Dependent Motion Segmentation in Moving Camera Videos: A Survey <s> 2) FEATURE TRAJECTORY CLUSTERING METHODS <s> Over the past few years, several methods for segmenting a scene containing multiple rigidly moving objects have been proposed. However, most existing methods have been tested on a handful of sequences only, and each method has been often tested on a different set of sequences. Therefore, the comparison of different methods has been fairly limited. In this paper, we compare four 3D motion segmentation algorithms for affine cameras on a benchmark of 155 motion sequences of checkerboard, traffic, and articulated scenes. <s> BIB001 </s> Dependent Motion Segmentation in Moving Camera Videos: A Survey <s> 2) FEATURE TRAJECTORY CLUSTERING METHODS <s> We examine the problem of segmenting tracked feature point trajectories of multiple moving objects in an image sequence. Using the affine camera model, this motion segmentation problem can be cast as the problem of segmenting samples drawn from a union of linear subspaces. 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 not correspond to any valid motion model. In this paper, we develop a robust subspace separation scheme that can deal with all of these practical issues in a unified framework. Our methods draw strong connections between lossy compression, rank minimization, and sparse representation. We test our methods extensively and compare their performance to several extant methods with experiments on the Hopkins 155 database. Our results are on par with state-of-the-art results, and in many cases exceed them. All MATLAB code and segmentation results are publicly available for peer evaluation at http://perception.csl.uiuc.edu/coding/motion/. <s> BIB002 </s> Dependent Motion Segmentation in Moving Camera Videos: A Survey <s> 2) FEATURE TRAJECTORY CLUSTERING METHODS <s> 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/. <s> BIB003 </s> Dependent Motion Segmentation in Moving Camera Videos: A Survey <s> 2) FEATURE TRAJECTORY CLUSTERING METHODS <s> The subspace segmentation problem is fundamental in many applications. The goal is to cluster data drawn from an unknown union of subspaces. In this paper we state the problem and describe its connection to other areas of mathematics and engineering. We then review the mathematical and algorithmic methods created to solve this problem and some of its particular cases. We also describe the problem of motion tracking in videos and its connection to the subspace segmentation problem and compare the various techniques for solving it. <s> BIB004 </s> Dependent Motion Segmentation in Moving Camera Videos: A Survey <s> 2) FEATURE TRAJECTORY CLUSTERING METHODS <s> Due to occlusions and objects' non-rigid deformation in the scene, the obtained motion trajectories from common trackers may contain a number of missing or mis-associated entries. To cluster such corrupted point based trajectories into multiple motions is still a hard problem. In this paper, we present an approach that exploits temporal and spatial characteristics from tracked points to facilitate segmentation of incomplete and corrupted trajectories, thereby obtain highly robust results against severe data missing and noises. Our method first uses the Discrete Cosine Transform (DCT) bases as a temporal smoothness constraint on trajectory projection to ensure the validity of resulting components to repair pathological trajectories. Then, based on an observation that the trajectories of foreground and background in a scene may have different spatial distributions, we propose a two-stage clustering strategy that first performs foreground-background separation then segments remaining foreground trajectories. We show that, with this new clustering strategy, sequences with complex motions can be accurately segmented by even using a simple translational model. Finally, a series of experiments on Hopkins 155 dataset and Berkeley motion segmentation dataset show the advantage of our method over other state-of-the-art motion segmentation algorithms in terms of both effectiveness and robustness. <s> BIB005 </s> Dependent Motion Segmentation in Moving Camera Videos: A Survey <s> 2) FEATURE TRAJECTORY CLUSTERING METHODS <s> 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. <s> BIB006
Apart from feature based parametric methods, there is another type of very important method for mixed motion segmentation. That is feature trajectory clustering based methods. Feature trajectory clustering based methods focus on the classification of trajectories of selected features into different groups (subspaces) BIB004 ,  . These methods have been described in the literature reviews such as BIB001 and  . BIB002 , BIB003 ). Similar to feature based parametric methods, feature trajectory clustering methods also rely much on the robust feature extraction and tracking algorithms to obtain the key trajectory features of motions BIB005 , BIB006 . In addition, as they only output a segmentation with sparse key features, postprocessing is necessary to obtain a dense segmentation. Although several cases of camera motions can be well handled through feature based methods, in which, a simplified orthographic camera model similar to perspective camera is often assumed, and the focal length of a camera is required to be long enough to avoid any perspective distortions on the depth of 3D points. These requirements cannot be satisfied in many practical applications.