A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3021)


We present an analytic solution to the problem of estimating multiple 2-D and 3-D motion models from two-view correspondences or optical flow. The key to our approach is to view the estimation of multiple motion models as the estimation of a single multibody motion model. This is possible thanks to two important algebraic facts. First, we show that all the image measurements, regardless of their associated motion model, can be fit with a real or complex polynomial. Second, we show that the parameters of the motion model associated with an image measurement can be obtained from the derivatives of the polynomial at the measurement. This leads to a novel motion segmentation algorithm that applies to most of the two-view motion models adopted in computer vision. Our experiments show that the proposed algorithm outperforms existing algebraic methods in terms of efficiency and robustness, and provides a good initialization for iterative techniques, such as EM, which is strongly dependent on correct initialization.


Expectation Maximization Motion Model Image Pair Image Measurement Algebraic Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Center for Imaging ScienceJohns Hopkins UniversityBaltimoreUSA
  2. 2.National ICT AustraliaCanberraAustralia
  3. 3.Dept. of Elect. and Comp. Eng.UIUCUrbanaUSA

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