Tractable Algorithms for Robust Model Estimation
Journal article, 2015

What is the computational complexity of geometric model estimation in the presence of noise and outliers? We show that the number of outliers can be minimized in polynomial time with respect to the number of measurements, although exponential in the model dimension. Moreover,for a large class of problems, we prove that the statistically more desirable truncated L2-norm can be optimized with the same complexity. In a similar vein, it is also shown how to transform a multi-model estimation problem into a purely combinatorial one—with worst-case complexity that is polynomial in the number of measurements but exponential in the number of models. We apply our framework to a series of hard fitting problems. It gives a practical method for simultaneously dealing with measurement noise and large amounts of outliers in the estimation of low-dimensional models. Experimental results and a comparison to random sampling techniques are presented for the applications rigid registration, triangulation and stitching.


Olof Enqvist

Chalmers, Signals and Systems, Signal Processing and Biomedical Engineering

Erik Ask

Lund University

Fredrik Kahl

Chalmers, Signals and Systems, Signal Processing and Biomedical Engineering

K. Aström

Lund University

International Journal of Computer Vision

0920-5691 (ISSN) 15731405 (eISSN)

Vol. 112 1 115-129

Subject Categories

Computer Vision and Robotics (Autonomous Systems)

Medical Image Processing



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