text: We present a novel method for motion segmentation called LAAV (Locally Affine Atom Voting). Our model's main novelty is using sets of features to segment motion for all features in the scene. LAAV acts as a pre-processing pipeline stage for features in the image, followed by a fine-tuned version of the state-of-the-art Random Voting (RV) method. Unlike standard approaches, LAAV segments motion using feature-set affinities instead of pair-wise affinities between all features; therefore, it significantly simplifies complex scenarios and reduces the computational cost without a loss of accuracy. We describe how the challenges encountered by using previously suggested approaches are addressed using our model. We then compare our algorithm with several state-of-the-art methods. Experiments shows that our approach achieves the most accurate motion segmentation results and, in the presence of measurement noise, achieves comparable results to the other algorithms.
  @cite_16: 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.
  @cite_20: Low-Rank Representation (LRR) [16, 17] is an effective method for exploring the multiple subspace structures of data. Usually, the observed data matrix itself is chosen as the dictionary, which is a key aspect of LRR. However, such a strategy may depress the performance, especially when the observations are insufficient and or grossly corrupted. In this paper we therefore propose to construct the dictionary by using both observed and unobserved, hidden data. We show that the effects of the hidden data can be approximately recovered by solving a nuclear norm minimization problem, which is convex and can be solved efficiently. The formulation of the proposed method, called Latent Low-Rank Representation (LatLRR), seamlessly integrates subspace segmentation and feature extraction into a unified framework, and thus provides us with a solution for both subspace segmentation and feature extraction. As a subspace segmentation algorithm, LatLRR is an enhanced version of LRR and outperforms the state-of-the-art algorithms. Being an unsupervised feature extraction algorithm, LatLRR is able to robustly extract salient features from corrupted data, and thus can work much better than the benchmark that utilizes the original data vectors as features for classification. Compared to dimension reduction based methods, LatLRR is more robust to noise.
  @cite_23: Many motion segmentation algorithms based on manifold clustering rely on a accurate rank estimation of the trajectory matrix and on a meaningful affinity measure between the estimated manifolds. While it is known that rank estimation is a difficult task, we also point out the problems that can be induced by an affinity measure that neglects the distribution of the principal angles. In this paper we suggest a new interpretation of the rank of the trajectory matrix and a new affinity measure. The rank estimation is performed by analysing which rank leads to a configuration where small and large angles are best separated. The affinity measure is a new function automatically parametrized so that it is able to adapt to the actual configuration of the principal angles. Our technique has one of lowest misclassification rates on the Hopkins155 database and has good performances also on synthetic sequences with up to 5 motions and variable noise level.
  @cite_17: In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures corresponding to several classes or categories the data belongs to. In this paper, we propose and study an algorithm, called Sparse Subspace Clustering (SSC), to cluster data points that lie in a union of low-dimensional subspaces. The key idea is that, among infinitely many possible representations of a data point in terms of other points, a sparse representation corresponds to selecting a few points from the same subspace. This motivates solving a sparse optimization program whose solution is used in a spectral clustering framework to infer the clustering of data into subspaces. Since solving the sparse optimization program is in general NP-hard, we consider a convex relaxation and show that, under appropriate conditions on the arrangement of subspaces and the distribution of data, the proposed minimization program succeeds in recovering the desired sparse representations. The proposed algorithm can be solved efficiently and can handle data points near the intersections of subspaces. Another key advantage of the proposed algorithm with respect to the state of the art is that it can deal with data nuisances, such as noise, sparse outlying entries, and missing entries, directly by incorporating the model of the data into the sparse optimization program. We demonstrate the effectiveness of the proposed algorithm through experiments on synthetic data as well as the two real-world problems of motion segmentation and face clustering.
summary: The Multiview approach utilizes the trajectory of the feature points. PAC @cite_23 and SSC @cite_17 methods have quite accurate results in multiple motion cases in a sequence and are also robust to noise. However, those algorithms are extremely slow. Latent low-rank representation-based method (LatLRR) @cite_20 is faster and more accurate, but this method becomes degraded in extremely noisy environments. The ICLM-based approach @cite_16 is very fast, but has lower accuracy than other state-of-the-art approaches. In addition, while Multiview approaches are more accurate than Two-view approaches, they do not have good performance when there are only a few frames.