Estimation of multiple motions: regularization and performance evaluation

Abstract

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.

Estimation of multiple motions using block matching and Markov random fields

“…Single moving points leading to non-smooth motion vector fields are unlikely to appear. Regularization of the motion vector fields is widely used for the optical flow estimation and its extension to multiple motions [5]. Since motion estimation here deals with statistical observations rather than with functional minimization problems, we choose to increase robustness against noise by using a stochastic framework based on Markov random fields (similar to how it was used in [17] for motion detection and in [11] for single motion estimation) in combination with the block-matching constraint.…”

“…The block-matching constraint will be derived from the phased-based method for multiple motion estimation [4,5]. In this method, the image sequence is modeled as an additive superposition of N independent moving layers.…”

“…A phase-based solution for the estimation of two transparent overlaid motions was proposed by Vernon [4]. This method has also been generalized for an arbitrary number of N motions in [5]. This generalization led to solutions for extracting the N motions at a single point as well as for separating the moving image layers.…”

“…In this paper we extend this algorithm to use a stochastic framework with a confidence test and Markov random fields. The algorithm is derived from the phase-based solution for the Fourier-domain equations for transparent motions [4,5]. The distortion caused by occluding regions is also analyzed and we show how to apply the algorithm to estimate motions at occlusions.…”

Estimation of Multiple Orientations and Multiple Motions in Multi-Dimensional Signals

“…In order to estimate the mixed-motion parameters we can choose one of the methods proposed in [17,23]. Then the nonlinear problem is solved by decomposing the MMP into the individual motion components.…”