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The Scientific World Journal
Volume 2013, Article ID 878417, 15 pages
Research Article

Analytical Analysis of Motion Separability

School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Corner of Plenty Road and McKimmies Road, Bundoora, Victoria 3083, Australia

Received 29 August 2013; Accepted 26 September 2013

Academic Editors: S.-S. Liaw and Z. Yang

Copyright © 2013 Marjan Hadian Jazi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Motion segmentation is an important task in computer vision and several practical approaches have already been developed. A common approach to motion segmentation is to use the optical flow and formulate the segmentation problem using a linear approximation of the brightness constancy constraints. Although there are numerous solutions to solve this problem and their accuracies and reliabilities have been studied, the exact definition of the segmentation problem, its theoretical feasibility and the conditions for successful motion segmentation are yet to be derived. This paper presents a simplified theoretical framework for the prediction of feasibility, of segmentation of a two-dimensional linear equation system. A statistical definition of a separable motion (structure) is presented and a relatively straightforward criterion for predicting the separability of two different motions in this framework is derived. The applicability of the proposed criterion for prediction of the existence of multiple motions in practice is examined using both synthetic and real image sequences. The prescribed separability criterion is useful in designing computer vision applications as it is solely based on the amount of relative motion and the scale of measurement noise.