We formulate a general energy and method for segmentation that is designed to have preference for segmenting the coarse structure over the fine structure of the data, without smoothing across boundaries of regions. The energy is formulated by considering data terms at a continuum of scales from the scale space computed from the Heat Equation within regions, and integrating these terms over all time. We show that the energy may be approximately optimized without solving for the entire scale space, but rather solving time-independent linear equations at the native scale of the image, making the method computationally feasible. We provide a multi-region scheme, and apply our method to motion segmentation. Experiments on a benchmark dataset shows that our method is less sensitive to clutter or other undesirable fine-scale structure, and leads to better performance in motion segmentation.
We present a novel variational approach for segmenting the image plane into a set of regions of parametric motion on the basis of two consecutive frames from an image sequence. Our model is based on a conditional probability for the spatio-temporal image gradient, given a particular velocity model, and on a geometric prior on the estimated motion field favoring motion boundaries of minimal length. Exploiting the Bayesian framework, we derive a cost functional which depends on parametric motion models for each of a set of regions and on the boundary separating these regions. The resulting functional can be interpreted as an extension of the Mumford-Shah functional from intensity segmentation to motion segmentation. In contrast to most alternative approaches, the problems of segmentation and motion estimation are jointly solved by continuous minimization of a single functional. Minimizing this functional with respect to its dynamic variables results in an eigenvalue problem for the motion parameters and in a gradient descent evolution for the motion discontinuity set. We propose two different representations of this motion boundary: an explicit spline-based implementation which can be applied to the motion-based tracking of a single moving object, and an implicit multiphase level set implementation which allows for the segmentation of an arbitrary number of multiply connected moving objects. Numerical results both for simulated ground truth experiments and for real-world sequences demonstrate the capacity of our approach to segment objects based exclusively on their relative motion. Motion is a strong cue for unsupervised object-level grouping. In this paper, we demonstrate that motion will be exploited most effectively, if it is regarded over larger time windows. Opposed to classical two-frame optical flow, point trajectories that span hundreds of frames are less susceptible to short-term variations that hinder separating different objects. As a positive side effect, the resulting groupings are temporally consistent over a whole video shot, a property that requires tedious post-processing in the vast majority of existing approaches. We suggest working with a paradigm that starts with semi-dense motion cues first and that fills up textureless areas afterwards based on color. This paper also contributes the Freiburg-Berkeley motion segmentation (FBMS) dataset, a large, heterogeneous benchmark with 59 sequences and pixel-accurate ground truth annotation of moving objects. The accuracy of optical flow estimation algorithms has been improving steadily as evidenced by results on the Middlebury optical flow benchmark. The typical formulation, however, has changed little since the work of Horn and Schunck. We attempt to uncover what has made recent advances possible through a thorough analysis of how the objective function, the optimization method, and modern implementation practices influence accuracy. We discover that “classical” flow formulations perform surprisingly well when combined with modern optimization and implementation techniques. Moreover, we find that while median filtering of intermediate flow fields during optimization is a key to recent performance gains, it leads to higher energy solutions. To understand the principles behind this phenomenon, we derive a new objective that formalizes the median filtering heuristic. This objective includes a nonlocal term that robustly integrates flow estimates over large spatial neighborhoods. By modifying this new term to include information about flow and image boundaries we develop a method that ranks at the top of the Middlebury benchmark. We describe a system for representing moving images with sets of overlapping layers. Each layer contains an intensity map that defines the additive values of each pixel, along with an alpha map that serves as a mask indicating the transparency. The layers are ordered in depth and they occlude each other in accord with the rules of compositing. Velocity maps define how the layers are to be warped over time. The layered representation is more flexible than standard image transforms and can capture many important properties of natural image sequences. We describe some methods for decomposing image sequences into layers using motion analysis, and we discuss how the representation may be used for image coding and other applications. > We propose a method to detect disocclusion in video sequences of three-dimensional scenes and to partition the disoccluded regions into objects, defined by coherent deformation corresponding to surfaces in the scene. Our method infers deformation fields that are piecewise smooth by construction without the need for an explicit regularizer and the associated choice of weight. It then partitions the disoccluded region and groups its components with objects by leveraging on the complementarity of motion and appearance cues: Where appearance changes within an object, motion can usually be reliably inferred and used for grouping. Where appearance is close to constant, it can be used for grouping directly. We integrate both cues in an energy minimization framework, incorporate prior assumptions explicitly into the energy, and propose a numerical scheme. Layered models allow scene segmentation and motion estimation to be formulated together and to inform one another. Traditional layered motion methods, however, employ fairly weak models of scene structure, relying on locally connected Ising Potts models which have limited ability to capture long-range correlations in natural scenes. To address this, we formulate a fully-connected layered model that enables global reasoning about the complicated segmentations of real objects. Optimization with fully-connected graphical models is challenging, and our inference algorithm leverages recent work on efficient mean field updates for fully-connected conditional random fields. These methods can be implemented efficiently using high-dimensional Gaussian filtering. We combine these ideas with a layered flow model, and find that the long-range connections greatly improve segmentation into figure-ground layers when compared with locally connected MRF models. Experiments on several benchmark datasets show that the method can recover fine structures and large occlusion regions, with good flow accuracy and much lower computational cost than previous locally-connected layered models.