Mixed-motion Segmentation Using Helmholtz Decomposition

Motion segmentation plays a central role in video analysis, such as the surveillance, human-computer interaction, action recognition, etc. Extensive studies have been done on the stationary camera scenarios. Recently, more attentions are focusing on dynamic backgrounds with several moving objects in the scene. In many applications, the background motion is of much less interest, and solely the local object motion is expected. Several approaches have been proposed for global motion estimation and motion segmentation (the global motion and the object motion are also named as inlier and outlier, respectively). The work in [6] introduced a parametric form which assumed the global motion model from simple translation to general perspective transformation using different parameters. A joint global motion estimation and segmentation method was proposed in [2]. It iteratively updates the inlier model by segmenting the outlier out. A regression scheme, using gradient descent (GD) [6] or least squares (LS) [5], is also applied to refine the inlier model. An outlier rejection filter in [1] explicit filters motion vectors by checking their similarity in a pre-defined window. RANSAC in [3] is a statistical method which estimates the inlier model by iteratively updating the probability of inlier. All above methods are 2D based methods. They require the multiple motions to be independent. But for interdependent motions, they may fail to deal with. Considering this, it is better to place different motions on different layers in higher dimensional space. To this end, our method transforms 2D motion field into 3D surfaces. Local extremes on the surface such as peaks, ridges and valleys depict local motions while smoothing places represent the global motion. The 3D surface is calculated using Helmoholtz decomposition. In [4], a particle filter based on Helmholtz decomposition was proposed for flow estimation. Following is its fundamental theory. For an arbitrary flow field ξ, it is decomposed into two components: curl-free (divergence) component ∇E and divergence-free (curl) component ∇ × W , where E and W are what we want to obtain the 3D potential surfaces. The