Robust Fitting in Computer Vision: Easy or Hard?

• Published in: International journal of computer vision Vol. 128; no. 3; pp. 575 - 587
• Main Authors: Chin, Tat-Jun, Cai, Zhipeng, Neumann, Frank
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2020; Springer; Springer Nature B.V
• Subjects: Algorithms; Analysis; Artificial Intelligence; Computer Imaging; Computer Science; Computer vision; Hardness; Image Processing and Computer Vision; Inliers (landforms); Machine vision; Maximization; Optimization; Pattern Recognition; Pattern Recognition and Graphics; Robustness; Vision; Robust fitting; Consensus maximisation; Inlier set maximisation; Computational hardness
• ISSN: 0920-5691; 1573-1405
• DOI: 10.1007/s11263-019-01207-y

Robust model fitting plays a vital role in computer vision, and research into algorithms for robust fitting continues to be active. Arguably the most popular paradigm for robust fitting in computer vision is consensus maximisation , which strives to find the model parameters that maximise the number of inliers. Despite the significant developments in algorithms for consensus maximisation, there has been a lack of fundamental analysis of the problem in the computer vision literature. In particular, whether consensus maximisation is “tractable” remains a question that has not been rigorously dealt with, thus making it difficult to assess and compare the performance of proposed algorithms, relative to what is theoretically achievable. To shed light on these issues, we present several computational hardness results for consensus maximisation. Our results underline the fundamental intractability of the problem, and resolve several ambiguities existing in the literature.