The ability to identify the static background in videos captured by a moving camera is an important pre-requisite for many video applications (e.g. video stabilization, stitching, and segmentation). Existing methods usually face difficulties when the foreground objects occupy a larger area than the background in the image. Many methods also cannot scale up to handle densely sampled feature trajectories. In this paper, we propose an efficient local-to-global method to identify background, based on the assumption that as long as there is sufficient camera motion, the cumulative background features will have the largest amount of trajectories. Our motion model at the two-frame level is based on the epipolar geometry so that there will be no over-segmentation problem, another issue that plagues the 2D motion segmentation approach. Foreground objects erroneously labelled due to intermittent motions are also taken care of by checking their global consistency with the final estimated background motion. Lastly, by virtue of its efficiency, our method can deal with densely sampled trajectories. It outperforms several state-of-the-art motion segmentation methods on public datasets, both quantitatively and qualitatively.
Trajectory-based motion segmentation methods usually produce multiple independent motion groups; however, they usually stop short of actually identifying the background motion, or just use a simple background metric such as size. Furthermore, due to the computational demand of the 3D motion segmentation methods @cite_19 @cite_16 @cite_4 @cite_23 , these works lack the ability to deal with large amount of feature trajectories. For long and densely sampled feature trajectories, some fast 2D methods @cite_1 @cite_0 may be used. However, their results may become over-segmented when the figure-ground is complex, for instance, scenes with large depth variation. Our method not only processes large amount of trajectory in an efficient way, but also handle videos with complex scene structures.
@cite_4 @cite_1 @cite_0 @cite_19 @cite_23 @cite_16
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In this paper, we study the problem of segmenting tracked feature point trajectories of multiple moving objects in an image sequence. Using the affine camera model, this problem can be cast as the problem of segmenting samples drawn from multiple linear subspaces. In practice, due to limitations of the tracker, occlusions, and the presence of nonrigid objects in the scene, the obtained motion trajectories may contain grossly mistracked features, missing entries, or corrupted entries. In this paper, we develop a robust subspace separation scheme that deals with these practical issues in a unified mathematical framework. Our methods draw strong connections between lossy compression, rank minimization, and sparse representation. We test our methods extensively on the Hopkins155 motion segmentation database and other motion sequences with outliers and missing data. We compare the performance of our methods to state-of-the-art motion segmentation methods based on expectation-maximization and spectral clustering. For data without outliers or missing information, the results of our methods are on par with the state-of-the-art results and, in many cases, exceed them. In addition, our methods give surprisingly good performance in the presence of the three types of pathological trajectories mentioned above. All code and results are publicly available at http: perception.csl.uiuc.edu coding motion . Extracting 3D shape of deforming objects in monocular videos, a task known as non-rigid structure-from-motion (NRSfM), has so far been studied only on synthetic datasets and controlled environments. Typically, the objects to reconstruct are pre-segmented, they exhibit limited rotations and occlusions, or full-length trajectories are assumed. In order to integrate NRSfM into current video analysis pipelines, one needs to consider as input realistic -thus incomplete- tracking, and perform spatio-temporal grouping to segment the objects from their surroundings. Furthermore, NRSfM needs to be robust to noise in both segmentation and tracking, e.g., drifting, segmentation "leaking", optical flow "bleeding" etc. In this paper, we make a first attempt towards this goal, and propose a method that combines dense optical flow tracking, motion trajectory clustering and NRSfM for 3D reconstruction of objects in videos. For each trajectory cluster, we compute multiple reconstructions by minimizing the reprojection error and the rank of the 3D shape under different rank bounds of the trajectory matrix. We show that dense 3D shape is extracted and trajectories are completed across occlusions and low textured regions, even under mild relative motion between the object and the camera. We achieve competitive results on a public NRSfM benchmark while using fixed parameters across all sequences and handling incomplete trajectories, in contrast to existing approaches. We further test our approach on popular video segmentation datasets. To the best of our knowledge, our method is the first to extract dense object models from realistic videos, such as those found in Youtube or Hollywood movies, without object-specific priors. We present a novel optimisation framework for the estimation of the multi-body motion segmentation and 3D reconstruction of a set of point trajectories in the presence of missing data. The proposed solution not only assigns the trajectories to the correct motion but it also solves for the 3D location of multi-body shape and it fills the missing entries in the measurement matrix. Such a solution is based on two fundamental principles: each of the multi-body motions is controlled by a set of metric constraints that are given by the specific camera model, and the shape matrix that describes the multi-body 3D shape is generally sparse. We jointly include such constraints in a unique optimisation framework which, starting from an initial segmentation, iteratively enforces these set of constraints in three stages. First, metric constraints are used to estimate the 3D metric shape and to fill the missing entries according to an orthographic camera model. Then, wrongly segmented trajectories are detected by using sparse optimisation of the shape matrix. A final reclassification strategy assigns the detected points to the right motion or discards them as outliers. We provide experiments that show consistent improvements to previous approaches both on synthetic and real data. Motion segmentation is an important task for intelligent transportation systems. In this paper, inspired by the fact that a feature point trajectory can be sparsely represented as a combination of several feature point trajectories that share coherent transformations, an efficient and effective motion segmentation method with a sparsity constraint is proposed. Specifically, we first propose an accumulated scheme to efficiently integrate motion information from all the frames of a video sequence to construct a correlation matrix. Then, a sparse affinity matrix is built on the correlation matrix by using information-theoretic principles, where the nonzero elements in the same row of the sparse affinity matrix correspond to the feature point trajectories more likely belonging to the same motion. Thereafter, a segment and merge procedure is proposed to effectively estimate the number of motions via the sparse affinity matrix. Finally, by applying spectral clustering on the sparse affinity matrix, different motions in the video sequence are accurately segmented based on the estimated number of motions. Experimental results on the Hopkins 155 and the 62-clip datasets demonstrate that the proposed method achieves superior performance compared with several state-of-the-art methods. We consider the problem of segmenting multiple rigid-body motions from point correspondences in multiple affine views. We cast this problem as a subspace clustering problem in which point trajectories associated with each motion live in a linear subspace of dimension two, three or four. Our algorithm involves projecting all point trajectories onto a 5-dimensional subspace using the SVD, the PowerFactorization method, or RANSAC, and fitting multiple linear subspaces representing different rigid-body motions to the points in ?5 using GPCA. Unlike previous work, our approach does not restrict the motion subspaces to be four-dimensional and independent. Instead, it deals gracefully with all the spectrum of possible affine motions: from two-dimensional and partially dependent to four-dimensional and fully independent. Our algorithm can handle the case of missing data, meaning that point tracks do not have to be visible in all images, by using the PowerFactorization method to project the data. In addition, our method can handle outlying trajectories by using RANSAC to perform the projection. We compare our approach to other methods on a database of 167 motion sequences with full motions, independent motions, degenerate motions, partially dependent motions, missing data, outliers, etc. On motion sequences with complete data our method achieves a misclassification error of less that 5 for two motions and 29 for three motions. Consider a video sequence captured by a single camera observing a complex dynamic scene containing an unknown mixture of multiple moving and possibly deforming objects. In this paper we propose an unsupervised approach to the challenging problem of simultaneously segmenting the scene into its constituent objects and reconstructing a 3D model of the scene. The strength of our approach comes from the ability to deal with real-world dynamic scenes and to handle seamlessly different types of motion: rigid, articulated and non-rigid. We formulate the problem as hierarchical graph-cut based segmentation where we decompose the whole scene into background and foreground objects and model the complex motion of non-rigid or articulated objects as a set of overlapping rigid parts. We evaluate the motion segmentation functionality of our approach on the Berkeley Motion Segmentation Dataset. In addition, to validate the capability of our approach to deal with real-world scenes we provide 3D reconstructions of some challenging videos from the YouTube-Objects dataset. Point trajectories have emerged as a powerful means to obtain high quality and fully unsupervised segmentation of objects in video shots. They can exploit the long term motion difference between objects, but they tend to be sparse due to computational reasons and the difficulty in estimating motion in homogeneous areas. In this paper we introduce a variational method to obtain dense segmentations from such sparse trajectory clusters. Information is propagated with a hierarchical, nonlinear diffusion process that runs in the continuous domain but takes superpixels into account. We show that this process raises the density from 3 to 100 and even increases the average precision of labels. Common techniques in structure from motion do not explicitly handle foreground occlusions and disocclusions, leading to several trajectories of a single 3D point. Hence, different discontinued trajectories induce a set of (more inaccurate) 3D points instead of a single 3D point, so that it is highly desirable to enforce long continuous trajectories which automatically bridge occlusions after a re-identification step. The solution proposed in this paper is to connect features in the current image to trajectories which discontinued earlier during the tracking. This is done using a correspondence analysis which is designed for wide baselines and an outlier elimination strategy using the epipolar geometry. The reference to the 3D object points can be used as a new constraint in the bundle adjustment. The feature localization is done using the SIFT detector extended by a Gaussian approximation of the gradient image signal. This technique provides the robustness of SIFT coupled with increased localization accuracy. Our results show that the reconstruction can be drastically improved and the drift is reduced, especially in sequences with occlusions resulting from foreground objects. In scenarios with large occlusions, the new approach leads to reliable and accurate results while a standard reference method fails. When trying to extract 3D scene information and camera motion from an image sequence alone, it is often necessary to cope with independently moving objects. Recent research has unveiled some of the mathematical foundations of the problem, but a general and practical algorithm, which can handle long, realistic sequences, is still missing. In this paper, we identify the necessary parts of such an algorithm, highlight both unexplored theoretical issues and practical challenges, and propose solutions. Theoretical issues include proper handling of different situations, in which the number of independent motions changes: objects can enter the scene, objects previously moving together can split and follow independent trajectories, or independently moving objects can merge into one common motion. We derive model scoring criteria to handle these changes in the number of segments. A further theoretical issue is the resolution of the relative scale ambiguity between such changes. Practical issues include robust 3D reconstruction of freely moving foreground objects, which often have few and short feature tracks. The proposed framework simultaneously tracks features, groups them into rigidly moving segments, and reconstructs all segments in 3D. Such an online approach, as opposed to batch processing techniques, which first track features, and then perform segmentation and reconstruction, is vital in order to handle small foreground objects. In moving camera videos, motion segmentation is commonly performed using the image plane motion of pixels, or optical flow. However, objects that are at different depths from the camera can exhibit different optical flows even if they share the same real-world motion. This can cause a depth-dependent segmentation of the scene. Our goal is to develop a segmentation algorithm that clusters pixels that have similar real-world motion irrespective of their depth in the scene. Our solution uses optical flow orientations instead of the complete vectors and exploits the well-known property that under camera translation, optical flow orientations are independent of object depth. We introduce a probabilistic model that automatically estimates the number of observed independent motions and results in a labeling that is consistent with real-world motion in the scene. The result of our system is that static objects are correctly identified as one segment, even if they are at different depths. Color features and information from previous frames in the video sequence are used to correct occasional errors due to the orientation-based segmentation. We present results on more than thirty videos from different benchmarks. The system is particularly robust on complex background scenes containing objects at significantly different depths. We propose a detection-free system for segmenting multiple interacting and deforming people in a video. People detectors often fail under close agent interaction, limiting the performance of detection based tracking methods. Motion information often fails to separate similarly moving agents or to group distinctly moving articulated body parts. We formulate video segmentation as graph partitioning in the trajectory domain. We classify trajectories as foreground or background based on trajectory saliencies, and use foreground trajectories as graph nodes. We incorporate object connectedness constraints into our trajectory weight matrix based on topology of foreground: we set repulsive weights between trajectories that belong to different connected components in any frame of their time intersection. Attractive weights are set between similarly moving trajectories. Information from foreground topology complements motion information and our spatiotemporal segments can be interpreted as connected moving entities rather than just trajectory groups of similar motion. All our cues are computed on trajectories and naturally encode large temporal context, which is crucial for resolving local in time ambiguities. We present results of our approach on challenging datasets outperforming by far the state of the art. Given point correspondences in multiple perspective views of a scene containing multiple rigid-body motions, we present an algorithm for segmenting the correspondences according to the multiple motions. We exploit the fact that when the depths of the points are known, the point trajectories associated with a single motion live in a subspace of dimension at most four. Thus motion segmentation with known depths can be achieved by methods of subspace separation, such as GPCA or LSA. When the depths are unknown, we proceed iteratively. Given the segmentation, we compute the depths using standard techniques. Given the depths, we use GPCA or LSA to segment the scene into multiple motions. Experiments on the Hopkins 155 motion segmentation database show that our method compares favorably against existing affine motion segmentation methods in terms of segmentation error and execution time. Existing approaches to camera tracking and reconstruction from a single handheld camera for Augmented Reality (AR) focus on the reconstruction of static scenes. However, most real world scenarios are dynamic and contain multiple independently moving rigid objects. This paper addresses the problem of simultaneous segmentation, motion estimation and dense 3D reconstruction of dynamic scenes. We propose a dense solution to all three elements of this problem: depth estimation, motion label assignment and rigid transformation estimation directly from the raw video by optimizing a single cost function using a hill-climbing approach. We do not require prior knowledge of the number of objects present in the scene — the number of independent motion models and their parameters are automatically estimated. The resulting inference method combines the best techniques in discrete and continuous optimization: a state of the art variational approach is used to estimate the dense depth maps while the motion segmentation is achieved using discrete graph-cut based optimization. For the rigid motion estimation of the independently moving objects we propose a novel tracking approach designed to cope with the small fields of view they induce and agile motion. Our experimental results on real sequences show how accurate segmentations and dense depth maps can be obtained in a completely automated way and used in marker-free AR applications. The problem of rigid motion segmentation of trajectory data under orthography has been long solved for non-degenerate motions in the absence of noise. But because real trajectory data often incorporates noise, outliers, motion degeneracies and motion dependencies, recently proposed motion segmentation methods resort to non-trivial representations to achieve state of the art segmentation accuracies, at the expense of a large computational cost. This paper proposes a method that dramatically reduces this cost (by two or three orders of magnitude) with minimal accuracy loss (from 98.8 achieved by the state of the art, to 96.2 achieved by our method on the standard Hopkins 155 dataset). Computational efficiency comes from the use of a simple but powerful representation of motion that explicitly incorporates mechanisms to deal with noise, outliers and motion degeneracies. Subsets of motion models with the best balance between prediction accuracy and model complexity are chosen from a pool of candidates, which are then used for segmentation. We present a novel method to obtain a 3D Euclidean reconstruction of both the background and moving objects in a video sequence. We assume that, multiple objects are moving rigidly on a ground plane observed by a moving camera. The video sequence is first segmented into static background and motion blobs by a homography-based motion segmentation method. Then classical "Structure from Motion" (SfM) techniques are applied to obtain a Euclidean reconstruction of the static background. The motion blob corresponding to each moving object is treated as if there were a static object observed by a hypothetical moving camera, called a "virtual camera". This virtual camera shares the same intrinsic parameters with the real camera but moves differently due to object motion. The same SfM techniques are applied to estimate the 3D shape of each moving object and the pose of the virtual camera. We show that the unknown scale of moving objects can be approximately determined by the ground plane, which is a key contribution of this paper. Another key contribution is that we prove that the 3D motion of moving objects can be solved from the virtual camera motion with a linear constraint imposed on the object translation. In our approach, a planartranslation constraint is formulated: "the 3D instantaneous translation of moving objects must be parallel to the ground plane". Results on real-world video sequences demonstrate the effectiveness and robustness of our approach. We present an unsupervised approach for learning a layered representation of a scene from a video for motion segmentation. Our method is applicable to any video containing piecewise parametric motion. The learnt model is a composition of layers, which consist of one or more segments. The shape of each segment is represented using a binary matte and its appearance is given by the rgb value for each point belonging to the matte. Included in the model are the effects of image projection, lighting, and motion blur. Furthermore, spatial continuity is explicitly modeled resulting in contiguous segments. Unlike previous approaches, our method does not use reference frame(s) for initialization. The two main contributions of our method are: (i) A novel algorithm for obtaining the initial estimate of the model by dividing the scene into rigidly moving components using efficient loopy belief propagation; and (ii) Refining the initial estimate using ? β-swap and ?-expansion algorithms, which guarantee a strong local minima. Results are presented on several classes of objects with different types of camera motion, e.g. videos of a human walking shot with static or translating cameras. We compare our method with the state of the art and demonstrate significant improvements. We propose a novel algorithm for segmenting multiple motions of different types from point correspondences in multiple affine or perspective views. Since point trajectories associated with different motions live in different manifolds, traditional approaches deal with only one manifold type: linear subspaces for affine views, and homographic, bilinear and trilinear varieties for two and three perspective views. As real motion sequences contain motions of different types, we cast motion segmentation as a problem of clustering manifolds of different types. Rather than explicitly modeling each manifold as a linear, bilinear or multilinear variety, we use nonlinear dimensionality reduction to learn a low-dimensional representation of the union of all manifolds. We show that for a union of separated manifolds, the LLE algorithm computes a matrix whose null space contains vectors giving the segmentation of the data. An analysis of the variance of these vectors allows us to distinguish them from other vectors in the null space. This leads to a new algorithm for clustering both linear and nonlinear manifolds. Although this algorithm is theoretically designed for separated manifolds, our experiments demonstrate its performance on real data where this assumption does not hold. We test our algorithm on the Hopkins 155 motion segmentation database and achieve an average classification error of 4.8 , which compares favorably against state-of-the art multiframe motion segmentation methods. Our goal is to segment a video sequence into moving objects and the world scene. In recent work, spectral embedding of point trajectories based on 2D motion cues accumulated from their lifespans, has shown to outperform factorization and per frame segmentation methods for video segmentation. The scale and kinematic nature of the moving objects and the background scene determine how close or far apart trajectories are placed in the spectral embedding. Such density variations may confuse clustering algorithms, causing over-fragmentation of object interiors. Therefore, instead of clustering in the spectral embedding, we propose detecting discontinuities of embedding density between spatially neighboring trajectories. Detected discontinuities are strong indicators of object boundaries and thus valuable for video segmentation. We propose a novel embedding discretization process that recovers from over-fragmentations by merging clusters according to discontinuity evidence along inter-cluster boundaries. For segmenting articulated objects, we combine motion grouping cues with a center-surround saliency operation, resulting in “context-aware”, spatially coherent, saliency maps. Figure-ground segmentation obtained from saliency thresholding, provides object connectedness constraints that alter motion based trajectory affinities, by keeping articulated parts together and separating disconnected in time objects. Finally, we introduce Gabriel graphs as effective per frame superpixel maps for converting trajectory clustering to dense image segmentation. Gabriel edges bridge large contour gaps via geometric reasoning without over-segmenting coherent image regions. We present experimental results of our method that outperform the state-of-the-art in challenging motion segmentation datasets. We address the problem of Foreground Background segmentation of “unconstrained” video. By “unconstrained” we mean that the moving objects and the background scene may be highly non-rigid (e.g., waves in the sea); the camera may undergo a complex motion with 3D parallax; moving objects may suffer from motion blur, large scale and illumination changes, etc. Most existing segmentation methods fail on such unconstrained videos, especially in the presence of highly non-rigid motion and low resolution. We propose a computationally efficient algorithm which is able to produce accurate results on a large variety of unconstrained videos. This is obtained by casting the video segmentation problem as a voting scheme on the graph of similar (‘re-occurring’) regions in the video sequence. We start from crude saliency votes at each pixel, and iteratively correct those votes by ‘consensus voting’ of re-occurring regions across the video sequence. The power of our consensus voting comes from the non-locality of the region re-occurrence, both in space and in time – enabling propagation of diverse and rich information across the entire video sequence. Qualitative and quantitative experiments indicate that our approach outperforms current state-of-the-art methods. We present an approach for motion segmentation using independently detected keypoints instead of commonly used tracklets or trajectories. This allows us to establish correspondences over non- consecutive frames, thus we are able to handle multiple object occlusions consistently. On a frame-to-frame level, we extend the classical split-and-merge algorithm for fast and precise motion segmentation. Globally, we cluster multiple of these segmentations of different time scales with an accurate estimation of the number of motions. On the standard benchmarks, our approach performs best in comparison to all algorithms which are able to handle unconstrained missing data. We further show that it works on benchmark data with more than 98 of the input data missing. Finally, the performance is evaluated on a mobile-phone-recorded sequence with multiple objects occluded at the same time.