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7 May 2003Estimation of multiple motions: regularization and performance evaluation
This paper deals with the problem of estimating multiple transparent
motions that can occur in computer vision applications, e.g. in the
case of semi-transparencies and occlusions, and also in medical
imaging when different layers of tissue move independently. Methods
based on the known optical-flow equation for two motions are
extended in three ways. Firstly, we include a regularization term
to cope with sparse flow fields. We obtain an Euler-Lagrange system
of differential equations that becomes linear due to the use of the
mixed motion parameters. The system of equations is solved for the
mixed-motion parameters in analogy to the case of only one motion.
To extract the motion parameters, the velocity vectors are treated
as complex numbers and are obtained as the roots of a complex
polynomial of a degree that is equal to the number of overlaid
motions. Secondly, we extend a Fourier-Transform based method
proposed by Vernon such as to obtain analytic solutions for more
than two motions. Thirdly, we not only solve for the overlaid
motions but also separate the moving layers. Performance is
demonstrated by using synthetic and real sequences.
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Ingo Stuke, Til Aach, Cicero Mota, Erhardt Barth, "Estimation of multiple motions: regularization and performance evaluation," Proc. SPIE 5022, Image and Video Communications and Processing 2003, (7 May 2003); https://doi.org/10.1117/12.476592