This paper deals with a challenging, frequently encountered, yet not properly investigated problem in two-frame optical flow estimation. That is, the input frames are compounds of two imaging layers -- one desired background layer of the scene, and one distracting, possibly moving layer due to transparency or reflection. In this situation, the conventional brightness constancy constraint -- the cornerstone of most existing optical flow methods -- will no longer be valid. In this paper, we propose a robust solution to this problem. The proposed method performs both optical flow estimation, and image layer separation. It exploits a generalized double-layer brightness consistency constraint connecting these two tasks, and utilizes the priors for both of them. Experiments on both synthetic data and real images have confirmed the efficacy of the proposed method. To the best of our knowledge, this is the first attempt towards handling generic optical flow fields of two-frame images containing transparency or reflection.
One of the first work for multiple optical flow computation is possibly due to Shiwaza al @cite_35 @cite_46 . By assuming the two underlying flow fields to be constant ( pure translating), they derived a generalized brightness constancy constraint for the multi-motion case. However, this constant motion assumption is restrictive, not applicable for general flow fields with complex motions. Nevertheless, their method, being one of the first, has inspired a number of variants and extensions @cite_14 @cite_34 @cite_23 @cite_4 . Some variants operate in the Fourier domain, @cite_25 @cite_30 @cite_24 .
@cite_30 @cite_35 @cite_14 @cite_4 @cite_24 @cite_23 @cite_46 @cite_34 @cite_25
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We extend the principle of phase-based techniques for measuring optical flow and binocular disparity to multiple motion estimation. We analyse multiple optical flows by estimating phase gradients (instantaneous fre­ quencies) from a set of independent bandpass quadrature filter pairs. Our approach is similar to that of Shizawa and Mase [22], in which nth-order differential operators are required to compute n simultaneous velocity es­ timates. The approach presented here only requires a set of band-pass filters and their first derivatives. In this paper a mechanism for computing multiple motion models along with the corresponding regions of support for a sequence of images is presented. The mechanism is an indirect parametric motion estimation technique. Firstly, a robust technique based on the fundamental constraint equation of multiple optical flow is used to estimate a dense multiple vector field of the scene. Secondly, from the recovered low-level data, motion models and their corresponding regions of support are estimated through a variant of the expectation-maximisation (EM) algorithm. The proposed algorithm is shown to provide good motion estimates and regions of support. Using low-order global motion hypotheses and the assumption that there are no more than two motions at a single point, it is possible to successfully decompose motion stimuli that contain additively combined transparent layers. It is assumed that the space of flow fields is sufficiently smooth that a relatively coarse sampling of the flow parameter(s) will produce a set of vector fields that can be combined to reasonably approximate the actual motions in the scene. The definition of support from an exclusively spatial notion is extended to include the spatio-temporal energy domain. The key insight is that when processing transparent motion displays, the support of a motion hypothesis should exist over both a region of space and velocity, so that it can be isolated both spatially and in terms of local velocity. > A unified theoretical framework for motion transparency and motion boundaries by devising fundamental constraint equations of multiple optical flow is proposed. This framework can handle flow discontinuities at motion boundaries as well as flow multiplicities due to transparency of objects in a unified manner. The constraint equations are formulated by a composition of homogeneously parametrized differential operators on the space-time image. Fitting algorithms for the constraints which result in eigensystem analyses are described. To determine the number of flows, the authors use the margin energy, a measure of goodness of fit which is the difference between the first and the second lower eigenenergy of the eigensystem. They also hypothesize a criterion for multiplicity. The measure and the criterion are derived from the analogy of quantum mechanics. It is demonstrated that the margin energy can determine the transparency and discontinuities of the flow field as regions of more than one flow. > This paper is concerned with the estimation of the motions and the segmentation of the spatial supports of the different layers involved in transparent X-ray image sequences. Classical motion estimation methods fail on sequences involving transparent effects since they do not explicitly model this phenomenon. We propose a method that comprises three main steps: initial block-matching for two-layer transparent motion estimation, motion clustering with 3D Hough transform, and joint transparent layer segmentation and parametric motion estimation. It is validated on synthetic and real clinical X-ray image sequences. Secondly, we derive an original transparent motion compensation method compatible with any spatiotemporal filtering technique. A direct transparentmotion compensation method is proposed. To overcome its limitations, a novel hybrid filter is introduced which locally selects which type of motion compensation is to be carried out for optimal denoising. Convincing experiments on synthetic and real clinical images are also reported. The measurement of multiple velocities using phase-based methods is discussed. In particular, phase gradients (instantaneous frequency) from different bandpass channels (quadrature filter outputs) are used to estimate multiple image velocities in a single neighborhood. The approach is similar to that of M. Shizawa and K. Mase (1990) in which nth-order differential operators are required to compute n simultaneous velocity estimates. However, to use instantaneous frequency, the output of each channel must be differentiated only once. >