultra-fast, it lacks accuracy as only localized data are considered. To remedy this drawback, with the observation that “not all residuals are trustworthy”, we propose to unearth the uncertainty from the sampled points by means of Gaussian process. Thereby, we introduce a novel Local Optimization (LO) strategy that is robust to both heavy outliers and bad-conditioned sampling cases, to complement the inaccuracy of the sampler. With some particular considerations for the degenerate case of the epipolar geometry, the proposed TOPSAC is applied to solving geometric estimation problems, and achieves the best of both worlds in accuracy and efficiency on both synthesized and real-world datasets, often demonstrating up to an order of magnitude speedup compared to traditional methods while maintaining state-of-the-art accuracy. It shows high speed and robustness, even under extreme view changes, heavy outliers, and dominant planes where others fail.