In this paper, we propose a new framework for segmenting feature-based moving objects under affine subspace model. Since the feature trajectories in practice are high-dimensional and contain a lot of noise, we firstly apply the sparse PCA to represent the original trajectories with a low-dimensional global subspace, which consists of the orthogonal sparse principal vectors. Subsequently, the local subspace separation will be achieved via automatically searching the sparse representation of the nearest neighbors for each projected data. In order to refine the local subspace estimation result and deal with the missing data problem, we propose an error estimation to encourage the projected data that span a same local subspace to be clustered together. In the end, the segmentation of different motions is achieved through the spectral clustering on an affinity matrix, which is constructed with both the error estimation and sparse neighbors optimization. We test our method extensively and compare it with state-of-the-art methods on the Hopkins 155 dataset and Freiburg-Berkeley Motion Segmentation dataset. The results show that our method is comparable with the other motion segmentation methods, and in many cases exceed them in terms of precision and computation time.
@cite_15: 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.
@cite_10: We propose a method based on sparse representation (SR) to cluster data drawn from multiple low-dimensional linear or affine subspaces embedded in a high-dimensional space. Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all other data points. In general, finding such a SR is NP hard. Our key contribution is to show that, under mild assumptions, the SR can be obtained exactly' by using l1 optimization. The segmentation of the data is obtained by applying spectral clustering to a similarity matrix built from this SR. Our method can handle noise, outliers as well as missing data. We apply our subspace clustering algorithm to the problem of segmenting multiple motions in video. Experiments on 167 video sequences show that our approach significantly outperforms state-of-the-art methods.
@cite_6: This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a high-dimensional space and with an unknown number of subspaces are also presented. Our experiments on low-dimensional data show that GPCA outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as k-subspaces and expectation maximization. We also present applications of GPCA to computer vision problems such as face clustering, temporal video segmentation, and 3D motion segmentation from point correspondences in multiple affine views.
@cite_12: In this paper, based on ideas from lossy data coding and compression, we present a simple but effective technique for segmenting multivariate mixed data that are drawn from a mixture of Gaussian distributions, which are allowed to be almost degenerate. The goal is to find the optimal segmentation that minimizes the overall coding length of the segmented data, subject to a given distortion. By analyzing the coding length rate of mixed data, we formally establish some strong connections of data segmentation to many fundamental concepts in lossy data compression and rate-distortion theory. We show that a deterministic segmentation is approximately the (asymptotically) optimal solution for compressing mixed data. We propose a very simple and effective algorithm that depends on a single parameter, the allowable distortion. At any given distortion, the algorithm automatically determines the corresponding number and dimension of the groups and does not involve any parameter estimation. Simulation results reveal intriguing phase-transition-like behaviors of the number of segments when changing the level of distortion or the amount of outliers. Finally, we demonstrate how this technique can be readily applied to segment real imagery and bioinformatic data.
During the last decades, either the subspace-based techniques @cite_10 @cite_12 or the affinity-based methods @cite_15 @cite_6 have been receiving an increasing interest on segmentation of different types of motions from a real video.